On Antihyperon-Hyperon Production in Antiproton-Proton Collisions with the PANDA Experiment

Transcription

1 On Antihyperon-Hyperon Production in Antiproton-Proton Collisions with the PANDA Experiment A Thesis submitted for the degree of Master of Science in Engineering Physics Catarina E. Sahlberg Department of Nuclear and Particle Physics Uppsala University March 2007

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3 Abstract The PANDA project is an international particle physics collaboration, aimed at investigating unsolved questions regarding the strong interaction. This will be done through the construction of a state-of-the-art particle detector, to allow detection of particles produced in antiproton-proton annihilation in experiments planned to be preformed at the future FAIR research centre in Darmstadt, Germany. The aim of this work is to contribute to the development of a software for simulations of reactions in the PANDA experiment. An event generator for the reaction pp ΛΛ pπ + pπ was created, with regard to spin observables and target properties. Experimental information for the differential cross section of the pp ΛΛ reaction, Λ/Λ-polarisation and Λ-Λ spin correlation was considered.

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5 Contents 1 Introduction 1 2 Theoretical Background Introduction Matter Particles Quarks Leptons Forces and Force Carriers Hadrons The Quark Model Hadrons within the Quark Model Exotic Hadrons Open Questions Confinement The Origin of Mass Symmetries Parity Charge conjugation Time Reversal G-parity Broken Symmetries Note on the Units The PANDA Project Introduction Physical Motivation FAIR Detector Interaction Region Target Spectrometer Forward Spectrometer Software The pp ΛΛ pπ + pπ Reaction The pp System The pp ΛΛ Reaction Coordinate System Production Kinematics iii

6 4.2.3 Spin Observables Symmetries Cross Section Decay of Λ The Λ pπ Decay Channel Angular Distribution Simulations Introduction Event Generation Extended Target Decay Vertices Differential Cross Section Polarisation Spin Correlations Reconstruction Extended Target Momentum of Λ from Opening Angles Production Angle of Λ Conclusion and Outlook Summary and Conclusion Outlook A Statistics 69 A.1 The Method of Moments A.2 Weighting A.3 Random Number Generation A.3.1 Transformation Method A.3.2 Rejection Method B Relativistic Kinematics 73 B.1 Four-vectors B.2 Reference Frames B.3 Lorentz Transformation B.4 Mandelstam Variables B.4.1 Invariant Mass B.4.2 Four-momentum Transfer C Momentum in two-body decay 79 iv

7 Chapter 1 Introduction In 1947, during an experiment studying the interactions of cosmic rays, G. Rochester and C. Butler discovered a new type of particle. The particle had a surprisingly long life time, approximately 13 orders of magnitude longer than what had been expected. This property of the particle along with the fact that it decayed via the weak interaction although being produced through the strong interaction, puzzled scientists. In the following years Rochester and Butler found other particles which showed similar such strange properties. These particle were assigned a property dubbed strangeness, and the particles were later to be referred to as strange particles. [1] The discovery of the strange particles caused great excitement at the time, since they indicated the existence of a new form of matter which was completely unexpected at the time.[2] With this and other contemporary discoveries, the notion of a particle zoo was created, which referred to the multitude of new particles that were being discovered.[1] In 1964 Gell-Mann postulated the existence of quarks to organize these particles, which lay the foundation of modern particle physics. Today, particle physics is one of the most active and expanding fields of physics. It sets out to explain the universal principles that govern even everyday phenomena by studies of the most elementary levels of the universe. The goal of particle physics is to gain understanding of the building blocks of matter and the forces between these that makes them stay together. To address questions regarding these issues, particle physicists seek to create experiments that might show properties of the elementary interactions, by isolating and identifying reactions between elementary particles. Although experiments studying naturally occurring particles for instance in cosmic rays, similar to the experiments of Rochester and Butler, are still performed, most of the particle physics experiments today are made in large accelerator facilities. Here a beam of particles is created, and then sent to collide with another beam of particles or a slab of some material. The reactions between the beam particles and the colliding particles are then carefully detected and analysed. All of these experiments rely on sophisticated detectors that employ a range of advanced technologies to measure and record particle properties. In Germany, a new particle accelerator facility called FAIR (Facility for Antiproton and Ion Research) is being built that will be able to produce beams of antiprotons with higher intensities and energy resolutions than ever before. 1

8 It will be suited for a number of experiments, of which the PANDA experiment is one of the most prominent. The PANDA project is focused on developing a state-of-the-art particle detector to be used in the accelerator to study the properties of the force that enables the production of strange particles, the strong force. It will make use of a beam of antiprotons accelerated to high momenta, colliding with an internal target of protons. The aim of this Diploma thesis is to make a contribution to the development of a computer framework for simulations of the reactions thought to take place at the PANDA detector. This work has focused on the production of the lightest antihyperon-hyperon pair decaying to a proton-pion and an antiproton-pion pair, i.e. the reaction pp ΛΛ pπ + pπ where the Λ particle happens to be the second of the strange particles discovered by Rochester and Butler. The work includes the construction of an event generator for this reaction, with particles produced according to distributions based on experimentally determined differential cross sections, polarisations and spin correlations. Regard has also been taken to the properties of the two main target types envisioned for PANDA. Although the work is limited to the discussion of Λ particle production and decay, the methods presented here should be possible to implement on other production and decay channels as well. This report starts with giving a brief introduction to particle physics in Chapter 2, to make the reader up to date with the theoretical background of the PANDA project. This chapter also treats some of the unresolved questions that explains the importance of the project. The project itself is described in the following chapter. Chapter 4 discusses the theory specific to the simulations that have been investigated and the work with the simulations is described in Chapter 5. The report is finished with a short conclusion and outlook. In the appendices some awkward but relevant theory and derivations are presented. 2

