Nucleon Form Factors John Arrington Argonne National Lab
Nucleon Form Factors John Arrington Argonne National Lab Hall A Collaboration Meeting 4 Jan 2007
Early History of the Proton 2
Electron Scattering and Form Factors 3
Proton Form Factors 4
Nucleon Form Factors n Fundamental properties of the nucleon – Connected to charge, magnetization distribution – Crucial testing ground for models of the nucleon internal structure – Necessary input for experiments probing nuclear structure, or trying to understand modification of nucleon structure in nuclear medium n Early measurements found: – Neutron form factor small – Others well approximated by dipole form – Only proton magnetic form factor measured precisely over large Q 2 range 5
Significant Program Over Next 40+ Years 6
Unpolarized Elastic e-N Scattering n Nearly all of these measurements used Rosenbluth separation s. R = ds/d. W [e(1+t)/s. Mott] = t. GM 2 + e. GE 2 t = Q 2/4 M 2 Reduced sensitivity to… • GM if t<<1 (low Q 2) • GE if t>>1 • GE if GE 2<<GM 2 (e. g. neutron) e. GE 2 Form factor extraction is very sensitive to angle-dependent corrections in these cases Lack of a free neutron requires deuteron target: correct for proton contribution and nuclear effects (e. g. FSI, MEC) t. GM 2 q=180 o q=0 o 7
Nucleon Form Factors n Fundamental properties of the nucleon – Connected to charge, magnetization distribution – Crucial testing ground for models of the nucleon internal structure – Necessary input for experiments probing nuclear structure, or trying to understand modification of nucleon structure in nuclear medium – Rosenbluth (L-T) technique has severe limitations in some regions n Recent revolution (last 10 yrs) due to new experimental techniques – Dramatically improved precision, Q 2 coverage – Most previous data now obsolete (or incorrect) – New program of parity-violating measurements – Revelation of importance of two-photon exchange n Driving renewed activity on theory side – Models trying to explain all four EM FFs – Trying to explain data at both low and high Q 2 – Model-independent interpretations of, e. g. flavor dependence 8
New techniques: Polarization and A(e, e’N) n Mid ’ 90 s brought measurements using improved techniques – Polarized beams with polarized target or recoil polarimeter – Large, efficient neutron detectors for 2 H(e, e’n) – Improved models for nuclear corrections L/T: t. GM 2 + e. GE 2 Pol: GE/GM Bigbite in Hall A at JLab Polarized 3 He target Focal plane polarimeter 9
Example: GE /GM from Recoil Polarization Note that PL and PT (or Ax, Az) depend only on GE/GM Need additional data to separate GE and GM (e. g. se-p) GMn measurements require nuclear targets (polarized 2 H or 3 He) Similar expressions for cross section asymmetry from polarized target 10
Nucleon Form Factors: Recent Advancements n Neutron form factor measurements – 1997: Mainly d(e, e’) - limited (e, e’n), (e, e’n/e, e’p), polarization data – Uncertainties and scatter made it difficult to evaluate models GMn as of 1997: Inclusive, ratio, and polarization measurements Since 1997: new polarization, ratio measurements (+CLAS preliminary) 11
Nucleon Form Factors: Recent Advancements n Neutron form factor measurements as of ~1997 – GEn very poorly known – Mostly from elastic e-d very large model-dependence GEn as of 1997: elastic e-d and polarization measurements Since 1997: 2 H and 3 He polarized target and recoil polarization data, along with improved e-d analysis and projected future measurements 12
Nucleon Form Factors: Recent Advancements n Proton form factor measurements from Rosenbluth separations – GMp well measured to 10 Ge. V 2, data out to 30 Ge. V 2 – GEp well known to 1 -2 Ge. V 2, data to ~6 Ge. V 2 mp. GEp/GMp from inclusive Rosenbluth measurements GMp from inclusive measurements – data extend to 30 Ge. V 2 New data: Recoil polarization and p(e, p) “Super-Rosenbluth” With TPE corrections (Blunden, et al. ), GMp shifts by up to 2 -3 sigma, maybe more 13
