Measurement of the Neutron Magnetic Form Factor at High Q 2 Using the Ratio Method on Deuterium (PR )

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1 Measurement of the Neutron Magnetic Form Factor at High Q Using the Ratio Method on Deuterium (PR1-7-14) A New Proposal for the Jefferson Lab 1-GeV Upgrade Program in Hall B Follow-on to PAC3 Letter of Intent LOI Outline 1. Scientific Motivation and Previous Measurements.. The Ratio Method. 3. Event Selection and Simulations. 4. Corrections and Uncertainties. 5. Summary and Run-Time Estimate. PAC3 Meeting, August 6-8, 7 1

2 Collaborators G.P. Gilfoyle W.K. Brooks, S.Stepanyan M.F. Vineyard University of Richmond Jefferson Lab Union College M. Holtrop K. Hafidi M. Garcon UNH ANL DAPNIA/SPhN-Saclay P. Kroll S. Jeschonnek S.E. Kuhn, J.D. Lachniet, L.B. Weinstein Universität Wuppertal Ohio State University Old Dominion University and the CLAS Collaboration - Spokesperson - Contact person. - Theory support. The physics impact of the experiment is high. The group has already successfully performed similar measurements at 6 GeV. This measurement is an important part of the Jlab program to study the 4 elastic nucleon form factors. - PAC3 report on LOI PAC3 Meeting, August 6-8, 7

3 G n M Scientific Motivation is a fundamental quantity describing the charge and magnetization in the neutron. In the infinite-momentum-frame the parton charge density in transverse space is ρ(b) = dq Q π J (Qb) (G.Miller, arxiv:75.49v [nucl-th]). ( GE (Q )+τg M (Q ) 1+τ 1 b ρ[fm ] Measurements at large Q will render the results above more precise or potentially change them considerably (Ibid.). Elastic form factors (G n M, Gn E, Gp M, and Gp E ) provide key constraints on the generalized parton distributions (GPDs) which hold the promise of a three-dimensional picture of the nucleon. High-quality data on the neutron form factors in a wide t range would be highly valuable for pinning down the differences in the spatial distribution of u and d quarks... drastic differences in the behavior of u and d contributions to the form factors ) (M.Diehl, Th. Feldmann, R. Jakob, and P.Kroll, hep-ph/48173v). PAC3 Meeting, August 6-8, 7 3

4 Part of a broad effort to understand how nucleons are constructed from the quarks and gluons of QCD (NSAC Long Range Plan, April, ). Fundamental challenge for lattice QCD (J.D. Ashley, D.B. Leinweber, A.W. Thomas and R.D. Young, Eur. Phys. J. A 15, 487 ()). There are drastic differences in the u and d quark contributions that require high-q data to sort out (M. Diehl, et al. Eur.Phys.J.C 39 (5) 1). Required for extracting the strange quark distributions in the proton. The magnetic form factor for the neutron extrapolated from lattice data with lattice spacings a =.93 fm (single line), a =.68 fm (dash-dot line) and a =.51 fm (dotted line) and compared to experimental results. PAC3 Meeting, August 6-8, 7 4

5 World Data on G n M G D ) n n /(µ M G CLAS Preliminary Lung Xu Kubon Anderson Bartel Anklin Arnold Q (GeV/c) :46:39 The world data on G n M scaled by the dipole approximation where G D (Q )=1/(1+(Q /Λ)) and Λ=.71 (GeV/c). The proposed measurement will extend the upper limit to Q =14(GeV/c). PAC3 Meeting, August 6-8, 7 5

6 Q (GeV/c) Entries The CLAS1 Detector and Dual Target Cell Vacuum Hydrogen Cell Deuterium Cell The dual target enables us to collect highprecision, consistent calibration data so systematic uncertainties 3%. Counts D(e,e p)n E = 11 GeV Black - Thrown events Red - Accepted events hqep :49: Q (GeV/c) CLAS1 acceptance for quasi-elastic e p events calculated with FASTMC (CLAS1 parameterized simulation). Range is Q = 14(GeV/c). PAC3 Meeting, August 6-8, 7 6

