A dissertation presented to. the faculty of. the College of Arts and Science of Ohio University. In partial fulfillment

Photoproduction of K + Λ/Σ and K Σ + from the proton using CLAS at Jefferson Lab A dissertation presented to the faculty of the College of Arts and Science of Ohio University In partial fulfillment of the requirements for the degree Doctor of Philosophy Wei Tang December 212 212 Wei Tang. All Rights Reserved.

2 This dissertation titled Photoproduction of K + Λ/Σ and K Σ + from the proton using CLAS at Jefferson Lab by WEI TANG has been approved for the Department of Physics and Astronomy and the College of Arts and Science by Kenneth H. Hicks Professor of Physics and Astronomy Robert Frank Dean, College of Arts and Science

ABSTRACT 3 TANG, WEI, Ph.D., December 212, Physics Photoproduction of K + Λ/Σ and K Σ + from the proton using CLAS at Jefferson Lab (191 pp.) Director of Dissertation: Kenneth H. Hicks This dissertation presents measurements of the differential and total cross sections of the photoproduction γ + p K + + Λ and γ + p K + + Σ using the CLAS g11a data collected at experimental Hall-B, Jefferson Lab. These measurements are the world s first high statistics measurements of K + Λ and K + Σ photoproduction. The cross section covers the incident photon energy range from 1.75 GeV to 3.85 GeV for K + Λ and from 1.85 GeV to 3.75 GeV for K + Σ in the CLAS lab frame, Also, the Λ recoil polarization of the K + Λ reaction channel is measured. The differential cross sections of γ + p K + Σ + were measured as a calibration reaction and those results are compared with the previous CLAS, SAPHIR and CBELSA measurements. The K + Λ recoil polarization was calibrated by checking the K + Λ polarization and comparing with previous CLAS measurements.

TABLE OF CONTENTS 4 Page Abstract......................................... 3 List of Tables...................................... 8 List of Figures...................................... 1 1 Introduction..................................... 13 1.1 Strong Force and Quantum Chromodynamics................ 13 1.2 Quark Model................................. 16 1.3 Missing Resonance Problem......................... 22 1.4 Controversial K (8) or κ Meson...................... 24 1.5 Theoretical Models for the K Photoproduction............... 26 1.5.1 Zhao Model.............................. 28 1.5.2 Oh and Kim Model.......................... 29 1.5.3 Ozaki-Nagahiro-Hosaka Model................... 32 1.5.4 Thornber Model........................... 35 1.6 Previous Measurements of K Y Photoproduction.............. 35 1.6.1 γp K Σ +, CLAS 26...................... 36 1.6.2 γp K Σ +, CBELSA/TAPS 28................. 36 1.6.3 γp K Σ +, LEPS 212....................... 38 1.6.4 γp K + Λ, CLAS 26....................... 4 1.6.5 γp K + Λ, SAPHIR 25..................... 41 1.7 Summary................................... 42 2 Jefferson Lab, CEBAF and the CLAS Detector.................. 43 2.1 CEBAF.................................... 43 2.2 The Hall-B Tagging System......................... 47 2.3 The g11a Target................................ 51 2.4 The CLAS Detector.............................. 52 2.4.1 Start Counter............................. 52 2.4.2 Superconducting Toroidal Magnet.................. 53 2.4.3 Drift Chambers............................ 54 2.4.4 The Time of Flight System...................... 56 2.4.5 Other Sub-detecting Systems..................... 57 2.5 Beamline Devices............................... 57 2.6 Trigger System and Data Acquisition..................... 58 2.7 Summary................................... 58

5 3 Event Selection................................... 59 3.1 Channels of Interest.............................. 59 3.2 Excluded Runs................................ 61 3.2.1 CLAS Standard Corrections to the Data............... 62 3.3 Particle Identification and Photon Selection................. 68 3.3.1 Particle Identification......................... 68 3.3.2 Photon Selection........................... 69 3.4 Summary................................... 71 4 Cuts on the Data................................... 72 4.1 Removed TOF Scintillator Paddles...................... 72 4.2 Fiducial Cut.................................. 72 4.3 Z-axis Vertex Cut............................... 75 4.4 Two-pion and Three-pion Missing Mass Loose Cut............. 75 4.5 Three-pion Missing Mass Cut for K + Λ Channel............... 77 4.6 Three-pion Mass Cut for K + Σ Channel................... 77 4.7 Removing Background By Sideband Subtraction Method.......... 77 4.8 Summary................................... 83 5 Detector Acceptance and Experimental Yields................... 85 5.1 Detector Acceptance............................. 85 5.1.1 Event Generation........................... 85 5.1.2 GSIM and GPP............................ 86 5.1.3 Summary Of Generated Monte Carlo Files............. 86 5.1.4 Trigger Corrections.......................... 87 5.1.5 The Detector Acceptance for K + Λ and K + Σ............ 88 5.2 Yields from the Experimental Data...................... 91 5.2.1 Template Fitting for K + Λ...................... 91 5.2.2 Extracting the Counts for K + Σ................... 96 5.3 Summary................................... 97 6 Normalization and Cross Section Results...................... 99 6.1 Photon Beam Flux.............................. 99 6.2 Target Density................................. 11 6.3 Differential Cross Sections Results...................... 11 6.4 Extracting the Total Cross Section...................... 12 6.5 Comparison with Theoretical Calculations................. 16 6.6 Summary................................... 17

6 7 Systematic Analysis................................. 118 7.1 The Systematic Uncertainty from the Cuts.................. 118 7.1.1 Fiducial Cut............................. 118 7.1.2 Z-axis Vertex Cut.......................... 119 7.1.3 K and K + Missing Mass Loose Cut................ 12 7.1.4 Cut On Λ Mass for K + Λ....................... 121 7.1.5 Cut On K + Mass for K + Σ..................... 121 7.1.6 Sideband Subtraction......................... 121 7.1.7 Summary of Systematic Uncertainties from Cuts.......... 122 7.2 Systematic Uncertainty from the Yield.................... 123 7.3 Systematic Uncertainty from the Monte Carlo................ 124 7.4 Other Systematic Uncertainties........................ 125 7.4.1 Photon Selection Uncertainty.................... 125 7.4.2 Unapplied Start Counter Correction................. 125 7.4.3 Other Sources of Uncertainty..................... 126 7.5 Summary of Systematic Uncertainty..................... 126 7.6 Summary................................... 127 8 γp K Σ + Differential Cross Sections....................... 128 8.1 Particle Identification and Cuts........................ 128 8.2 Two Methods................................. 129 8.3 Differential Cross Sections of K Σ +..................... 131 8.4 Comparison with Other Data......................... 132 8.5 Summary................................... 135 9 Λ Recoil Polarization................................ 136 9.1 Recoil Polarization of K + Λ Photoproduction................ 138 9.1.1 Particle Identification......................... 138 9.1.2 Cuts on the Data........................... 139 9.1.3 K + Λ Recoil Polarization....................... 141 9.1.4 Systematic Uncertainty Study of K + Λ Recoil Polarization..... 142 9.2 Calibration Check: K + Λ Recoil Polarization................. 144 9.3 Summary................................... 145 1 Conclusion..................................... 149 Appendix A: Energy Transformation.......................... 163 Appendix B: Numerical Values of the K + Λ Photoproduction Differential Cross Section Result.................................... 166

7 Appendix C: Numerical Values of the K + Σ Photoproduction Differential Cross Section Result.................................... 175 Appendix D: The K + Λ Differential Cross Section Comparison Between the Template Fitting and Ordinary Fitting Methods.................. 184 Appendix E: The Effect of Trigger Correction on K + Λ Differential Cross Section.. 185 Appendix F: Events Discarded and Left by Each Cut of K + Λ Channel........ 188 Appendix G: The Dalitz Plots of MM 2 (K + ) vs. MM 2 (Σ + (1385)) for K + Λ Channel. 19

LIST OF TABLES 8 Table Page 1.1 Some properties of the four elementary forces.................. 14 1.2 Some quantum numbers of the u, d and s light quarks.............. 17 1.3 Meson states and their corresponding quantum numbers............. 19 1.4 Name scheme for Baryons............................ 2 1.5 The status of the N resonances.......................... 23 3.1 Some physical properties of K +, Λ and Σ.................... 6 3.2 Some physical properties of K S and K L..................... 6 3.3 Excluded problematic Runs[56].......................... 62 3.4 Excluded other Runs............................... 63 3.5 Summary of the CLAS standard corrections................... 67 4.1 Removed TOF scintillator paddles[75]...................... 73 4.2 Cuts applied and their descriptions and(or) parameters.............. 84 5.1 GSIM s ffread card s inputing parameters.................... 87 5.2 gpp s inputing parameters and their meanings.................. 88 5.3 The summary of generated Monte Carlo files.................. 88 7.1 Summary of systematic uncertainties from all the cuts.............. 123 7.2 Summary of systematic uncertainties from other soureces............ 126 7.3 Summary of systematic uncertainties....................... 127 8.1 Binning for each dataset. The energy has unit of GeV............... 133 9.1 Cuts applied for the recoil polarization measurement.............. 14 9.2 systematic uncertainties for K + Λ recoil polarization.............. 143 9.3 Cuts for K + Λ recoil polarization......................... 145 A.1 Energy transformation table........................... 164 A.2 Energy transformation table........................... 165 B.1 The Table for the differential cross section of K + Λ (1)............. 166 B.2 The Table for the differential cross section of K + Λ (2)............. 167 B.3 The Table for the differential cross section of K + Λ (3)............. 168 B.4 The Table for the differential cross section of K + Λ (4)............. 169 B.5 The Table for the differential cross section of K + Λ (5)............. 17 B.6 The Table for the differential cross section of K + Λ (6)............. 171 B.7 The Table for the differential cross section of K + Λ (7)............. 172