9 Chapter 2 Theoretical Background This chapter discusses the general theoretical background for the work. It gives a brief introduction to the Standard Model of particle physics (Section 2.1), and thereafter a description of the different parts of this theory: fundamental particles (Section 2.2), force carriers (Section 2.3) and non-elementary particles (Section 2.4). This is completed with a discussion of some of the complications with the Standard Model and some remaining question within the field of hadron physics (Section 2.5). The chapter is ended with a discussion of symmetries in quantum mechanics (Section 2.6) and a note on the units used in this work (Section 2.7). 2.1 Introduction The so-called Standard Model of Particles and Forces is a quantum field theory that describes all the current knowledge about particle physics. It describes the fundamental particles, of which all matter is composed, and the interaction between these. The Standard Model includes 12 fundamental matter particles and their antiparticles, 12 force carrying particles that are responsible for the interaction between the matter particles, as well as a number of thus far unobserved particles that has been predicted based on the theory. 2.2 Matter Particles The fundamental particles that make up the matter of the world can be organized in two groups, the quarks and the leptons. These are both fermions 1 of spin 1/2 and, as far as we know point-like Quarks There are six known quarks, ordered in three different categories, or generations, depending on their mass and charge properties (see Table 2.1). The first generation of quarks consists of the light up (u) and down (d) quarks, the second generation of the strange (s) and the charm (c) quark, and the third generation of the heavy bottom (b) and top (t) quarks. 1 Particles of half-integer spin. 3

10 Generation Name Symbol Charge Mass Flavour Antie [MeV/c 2 ] particle 1 Up Down u d +2/3 1/ I 3 = +1/2 I 3 = 1/2 u d 2 Strange s 1/3 95 ± 25 S = 1 s Charm c +2/ ± 90 C = 1 c 3 Bottom b 1/ ± 70 B = 1 b Top t +2/ ± 2100 T = 1 t Table 2.1: The properties of the six quarks.[3] All quarks carry baryon number 1/3 and spin 1/2. The anti-quarks have the same mass as their respective quark, but opposite flavour, electric charge and baryon number. All quarks carry a property called flavour (see column 6 of Table 2.1). The flavour of the u and d is the isospin (I), the up quark carry half a unit of positive third component isospin while the down quark carry half a unit of negative third component isospin. The s quark carry one unit of negative strangeness (S), the c quark one unit of charm (C), the b quark one unit of negative bottomness or beauty ( B) and the t quark one unit of topness or truth (T ). Quarks and antiquarks cannot be observed individually due to the property of the strong interaction and are always confined in particles called hadrons. The quarks are fermions and as such they have to obey the Pauli exclusion principle. But since they all have the same spin, in order to be distinguishable they carry an additional quantum number, called colour charge. Quarks carry either red, blue or green colour, while antiquarks carry antired, antiblue or antigreen colour. The only objects that can be observed are colourless, which arises from the fact that a colour together with its corresponding anticolour, or all three colours together, produce colour neutral objects Leptons There are six known leptons, and in the same way as with the quarks, they can be organized in three generations, as is indicated in Table 2.2. The electron (e) and the electron neutrino (ν e ) make up the first generation, the muon (µ) and the muon neutrino (ν µ ) the second, and the tau (τ) and the tau neutrino (ν τ ) the third. The leptons carry a so-called lepton number, distinct for each generation. The total lepton number in a system is always conserved in any reaction. All visible matter in the universe is composed of the quarks and leptons of the first generation. Particles composed of quarks and leptons of higher generations are short lived and decays to particles composed of first generation fundamental particles. [4] 2.3 Forces and Force Carriers There are four fundamental forces, from which all other forces can be derived: the strong, the weak, the electromagnetic and the gravitational. The first three are included in the Standard Model, although efforts so far unsuccessful 4