Insight from New Measurements n New information on proton structure – GE, GM differ for the proton: different charge, magnetization distributions – Connection to GPDs: spin-space-momentum correlations Model-dependent extraction of charge, magnetization distribution of proton: J. Kelly, Phys. Rev. C 66, 065203 (2002) A. Belitsky, X. Ji, F. Yuan, PRD 69: 074014 (2004) G. Miller, PRC 68: 022201 (2003) 14
Insight from New Measurements n Can test models with data on both proton and neutron form factors – Previously, precise data and large Q 2 range only for GMp, lower precision and limited Q 2 range for GEp, GMn, little data for GEn n Data for all FFs at low Q 2 – GEp, GMn, GEn known to higher Q 2 and greater precision – GEp has changed dramatically, GMp also non-trivially modified n Soon, all four FFs known with high precision to 4 -5 Ge. V 2 – Complete data set in “quark core” and “pion cloud” region – Precise non-singlet (p-n) extraction over large range 15
Small Sample of Recent Calculations 16
Pion Cloud charge and magnetization density Dipole form factor within 5% for Q 2 < 1. 0 (Ge. V/c)2 Deviations from dipole at low Q 2 → effects of meson cloud e. g. Friedrich-Walcher parameterization: “smooth part” Slide courtesy of Michael Kohl “bump part” 17
Pion Cloud: Data minus “smooth” fit Slide courtesy of Michael Kohl 18
Pion Cloud: Some cautions n “Bump” is not simply the “pion’s contribution” – p np x% of the time implies x% of GEp(0) should be from the pion – Fourier transform of the “bump” does not isolate pion n Deviation from dipole(s) is just that – a deviation from the dipole form n Important to GEn, but not the story full Proton n Global analysis of high-precision data can, in a model-dependent way, tell us about the pion cloud n Precise comparison of low-Q FFs, e. g. GMp vs. GEp or GMp vs. GMn can provide additional information Neutron n Model-independent Information on differences. Still need model to tell pion cloud vs. relativistic effects, etc… 19
Parity Violating Elastic e-p Scattering n Nucleon charge, mag. distributions determined by quark distributions Experiment SAMPLE HAPPEX G 0 PVA 4 Q 2 0. 1* 0. 04* 0. 5 0. 1 -1 0. 4* 0. 7* 0. 1 0. 2* APV [ppm] 6 ppm 7 2 15 2 6 1 -10 1 5 - Notes 1997 deuterium 4 He * = backward angle Magneta for planned measurements 20
Nucleon Form Factors: Parity Violation n Parity-violating elastic electron scattering – APV depends on EM form factors, RC, and strangeness content – Combine with EM FF to perform full flavor decomposition of form factors into Gu(Q 2), Gd(Q 2), Gs(Q 2) Separation at Q 2=0. 1 Projected uncertainty Contours from R. D. Young, et al, PRL 97: 102002 (2006) Bands are latest HAPPEX: A. Acha, et al. , nucl-ex/0609002 21
Present Status n Recent and near-future measurements: 1997 -2007 – Most of the world’s high-Q 2 data – Most of the world’s high-precision data – Demonstrated problems with previous GEp AND GMp data – New program of parity violating elastic scattering n For non-singlet (p-n) form factors or flavor decomposition, need precise data covering similar Q 2 range, careful understanding of systematics, including correlations between measurements n TPE contributions – Effect on GEp (up to 100+%) much larger than for GMp (several %) – Impact of GMp corrections can be more important in global fitting – Corrections can propagate from proton to neutron (as extracted from 2 H) to strangeness contribution from parity measurements – While direct TPE corrections to parity violation are small, the effect of TPE corrections to the EM FFs changes the expected asymmetry. 22
Radiative Corrections: Beyond the Born Approximation 23
Tests of Two-Photon Exchange (’ 50 s and ’ 60 s) 24
Two-Photon Exchange Strikes Back n Proton form factor measurements – Comparison of precise Rosenbluth and Polarization measurements of GEp/GMp show clear discrepancy at high Q 2 n Two-photon exchange corrections believed to explain the discrepancy P. A. M. Guichon and M. Vanderhaeghen, PRL 91, 142303 (2003) n Compatible with e+/e- ? n Still lack direct evidence of effect on cross section – Beam normal spin asymmetry the only observable in elastic e -p where TPE observed M. K. Jones, et al. , PRL 84, 1398 (2000) O. Gayou, et al. , PRL 88, 092301 (2003) I. A. Qattan, et al. , PRL 94, 142301 (2005) 25