7 The Ratio Method - Some Necessary Background Express the cross section in terms of the Sachs form factors. dσ dω = σ Mott ( G E + τ ǫ G M ) ( τ ) τ = Q 4M ǫ = (1 + τ) tan ( θ ) σ Mott = α E cos ( θ ) 4E 3 sin 4 ( θ ). Kinematic definitions - The angle θ pq is between the virtual photon direction and the direction of the ejected nucleon. e Scattering Plane e θ φ e pq Reaction Plane P θ pq We can now take the ratio of the e p and e n cross sections (the ratio method). Q R = dσ dω (D(e, e n)) dσ dω (D(e, e p)) = a(q ) G n E +τg n M 1+τ + τg n M tan ( θ ) G p E +τg p M 1+τ + τg p M tan ( θ ) PAC3 Meeting, August 6-8, 7 7

8 The Ratio Method - Outline and Advantages Outline 1. Selecting quasielastic events: inelastic background, acceptance matching.. Neutron detection efficiency. 3. Proton detection efficiency. GOAL: 3% systematic uncertainty 4. Estimates of uncertainties. Advantages Use deuterium as a neutron target. Reduces sensitivity to changes in running conditions, nuclear effects, radiative corrections, Fermi motion corrections. Importance of in-situ calibrations of neutron and proton detection efficiencies. Take advantage of the experience from the CLAS measurement of G n M. Vacuum Hydrogen Cell Deuterium Cell PAC3 Meeting, August 6-8, 7 8

9 Selecting Quasielastic Events Select e p events using the CLAS1 tracking system for electrons and protons. Use TOF and calorimeters as independent detectors for neutrons. The main focus here will be on the calorimeters since they are more efficient. Apply a θ pq cut to select quasi-elastic events plus W < 1. (GeV/c ). 3 Match acceptances using quasi- elastic electron kinematics to determine if the nucleon CLAS E5 data 4. GeV W cut all ep events Angle between q and nucleon p. lies in CLAS1 acceptance. 1 θ pq < 3 degrees Neutrons and protons treated exactly the same whenever possible. The CLAS G n M consistency check W (GeV ) measurement at 4 GeV overlaps the proposed measurement to provide a Impact of inelastic background will be greater at large Q due to increasing width of W requiring simulation. PAC3 Meeting, August 6-8, 7 9

10 Entries Monte Carlo Simulation 1. Quasielastic events elastic form factors.. Inelastic events proton and deuteron data (P. Stoler, Phys. Rep., 6, 13 (1993), L.M.Stuart, et al., Phys. Rev. D58 (1998) 33). 3. For exit channel use elastic form factors and the genev program (for inelastic events) ( M.Ripani and E.M.Golovach based on P.Corvisiero, et al., Nucl. Instr. and Meth., A346, 433 (1994)). 4. Use FASTMC (CLAS1 parameterized Monte Carlo) to simulate the CLAS1 response. 5. Validate the Monte Carlo simulation. d σ /d Ω de [nb/sr GeV] W GeV Counts :37:36 E = 11 GeV Inclusive Electrons Q = 6-7 (GeV/c) Red - quasielastic Green - Inelastic Black - Sum hw W (GeV/c ) Simulated (top panel) and measured (lower panel) inclusive electron spectra (L.M.Stuart, et al., Phys. Rev. D58 (1998) 33). PAC3 Meeting, August 6-8, 7 1

11 Selecting Quasielastic Protons - The θ pq Cut Counts 5 15 D(e,e p)n 11 GeV Q = 6-7 (GeV/c) Red - Quasielastic Green - Inelastic Black - Total :6: (deg) θ pq Distribution of θ pq for the simulations and angular resolution of CLAS1 for charged particles in the forward tracking system from GSIM1. PAC3 Meeting, August 6-8, 7 11

12 Selecting Quasielastic Protons - W Spectra Counts W cut E = 11 GeV D(e,e p)x Q = 6-7 (GeV/c) Red - Quasielastic Green - Inelastic Black - Sum Counts W cut E = 11 GeV D(e,e p)x Q = 6-7 (GeV/c) Red - Quasielastic Green - Inelastic Black - Sum o < 3 θ pq Counts W cut D(e,e p)n o θ pq < 3 ep final state only W (GeV/c ) :: W (GeV/c ) W (GeV/c ) W spectra for the e p final state. The left-hand panel has no θ pq cut and the middle panel shows the effect of requiring θ pq < 3. The right-hand panel is for θ pq < 3 and only e p in the final state (the multi-particle veto). PAC3 Meeting, August 6-8, 7 1