11 Generation Name Symbol Charge Mass Antie [MeV/c 2 ] particle 1 Electron Electron neutrino e ν e < 2 10 e + ν e 6 2 Muon neutrino ν µ 0 < 0.19 ν µ Muon µ µ 3 Tau τ τ Tau neutrino ν τ 0 < ν τ Table 2.2: The properties of the six leptons.[3] The anti-leptons have the same mass as their respective lepton, but opposite lepton number and electric charge. have been made to include the last as well. But since the gravitational force is significantly weaker than the others on the level of particle physics, it can be neglected. Each force within the Standard Model is mediated by gauge bosons, and couple to a certain property of the particles on which it acts. The properties of the gauge bosons are listed in Table 2.3. The notation J P C refers to the quantum numbers of the gauge bosons where J is the total spin, P is parity and C is C-parity. Parity and C-parity will be discussed in greater detail in Section 2.6. Force Name Symbol Charge Mass J P C e [GeV/c 2 ] Electromagnetic Photon γ Weak Z boson Z ± W boson W ± ± ± Strong Gluon g Table 2.3: The properties of the four gauge bosons.[3] The electromagnetic interaction is mediated by the exchange of massless photons and acts on the electrical charge. It has infinite range and is practically the only force within the Standard Model that we notice in our daily life. The electromagnetic force is responsible for keeping the electrons and nucleons of the atom together, as well as keeping together the different atoms in a molecule. The phenomena involving the electromagnetic interaction is described in the theory of Quantum Electrodynamics (QED). [5] The weak interaction is mediated by the heavy bosons Z 0, W + and W, and acts on the flavour of particles. It has a relative short range, about m, and is the only force that can violate the conservation of flavour in an interaction. Therefore it plays a major role in the process of a nuclear decay, for example β decay in which a neutron is converted into a proton together with an emission of an electron and an electron neutrino. [5] The strong interaction is carried by massless particles called gluons and couples to the colour charge of the particles. The strong force has a smaller range than the weak force, only about m and is the force that creates the interaction between quarks. It is also responsible for binding the nucleons together inside the nucleus. The theory describing the strong interaction is called Quantum Chromodynamics (QCD). Unlike the one photon of the electromagnetic 5

12 interaction, and the three W and Z bosons of the weak interaction, the Standard model includes eight independent gluons for the strong interaction. And unlike the photon, which is electrically neutral, the gluons themselves carry colour charge, which means that they can interact among themselves. It is this property that causes the quarks to be confined within the hadrons. Gluons are thought to simultaneously carry both colour and anticolour. [5] 2.4 Hadrons Particles composed of quarks and gluons are called hadrons, defined by their interactions via the strong force. The hadrons can be either baryons, defined as particles of baryon number B = 1, or mesons, defined as particles of baryon number B = 0, where the baryon number of a particle is the sum of the baryon number of its constituents. Hadrons are seen as containing both so-called valence quarks and possibly also valence gluons and a sea made up of virtual gluons and antiquark-quark pairs. The valence quarks (and gluons) give the hadron its characteristic quantum numbers and also its dynamical properties regarding mechanisms in decay and particle production. Hence, when discussing the constituents of a particle, it is the valence quarks that are referred to. The quark-gluon sea has no effect on the quantum numbers, but determines other properties of the hadron, such as the electric charge distribution and magnetic moment within the particle. [6] The Quark Model The quark model is a mean of structuring the hadrons, based on their quantum numbers. The quark model predates the theory of QCD, and was developed by Gell-Mann in order to classify the multitude of particles that was being discovered in the 50 s and 60 s. It was soon understood that the observed particles could not all be elementary particles. Gell-Mann (together with Nishijima) begun by classifying the hadrons, and went on to postulate the existence of the quarks as the particles composing the hadrons. The quark model describes essentially all hadrons that have been observed thus far. It is, however, far too simple to include all hadrons that can be predicted by the theory of QCD. Particles that cannot be described by the quark model are called exotic hadrons. The quark model organizes the hadrons in a structure based on their I, C and Y quantum numbers, where I is the particle isospin, C is the charm, and Y is the hypercharge. The hypercharge is defined as Y S + C + B + T + B, where S is strangeness, C is charm, B is bottomness, T is topness and B is baryon number. The hadrons reflect the properties of their constituents, and thus the quantum numbers of a hadron can be found by considering the quantum numbers of its valence quarks. Figure 2.1 shows the structure of the quark model Hadrons within the Quark Model Hadrons that can be classified according to the quark model are normally referred to as ordinary hadrons, as opposed to the exotic ones that are found outside of this model. The hadrons within the quark model are either baryons 6

13 (a) (b) (c) (d) Figure 2.1: Quark model structuring of the hadrons showing the baryon octet (a) and decuplet (b) as well as the meson pseudoscalar (c) and vector (d) 20- plets.[3] The axes of the coordinate system are I, C and Y, where I is the particle isospin, C is the charm, and Y is the hypercharge. 7