Two-Photon Exchange Measurements n Comparisons of e+-p and e--p scattering [VEPP-III, Hall B] Evidence (3 s level) for TPE in existing data J. Arrington, PRC 69, 032201(R) (2004) World’s data Novosibirsk JLab – Hall B n e dependence of polarization transfer and unpolarized se-p [Hall C] – More quantitative measure of the discrepancy – Test against models of TPE at both low and high Q 2 n TPE effects in Born-forbidden observables [Hall A, Hall C, Mainz] – Target single spin asymmetry, Ay in e-n scattering – Induced polarization, py, in e-p scattering – Vector analyzing power, AN, in e-p scattering (beam normal spin asymmetry) 26
Status of TPE n Significant progress in theoretical understanding – Multiple calculations that explain most of the effect at high Q 2 – Hadronic calculations appear sufficient up to 2 -3 Ge. V 2 n Experimental program will quantify TPE for several e-p observables – Precise test of calculations in explaining discrepancy – Tests against different observables n Want calculations well tested for elastic e-p, reliable enough to be used for other reactions Before TPE After TPE (Blunden, et al) 27
TPE Beyond the Elastic Cross Section n Two-photon exchange (TPE) corrections – Precise tests of TPE calculations for the proton – Calculations for several observables for proton and neutron – Important direct and indirect consequences on other experiments • High-precision quasi-elastic expts. D. Dutta, et al. , PRC 68, 064603 (2003) J. Arrington, PRC 69, 022201(R) (2004) • - N scattering measurements H. Budd, A. Bodek, and J. Arrington, hepex/0308005 P. Blunden and I. Sick, PRC 72, 057601 (2005) • Proton charge radius, hyperfine splitting • Strangeness from parity violation • Neutron form factor measurements S. Brodsky, et al. , PRL 94, 022001 (2005) A. Afanasev and C. Carlson, PRL 94, 212301 (2005) J. Arrington and I. Sick, nucl-th/0612079 P. Blunden, W. Melnitchouk, and J. Tjon, PRC 72, 034612 (2005) A. Afanasev, et al. , PRD 72, 013008 (2005) 28
Example: TPE Effects on Parity Measurements n Direct TPE effect small (top left) n Total effect (bottom left) noticably larger n TPE effect goes thru zero for Q 2~0. 3 Ge. V 2 29
Summary: Next few years n Results for GEn at high Q 2 n New measurements of GEp/GMp at high Q 2 – Look for zero crossing of GEp n Tests of TPE corrections – Cross section, polarization, Born-forbidden observables n Parity measurements (HAPPEX, G 0, A 4) – Strangeness contributions n Global analysis of form factor, TPE measurements – Extract corrected proton, neutron, and strangeness form factors – Precise, complete data set for nucleon form factors to moderate Q 2 n 12 Ge. V upgrade: More to come… 30
Nucleon Form Factors at Jefferson Lab n Part of the initial scientific mission of CEBAF n A promise fulfilled – Nearly complete set of measurements – Driving rapid progress in theory n Delivered more than initially expected – New: Parity program – Unexpected: Decrease of GE/GM at high Q 2 – New: Two-photon exchange n Hall A had a major role in nearly all aspects of the program – Polarimeter: GEp/GMp at high Q 2 “Super-Rosenbluth”, TPE – Polarized 3 He: GEn at high Q 2 , GMn at low Q 2 – Parity program: Strangeness contributions – More to come: TPE measurements, Low Q 2 GEp/GMp proposal, … 31
For more information… Nucleon form factors: C. F. Perdrisat, V. Punjabi, and M. Vanderhaeghen, ar. Xiv: hep-ph/0612014 (2006) J. Arrington, C. D. Roberts, and J. M. Zanotti, ar. Xiv: nucl-th/0611050 (2006) C. E. Hyde-Write and K. de Jager, Ann. Rev. Nucl. Part. Sci. 54, 217 (2004) H. Gao, Int. J. Mod. Phys. E 12, 1 (2003); Erratumibid 567, (2003) Parity, GPDs, TPE, etc…: E. J. Beise, M. L. Pitt, and D. T. Spayde, Prog. Part. Nucl. Phys. 54, 289 (2005) D. H. Beck and R. D. Mc. Keown, Ann. Rev. Nucl. Part. Sci. 51, 189 (2001) D. H. Beck and B. R. Holstein, Int. J. Mod. Phys. E 10, 1 (2000) K. Kumar and P. Souder, Prog. Part. Nucl. Phys. 45, S 333 (2000) X. Ji, Ann. Rev. Nucl. Part. Sci. 54, 413 (2004) M. Vanderhaeghen and C. E. Carlson – coming in 2007 32
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