13 Selecting Quasielastic Neutrons - W Spectra Counts E = 11 GeV D(e,e n)x Q = 6-7 (GeV/c) o < 3 θ pq W cut Counts W cut D(e,e n)p o < 3 θ pq en only final state Red - quasielastic Green - inelastic Black - Sum W (GeV/c ) W (GeV/c ) Comparison of the simulated W spectra for the D(e,e n)x (left-hand panel) and D(e,e n)p reactions (right-hand panel) with θ pq < 3 in both. PAC3 Meeting, August 6-8, 7 13

14 Selecting Quasielastic Events - Angular Distributions Counts D(e,e n)p E = 11 GeV Q = 6-7 (GeV/c) Counts 5 D(e,e p)n 11 GeV Q = 6-7 (GeV/c) Red - Quasielastic Green - Inelastic Black - Total (deg) θ pq :6: (deg) θ pq Angular distribution of θ pq neutrons (left-hand panel) for the quasielastic (red), inelastic (green), and total (black) contributions (left-hand panel) and protons (right-hand panel). PAC3 Meeting, August 6-8, 7 14

15 Suppressing the Inelastic Background Reduce the maximum value of θ pq. Plots below show effect of reducing the maximum angle from 3. (left-hand panel) to 1.5 (right-hand panel) for Q = 6 7(GeV/c). W GeV Counts W cut D(e,e n)p o < 3 θ pq en only final state Counts 5 15 W cut o < 1.5 θ pq W (GeV/c ) W (GeV/c ) Calculate the background using the dependence of the spectra on the maximum θ pq, multiple-particle veto, and other kinematic quantities to tune the simulation. PAC3 Meeting, August 6-8, 7 15

16 Selecting Quasielastic Events - Acceptances hqaccep Entries 197 Proton Acceptance Neutron Acceptance Q (GeV/c) Q (GeV/c) Acceptance for the D(e,e p)n (left-hand panel) and D(e,e n)p (right-hand panel) in CLAS1 (forward EC only) for 11 GeV. Calculated with FASTMC (parameterized Monte Carlo simulation of CLAS1). PAC3 Meeting, August 6-8, 7 16

17 Ratio Method Calibrations - Proton Detection Efficiency 1. Use ep e p elastic scattering from hydrogen target as a source of tagged protons.. Select elastic e p events with a W cut. 3. Identify protons as positive tracks with a coplanarity cut applied. 4. Use the missing momentum from ep e X to predict the location of the proton and search the TOF paddle or an adjacent one for a positively-charged particle. 5. Calibration data taken simultaneously with production data using the dual-cell target shown here. Vacuum Hydrogen Cell Deuterium Cell PAC3 Meeting, August 6-8, 7 17

18 Ratio Method Calibrations - Neutron Detection Efficiency 1. Use the ep e π + n reaction from the hydrogen target as a source of tagged neutrons in the TOF and calorimeter.. For electrons, use CLAS1 tracking. For π +, use positive tracks, cut on the difference between β measured from tracking and from time-of-flight to reduce photon background. 3. For neutrons, ep eπ + X for.9 < m X <.95 GeV/c. 4. Use the predicted neutron momentum p n to determine the location of a hit in the fiducial region and search for that neutron. 5. The CLAS G n M results. 6. GSIM1 simulation results for CLAS1 are shown in the inset. Proposed measurement will extend to higher momentum where the efficiency is stable. Calorimeter efficiency EC Neutron Efficiency o θ n = - 5 GSIM1 simulation p (GeV/c) n o PAC3 Meeting, August 6-8, 7 18