14 consisting of three quarks (qqq) or mesons consisting of a quark and an antiquark (qq). Baryons are fermions, while mesons are bosons. Name Symbol Quark Mass J P C Mean life Antistructure [MeV/c 2 ] [s] particle Proton p uud /2 + > p Neutron n ddu / ± 0.8 n Delta udd / Lambda Λ uds / Λ Sigma Σ uds / Σ Xi Ξ uss / Ξ Table 2.4: The properties of some baryons.[3] All baryons have baryon number 1, and all antibaryons have baryon number -1. A list of some important ordinary baryons and their properties is presented in Table 2.4. The only stable baryon is the proton, which has a mean life that by far exceeds the estimated age of the universe, which is currently approximated to 13.7 billion years [7]. Protons and neutrons form the nucleus of an atom, and are therefore referred to as nucleons. Bound neutrons are stable, since it is energetically impossible for them to decay within a stable nucleus. Baryons that have non-zero strangeness, but zero charm, bottomness and topness are called hyperons. The lightest of the hyperons is the Λ hyperon. The hyperons are relatively long lived. All decay via the weak interaction apart for the Σ 0 that decay electromagnetically directly or through a series of decays to a nucleon and one or more mesons. The hyperons do not normally form bound states, but can occur in short lived so-called hypernuclei. Some important mesons and their properties are presented in Table 2.5. Note that the neutral pion, π 0, is its own antiparticle. The only relatively stable meson are the charged pions and the kaons, which means that they are the only mesons that can be detected before they decay. In certain models of the strong interaction, the interaction is mediated by mesons through a so-called meson exchange. Name Symbol Quark Mass J P C Mean life Antistructure [MeV/c 2 ] [s] particle Pion π 0 (uu dd) π 0 π + ud π Kaon K + us K K(L) 0 ds K 0 D meson D + cd D D 0 cu D 0 Table 2.5: The properties of some mesons.[3]. 8

15 2.4.3 Exotic Hadrons The theory of QCD predicts the ordinary hadrons, but it does not rule out the possible existence of other, more complex, types of particles, provided these are colour neutral. However, the existence of such hypothetical particles, referred to as exotic hadrons, remains a subject of controversy. Exotic hadrons could be consisting of just quarks, such as the tetraquarks (qqqq) or the pentaquarks (qqqqq). It is also possible that gluons could form compounds, either on their own creating glueballs (gg) or in combination with quarks forming so-called hybrids (qqg-mesons or qqqg-baryons). [2] The exotic hadrons can be of two different categories. The first type are those with quantum numbers that cannot be fitted into the schematic system of the quark model. This could be either particles with anomalous flavour or charge, or particles with anomalous spin-parity quantum numbers. The detection of particles with such forbidden quantum numbers would thus indicate the existence of exotic hadrons. So far, the only available candidates for particles within this category are mesons with spin-parity J P C = 1 +, although these results are not conclusive. [6] The second type are those exotic hadrons that have coinciding quantum numbers with other ordinary hadrons, but with a different valence structure, resulting in anomalous dynamical properties. These are called cryptoexotic, or hidden-exotic hadrons. All of the serious candidates for exotic particles are found within this category, for example baryons with hidden strangeness (qqqss) and mesons with hidden charm (qqcc). [6] 2.5 Open Questions Apart from wanting to find the particles predicted by QCD discussed in the previous section, research in the field of hadron physics is made to answer some of the existing unsolved questions. These include the question of confinement of the quarks in hadrons, and the question regarding the origin of the mass of the hadrons Confinement Unlike all other forces, which grows weaker with distance, the impact of the strong force is small at close distances, and grows stronger if the distance is increased. This is a part of the explanation to the question of confinement of the quarks. If trying to separate the constituents of a meson that is trying to separate the quark from the antiquark the gluonic field of the strong force would eventually get so large that a new quark and anti-quark would be formed, in between the separated pair. Consequently, two antiquark-quark pairs would be formed, replacing the one pair that existed in the beginning. To explain why this mechanism occurs is one of the remaining tasks of hadron physics. [8] The Origin of Mass From Tables 2.1 and 2.4, it is evident that the mass of a nucleon (proton or neutron) is significantly larger than the sum of the masses of its three constituent 9

16 valence quarks. The rest of the nucleon mass has to be attributed to the kinetic energy of the quarks and to the energy of the interactions between these. Analogously, only a part of the spin of the nucleon can be attributed to the valence quarks, but must be explained by other means. These effects of mass generation are not described by the standard model, but there is hope that new experiments will shed some light on this issue. [9] 2.6 Symmetries The concept of symmetry is important in quantum mechanics, and particularly in particle physics. The standard model has three related symmetries of the matter universe, namely: parity (P ), which is the reflection of space; charge conjugation (C), which is the reflection to the antimatter universe; and time reversal (T ), which is the reflection of time Parity The operation of parity reverses the momentum of a particle, but conserves the direction of its spin. Consequently it changes the handedness of a system, turning a right handed system into a left handed and vice versa. The operation of parity can be seen as turning a system into its mirror image, for which the same physical laws are assumed to be valid as for the original system. If the spatial part of the wave function for a system is symmetric under the parity operation, it is said to have even parity, in particle physics denoted P = +. If it on the other hand is antisymmetric under the operation, the state is said to have odd parity, denoted P =. The parity of a composite system is given by the parity of its constituents, according to P = P 1 P 2 ( 1) L, (2.1) where P i denotes the parity of the constituents, and L is the orbital angular between the constituents. [2] Charge conjugation The operation of charge conjugation turns a particle into its antiparticle, conserving the direction of the spin. The operation can be seen as taking a system in the matter world and turning into its image in the antimatter world, where the same physical laws are assumed to be applicable as in the matter world. The eigenvalues of the charge conjugation operator are called the C-parity of the system. However, it is only a very few particles that have wave functions that are eigenstates to the charge conjugation operator; only the truly neutral particles such as γ and π 0 will have an associated C-parity. This is because such particles are their own antiparticles. The C-parity of a composite system made up of a particle-antiparticle pair is given by the C-parity of its constituents, but has different formulae depending on if the particles are fermions or bosons. For bosons it is given by C = ( 1) L, (2.2) 10