B.8 The Table for the differential cross section of K + Λ (8)............. 173 B.9 The Table for the differential cross section of K + Λ (9)............. 174 C.1 The Table for the differential cross section of K + Σ (1)............. 175 C.2 The Table for the differential cross section of K + Σ (2)............. 176 C.3 The Table for the differential cross section of K + Σ (3)............. 177 C.4 The Table for the differential cross section of K + Σ (4)............. 178 C.5 The Table for the differential cross section of K + Σ (5)............. 179 C.6 The Table for the differential cross section of K + Σ (6)............. 18 C.7 The Table for the differential cross section of K + Σ (7)............. 181 C.8 The Table for the differential cross section of K + Σ (8)............. 182 C.9 The Table for the differential cross section of K + Σ (9)............. 183 F.1 Event number impacted by each cut for the experimental data.......... 188 F.2 Event number impacted by each cut for the Monte Carlo data.......... 189 9

LIST OF FIGURES 1 Figure Page 1.1 The elementary particles............................. 15 1.2 Pseudoscalar and vector meson nonets...................... 19 1.3 Spin- 1 ground state baryons octet........................ 21 2 1.4 Typical Feynman diagrams used in isobar model calculation.......... 27 1.5 The diagram of reggeized models......................... 28 1.6 The predicted differential cross sections dσ dω K + Σ and γp K Σ +.. 3 1.7 The predicted total cross sections of γp K + Σ and γp K Σ +....... 31 1.8 The tree diagrams used in the Oh and Kim model................ 32 1.9 The total cross sections from Oh and Kim Model................ 33 1.1 The total cross sections from ONH Model.................... 34 1.11 The total cross sections from Oh and Kim Model and ONH Model....... 34 1.12 [The total cross sections ratio from Thornber Model............... 35 1.13 The differential cross section of γp K Σ + measured at CLAS........ 37 1.14 The differential cross section of γp K Σ + measured at CBELSA/TAPS... 38 1.15 The decay angular distribution for γp K Σ + from LEPS........... 39 1.16 The spin density matrix elements extracted from γp K Σ +.......... 4 1.17 The preliminary K + Λ total cross section from CLAS.............. 41 2.1 An Aerial view of Jefferson Lab......................... 44 2.2 The machine configuration of the CEBAF.................... 45 2.3 A model of cryomodule.............................. 46 2.4 cross section view of Superconducting Radio Frequency Niobium cavities... 47 2.5 Schematic diagram of the Hall-B Tagging system................ 5 2.6 Schematic diagram of how the E and T planes work............... 5 2.7 Schematic diagram of the tagger readout system................. 51 2.8 Schematic diagram of the g11a target...................... 52 2.9 A photograph of the CLAS detector....................... 53 2.1 The schematic plot of the Start Counter..................... 54 2.11 A photograph of the superconducting toroidal magnet during the construction. 55 2.12 A schematic plot of the CLAS detector...................... 56 2.13 A schematic plot of one sector of the CLAS TOF system............ 57 3.1 The Eloss correction effect on pions....................... 64 3.2 The tagger corrections for g11a data....................... 66 3.3 The tagger corrections effect on the K + Λ.................... 66 3.4 The momentum corrections effect on the K + Λ................. 67 3.5 The TOF difference spectrum for pions...................... 7 4.1 The fiducial cuts on both π + and π........................ 74

4.2 Z-axis vertex cut................................. 76 4.3 Cut of Λ and K +................................. 78 4.4 The reconstructed two-pion mass of the K S ditributions............. 8 4.5 Reconstructed three-pion mass and missing mass................ 82 4.6 The plot of reconstructed three-pion mass of K +................ 83 4.7 The plot of reconstructed three-pion missing mass................ 84 5.1 Examples of Breit-Wigner fitting on K + peak.................. 9 5.2 Examples of Gaussian fitting of Σ peak..................... 91 5.3 Detector Efficiency for γ + p K + + Λ..................... 92 5.4 Detector Efficiency for γ + p K + + Σ.................... 93 5.5 Merged K + and Σ + (1385) plots......................... 95 5.6 Merged K + and Σ + (1385) plots......................... 96 5.7 An examples of the template fitting........................ 97 5.8 Examples of fitting of the Λ and Σ peak..................... 98 6.1 The plot of g11a gflux............................... 1 6.2 Differential cross sections of γ + p K + + Λ.................. 13 6.3 Differential cross sections of γ + p K + + Σ................. 14 6.4 Legendre polynomial fitting of γ + p K + + Λ................ 18 6.5 Legendre polynomial fitting of γ + p K + + Σ................ 19 6.6 Plots of the Legendre Polynomial fitting parameters for K + Λ.......... 11 6.7 Total cross section extracted for K + Λ...................... 111 6.8 Plots of Legendre Polynomials fitting parameters................ 112 6.9 Total cross sections of γp K + Λ........................ 113 6.1 Total cross sections of γp K + Σ........................ 113 6.11 Comparison of total cross sections of γp K + Λ................ 114 6.12 Theoretical differential cross sections of photoproduction γ + p K + + Λ.. 115 6.13 Comparison of total cross sections of γp K + Λ with theoretical models... 116 6.14 The total cross section ratio of the reactions γp K Σ + to γp K + Λ.... 117 7.1 Fiducial cut systematic uncertainties for K + Λ................. 119 7.2 Fiducial cut systematic uncertainties for K + Σ................. 12 7.3 Z vertex systematic uncertainty for K + Λ and K + Σ.............. 12 7.4 Λ mass cut and K + mass cut systematic uncertainty............... 121 7.5 Systematic uncertainty from sideband subtraction................ 122 7.6 The systematic uncertainty from different fitting strategies............ 124 7.7 The systematic uncertainty from the Monte Carlo................ 125 8.1 Plot of the neutron mass............................. 129 8.2 Fitting of Σ + and K S................................ 131 8.3 The differential cross sections of K Σ +...................... 132 8.4 K Σ + cross section comparison.......................... 134 11

9.1 Schematic plot of the Λ recoil polarization measurement............ 137 9.2 Particle Identification for K + and p........................ 14 9.3 Plots of K + and Λ after all the cuts........................ 141 9.4 The recoil polarization of γ + p K + + Λ................... 142 9.5 The systematic uncertainty for the recoil polarization.............. 143 9.6 The recoil polarization of γ + p K + + Λ.................... 146 9.7 The recoil polarization of γ + p K + + Λ(two tracks)............. 147 9.8 2 and 3 particle track recoil polarization result for K + Λ............. 148 1.1 Comparison of total cross sections of K + Λ with K + Λ............. 152 A.1 Schematic plot of two particles scattering.................... 163 D.1 Differential cross sections of γ + p K + + Λ.................. 184 E.1 Comparison of the K + Λ differential cross sections............... 186 E.2 The distribution of the relative differential cross section differnce between the calculation with the trigger efficiency and without it............... 187 G.1 The Dalitz plots of experimental data....................... 19 G.2 The Dalitz plots of experimental data....................... 191 12

1 INTRODUCTION 13 The motivation of this analysis is to measure the differential and total cross sections of the photoproduction γ + p K + + Λ and γ + p K + + Σ as well as the Λ recoil polarization of the first reaction channel. The cross section measurement of K + Λ and K + Σ will provide the information of the N baryon excited states for the missing resonance problem and can be also used to study the controversial κ(8) meson as a test of theoretical models for the strange vector meson production. The Λ recoil polarization result will provide more information for the theoretical model development. In the following sections of this chapter, some general background information is discussed. 1.1 Strong Force and Quantum Chromodynamics It is generally accepted that there are four fundamental forces in nature: gravity, electromagnetism, the strong and weak force. Gravity is a long range universal force that causes every object to attract to every other object. The gravitational force between two objects is proportional to their masses and the inverse square of their distance, namely, F G = G m1 m 2 r 2 where G is the newtonian gravitational constant, m 1, m 2 are the masses of the two subjects, and r is the distance between them. Electromagnetism is also a long range force but only limited to objects with charge, which causes two objects of the same charge to repel each other, while two objects of opposite charge to attract each other. The dynamics of those charged objects follow Maxwell s equations and the Lorentz Law. The strong and weak forces, on the other hand, are short range forces that are only effective within a very small distance. They are the forces that govern the nucleons and quarks, where the strong force has a strengh of 1 5 times of that of the weak force. In general, the strong force is responsible for holding the quarks and nucleons together and the weak force is responsible for radioactive decay and interactions that include neutrino(s).