19 The Ratio Method - Systematic Errors G n M is related to the e n/e p ratio R by G n M = ± [ R ( ) ( ) σ p mott 1+τn σmott n 1+τ p (G ) ] p E + τ p ε p G p M G n ε n E τn where the subscripts refer to neutron (n) and proton (p). Upper limits on systematic error from the CLAS measurement ( G n M /Gn M =.7%). Quantity δg n M /Gn M 1 Quantity δgn M /Gn M 1 Neutron efficiency parameterization < 1.5 θ pq cut < 1. proton σ < 1.5 G n E <.7 neutron accidentals <.3 Neutron MM cut <.5 neutron proximity cut <. proton efficiency <.4 Fermi loss correction <.9 Radiative corrections <.6 Nuclear Corrections <. Investigate the largest contributors (the top two rows in the table) and assume the other maximum values stay the same. Goal: 3% systematic uncertainty PAC3 Meeting, August 6-8, 7 19

20 Other elastic form factors - Systematic uncertainty ( G n M /Gn M 1) based on differences in the proton reduced cross section parameterizations of Bosted and Arrington-Melnitchouk. Systematic Uncertainty Studies Neutron Detection Efficiency - Simulate the uncertainty associated with fitting the shape of the measured neutron detection curves. n /G M n G M :56:7 E = 11 GeV Q (GeV/c) PAC3 Meeting, August 6-8, 7

21 Systematic Uncertainties - Summary Quantity δg n M /Gn M 1 Quantity δgn M /Gn M 1 Neutron efficiency parameterization <.7(1.5) θ pq cut < 1.(1.7) proton σ < 1.5(1.5) G n E <.7(.5) neutron accidentals <.3 Neutron MM cut <.5 neutron proximity cut <. proton efficiency <.4 Fermi loss correction <.9 Radiative corrections <.6 Nuclear Corrections <. Summary of expected systematic uncertainties for CLAS1 G n M measurement ( G n M /Gn M =.4%(.7)). Red numbers represent the previous upper limits from the CLAS measurement. PAC3 Meeting, August 6-8, 7 1

22 Anticipated Results and Beam Request Expected Q range and systematic uncertainty of 3% and world data for G n M. n /µ M n G D G Lung Xu Kubon Bartel Anklin Arnold CLAS Preliminary CLAS1 anticipated Anderson Will almost triple the current 1 Q range..8 Need to obtain statistical precision as good as the anticipated systematic uncertainty Q (GeV/c) We request 56 PAC days of beam time at 11 GeV at a luminosity per nucleon of cm s 1. PAC3 Meeting, August 6-8, 7

23 Anticipated Results and Beam Request Expected Q range and systematic uncertainty of 3% and world data for G n M. n /µ M n G D G Lung Xu Kubon Bartel Anklin Arnold CLAS Preliminary CLAS1 anticipated Anderson Will almost triple the current 1 Q range..8 Need to obtain statistical precision as good as the anticipated systematic uncertainty..6 Solid - Lomon Dashed - Guidal Dotted - Miller Q (GeV/c) We request 56 PAC days of beam time at 11 GeV at a luminosity per nucleon of cm s 1. Lomon, Phys.Rev.C () G. MIller, Phys. Rev. C 66, 31(R) () M.Guidal, M.K. Polyakov, A.Radyushkin, and M. Vanderhaeghen, Phys. Rev. D 7, 5413 (5). PAC3 Meeting, August 6-8, 7 3

24 Conclusions The neutron magnetic form factor is a fundamental quantity and extending the Q range and coverage will probe deeper into hadronic structure, provide essential constraints on GPDs, and challenge lattice QCD. The CLAS1 detector will provide wide kinematic acceptance (Q = 3 14(GeV/c) ) and independent measurements of neutrons with its calorimeters and TOF systems. We propose to use the ratio method on deuterium to reduce our sensitivity to a variety of sources of systematic uncertainty and limit systematic uncertainties to less than 3%. To keep systematic uncertainties small we will measure the detection efficiencies with a unique dual-cell target. Production and calibration data will be taken simultaneously. We request 56 PAC days of beam time at 11 GeV and a luminosity per nucleon of cm s 1 to obtain statistical precision in the highest Q bin as good as the anticipated systematic uncertainty. PAC3 Meeting, August 6-8, 7 4

25 Run Statistics Q Proton Neutron Proton Proton Neutron Neutron (GeV/c) Rate (s 1 ) Rate (s 1 ) Counts Error Counts Error Rates and statistical uncertainties for quasielastic scattering. All bins are ±.5 (GeV/c). Based on 56 PAC days of beam time and a luminosity per nucleon of cm s 1. δg n M G n M PAC3 Meeting, August 6-8, 7 5