17 where L is the orbital angular momentum of the composite system. For fermions, on the other hand, it is given by C = ( 1) L+S, (2.3) where L is the angular momentum of the composite system, and S is the spin angular momentum of the system. [2] Time Reversal The operation of time reversal changes the direction of time, but keeps all another quantities conserved. This symmetry is rather counter intuitive, and in fact, the overall universe does not seem to be symmetric under the change of the direction of time. In this larger picture, the notion of time is closely intertwined with the idea of entropy, giving a distinct notion of past and future based on the increase or decrease of the entropy. In particle physics, however, the universe is seen on a much smaller scale, where global quantities such as entropy has no real meaning. When viewing the world from this scale, local properties show a fine symmetry under the operation of time reversal G-parity G-parity is not a symmetry as such, but combination of charge conjugation and a rotation. It is given by the C operation in addition to a rotation of the angle π around one of the axis of the isospin space of a particle. As with the charge conjugation, the G operation will only have eigenvalues for neutral systems. The G-parity of a system of a boson and antiboson pair is given by G = ( 1) S+I, (2.4) where S is the spin angular momentum of the composite system and I is the isospin. For a fermion-antifermion pair the G-parity is given by G = ( 1) L+S+I, (2.5) where S is the spin angular momentum of the composite system, L is the orbital angular momentum and I is its isospin. [2] Broken Symmetries The parity and the charge conjugation is conserved in both the strong and electromagnetic interaction, but is broken by the weak interaction. Since the strong interaction also conserves the isospin, this means that also the G-parity is conserved in this interaction. It is not, however, conserved in the weak and in the electromagnetic interactions, since these do not conserve isospin. The standard model predicts that if applying all three symmetry operators at the same time, the result would always show symmetry. This phenomenon is called CP T invariance, and has so far proved to be true. There are, however, systems that show a broken symmetry under the combined C and P operations. This also means, under the assumption of CP T invariance, that the T symmetry must be broken, and that the system thus shows a preference for one direction of time. This violation of CP -symmetry, 11

18 and thereby of T -symmetry as well, has so far only been observed in the weak interaction. The breaking of the CP -symmetry might give an explanation to why the world is made up of only matter and not equal parts of matter and antimatter, as is predicted by the theory of the Big Bang. 2.7 Note on the Units In most fields of physics, it is often convenient to use a system of units appropriate to that specific field. Particle physics is no exception, and has thus adopted a system of so-called natural units. The system is chosen so that the two fundamental constants of quantum mechanics, the reduced Planck s constant,, and the speed of light in vacuum, c, are set to unity. These two constants would in conventional SI-units be given by h 2π = Js = MeVs c = ms 1. In the system where = c = 1, can be seen as one unit of action, and c as one unit of speed, and with the addition of one unit of energy as 1 ev, the system of units is completely defined. [10] By adopting the system of natural units, and c can be omitted in formulas, which leads to considerable simplifications. The dimension of all quantities will also have some power of energy; mass (m), momentum (mc) and energy (mc 2 ) are expressed in MeV, and both time ( /mc) and length ( /mc 2 ) are described in units of MeV 1. It is, however, easy to convert a quantity back to practical units by using the conversion factor c = MeVm. In the remainder of this work, these natural units will be used in calculations, although some quantities will be given in SI-units. 12

19 Chapter 3 The PANDA Project This chapter will address the PANDA project, including a short introduction (Section 3.1), physical motivations to the experiments (Section 3.2) and a description of the facility where the experiment will take place (Section 3.3). The detector itself will be described in Section 3.4 and the computational framework of the experiment in Section Introduction The PANDA (antiproton ANihilations DArmstadt) project is an international collaboration, involving more than 300 researchers, at 40 different institutions in 15 countries worldwide.[11] The project started a few years back, and will continue for many years to come. The aim of the project is to study the properties of the strong interaction. This will be done by accelerating antiprotons to large speeds and letting them collide with protons, and observing the outcome of these collisions. In order to do this, two things are required: Firstly, an advanced accelerator facility to obtain the required energies and intensities of the antiprotons and secondly, a sophisticated detector system to be able to the detect the produced particles. To meet the first requirement, the PANDA experiment will take place at the Gesellschaft für Schwerionenforschung (GSI) in the German city of Darmstadt, where a new accelerator facility called FAIR (Facility for Antiproton and Ion Research) is currently being built. FAIR will be able to provide the experiment with antiprotons accelerated to the necessary energies and intensities, and thus it is envisioned that predicted particles never seen before will able to be detected. The second requirement will be met by the construction of a state-of-the-art detector. This detector is the heart of the PANDA project. It is currently in its research and development phase, and is planned to start taking data at the High Energy Storage Ring (HESR) at FAIR in 2012.[12] The hope is that experiments like PANDA will be of decisive importance for developing an understanding of the properties of the strong force, and also both confirm earlier predictions made from QCD and at the same time generate observations that can serve as an input to the development of the theory. 13