14 Physicists put all particles into two catergories: bosons and fermions, by their spins. If a particle has an integer value of spin, then it is a boson, otherwise, it is a fermion. From the modern scientific point of view, our world is made up from (only) elementary particles, including three generations of quarks and leptons, and the gauge bosons. The quarks and leptons are fermions, and they both have corresponding anti-particles. The quarks and gluons also have a quantum property called color charge, unlike the electric charge, which has three different values: red, green and blue. The cause of the four fundamental forces thus can be interpreted as exchanging gauge bosons between particles. Table 1.1 summarizes some properties of the four fundamental forces and Figure 1.1 lists those elementary particles and some of their properties. Table 1.1: Some properties of the four elementary forces, where the coupling measures the strength of the force. Table sources: Reference[1] Interaction Coupling Boson Mass(GeV/c 2 ) Range(cm) Typical time(s) Gravity 1 39 graviton - Electromagnetism 1 137 photon 1 2 Weak Force 1 5 W ±, Z 8,9 1 16 1 1 Strong Force 1 gluons < 1 13 1 23 As one of the main forces that govern the interactions of nucleons and quarks, the strong force is very complicated. The theory behind the strong force is a highly nonlinear theory called Quantum Chromodynamics (QCD). The Largrangian of the QCD that describes the dynamics of the quarks and gluons has the form[3, 7, 8]: L QCD = q i (i µ γ µ δ i j - g λa i j 2 Aa µγ µ - mδ i j )q j - 1 4 Fa µνf µν a, F µν a = µ A ν a - ν A µ a - g f abc A µ b Aν c

where A µ a are the gluon fields, q i are the quark fields, g is the coupling constant, f abc is the structure constants of SU(3) and λ a are the Gell-Mann matrices. The λa 2 are the generator of SU(3). The sub index a (= 1,..., 8) represents different SU(3) representations, and the sub index i (= 1, 2, 3) represents the different color of quarks. The F µν a represents the non-linear properties of the SU(3), which gives rise to the high order (trilinear and quadratic) non-linear terms in the theory, so that gluons not only interact with quarks but also couple to themselves. It is because those gluons interact with other gluons that makes the strong force so complicated. 15 Figure 1.1: The elementary particles, which include three generations of quarks and leptons, and the exchanged gauge bosons for each fundamental force. The table does not list the graviton, which is the expected exchanged boson for gravity, but has not been found yet. Image Sources: Reference[2] Because of the complexity of the QCD, it is impossible to solve it analytically, so approximations have to be used. At the extreme of high energy, due to asymptotic

16 freedom, the interaction between quarks becomes weaker, which allows the use of the perturbative calculations of QCD (pqcd). However, for a lower energy range, there is no such perturbative theory that can be used. One of the most promising methods of calculating the QCD is called Lattice QCD (LQCD), which formulates QCD on a discrete Euclidean space and time hypercubic lattice with lattice spacing of a, where the nodes of the lattice represent the quark fields, while the links that connecting the nodes represent the gluon fields. LQCD allows non-perturbative calculations by numerical evaluation of the path integral that defines the theory. In principal, LQCD is an exact calculation of QCD from first principals as far as the lattice spacing parameters a. Practically, the calculation of LQCD is very difficult and is limited by the availability of computational resources and the efficiency of algorithms[4, 5]. Although major progress have been made by LQCD calculations in recent decades, our understanding of the strong force still relies mainly on experiments and some QCD-motivated models[3]. In the next section, the quark model will be discussed. For more information of LQCD, the readers could read material like Reference[4, 5, 6]. 1.2 Quark Model There are six different types or flavors of quarks, namely u, d, s, c, b and t. Quarks are spin 1 2 fermions, with baryon number 1 3 and positive parity by convention. Table 1.2 lists some quantum numbers of the u, d and s light quarks, where B stands for the baryon number, Q for the electric charge, I 3 for isospin projection, S for strangeness and Y for hypercharge. Y is defined as the sum of S and B, namely Y = S + B. The spin-independent potential between two quarks is usually taken as: V = 4 3 αs r + k r

Table 1.2: Some quantum numbers of the u, d and s light quarks. B stands for the baryon number, Q for the electric charge, I 3 for isospin projection, S for strangeness and Y for hypercharge. Table sources: Reference[7] 17 Quark Spin B Q I 3 S Y u 1 2 d 1 2 s 1 2 1 3 2 3 1 1 2 3 1-1 - 1 1 3 3 2 3 1 3-1 3-1 - 2 3 where α s is the strong coupling constant, the value of which depends on the momentum transfer and has a value of 1 for the momentum transfer < 1 GeV. The k is a constant of the string tension and has a numerical value.9 GeV/fm[3]. The - 4 3 αs r term arises from single gluon exchange and dominates at small r. The k r term dominates at large r and is associated with confinement. Because of this linear k r term, it is impossible to free a quark: attempts to free a quark from the quark potential simply results in production of new quark-antiquark pairs[8]. Hence, there are no single quark states. Quarks are always dressed and confined in some color singlet (or colorless) bound states called hadrons 1. According to Particle Data Group (PDG) s review of the quark model[9], the quark model is generally defined as the description of hadronic properties that strongly emphasizes the role of the minimum-quark-content part of the wave function of a hadron. There are two types of hadrons, one is called a baryon which has the baryon number of 1 and the other is called a meson with the baryon number of. In most cases, the baryons have the valence quark structure of qqq, while the mesons have the valence quark structure 2 of qq. However, there might also be states like the glueball (gg, ggg,...), hybrid 1 The only exception goes with the top quark t, which has a mean life time much shorter than the timescale of the strong interactions, thus it will decay before it gets hadronized. 2 The q represents the quark, q represents the anti-quark and g represents the gluon.

18 (qgq, qggq,... ), tetraquark (qqqq), pentaquark (qqqqq) and etc. Those states are not forbidden by the QCD fundamental rules but have not been found yet. Baryons and mesons are classified by their quantum numbers. Because the gluons only carry the quantum number of color charge, and the color charge is believed to be permanently confined, most of the quantum numbers of hadrons are given by quantum numbers of their constituent quarks and antiquarks[9]. Mesons, as bound states of qq, are classified in J PC or 2S +1 L J states[1], where S, L, J, P and C represent the spin, orbital angular momentum, total angular momentum, parity and charge conjugation of the mesons, respectively. The L =, 1, 2, 3..., states are usually written as S, P, D, F,... states. The following is the relationship of these quantum numbers: J = L S or J = L S,..., L + S, P = ( 1) L+1, C = ( 1) L+S. The J = states are pseudoscalars (J PC = + ) and scalars (J PC = ++ ), the J = 1 states are vectors (J PC = 1 ), pseudo-vectors (J PC = 1 + ) and axial vectors (J PC = 1 ++ ), the J = 2 states are tensors and so forth. Table 1.3 lists some meson states and their corresponding quantum numbers. Figure 1.2 shows a plot of pseudoscalar and vector mesons in a nonet structure accroding to their hypercharge Y and isospin projection I 3, where the mesons with the light background are the vector mesons, which are the excited states of the psudoscalar mesons. Instead of having the structure of qq, the glueballs and hybrids can also be represented by J PC states, those particles are called exotic mesons and also belong to the meson family. For more information of mesons, [3, 7, 8, 9, 1, 11, 12] are good references.

Table 1.3: Meson states and their corresponding quantum numbers. Table Sources: [1] 19 State S L J P C J PC Mesons Name 1 S - + + π, η, η, K pseudoscalar 3 S 1 1 1 - - 1 ρ, ω, φ, K vector 1 P 1 1 1 + - 1 + b 1, h 1, h 1, K 1 pseudo-vector 3 P 1 1 + + ++ a, f, f, K scalar 3 P 1 1 1 1 + + 1 ++ a 1, f 1, f 1, K 1 axial vector 3 P 2 1 1 2 + + 2 ++ a 2, f 2, f 2, K 2 tensor Figure 1.2: Pseudoscalar and vector meson nonets. The mesons with a light background are vector meson, while the others are the psudoscalar mesons. On the other hand, baryons, as bound states of qqq, are identified by their names and masses. Currently about 12 baryons and baryon resonances are known. The naming

scheme of baryons is bases on the constituent light u, d and s quarks[13, 14]: baryons that contain three u and/or d quarks are named either N or which depends on whether their isospin is 1 or 3. Baryons with two u and/or d quarks are named either Λ or Σ which 2 2 depends on whether their isospin is or 1, if the third quark is a c or b quark, the c or b will be identified by a subscript like Λ c or Λ b. Baryons with one u or d quark, which have isospin of 1, are named Ξ, and one or two subscripts are used if one or both two other 2 quarks are c or b quarks, i.e. Ξ c, Ξ cc. Baryons with no u or d quarks are named Ω, and the c or b quark constituent(s) is(are) indicated with subscripts like Ω c and Ω cc. Baryons that decay strongly also have their masses as part of their names, i.e. Σ(1385), Λ(145). Baryon resonance states are represented by adding L 2I,2J behind the particle name, where L is the lowest orbital angular momentum. When the resonance decays into its ground state and a pseudoscalar meson, I and J are isospin and total angular momentum of the resonance. Table 1.4 summarizes the naming scheme for the baryons that are made of 2 light constituent u, d and s quarks. Figure 1.3 shows the spin- 1 2 ground states baryon plotted in a octet structure according to their hypercharge Y and isospin projection I 3. Table 1.4: Name scheme for Baryons that are made of light u, d and s valence quarks. Constituent Quarks Isospin Name u or d, no s 1/2 N u or d, no s 3/2 two u or d and one s Λ two u or d and one s 1 Σ one u or d and two s 1/2 Ξ three s Ω

21 Figure 1.3: Spin- 1 2 ground state baryons octet. Baryons are fermions, hence they obey the Pauli Exclusion Principle, which says that the wave functions are antisymmetric under the interchange of two equal-mass quarks. Since the color part of baryons is a completely antisymmetric state of the three colors, thus the baryon wave functions have the form of[9]: qqq> A = space, spin, flavor> s color> A, where A and S represent antisymmetry and symmetry. So far, all established baryons are made of three valence quarks, particles that have a baryon number of 1 are generally considered as members of the baryon family. Baryons that have a valence quark structure other than qqq are called exotic baryons, which include the hot topics particle pentaquark (qqqqq) that attracted much attention at the begining of this century. Even though lots of searches have been made for the pentaquark, their

22 existence is still controversial. For more information of baryons and baryon related topic, [7, 8, 9, 13, 15] are good references. 1.3 Missing Resonance Problem As one of the powerful tools in the field of particle physics, the quark model is not only used to help us understand the physics behind those experimental data, but also used to make predictions that have not been found experimentally. Hence the quark model is a help to guide the direction for experimental hadronic physics. One of those examples is the prediction of the baryon resonance states from different quark models [16, 17, 18, 19, 2, 21, 22]. According to quark model predictions, a lot of baryon resonance states exist. However only a small portion of those predicted states were established experimentally, and this is known as the Missing Resonance Problem. In the PDG s[23] most recent review of N and Resonances about 45 Nucleon resonance states are predicted by quark models up to an excitation energy of 2.4 GeV, but only 12 are established and 7 are tentative. Table 1.5 shows those states. A baryon resonance state is established only if it has been seen in at least two independent analyses of elastic scattering (πn πn and KN KN reactions), and if the relevant partial-wave amplitudes do not behave erratically or have large errors. The meaning of the star rating is listed at the end of the table, and more information of the baryon star rating could be found in [24]. Naturally, the Missing Resonance Problem leads to two conclusions: one is those missing resonance states simply do not exist, the other is those missing resonance states do exist but have not been found experimentally. For the first conclusion, several solutions have been proposed like the approximations of the models lead to inaccurate predictions, or that the di-quark structure inside a baryon might reduce the number of predicted resonnace states. However, none of those solutions seems to be working very well; the