26 Procedure for Quasielastic Simulation Pick a Q weighted by the elastic cross section. Pick p f and cos θ of the target nucleon weighting it by the combination of the Hulthen distribution and the effectivebeam-energy effect. Boost to the rest frame of the nucleon and rotate coordinates so the beam direction is along the z axis. Calculate a new beam energy in the nucleon rest frame. Choose an elastic scattering angle in the nucleon rest frame using the Brash parameterization. Transform back to the laboratory frame. -1 dp/dp (GeV/c) Hulthen Distribution 1 1 Hulthen distribution p (GeV/c) PAC3 Meeting, August 6-8, 7 6

27 Procedure for Inelastic Simulation - 1 Use existing measurements of inelastic scattering on the proton (P. Stoler, Phys. Rep., 6, 13 (1993)). For the neutrons use inelastic scattering from deuterium (L.M.Stuart, et al., Phys. Rev. D58 (1998) 33). Data don t cover the full CLAS1 range, but n p ratios are roughly constant. Inelastic cross sections as a function of ω = 1 + W /Q. PAC3 Meeting, August 6-8, 7 7

28 Procedure for Inelastic Simulation - Pick a Q weighted by the measured cross sections. Pick p f and cos θ of the nucleon weighted by the Hulthen distribution and the effective-beam-energy effect for inelastic scattering. Boost to the rest frame of the nucleon and rotate coordinates so the beam direction is along the z axis. Calculate a new beam energy in the nucleon rest frame. Choose the final state using genev (M.Ripani and E.N.Golovach based on P.Corvisiero, et al., NIM A346, (1994) 433.). Transform back to the laboratory frame. pf GeV c cos Θ PAC3 Meeting, August 6-8, 7 8

29 Selecting Quasielastic Neutrons - Angular Distributions θ pq for neutrons htheta_pqn1 Entries Counts 1 8 D(e,e n)p E = 11 GeV Q = 6-7 (GeV/c) (deg) σ θ GSIM1 Neutron Simulation of CLAS o o θ n = - 5 blue-ec red- PCAL+EC (deg) θ pq (GeV/c) p n Angular distribution of θ pq for the quasielastic (red), inelastic (green), and total (black) contributions (left-hand panel) and a GSIM1 simulation of the angular resolution of CLAS1 for neutrons in the forward tracking system (right-hand panel). PAC3 Meeting, August 6-8, 7 9

30 Ratio Method Calibrations - Neutron Detection Efficiency - 1. Acceptance for neutrons in D(e,e n)p. p n 1 (GeV/c) n p vs. θ n 9 8 E = 11 GeV hpnthetan Entries Acceptance for neutrons in p(e,e π + )n. p n (GeV/c) p n vs. θ for e-π + n events p(e,e π + )n 11 GeV Accepted Events Q = -14 (GeV/c) θ n (deg) hpnthetan Entries (GeV/c) p n p(e,e π + )n 11 GeV Accepted Events Q = 7-14 (GeV/c) hpnthetan Entries Mean x.83 Mean y 4.7 RMS x 3.38 RMS y θ n (deg) θ n (deg) PAC3 Meeting, August 6-8, 7 3

31 Systematic Uncertainties - Neutron Detection Efficiency Characterize the neutron detection efficiency ǫ n with the expression ǫ n = S ( exp( p n p a ) ) where S is the height of the plateau in ǫ n for p n > GeV/c, p is a constant representing the position of the middle of the rapidly rising portion of the ǫ n, and a controls the slope of the ǫ n in the increasing ǫ n region. Fit the ǫ n with a third-order polynomial and a flat region. Use the original ǫ n and the fit in reconstructing the neutrons and compare. Neutron Detection Efficiency Efficiency n /G M n G M χ / ndf = 8.18 / -3 p.5984 ±.118 p ±.1715 p.1496 ± p (GeV/c) n E = 11 GeV :56: Q (GeV/c) PAC3 Meeting, August 6-8, 7 31