20 3.2 Physical Motivation The physics program for the PANDA experiment includes many different topics all related to the properties of the strong interaction. As a start, experiments such as precision spectroscopy of charmonium, the search for exotic objects such as hybrids and glueballs, the study of the properties of charmed hadrons and γ-ray spectroscopy of hypernuclei are foreseen.[9] Charmonium, for example the J/ψ meson, is a bound state of a charmed quark and antiquark pair, cc. It was named in analogy with positronium, the bound state of an electron and a positron. Since charmonium has a net zero charm, it is often said that its states contain hidden charm. The charm quarks are relatively massive, making their motion almost non-relativistic and the potential they move in almost static.[4] This gives the charmonium a positronium like spectrum, with energy levels described by the potential between the charmed quark and antiquark. Studies of the charmonium spectrum would therefore give information about properties of the interaction between the quarks. The physics program studying charmonium states would include precise measurement of mass, width and decay branches of all states through spectroscopy.[13] Hybrids and glueballs are discussed in Section Here, the aim of the PANDA project is to establish the predictions from QCD regarding these, using high statistics measurement and advanced spin-parity analysis.[13] Such studies of heavier quarks would give insights in the gluon interaction responsible for the generation of a part of the hadron masses. Hypernuclei are nuclei that contain not only nucleons, but also one or more hyperons. Precision γ-ray spectroscopy of hypernuclei will gain knowledge about their structure and the nature of the interaction between nucleons and hyperons as well as between hyperons and other hyperons.[13] Further along the project, other subjects of study are envisioned. These will include the search for CP -violation in the strange and charmed regions, i.e. in the decays of D mesons or in the ΛΛ system, as well as spectroscopy of D meson decay in the search for rare leptonic and hadronic decay. [13] 3.3 FAIR The new international research facility FAIR will be a major upgrade of the current GSI facility. The construction of the new parts is planned to start this year (2007), with the first experiments taking place in 2012, and the whole construction being completed by The costs for this building project are estimated at approximately 1.2 billion euro, 65 percent of which is paid by the German government. It is estimated that four different experiments will be able to run simultaneously at the facility. [14] The outlines for the existing GSI and the upcoming are shown in Figure 3.1, where the existing GSI facility with its linear accelerator UNILAC is shown to the left; and the upcoming FAIR facility to the right with the double ring synchrotron SIS 100/200 and the High-Energy Storage Ring (HESR). The new double ring synchrotron accelerator, which has a circumference of about 1.1 km, will use the current GSI facility as an injector. The SIS 100/200 will produce high energy protons, which will be used to create an antiproton beam. The antiprotons will be collected and stochastically cooled in the CR 14

21 Figure 3.1: The existing GSI facility to the left (shaded area) and the new FAIR facility to the right. [12] and RESR rings, and then injected into the 574 m long HESR. The HESR is envisioned to be able to store antiprotons of momenta from about 1.5 up to 15 GeV at a time. [15] 3.4 Detector The PANDA detector is designed to be a versatile system, able to measure both electromagnetic and hadronic final states. The event rate, i.e. the number of particle reactions per second, is estimated to per second. The goal is to make the detector cover nearly the full solid angle. To manage this, the detector is composed of two parts: a cylindrical target spectrometer and an extensive forward spectrometer. [15] Figure 3.2 is showing a cross section view of the PANDA detector in the horizontal xz-plane. The coordinate system of the detector is given by the accelerated beam going along the z-axis, and the target beam travelling in the negative y-direction. Although the design, location and properties of most of the detector subssystem are decided, there are still some unsettled questions. In some parts more than one solution is possible, and the question to answer is which one of these that would be optimal, in that it could fulfill all the requirements while at the same time keeping the costs at a minimum Interaction Region The detector in the PANDA experiment makes use of an internal target of protons. Various target options are being considered, although the two most 15

22 Figure 3.2: The PANDA detector in the xz-plane, showing the antiproton beam coming in from the left, and the proton target going into the page. [16] prominent are a cluster jet target and a pellet target. The cluster jet target equipment produces a jet of ultra-dense hydrogen that is sent through the antiproton beam. The pellet target consists of a stream of small pellets made from frozen hydrogen that is sent through the beam. Both these targets are constructed in such a way so that the horizontally incoming beam will hit the target particles, arriving to the interaction region in a vertical stream. The interaction between the beam and target will then occur in a volume that depends on the beam and target widths, centred around the origo of the detector system. The pellet target can be somewhat cumbersome to use, and the cluster jet is thus favourable from a practical point of view. However, the cluster jet has not yet managed to deliver the luminosity desired for PANDA, although efforts to attain this are still being made. Furthermore, the cluster jet creates larger interaction region, which complicates the reconstruction of events, in particular when dealing with produced particle of short life times. Currently, a solution is foreseen where both target options would be possible to use in the detector, depending on the requirements of the specific experiment. [4] Target Spectrometer The target spectrometer (TS) is a detector system with cylindrical symmetry that detects particle emitted at relatively large angles. The planned outline is shown in Figure 3.2, and the different components, from the interaction region and outwards are the following [13]: MVD A micro-vertex detector (MVD) for detection of charge particles is directly located around the interaction region. The MVD is arranged in a barrel structure with five layers together with four additional layers in the 16