23 Table 1.5: The status of the N resonances. Table Sources:[23] Particle L 2I2J Overall status Particle L 2I2J Overall status N(144) P 11 N(199) F 17 N(152) D 13 N(2) F 15 N(1535) S 11 N(28) D 13 N(165) S 11 N(29) S 11 N(1675) D 15 N(21) P 11 N(168) F 15 N(219) G 17 N(17) D 13 N(22) D 15 N(171) P 11 N(222) H 19 N(172) P 13 N(225) G 19 N(19) P 13 Existence is certain, and properties are at least fairly well explored. Existence ranges from very likely to certain, but further confirmation is desirable and/or quantum numbers, branching fractions, etc. are not well determined. Evidence of existence is only fair. Evidence of existence is poor. approximation of the calculating models could not explain so many unobserved predicted states, while the di-quark structure inside a baryon lacks any experimental evidence. On the other hand, the establishment of baryon resonance states are difficult due to the increasingly smaller elastic width (with increasing resonance mass) and the overlapping resonances with their large widths. In addition, the PDG established resonance states

24 mostly in the analyses of πn elastic scattering. Resonance states that couple weakly to πn will be missing [25]. Hence searching with an electromagnetic probe like photons or electrons on protons might let us find those missing resonance states. Also, analysis of data in different final states, for example ππn, ωn and KΛ, might help us find those missing states. Actually, the quark model calculation[26] of strange decays of nonstrange baryons predicted several missing baryon resonance states, and a recent measurement of the K + Λ photoproduction and its aftermath analysis showed the evidence of a resonance-like structure around 1.9 GeV[27]. The model also predicted many other excited final states decaying strongly to KΛ(145), KΛ(152), KΣ (1385), K Λ and K Σ. For K + Λ photoproduction, the model predicted that several low-lying weakly established negative-parity nucleon resonances should contribute strongly to this reaction, and the well established state N(29) could be seen in this reaction channel as well. The confirmation of the existence or non-existence of those baryon resonance states could help us rule out or confirm certain theoretical pictures and let us have more insightful understanding of the strong interaction. To search for the missing baryon resonance states from the photoproduction of the strangeness production of K is one of the main motivations for this analysis. 1.4 Controversial K (8) or κ Meson As discussed in the previous section, mesons can be catergorized into different groups by their quantum numbers. Figure 1.2 lists the nonets for the pseudoscalar and the vector mesons. Similarly according to the quark model prediction, there also exists a nonet for the scalar mesons, which have total angular momentum of and positive parity and charge conjugation (see Table 1.3). However, the identification of the scalar mesons is very difficult and a long-standing puzzle[28], which is due to several reasons. For example

25 the much wider decay widths of these scalar mesons make it difficult to distinguish resonances and background. Also several decay channels open up within a narrow mass interval and the glueballs ((gg, ggg,...), or multiquark states(qqqqq, qqqq,... ) that have the same quantum number of J PC = ++ might be mixed with the scalar mesons. Currently only the K (143) is confirmed as a strange scalar meson. The f (6) or σ, K (8) or κ, a (98), f (98), f (137), f (15), f (171) and a (145) have the J PC = ++, and are the scalar meson candidates. Within those particles, the σ, a (98) and f (98) are often considered as meson-meson resonances or tetraquarks (qqqq), and the f (137) and f (171) are expected to mix with the f (15), while the latter two have been proposed as candidates for the scalar glueball[9, 1, 11, 12, 29]. As one of the candidates that falls into the scalar meson nonet, the κ is expected to have an isospin value of 1 2, a mass between3 7 and 9 MeV, and a resonance width as broad as 5 MeV. The first experimental evidence of the κ was found in 1963[37], where an enhancement occurred in the reaction π p Σ K + π at the mass of 726 MeV/c 2. After that, continuous evidences of the κ have been seen in many phenomenological analysis between 7 and 9 MeV, several most recent ones are listed as [3, 31, 32, 33, 34]. However, confirmation of the κ is very difficult and its existence is still controverial. In fact the κ is omitted from PDG s Summary Table[35] and is only listed in its complete volume of the review of particle physics book[36] with the comment of needs confirmation. The confirmation of κ is significant in the understanding of the scalar mesons and the establishment of the scalar meson nonet. The K photoproduction provides a good opportunity to study the controversial κ meson, since it allows the exchange of κ in the t-channel, while the ground state K photoproduction prohibits the κ exchange because the 3 In the field of the particle physics, the natural unit is the conventional unit that been used, in which the Planck s constant and the velocity of light c are set to the unit, and quantities like mass, momentum and energy are measured in units of GeV (1 GeV = 1 3 MeV = 1 9 electron volts), while the length and time are in units of GeV 1 [7].

26 reaction κ Kγ breaks the angular momentum and parity conservation laws. A measurement of the K photoproduction observables thus could provide the data to test the theoretical models that include the κ exchange, which is another motivation of this analysis. 1.5 Theoretical Models for the K Photoproduction The models that are currently available for the K photoproduction are all effective Lagrangian models, which fall into two groups: isobar models and reggeized meson exchange models. Isobar models evaluate tree-level Feynman diagrams, which include resonant and nonresonant exchanges of baryons and mesons. Figure 1.4 shows the typical Feynman diagrams used in isobar model calculations. These plots are: (a) s-channel exchange, (b) t-channel exchange, (c) u-channel exchange, (d) contact or seagull terms. P A, P B, P C and P D represent each particle s four-momenta (E, P). Because of the requirement of the energy and momentum conservation laws, P A + P B = P C + P D, and E 2 = P 2 + m 2, only two of the variables are independent. It is conventional to define three Mandelstam variables: s = (P A + P B ) 2, t = (P A - P C ) 2, u = (P A - P D ) 2. To describe the physics process completely, all possible Feynman diagrams that could lead to the final state are required to be taken into account in the calculation. One advantage of the isobar models is that they identify the dominant contributions to the final states. On the other hand, there are many adjustable parameters in the models, which are generally fixed by fitting to the previous experimental data of the same reaction channels

27 Figure 1.4: Typical Feynman diagrams used in isobar models calculation. The plots are: (a) s-channel exchange, (b) t-channel exchange, (c) u-channel exchange, (d) contact or seagull terms. P A, P B, P C and P D represent each particle s four-momenta (E, P). or the channels that have a similar reaction mechanism. Tuning and fixing of those parameters can be tricky. The reggeized models also use the Effective Lagrangian approach. However, rather than focus on selecting of all possible s, t and u channel reaction processes, the reggeized models emphasis the t-channel mesons exchange, which is expected to dominant the reaction at energies above the resonance region. The standard propagators in the Lagrangian are replaced by Regge propagators, which take into account an entire family of exchanged particles with the same quantum number instead of one meson exchange. Figure 1.5 shows the diagram of the reggeized models, where the Lagrangian propagators for the t-channel diagram is reggeized from s t m 2 to s J t m 2 J and finally to s α(t). When s is

large, the sum goes over each exchanged meson J with the same quantum numbers. Here s, t are Mandelstam variables and α(t) is the regge trajectory. 28 Figure 1.5: The diagram of reggeized Models, where the Lagrangian propagators for the t-channel diagram is reggeized from s to s J term and finally to s α(t) when s is t m 2 t m 2 J large, where sum goes over each exchanged meson J with same quantum number. s, t are Mandelstam variables and α(t) is regge trajectory. Image Sources: [38] The Regge approach was originally applied to high energy hadron reactions, thus the reggeized model might not be able to produce our results in detail, but at least it can tell us about how t-channel mesons exchange affects the reaction. In the following sections, those models are discussed in detail. 1.5.1 Zhao Model The Zhao model[39] is one of a few models available for K photoproduction. It is an isobar quark model that is based on the quark-meson couplings. The model assumes that SU(3) is flavor blind, in other words, it treats the s quark in the same way as the u and d

29 quarks except its different mass. Apart from the commonly used quark model parameters, the Zhao model only has two basic tunable parameters, which correspond to the vector and tensor couplings for quark-k interactions. The quark-meson coupling term of the Zhao model has the form: H m = -ψ l (aγ µ + ib 2m q σ µν q ν )V µ ψ l where ψ l (ψ l ) is the quark (anti-quark) field, V µ is the vector meson field, a and b are tunable coupling parameters for the vector and tensor couplings of quark-k interactions. Figure 1.6 shows the first prediction of the differential cross section dσ for γp dω K + Σ and γp K Σ + photoproduction. The vector and tensor coupling parameters a and b were set as -2.8 and -5.9, respectively, which were derived from ω photoproduction[4] using GRAAL data[41]. The dashed and solid curves in the plots are predictions with and without t-channel kaon exchange. From the plots we can see that the predicted K + Σ differential cross sections have a strong peaking at forward angles, which is due to the contribution from t-channel K exchange as well as the seagull terms. Because of the neutral charge of K, the K Σ + reaction does not contains the contributions from these two terms. Figure 1.7 shows the predicted total cross sections 4 for the two channels with the same parameter settings. 1.5.2 Oh and Kim Model The Oh and Kim model[42, 43] is another model currently available for the K photoproduction. The model is also based on the effective Lagrangian that evaluates the tree diagrams for K photoproduction. The model at first was planned to be used for the study of the background production mechanisms of the Born terms, which include t-channel K, K and κ exchanges, s-channel ground state nucleon exchanges and 4 b, pronuced barn, is the unit used for the the cross section, where 1 b = 1 24 cm 2 and 1 b = 1 6 µb.