32 Systematic Uncertainties - Other Elastic Form Factors Systematic ( G n M /Gn M uncertainty 1) based on differences in the proton reduced cross section parameterizations of Bosted and Arrington-Melnitchouk. Systematic ( G n M /Gn M uncertainty 1) based on differences in G n E parameterizations of Kelly and BBBA5. PAC3 Meeting, August 6-8, 7 3

33 Neutron Electric Form Factor G n E G E,n /G D Kelly G E,n /G D BBBA5 Q (GeV ) World data on G n E. (C.E. Hyde-Wright and K.deJager, Ann. Rev. Nucl. Part. Sci. 54 (4) 54 and references therein.) The neutron electric form factor from Kelly and BBBA5 parameterizations as a function of Q (J. J. Kelly, Phys. Rev, C 7, 68 (4) and R. Bradford, A. Bodek, H. Budd and J. Arrington, hep-ph/617.) PAC3 Meeting, August 6-8, 7 33

34 Suppressing the Inelastic Background Additional analysis to improve the neutron angular resolution: different EC fitting algorithm, use pcal which has greater segmentation. Calculate the inelastic background. Calibrate the calculation with other information from CLAS1. D(e,e )X (L.M.Stuart, et al., Phys. Rev. D 58, 33 (1998)). Use D(e,e p)x and D(e,e n)x and study dependence of maximum θ pq, multiplicity veto (recall previous plot), and φ pq dependence. Use missing mass to study D(e,e p)n. Calculate the quasielastic lineshape. Calibrate the reaction with other information using other reactions as mentioned above. Inelastic background is small for W.9 GeV. Calculate lineshape with Sim1 and fit the low W portion of the W spectrum. PAC3 Meeting, August 6-8, 7 34

35 W Spectra at the Acceptance Edge D(e,e p)x o θ pq < W (GeV ) D(e,e n)x o θ pq < E = 11 GeV, Q = 1-14 (GeV/c) Red - quasielastic Green - inelastic Black - total W (GeV ) D(e,e p)x (deg) D(e,e n)x θ pq (deg) θ pq W spectra at the edge of the acceptance Q = 1 14(GeV/c) for protons (left-hand panel) and neutrons (right-hand panel). Both reactions include the multi-particle veto. PAC3 Meeting, August 6-8, 7 35

36 The Ratio Method - Corrections Nuclear effects: The e n/e p ratio for free nucleons can be altered here because we measure the quasielastic scattering from bound nucleons. This factor a(q ) was calculated and we compared results from Jeschonnek and Arenhoevel. Where the calculations overlap in Q, the average correction to R is.994 and we assigned a systematic uncertainty of.6%. Radiative corrections: Calculated for exclusive D(e,e p)n with the code EXCLURAD by Afanasev and Gilfoyle (CLAS-Note 5- ). The ratio of the correction factors for e n/e p events is close to unity. PAC3 Meeting, August 6-8, 7 36

37 Published Measurements of Elastic Form Factors G n M G p M n M /(µ n G D ) G Lung Xu Kubon Bartel Anklin Arnold G p E /Gp M Q (GeV/c) C.E. Hyde-Wright and K.deJager, Ann. Rev. Nucl. Part. Sci. 54 (4) 54 and references therein. PAC3 Meeting, August 6-8, 7 37

38 G n M and GPDs Elastic form factors (G n M, Gn E, Gp M, and Gp E ) provide key constraints to stabilize the parameterizations of generalized parton distributions (GPDs) which hold the promise of a three-dimensional picture of the nucleon. G n M (t) = +1 1 dx q (e qh q (x,ζ;t) + κe q E q (x,ζ;t)) High-quality data on the neutron form factors in a wide t range would be highly valuable for pinning down the differences in the spatial distribution of u and d quarks... drastic differences in the behavior of u and d contributions to the form factors (M.Diehl, Th. Feldmann, R. Jakob, and P.Kroll, hep-ph/48173v). PAC3 Meeting, August 6-8, 7 38

39 Effect of Fermi Motion The Fermi motion in the target can drive some of the nucleons out of the CLAS acceptance. This effect turns out to be small in the ratio and decreases as Q increases. Fraction of nucleons scattered into the EC acceptance at 4. GeV Fractional difference in the ratio correction factor between the Hulthen distribution and a flat distribution. PAC3 Meeting, August 6-8, 7 39