23 forward direction. The MVD barrel consists of pixel detectors while the forward layers are made up of microstrip detectors. STT/TPC The next layer will be either a Straw Tube Tracker (STT) or a Time Projection Chamber (TPC). The STT, consisting of self-supporting straws in double layers, is considered being a safe fall-back solution to the technically more challenging TPC. MDC There are two multi-wire drift chambers (MDC) positioned in the forward direction from the STT/TPC, to detect particles emitted at small forward angles. Their function is similar to the STT. TOF In the layer following the STT/TPC, as well as behind the second MDC, Time-Of-Flight counters (TOF) will be placed to measure the flight time of the produced particles. One option is to use fast scintillating materials in thin strips to be read by photomultiplier tubes. [4] DIRC Outside of the cylindrical TOF there is a Detector of Internally Reflected Čherenkov light (DIRC), which is a type of Ring Imaging Čherenkov Counter (RICH). The DIRC is composed of quarts rods, in which the Čherenkov light is internally reflected to photon detectors at the edges. A second DIRC, made of quartz radiators, will be placed after the two MDC:s. EMC The next component is the Electromagnetic Calorimeter (EMC), made up of both a barrel part and a forwards and backwards layer. The EMC will likely be made of crystals of P bw O 4, which is a scintillating material that gives fast signals and has fair resolution. MUO All these components are all surrounded by a solenoid coil and iron yoke. The solenoid will yield a magnetic field of approximately 2 T. The iron yoke stops all produced particles, with the exception of muons. The last component of the TS, and the one furthest away from the interaction region, is therefore a set of muon counters (MUO) Forward Spectrometer The forward spectrometer (FS) is designed to detect particles emitted at relatively small angles, approximately at angles below 5 o in the vertical direction and below 10 o in the horisontal direction, as well as give additional information to that of the TS system for particles emitted at angles below 22 o. The outline is shown in Figure 3.2, and the components are the following, from the edge of the TS and downstream [13]: MDC A row of six vertically placed MDC:s is envisaged from the very edge of the TS and continuing more than half the length of the FS. These will be similar to those of the TS, and will detect the charged particles that are emitted at small angles. TOF Forward TOF:s will be placed behind the last MDC, as well as on both sides of the row of MDC:s, to detect and identify forward going particles with a moderate momentum. They will be made of plastic scintillating strips coupled to photomultiplier tubes. 17

24 RICH After the TOF:s, a Ring Imaging Čherenkov Counter (RICH) will be used. It is designed to compensate for the uncovered space of the DIRC in the forward region of the TS. The RICH will probably be made of some type of aerogel, connected to photon detectors. EMC Because of the size of the forward EMC, a less expensive alternative to the high-performance target EMC is sought. The solutions considered are either a lead-glass or a so-called Shashlyk EMC, both being about one order of magnitude cheaper than the target EMC, while at the same time only decreasing the resolution by a factor of two. HC A Hadron Calorimeter (HC) is placed right next to the EMC, consisting of steel and scintillator plates arranged in two layers. It will measure the energies of hadrons as well as energy losses of muons, MUO The outermost component of the FS will, similar to the TS, be a set of moun counters. 3.5 Software The antiproton-proton annihilations in the PANDA experiment have been simulated using so-called Monte Carlo methods 1 in software specific to this experiment. Such simulations are made to imitate the response of the proposed detector to get input for further improvements regarding materials and geometry and to make sure that the goals of PANDA are met. It is also important as a test bench for the development of the reconstruction and analysis software to be used for the experimental data from the actual experiment. [15] The PANDA framework is a complete simulation system, written in C++. All parts are not completely implemented yet, but the basic structure is. It consists of four major components: event generation, detector simulation, reconstruction and analysis. It uses the latest version of the CERN platform GEANT (GEometry ANd Tracking), Geant4 2, in the particle propagation and classes from the CERN analysis program ROOT 3 are used in the event generation. Both these systems enable the handling and analyzing of large amounts of data in efficient ways. 1 Monte Carlo methods are computational algorithms that are based on random numbers. They are often used when simulating the properties of physical systems. 2 Geant4 is an object-oriented software toolkit that uses Monte Carlo methods to simulate particle propagations in material.[17] 3 ROOT is an object-oriented software, developed at CERN and designed for particle physics data analysis.[18] 18