3 Figure 1.6: The predicted differential cross sections dσ dω of γp K + Σ and γp K Σ + photoproductions for E γ = 1.88, 2.1, 2.4 and 2.6 GeV by the Zhao model with a = -2.8 and b = -5.9 that were derived from ω photoproduction[4] using GRAAL data[41]. The dashed and solid curves are predictions with and without t-channel kaon exchange. Image Source: [39]. u-channel Λ, Σ and Σ exchanges. However, the s-channel nucleon resonance exchanges could be also added to the model. Figure 1.8 shows those Feynman diagrams used in the calculation, where the Y represents a hyperon, namely the Λ or Σ. The meaning of those plots are: (a) t-channel exchanges which includes the K, K and κ, (b) s-channel exchanges, which only include the ground state nucleon, (c) u-channel exchanges which include Λ, Σ and Σ, (d) seagull or contact term. For the K + Λ channel, the production amplitude then can be written as:

31 Figure 1.7: The predicted total cross sections of γp K + Σ and γp K Σ + photoproductions by the Zhao model with a = -2.8 and b = -5.9. The solid and dot-dashed curves are with the t-channel K exchange, the dotted and dashed curves are without the t-channel K exchange. Image Source: [39]. M = ε ν(k )µ Λ (p )M µν µ N (p)ε µ (γ), where µ Λ (p ) and µ N (p) are the Dirac spinors of the Λ and Nucleon, respectively, while ε ν(k ) and ε µ (γ) are the polarization vector of the K and the photon. M µν can be calculated for t, s, u and contact channels by evaluating each tree diagram, namely, M µν = M µν s + M µν t + M µν u + M µν c. The details of each production amplitude and the parameters used in the model can be found in [42, 43]. One attractive point of this model is that it includes a light κ meson exchange in the t-channel, which gives us a chance to study the controversial particle. Figure 1.9 shows the prediction of the total cross sections from Oh and Kim Model for (a) γp K + Λ and

32 Figure 1.8: The tree diagrams used in the Oh and Kim model, where the Y represents the hyperon, namely Λ or Σ. (a) t-channel exchanges which includes the K, K and κ, (b) s- channel exchanges, which only include the ground state nucleon, (c) u-channel exchanges which include Λ, Σ and Σ, (d) seagull or contact term. Image Source: [43] (b) γp K Σ + photoproduction, where the solid curves and the dashed curves are predicted total cross sections with and without the t-channel κ exchange, while the black dots in the left plot are the preliminary γp K + Λ total cross section measured at CLAS[44]. Both curves, with and without κ exchange contributions in plot (a) look reasonable, so it is difficult to isolate the real production mechanism even if we assume the experimental data and the model are correct. Therefore, more accurate differential and total cross section data and other observables, for example the spin desity matrix elements and polarization observables, are necessary for testing of the model. 1.5.3 Ozaki-Nagahiro-Hosaka Model A third model that currently avaiable for the K Photoproduction is Ozaki Nagahiro Hosaka (ONH) Model[45], which is a reggeized model. The model takes into account all of the possible hadrons exchanged with the same quantum number expect spin, and the

33 Figure 1.9: The prediction of the total cross sections from Oh and Kim Model for (a) γp K + Λ and (b) γp K Σ + photoproductions, where the solid curves and the dashed curves are predicted total cross sections with and without the t-channel κ exchange, while the black dots in the left plot are the preliminary γp K + Λ total cross section from CLAS[44]. Image Source: [43] coupling constants and κ parameters are the same as that were used in Oh and Kim Model[42, 43]. The prediction of the γp K + Λ from this model is seen in Figure 1.1, where the red curves is the total cross section calculated from the model, while the black solid dots are the preliminary γp K + Λ total cross section from CLAS[44]. Even though the fitting of the data from the ONH model looks as good as the fitting from the Oh and Kim model, the production mechanisms of the two models are very different. In the Oh and Kim model, t-channel K exchange dominates the total cross sections and the t-channel K exchange and contact terms are mostly suppressed. In contrast, the ONH model does have a measurable contribution from t-channel K exchange and contact terms. This can be seen from Figure 1.11, where each contribution is drawn in the plots, where the left plot is from Oh and Kim Model, and the right plot is from ONH Model. Hence, to understand the K Λ photoproduction mechanism correctly,

34 Figure 1.1: The prediction of the total cross sections from ONH Model for γp K + Λ, where the red curves is the total cross section calculated from the model, while the black solid dots are the preliminary γp K + Λ total cross section from CLAS[44]. Image Source: [45]. the data of other observables, i.e. spin density matrix elements and polarization observables, are necessary. Figure 1.11: The prediction of the total cross sections from Oh and Kim Model and ONH Model for γp K + Λ, Each contribution to the total cross section is drawn. The left plot is from Oh and Kim Model and the right plot is from ONH Model. Image Source: [45].

35 1.5.4 Thornber Model The Thornber model[46] is a regge-pole model that was introduced in 1968. The predictions from this model include the cross section, spin density matrix elements and K decay angular distribution for γp K + Y photoproduction, where Y is either a Λ or Σ hyperon. Figure 1.12 shows the predicted cross section ratio of dσ dσ /( dt dt t=t min ) for γp K + Λ photoproduction, where t is the Mandelstam variable. More information of Thornber Model could be found in [46]. Figure 1.12: The total cross sections ratio of dσ dσ /( dt dt t=t min ) for γp K + Λ photoproduction from Thornber Model. Image Source: [46]. 1.6 Previous Measurements of K Y Photoproduction While K photoproduction has been studied for over 4 years, recent new accelerator and detector technologies have greatly improved the quality and quantity of the world data for those reaction channels. In this section, we will briefly discussed about the most recent K Y photoproduction measurements.

36 1.6.1 γp K Σ +, CLAS 26 The first high statistics data of the differential cross sections for the γp K Σ + photoproduction came from the CLAS Collaboration[47, 48, 49], where the measurement covered the incident bremsstrahlung photon 5 beam energies (E γ ) from 1.7 to 3. GeV. The measurement follows the reactions: γ + p K + Σ +, where K K + + π. Two particles, namely K + and π, were detected. K and Σ + were then reconstructed from the invariant mass and missing mass of K + and π following momentum and energy conservation laws. Figure 1.13 shows those measured differential cross sections from E γ = 1.8125 to E γ = 2.9125 GeV. where the black curves are fits from the Zhao model[39] with the parameters a and b set to -2.2 and.8, respectively. At lower photon energy, the data, in general, have a flat angular distribution. As the energy goes up, the forward and backward angles start to dominate, which indicates the t-channel and u-channel contributions. 1.6.2 γp K Σ +, CBELSA/TAPS 28 Other differential cross section data available for K Σ + photoproduction is from the CBELSA/TAPS Collaboration[5], where the data cover the incident bremsstrahlung photon energies from the production threshold to 2.5 GeV. The measurement follows the decay chains: γ + p π + K + Σ +, then, K π + π, Σ + π + p 5 bremsstrahlung photon is described in the Chapter 2

37 Figure 1.13: The differential cross section of γp K Σ + measured at CLAS, the black curves are the fitting from Zhao Model[39] with a = -2.2 and b =.8. Image Source: [48]. and finally, π γ + γ. in other words, γ + p 8γ + p. Nine particles (eight photons and one proton) were detected and used to reconstruct the reaction channel using the momentum and energy conservations. Figure 1.14 shows the differential cross section result of γp K Σ + photoproduction, where the empty squares are from CLAS[48], while the solid dots are from CBELSA/TAPS[5]. The solid and dash-dotted curves are calculations from the Zhao model with the parameter setting of a = 2.7, b = -1.7 and a = -2.2, b =.8, respectively. The dashed and dotted curves are calculation from the Oh and Kim model with and without the t-channel κ exchange. The

38 band at the bottom is the systematic uncertainty for CBELSA/TAPS data. In general, the CBELSA/TAPS[5] and the CLAS[48] data agree with each other. However, as the E γ goes up, there starts to be some discrepancies between the two datasets at the forward angle region. To solve these discrepancies between the two data, another accurate measurement is necessary. Figure 1.14: The differential cross section of γp K Σ + measured at CBELSA/TAPS, where the empty squares are from CLAS[48], while the solid dots are from CBELSA/TAPS[5]. The solid and dash-dotted curves are calculation from Zhao Model with the parameter setting of a = 2.7, b = -1.7 and a = -2.2, b =.8, respectively. The dashed and dotted curves are calculation from Oh and Kim model with and without the t-channel κ exchange. The band at the bottom is the systematic uncertainty for CBELSA/TAPS data. Image Source: [5]. 1.6.3 γp K Σ +, LEPS 212 The most recent measurement of γp K Σ + photoproduction is from the LEPS Collaboration[33], where they measured the angular distribution and spin density matrix elements of channel. The measurement used the linearly polarized photon beams

39 generated by the laser backscattering technique with energies from 1.85 to 2.96 GeV at forward production angles. Reconstruction of the reaction channel is the same as that used by the CLAS, where K + and π were detected and then used to reconstruct the K and the Σ + from their invariant mass M( K +,π ) and missing mass MM( K +,π ) using energy and momentum conservation laws. Figure 1.15 shows the decay angular distribution of cosθ K +, φ K +, (φ - Φ) K + and Φ K + in the Gotfried-Jackson frame 6 from this measurement, and Figure 1.16 shows the spin density matrix elements extracted from γp K Σ +. Those results could be used to test the available theoretical models as well as put constrain on the parameters of those models. Figure 1.15: The decay angular distribution of cosθ K +, φ K +, (φ - Φ) K + and Φ K + in the Gotfried-Jackson frame for γp K Σ +. Image Source: [33]. 6 The definitions of the Gotfried-Jackson frame and Helicity frames are shown in the chapter of K + Λ recoil polarization for detail.