25 Chapter 4 The pp ΛΛ pπ + pπ Reaction This chapter discusses some theoretical aspects for the reaction that is in focus of this work, the pp ΛΛ pπ + pπ reaction. It starts with treating the properties of the pp system (Section 4.1). Then the ΛΛ production in the pp annihilation (Section 4.2) is discussed, and the chapter finishes with treating the decay of the Λ hyperon (Section 4.3). 4.1 The pp System The collision of an antiproton beam with a beam of protons can result in several different reactions. At a beam energy of 2 GeV, about 40 percent of the collisions results in elastic scattering.[19] The rest is referred to as antiproton-proton inelastic scattering and annihilations. The latter will be considered here. To find out which particles are allowed in the final state from the pp annihilation process, the quantum numbers of the initial state needs to be considered. The quantum numbers of the proton and the antiproton are given in Table 4.1. Quantum number Symbol Proton Antiproton Electric charge Q +1 1 Baryon number B +1 1 Total spin J 1/2 1/2 Isospin I 1/2 1/2 Third component isospin I 3 +1/2 1/2 Parity P +1 1 Table 4.1: The quantum numbers of the proton and anitproton. The quantum numbers of the antiproton and proton are combined to establish the total quantum numbers of the initial pp system. The baryon number and charge are scalars and as such simply additive, while other quantum numbers are slightly more complicated to handle. The parity of the composed system is given by (see Section 2.6.1) P = P p P p ( 1) L, where L is the orbital angular 19

26 momentum of the system, and the spin and isospin can be found by treating theses quantities as vectors. Therefore the total quantum numbers of the initial pp system are: Electric charge, Q = 0; Baryon number, B = 0; Isospin, (I, I 3 ) = (1, 0) or (I, I 3 ) = (0, 0); Spin, S = 0 or S = 1 Parity, P = ( 1) L+1 In addition, the system also has zero strangeness and charm. Furthermore, the charge conjugation of the system is given by (cf. Section 2.6.2) C = ( 1) L+S and the G-parity (cf. Section 2.6.4) by G = ( 1) L+S+I. All these quantum numbers puts constraints on the possible final state particles that can occur in the pp annihilation. There is, however, a multitude of possible particles that can be produced in the antiproton-proton annihilation. Examples are two body processes such as pp Y Y, where Y denotes a hyperon or pp mm, where m denotes a meson or three body processes, such as pp Y Y π.[19] The channels of interest here are the hyperon decay channels, namely pp ΛΛ, pp ΛΣ 0, pp Σ 0 Λ, pp Σ + Σ +, pp Σ Σ, pp Ξ Ξ, pp Ξ 0 Ξ 0 and pp Ω Ω. All of the produced particles here decay via the weak interaction, with the exception of the Σ 0 that decays electromagnetically to Λγ. The Λ and the Σ ± all decay to Nπ, where N denotes a nucleon, whilst the other decay in one or more steps to a Λ particle and one or more pions. Thus, the most straightforward approach to study the hyperon production channels would be to start with the ΛΛ channel. This is also the only hyperon channel were high quality experimental data on relevant quantities such as spin observables are available.[20] Consequently, the subject of the following sections will be a more detailed discussion of the pp ΛΛ reaction. 4.2 The pp ΛΛ Reaction The reaction pp ΛΛ takes place via the strong interaction, which conserves parity and charge conjugation as well as flavour. The most interesting feature of the reaction is the process where strange quarks are created. There are two ways to look at the reaction, as depicted in Figure 4.1. Figure 4.1(a) shows the reaction in a so-called quarkline diagram. Here the proton and the Λ hyperon are viewed as composed of a diquark and a quark. The diquark has the same ud quantum numbers with isospin and spin zero for both the proton and the Λ and is indicated by the shaded areas in Figure 4.1(a). In this view, the important process is the annihilation of the uu quark pair and the production of an ss pair, whilst the diquarks of the proton and antiprotons are merely spectators to this process. The observables for the pp ΛΛ reaction should thus indicate properties of the underlying uu ss process. [21] An alternative way to view the pp ΛΛ reaction is through meson exchange, illustrated in Figure 4.1(b). In this model, a K + meson (consisting of a u and 20

27 (a) (b) Figure 4.1: Two different ways to view the reaction pp ΛΛ: (a) A quarkline diagram; (b) A meson exchange diagram. [20] an s quark), is exchanged and thus creating the strangeness of the final state. [21] Coordinate System The pp ΛΛ reaction has two initial and two final state particles, and thus only two truly independent momentum vectors, namely the initial momentum vector of the beam antiprotons p i and the momentum vector of one of the produced Λ particles p f. The plane formed by these two vectors is called the production plane, and is unique for each event. Using this information, a coordinate system for each of the Λ and Λ particles in each event, can be created. This is usually done in the Centre-of-Mass (CM) frame of the reaction, letting the z-axis of the coordinate system be in the direction of the Λ particle, i.e. in the direction of the vector p f. The y-direction is then taken as the direction of the normal of production plane, which will mean that the z- and y-directions are orthogonal. The x-direction is then chosen orthogonal to both the z- and the y-direction, and in such a way that the constructed coordinate system is right handed. This is illustrated in Figure 4.2, where θ is the production angle of the Λ particle in the centre of mass of the reaction. Figure 4.2: Coordinate system for the reaction pp ΛΛ as it is constructed in the CM frame of the reaction.[22] 21