4 Figure 1.16: The spin density matrix elements extracted from γp K Σ + for Gotfried- Jackson and Helicity frames. Image Source: [33]. 1.6.4 γp K + Λ, CLAS 26 Another recent measurement of the K + Λ photoproduction was from the CLAS Collaboration[44]. The analysis covered the incident bremsstrahlung photo energies from 1.5 to 3.8 GeV. The reconstruction of the reaction channel follows: γ + p K + + Λ, then, K + K + + π and Λ π + p. Three particles K +, π and p were detected, then the Λ was reconstructed from the invariant mass of π and p (M(π p)), and the π was reconstructed from the missing mass of K +, π and p (MM(K + π p)). This analysis was not finished and only the preliminary total cross section is available, which can be seen as the red triangles in Figure 1.17. From the plots, comparing the K + Λ cross section ( blue dots) with the K + Λ cross section shows that it is several times smaller.

41 Figure 1.17: The preliminary K + Λ photoproduction total cross section (red triangles) measured at CLAS. Image Source: [44]. 1.6.5 γp K + Λ, SAPHIR 25 According to the Reference[5], the SAPHIR Collaboration also did a study on the K + Λ photoproduction[51]. The measurement follows the decay channel: γ + p K + + Λ, then, K + K + π + and Λ π + p, π +, π and p were detected in the analysis. The differential cross sections of this measurement show a forward peaking of the K +. The total cross section is.35µb at E γ = 2.2 GeV.

42 1.7 Summary In this chapter, we first described some general background behind our analysis. Then we showed two motivations for our analysis: searching for the missing resonance states and a test of theoretical models including the t-channel κ meson exchange. After that we discussed about several theoretical models and the currently available datasets for K photoproductions. In the following chapters, we will give more detail about of our analysis.

2 JEFFERSON LAB, CEBAF AND THE CLAS DETECTOR 43 The data used for this analysis was taken from May 17th to July 29th in 24 using the CLAS detector in Hall-B at the Thomas Jefferson National Accelerator Facility (TJNAF), which is also known as Jefferson Lab or JLab, in Newport News, Virginia. The dataset, called g11a, was taken as a part of experiment E4-21, and the main goal of which was to search for the pentaquark Θ + with high statistics[52]. However, the use of a loose trigger that allowed for other final states of this experiment and the large statistics of the dataset also provide for many other final states, including our reaction of interest with final state K + Λ and K + Σ. Figure 2.1 shows an aerial view of the Jefferson Lab on August 3, 211. Currently, JLab has three experimental halls that are capable of running experiments, and those experimental halls are named Hall-A, Hall-B and Hall-C. The 4th experimental hall, called Hall-D, which will be focus on photon physics, is now under construction and is expected to deliver the first beam by 214. There are also other facilities such as the accelerator, Test Lab and many others at JLab. Like other photoproduction experiments, g11a used the incident photon beam to hit the target (which is liquid hydrogen), then the interaction between the photon and the target will generate some new particles. By detecting and collecting the information of those newly generated particles, as well as the incident photon and target information along with other experimental information, different reaction channels can be studied. In the following sections of this chapter, the hardwares used in the g11a experiment will be discussed. 2.1 CEBAF As a photoproduction experiment, the first thing is to make the incident photon beam. However, the accelerator at JLab is only able to provide electron beams directly to the

44 Figure 2.1: An Aerial view of Jefferson Lab on August 3, 211. Image Sources: Reference[53] experimental halls. To get the photon beams, one more step is needed. In this section, we will discuss the accelerator at JLab, and in the following section, we will show how to convert the electron beams to the photon beams by using the Tagging system at Hall-B. CEBAF is an abbreviation of the Continuous Electron Beam Accelerator Facility, which is funded by the US Department of Energy (DOE). The construction of CEBAF started in 1987, by 1995 it began to run the first physics experiments.[54], since then it experienced several upgrades. Currently CEBAF is able to provide electron beams to experimental Hall-A, Hall-B and Hall-C simultaneously with the minimum and maximum beam energy of.6 and 6 GeV, respectively. With the current upgrade, by 214, it will be able to extend the maximum electron beam energy to 12 GeV as well as provide beam to the newly constructed experimental Hall-D.

45 Figure 2.2 shows the machine configuration of CEBAF. To provide the electron beams to the experimental halls, the electrons are first generated by illuminating a GaAs photocathode with pulsed lasers, which are tuned such that each experimental hall receives electron beams every 2 ns[56]. Then these generated electrons will pass through two and a quarter Superconducting Radio Frequency (SRF) Niobium cavities, which will accelerate the electrons to 67 MeV. After this step, the electrons will be injected to the accelerator LINAC by the Injector. Figure 2.2: The machine configuration of the Continuous Electron Beam Accelerator Facility (CEBAF). Image Sources: Reference[57] The SRF technology and the use of up to 5 multipass beam recirculation are two of the most important features of the CEBAF. These features let CEBAF obtain a 1% duty factor and hence a quick acquisition of high statistics data. This minimizes the construction and operation cost, as well as allowing for future upgrades.

46 There are two LINACs in the CEBAF, which are called the South LINAC and the North LINAC respectively, each of which has a length of 7 8 mile, and contains 2 cryomodules and is able to accelerate the electrons by.6 GeV per pass[57]. Each cryomodule contains 8 SRF Niobium cavities, which adds up to 16 SRF Niobium cavities for each LINAC. Figure 2.3 shows a model of cryomodule, which contains several SRF Niobium cavities. The Helium refrigerator supplies helium to cool those cavities to -271 C during operation, at which temperature these cavities become superconducting. Radio frequency standing waves are set up and tuned in the cavities so that each bunch of electron will get a continuous accelerating electric force when it passes through the cavities (see Figure 2.4). Figure 2.3: A model of cryomodule which contains several Superconducting Radio Frequency (SRF) Niobium cavities. Image taken by Wei Tang. The Recirculation Arcs have 4 and 5 levels on the east and west sides of CEBAF respectively, which bend the beams with a magetic force and allow the beams to pass

47 Figure 2.4: A cross section view of Superconducting Radio Frequency (SRF) Niobium cavities. The Standing waves are tuned so that each bunch of electrons will get a continuous accelerating electric force when it passes through the cavities. Image Sources: Reference[58] through each LINAC up to five times (each time at different Recirculation Arc level) reaching a maximum energy around 6 GeV. With the current upgrade, 5 more newly designed cryomodules will be added to each LINAC and a new level will be added to the east side of the Recirculation Arc. After the upgrade, the CEBAF will be able to produce a maximum electron beam energy of 12 GeV. The Extraction Elements located at the end of south LINAC will split and transport the electron beam to the three experimental halls simultaneously, provided that no other hall uses the same beam energy. The number of beam passes (beam energy) and the beam intensity can be controlled by each experimental hall. 2.2 The Hall-B Tagging System CEBAF provides the continuous electron beams to each experimental hall, but to get the photon beams, one more step is needed. In the experimental Hall-B at Jefferson Lab, this is accomplished by the Tagging System. The photons, generated at Hall-B, are Bremsstrahlung photons. The technique used to generate the photons is the electron Bremsstrahlung process. When an electron is

48 decelerated by a nucleus, the electron will emit a photon. Because the nucleus is much heavier than the electron, the energy transfered to the nucleus is negligible, thus to obey the energy conservation law, the energy of the Bremsstrahlung photon equals the energy difference between the incident electron and the decelerated electron. If the incident electron has an energy above a few MeV, both the Bremsstrahlung photon and the decelerated electron will have a very small angle with respect to the incident electron, which is described by θ γ =.511/E and θ e = θ γ E γ /E e respectively[59], where E, E γ and E e are the incident electron energy, the Bremsstrahlung photon energy and the decelerated electron energy with units of MeV. For the g11a experiment, the incident electron beam had an energy of about 4 GeV. Hence, both θ γ and θ e are smaller than 1 mrad. By approximation, both the Bremsstrahlung photon and the decelerated electron are still travelling along the original incident electron direction at the scale of the Hall-B Tagging System. The Electron beams are provided by CEBAF as described in the previous section, while the target used for this electron Bremsstrahlung process is called radiator, which is a gold foil with a radiation length of 1 4 for g11a experiment. The radiation length L is the thickness of a material that reduce the mean energy of an electron beam by a factor of exponential e ( 2.71828), and it depends on the type of nucleus and is defined as[8]: 1 L = 4Z(Z+1)r2 e N 137A ln( 183 Z 1/3 ), and r e = e2 mc 2 where N is Avogadro s number, Z and A are the atomic number and mass number of the nucleus, while e and m are the electron charge and mass respectively. Although the photons produced for g11a experimental are unpolarized, the CLAS Tagging System is capable of producing circular polarization and linear polarization photon beams, where the former required CEBAF to provide the longitudinally polarized electron beams and the latter requires the radiator to be a thin diamond crystal. More details of producing polarized photon beam at experimental Hall-B can be found in the Reference[6]

49 After passing through the radiator, the beam is a mixture of electrons and photons. To remove the electrons from the beam and get the energies of the photons, a tagger magnet and two hodoscope scintillator planes were used. The tagger magnet is used to sweep away the charged electrons and only leave the photons in the beam. The magnet was set so that the non-interacting electrons are sent to the beam dump directly, while those recoil electrons hit the two hodoscope planes (see Figure 2.5). The two hodoscope planes were used to measure the momentum and timing of those recoil electrons. The first hodoscope plane, called the E plane, which contains 384 partially overlapping narrow scintillators (each scintillator of 2 cm long, 4 mm thick and a varied width ranging from 6 to 18 mm[59]) are used to measure the momentum of the recoil electrons. The momentum resolution of the E plane is 1 1 3 E. The second hodoscope, called T plane, which contains 61 relatively larger scintillators (each scintillator is 2 cm thick and a varied length and width) are used to provide the timing precision needed for the coincidence with any subsequent events triggered by the interaction of corresponding photons in the targets[59]. The T plane has a timing resolution 11 ps. The E and T planes are able to tag the Bremsstrahlung photon energies over a range between 2% and 95% of the incident electron energy E, with the maximum E up to 6 GeV. Figure 2.6 shows a schematic diagram of how the E and T planes work. The signal generated by the scintillators of E and T planes are collected by the photomultipliers and their output is sent to the tagger readout electronic system. The processed information from the tagger readout electronic system is used for the offline analysis. Figure 2.7 shows the schemetic diagram of the tagger readout electronic system. For more information of this tagger readout electronic system please see the Reference[59].

5 Figure 2.5: Schematic diagram of the Hall-B Tagging system. Image Sources: Reference[59] Figure 2.6: Schematic diagram of how the E and T planes work. Image Sources: Reference[59] The final parts of the Hall-B tagging systems are two sets of interchangeable collimators (see Figure 2.5), which are used to further define the Bremsstralung photon

51 Figure 2.7: Schematic diagram of the tagger readout system. Image Sources: Reference[59] beam position, and make the beam centered on the beamline. There are also two sweep magnets between the two collimators, which are used to clean up the charged particles generated by the photons in the collimator walls. 2.3 The g11a Target The target for the g11a experiment was liquid H 2, which is the most common target used at Hall-B. However, liquid targets like 3 He, 4 He and D 2, and solid targets like Fe, Pb and Al were also used for other experiments runned at Hall-B. The liquid H 2 used for g11a was filled in a cylindrical Kapton chamber with 2 cm radius and 4 cm length[61]. The target density was determined by using the temperature and pressure inside the Kapton chamber which were monitored once per hour during the g11a run. The average target density was.7177 g/cm 3 for the g11a experiment. The target was put at the center of the CLAS detector (see the following section for detail) Figure 2.8 shows the schematic drawing of the g11a target.

52 Figure 2.8: Schematic diagram of the g11a target. Image Sources: Reference[62] 2.4 The CLAS Detector The CEBAF large acceptance spectrometer (the CLAS detector) is used to detect particles generated from the interaction of the incident photons or electrons with the target. The CLAS detector is able to track charged particles that have the momenta larger than 2 MeV/c, and covers the polar angles from 8 to 142 over 8% of the azimuthal region. The CLAS detector contains many sub-detecting systems. In this section, we will briefly discuss those sub-detecting systems used in the g11a experiment. Figure 2.9 shows a photograph of the CLAS detector. 2.4.1 Start Counter The Start Counter is used in the photoproduction experiments, which measures the vertex time at which the incoming photon hit the target by detecting the outgoing particles. The g11a experiment used a newly designed Start Counter, explicitly for high intensity photon beam running. This new Start Counter was constructed of 24 2.2-mm thick scintillator paddles, with an average time resolution of 35 ps[63]. Even though

53 Figure 2.9: A photograph of the CLAS detector. Image Sources: Reference[53] we do not need the timing information from the Start Counter in our analysis, each event recorded in g11a data did require a Start Counter trigger. Figure 2.1 shows a schematic plot of the newly designed Start Counter. 2.4.2 Superconducting Toroidal Magnet One of the most important parts of the CLAS detector is the superconducting toroidal magnet, which generates the magnetic field to bent the outgoing particles to travel through the drift chambers (discussed in the next subsection) along non-linear paths. Those trajectories are used to determine the momenta of the outgoing particles. The magnet consists of 6 identical kidney shaped iron-free coils, each of which has four layers of 54 turns of aluminum-stabilized NbTi/Cu conductor[6]. During the operation the magnet was cooled to 4.5 K by liquid Helium. The magnet was designed with the maximum operating current of 386 A, where the magnetic field can reach 2.5 T in the forward

54 Figure 2.1: A schematic plot of the Start Counter, where the purple cylindrical tube represents the target Kapton chamber. Image Sources: Reference[63] direction. However, during rountine operations, the maximum current was limited to 3375 A. For the g11a experiment, the maximum current was set to 192 A, which leads to a maximum magnetic field 1.8 T. The setup of this field configuration bends negatively charged particles toward the beamline and positively charged paritcles away from the beamline, while keeping the azimuthal angle unchanged. Figure 2.11 shows a photograph of the superconducting toroidal magnet during construction. 2.4.3 Drift Chambers The Drift Chambers are used to determine the momentum of each charged particle by tracking its trajectory. As described in the previous subsection, the superconducting toroidal magnet has 6 identical coils, which naturally divide the drift chambers azimuthally into six sectors. For each sector there are 3 drift chambers located at different distance from the center of the CLAS detector. These three drift chambers are called region 1, 2 and 3 drift chambers, respectively. The region 1 chamber is the smallest

55 Figure 2.11: A photograph of the superconducting toroidal magnet during the construction. Image Sources: Reference[55] chamber, which surrounds the target in a low magnetic field. The region 2 chamber is relatively larger and sits between the magnet coils in an area of high magnetic field. The region 3 chamber is the largest one, which is located radially outside of the magnetic coils. Considering all six sectors, there are 18 drift chambers in total. The drift chambers were filled with 9% argon and 1% CO 2 gas. This choice considered several factors including reasonably low multiple scattering, reasonable gas gain, low cost and safety. For more information on the CLAS drift chamber system, [64] is a good reference. Figure 2.12 shows a schematic plot of the CLAS detector, where the purple region represents the drift chambers and cyan region is for the superconducting toroidal magnet.

56 Figure 2.12: A schematic plot of the CLAS detector. Image Sources: Reference[55] 2.4.4 The Time of Flight System The time of flight (TOF) system is used to measure the time and position of each charged particle that hit the TOF scintillators. This information was used for the particle identification in the off-line analysis. Like drift chambers, the TOF system also has six sectors, each of which has four panels with 57 scintillators in total. Those scintillators are 5.8 cm thick, 15 or 22 cm in width and with lengths from 32 to 45 cm. The TOF system covers the polar angles from 8 to 142 and the entire active range in azimuthal angle. The time resolution of the TOF system is about 8 ps to 16 ps, depending on the length of the scintillators. Figure 2.13 shows a schematic plot of one sector of the CLAS TOF system. More information of the CLAS TOF system can be found in reference[65].

57 Figure 2.13: A schematic plot of one sector of the CLAS TOF system. Image Sources: Reference[55] 2.4.5 Other Sub-detecting Systems As can be seen in Figure 2.12, The CLAS detector has some other sub-detecting systems like Cherenkov Counters for electron/pion separation and Electromagnetic Shower Counters for electron and high energy neutral particles identification. More information of these CLAS sub-detecting systems could be found in reference[6, 66, 67]. 2.5 Beamline Devices To diagnose the quality of the beam, several instruments are used along the beamline. The beam-position monitors (BPMs) measure the electron beam position coordinate (x, y) and the beam intensity. There are three BPMs locate at 36., 24.6 and 8.2 m upstream of the CLAS target, each of which consists of three RF cavities. For the photon beam experiments like g11a, only the first two BPMs were used.

58 The harp, which is made of two orthogonal tungsten and iron wires, is used to measure the beam profile by passing through the beam. The measurements were taken only when the CLAS detector is not taking the data. There are three harps in use located at 36.7, 22.1 and 15.5 m upstream of the CLAS target. A large lead-glass total absorption shower counter (TASC) was inserted into the photon beam to measure the absolute photon flux. The TASC has an efficiency of 1%, however, it can only be used at beam currents less than 1 pa. Two other devices, the Pair Spectrometer and the Pair Counter, that can be used at high photon beam currents, are used with the TASC to measure the photon flux. For more information of the beamline devices, please see reference[59, 6] 2.6 Trigger System and Data Acquisition There are two levels of the trigger system used in CLAS. The lever l trigger uses part or all available prompt information from the photomultipliers to determine if there is an event, while the level 2 trigger is used to clear the events that satisfy the level 1 trigger but have no tracks in the drift chambers. The g11a experiment used the CLAS level 1 trigger and required that at least two tracks were detected and these two tracks were not in the same sector. Once an event satisfied this condition, it was written to magnetic tape for future analysis. The Data Acquisition system used at g11a run was able to run at 5 khz. For more information of the Trigger and Data Acquisition systems, please see the Reference[6]. 2.7 Summary In this chapter, we gave an overview of the CEBAF accelerator, several sub-detecting systems of the CLAS detector and some beamline devices. In the following chapters, we will show the details of our analysis with the CLAS g11a data.

3 EVENT SELECTION 59 As the world s largest photoproduction dataset at the time when it was taken, the CLAS g11a data contains 2 billion triggers and take the storage space of 21 TB on the magnetic tape at JLab. Before the data is available for the physics analysis, a process called cooking is performed, which calibrates and converts the information that was recorded by each CLAS sub-detecting system into a form that is suitable for physics analysis. The cooking details of the g11a data are documented in reference[68]. In the following sections of this chapter, we will discuss the event selection of our analysis. 3.1 Channels of Interest The reaction channels that we are interested in are γ + p K + + Λ and γ + p K + + Σ, where K + is a vector meson with the valence quark structure of u s, while Λ and Σ are both hyperons that have the same valence quark structure of uds and isospins and 1, respectively. Table 3.1 lists some properties of these particles. Because K + is an unstable particle, it will quickly decay to Kπ (66.7% to K π + and 33.3% to K + π ) through the strong interaction. The K + can not be directly detected by the CLAS detector. By applying energy and momentum conservation laws, we can reconstruct the K + through its decay particles. In this analysis, we will reconstruct the K + from its K π + decay channel. Also, as the CLAS detector was designed for detecting charged particles and is not optimized for detecting neutral particles, hence we will not detect the K directly but will reconstruct it from its decay daughters as well. In addition, if a neutral particle decays outside of the Start Counter, there will not be a trigger for it, thus it will not be detected by the CLAS detector. The K is a mixture of 5% K S and 5% K L (see the properties of K S and K L in Table 3.2), where the mean lifetime of a K L is 5.116 1 8 s (see Table 3.2), while the shortest distance from the target center to the Start Counter is approximately 1 cm[63], which is much smaller than the decay length of

6 K L ( 15 m), thus almost all of K L will decay outside of the Start Counter and can not be directly detected by the CLAS detector. On the other hand, with the mean life time of.8958 1 1 s, K S has a decay length of 2.69 cm, thus most of K S will decay inside the Start Counter. Therefore we chose to reconstruct the K S (5% of K ) from its decay channel K S π + + π, which has a decay branching ratio of 69.2%. The fraction of events that miss the trigger can be corrected using Monte Carlo simulations. Table 3.1: Some physical properties of K +, Λ and Σ [35] K + Λ Σ Mass(GeV).89166 1.11568 1.19264 I(J P 1 ) 2 (1 ) ( 1 + ) 1( 1 + ) 2 2 Mean life(s) 1.3 1 23 2.63 1 1 7.4 1 2 Decay channel K π +, K + π pπ, nπ Λγ and ratio 66.7%, 33.3% 63.9%, 35.8% 1% Table 3.2: Some physical properties of K S and K L. l represents either e or µ[35] Mean life(s) decay mode decay ratio K S.8958 1 1 π π, π + π 3.7%, 69.2% K L 5.116 1 8 π π π, π + π π, π ± l ν l 19.5%, 12.5%, 67.6% In short, we will measure the differential and total cross sections of the photoproduction channels: γ + p K + + Λ and γ + p K + + Σ followed by

61 K + K + π + and K S π + + π. The K + and K S can be reconstructed from their decay daughters π + π π + and π + π, while the Λ and Σ can be reproduced from a combination of the π + π π + momenta and the incident photon energy E γ by using the energy and momentum conservation laws. Since two π + and one π are detected, we started our analysis from the + + - skimmed CLAS g11a data 7. 3.2 Excluded Runs The data taken at CLAS is grouped into Runs, each of which contains 2 to 4 sub-run files and is an independent accumulation of data. According to [68], the CLAS g11a data was taken between May the 17th and July the 29th in 24, which includes 421 production Runs that range from Run 4349 to Run 44133. Runs 4349 to 4417 were taken with the electron beam energy of 4.19 GeV, while Runs 4418 to 44133 were taken with the electron beam energy of 5.21 GeV. To avoid the potential systematic difference between the two different incident electron beam energy data, we only used Runs 43526 to 4417 for our analysis. Runs from 4349 to 43525 were also excluded because they were run for a commissioning study and were not to be used for physics analysis. Runs between 43526 and 4417 that have, for example, Drift Chamber (DC), TOF and Trigger problems were also excluded. In addition, Run or Sub-Run files that do not have corresponding gflux files were removed as well. The gflux files store the information of the incident photon flux for each Run, which will be used to normalize the cross section result (see the following chapters for more details). Without the gflux files, we could only get the yield from the data, but could not calculate the observables such as cross sections. Also, if a gflux file exists, and there is no corresponding experimental file, this gflux file 7 Because the g11a data is very big ( 21 TB), the processing requires too much computing resources. To reduce the complexity and computing time of this analysis, we used the skimmed + + - g11a data, which only contains events with at least two positive and one negative charged tracks. Although the skimmed + + - g11a data is a subset of the full g11a data, all the information that we need is contained in it.

62 was removed from the normalization as well. In other words, we have a one to one corresponding between the experimental files and the gflux files. The total number of sub-run files for 4.19 GeV energy electron beam is 9811, after excluding all of the problematic files, there are 8724 files left, which accounts for 88.9% of all the available + + - skimmed g11a data with the electron beam energy of 4.19 GeV. Even though 11.1% of the files were removed, we still have enough statistics for our analysis. Table 3.3 gives a summary of the excluded problematic Runs, while Table 3.4 shows the excluded Runs that do not have corresponding gflux files 8. Table 3.3: Excluded problematic Runs[56]. Runs Exclude Reason 4349-43525 Comissioning Runs 43675-43676 Trigger Configuration are different 43777-43778 Trigger Configuration are different 43981-43982 DC Problems listed in logbook 43989-43991 DAQ Problems listed in logbook 4499 TOF Problem 4413 Trigger Configuration are different 4418-44133 5.21 GeV Electron Beam Energy 3.2.1 CLAS Standard Corrections to the Data The CLAS standard correction packages were applied in our analysis to improve the quality of data. Those corrections include: energy loss (Eloss) corrections, tagger 8 Note that some sub-runs were also excluded for this reason, but not listed here, for example, the Sub-Run 4493 a18 was excluded but is not list in the table because the other 4493 Sub-Runs were good.

63 Table 3.4: Excluded Runs that do not have a corresponding gflux files. Exclude Runs 43529-43531 43535-43539 43542-43546 43559-4356 43573, 43597 4365-4367 43627-43628 4366-43665 43667-43671 43673-43674 43688-43691 43699-437 43711-43717 43723-43724 43727, 43768 43774-43775 43779-43781 43794-43795 4384-4386 43811 43861 43825-43826 43828-43831 43847-4385 43868-4387 43873, 43878 43893, 449 43898-43899 4397-43999 443-446 4415-4416 4424, 4437 4426-4435 4439-4442 4453-4454 447-4471 441 corrections and momentum corrections. In the following part, we will briefly discuss each of them. Eloss Corrections: The momentum of the charged particles in CLAS is determined by their tracks in the drift chambers. However, before those charged particles reach the region 1 drift chambers, they have to pass through various of materials which include the target, the target walls, the beam pipe, the start counter and even the air gap between the start counter and the region 1 drift chamber. During this trip, the particles will lose some energy. The CLAS Energy Loss correction software package (Eloss), which was written by Eugene Pasyuk[69] for the CLAS detector, was used to correct the energy loss of each detected charged particle due to the particle traveling through these materials. The energy correction by the Eloss is generally on the order of several MeV, however, for

64 the low momentum particles the correction could be quite substantial. The Eloss corrections were applied to all charged particles that are heavier than electrons. Figure 3.1 shows the Eloss correction effect for our detected pions, where the x-axis is the pion momentum, while the y-axis is the energy difference of these pions before and after the Eloss correction, which is defined as: δe= E cor - E non cor, where the E non cor and E cor are the pion energy before and after the Eloss correction, respectively. From Figure 3.1 we can see that the Eloss correction only has a very small effect on the detected pion energies..1.9.8.7 δe (GeV).6.5.4.3.2.1.5 1 1.5 2 2.5 3 p (GeV) Figure 3.1: The Eloss Correction effect of the detected pion energies. The x-axis is the pion momentum, and the y-axis is the energy difference of those pions as explained in the text. Both axis are in units of GeV. Tagger Corrections: As described in the Chapter 2, for a photoproduction experiment, the incident photon beam energies are determined by the E-counters of the

65 CLAS tagging system. However, as was first found in 23 [7, 71, 72], due to the mechanical sagging of the tagger, there are some alignment issues in the photon tagger s focal plane, which leads to an inaccurate reconstruction of photon energies from the raw tagger information. To correct the mechanical sagging of the CLAS tagger for the g11a dataset, the CLAS standard tagger correction was used, which is an empirical correction and was developed from γp pπ + π reaction by Michael Williams[56, 73]. Figure 3.2 shows the tagger correction needed as ploted versus the E-counter for the channel γp pπ + π using g11a dataset, which is a reproduction of the original result[56, 73]. Figure3.3 gives the tagger correction effect on our K + Λ and K + Σ channel. The left plot of Figure 3.3 shows the distribution of δe, which is defined as δe = E cor - E non cor, where E cor represents the incident photon energy after the tagger correction while E non cor is the incident photon energy before the tagger correction. The right plot of Figure3.3 shows three-pion missing mass (MM(π + π π + )) without(red) and with(blue) the tagger correction. The two straight lines represent the PDG mass value [35] for Λ and Σ, respectively. From these plots we can see that after applying the tagger correction, the photon energies are slightly corrected, and the Λ and Σ peaks are more centered on the PDG value. Momentum Correction: The momentum corrections are used to correct the charged particles momentum due to the discrepancies between the ideal magnetic field map of CLAS and the actual magnetic field when taking the data, and also to correct misalignments and wire sags of various components. The momentum corrections for the g11a dataset is also an empirical correction and was developed from the γp pπ + π reaction by Michael Williams[56, 73]. Figure 3.4 shows an example of the two-pion invariant mass (M(π + π )) plot of the K S (left) and the three-pion missing mass

66 Figure 3.2: Left: E γ /E beam versus E-counter for the reaction γp pπ + π using g11a data. Right: Gaussian mean value extracted for each E-counter from the left plot. Image Sources: [75] x 1 3 Counts 2 175 15 125 1 75 5 25 -.4 -.3 -.2 -.1.1.2.3.4 δe (GeV) Counts 3 25 2 15 1 5 1 1.1 1.2 1.3 1.4 1.5 MM(π + π + π - )(GeV/c 2 ) Figure 3.3: Left: the distribution of δe, which is defined as δe = E cor - E non cor, where E cor represents the incident photon energy after the tagger correction while E non cor is the incident photon energy before the tagger correction. Right: three-pion missing mass plot without(red) and with(blue) the tagger correction, the two straight lines represent the PDG mass[35] for the Λ and Σ, respectively. Both plots have the unit of GeV. (MM(π + π π + )) plot of the Λ(Σ ) (right) before (red curves) and after (blue curves) the momentum corrections, where the solid lines show the corresponding invariant mass value