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GEp at 9 GeV2 and the nucleon Form Factors

Or: what have elastic form factors revealed about the structure of the nucleon

C.F. Perdrisat

the College of William and Mary

2008 J Lab Users MeetingJ Lab, Newport News, J une 16, 2008

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Outline

Introduction

FF from Rosenbluth and recoil polarization

The proton Form Factor “discrepancy”

New Form Factor data: Proton and Neutron

Recently completed experiments in Hall C and A at JLab

Conclusions

(see also review in “Progress in Particle and Nuclear Physics”, C.F.P., V. Punjabi and

M. Vanderhaeghen, Prog. Part. Nucl. Phys. 59, 694-764, 2007)

and other reviews: J. Arrington et al.(06); C. Hyde-Wright and K. de Jaeger (04); H. Gao (03)

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Introduction

• At large Q2 electromagnetic Form Factors contain structure information on the many-body system of quarks and gluons of the nucleon. At low Q2 they inform us about the pion cloud.

• When obtained from experiment, the Form Factors are relativistic invariants only to the extent that the probe is a single virtual photon exchanged between electron and nucleon; higher order contributions destroy this invariance, which one might regain after applying a number of radiative corrections; the current status of these corrections is unsatisfactory.

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j=<e’||e> J=<p’||p>

Nucleon vertex:

F1 helicity conserving , F2 helicity non-conserving form factors

Alternately, the Sachs form factors

GE(Q2)=F1(Q2)- F2(Q2) GM(Q2)=F1(Q2)+F2(Q2)

Traditionally, it is assumed that in the Breit frame, and for very small Q2, GE and GM are Fourier transforms of charge- and current distributions.

ep elastic in Born approximation

)2(22

)2(1

', QFM

iQFpp

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Dirac Pauli

Rosenbluth vs. Recoil Polarization

Cross section

with

Reduced cross section:

Recoilpolarizationcomponents

Form Factor ratio:

)1/()2(2)2(2

Q

MpGQ

EpG

Mottdd

dd

22tan)1(21

124

2

eand

MQ

2

21222/)1(

MpGEpG

MpG

MpG

EpG

Mottdd

dd

reduced

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all Rosenbluth separation dataDivided by the dipole form factor GD=(1-Q2/0.71)-2

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Recoil Polarization Results

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So what is the cause for the different results?

First, radiative corrections at large Q2 are large and strongly ε-dependent.

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green for 1.75 GeV2

blue for 3.75 GeV2

red for 5 GeV2

Data from Andivahis et al.(1994)

R=[(1+)/][exp/Mott]=

=G2Mp+ G2

Ep/

Second, there is a scatter in size of calculated

corrections

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Vdh: code similar to Maximon and Tjon:with realistic energy cut, external radiative correction included.

Andivahis et al: based on Mo and Tsai,with improvements from Walker et al.

Bystritskiy, Kuraev, Tomasi-Gustafsson: with Drell-Yan structurestructure function (Drell-Yan parton picture). RC for electron to all orders.

Afanasev et al: two-photon correction

Interpolation from Hall A recoil polarization, GMp from Kelly fit

5 GeV2

Third, two-(hard)photon exchange might play a role.

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Afanasev, Brodsky,Carlson,Y.C. Chen, Vanderhaeghen, GPDs fitted to FF data,Guidal et al.(04)

Blunden Melnitchouk and Tjon (05):intermediate state a proton, includes finite size effects: effect on Pt order ≤ 3 %, increases with Q2

For example: Real part of Y2γ

1) ε-independence of GEp/GMp in recoil polarization

2) cross section difference in e+ and e- proton scattering

3) non-linearity of Rosenbluth plot

Also imaginary part 4) from induced out-of-

plane polarization5) single-spin target

asymmetry

eande

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Hall C 04-019, completed

Hall B 07-005; also Olympus/Doriswith refurbished BLAST detector

Hall C 05-017; being analyzed

by-product of 04-019/04-108?

Hall A 05-015 (3He )

Whether two-photon exchange is entirely responsible for the FF “crisis” is of course to be determined experimentally

Two-Gamma 04-019

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Some model calculations predict a greater sensitivity to 2γ for the polarization than for the cross section data

The preliminary data for Q2=2.5 GeV2 show no ε-dependence of GEp/GMp atthe 0.01 level

PRELIMINARY, not

to be quoted

Electric FF of the neutron

Two of the Hall A preliminary data shown (02-013), anticipated error for two more (5/2008)

All polarization results, including new Bates/BLAST data (Geis 2008)

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Magnetic FF of the neutron

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Preliminary Bates/BLAST results d(e,e’), Meitanis et al

PRELIMI

NARY

GEp/GD from selectedpolarization experiments,compared to the Kelly fit

GMp from polarization GEp/GMp, (Brash et al)

The form factors of the proton

Magnification of thesmall Q2 region of GEp/GD

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Proton: F2 /F1 and pQCD

Brodsky and Farrar (75):

Q2F2/F1 constant

Belitsky, Ji and Yuan (03):

Q2F2/F1 ln2(Q2/2)! !

Guidal et al (05):3 parameters model of GPDs

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New Theoretical Results

De Melo, Frederico, Pace, Pisano, Salmè: light front CQM with qqbar from Z-diagram, the source of the zero crossing. Zero crossing still near 9 GeV2 when GEp data taken out of fit

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Argument of F. Gross and collaborator (Gross, Ramalho and Peňa, 2008): zero crossing is quite natural, unlike the defunct “scaling” behavior.

Simple argument: as long as F1 and F2 are positive, and Q2F2/F1 behavior supports that, GE=F1-τF2 must become negative somewhere!

Gross al et al: oversimplifying GE/GM = (f1 - τf2)/(f1 + f2)= (1- τκ)/ (1 + τκ).f1 and f2 are quark Dirac and Pauli FF, κ is quark anomalous magnetic moment, approximately 2.

The zero crossing is then at Q2=2 GeV2!

Zero crossing of GEpis natural!

New Theoretical Results: 2γ

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Jain, Joglekar and Mitra use formalism of nonlocal fieldtheory; one free parameter: predict an ε dependence for theGEp /GMp ratio of polarization transfer (Definitively not seen)

Borisyuk and Kobushkin evaluate 2γ exchange in dispersion relation approach; different formalism, results similar to Arrington, Melnitchouk and Tjon (2007)

Kondratyuk and Blunden added 5low lying resonances to previouscalculation with nucleon and Δ using polarization data as “Born” FF:higher resonances ~ cancel each other.

Bystricky, Kuraev, Tomasi-Gustafsson, use structure function (Drell-Yan parton picture) method: includes RC for electron to all order. Say two-photon contribution negligible!

GEp(III), 04-108

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8.54 GeV2 point:181.3 Cb, 1.63 billion triggerscollectedNew equipment workedbeautifully: BigCal and FPPAnalyzing power at 5.4 GeV/cclose to Dubna value6.8 GeV2 point:160 million triggers5.2 GeV2 point:A test of the spin transport at χ=180o

Recent and future FF

Last year GEn in Hall A, Q2 of 1.20, 1.65, 2.48 and 3.43 GeV2; data are currently being analyzed!

Very recent Hall A investigation of GEp/GMp by recoil polarization,in range 0.3<Q2<0.7 GeV2, with small statistical uncertainty

After the 12 GeV upgrade

•LOI for Hall C GEp/GMp to 13 GeV2, with SHMS and BigCal, LOI 12-06-103, to be submitted at next PAC

•Approved experiment E12-07-109, GEp/GMp to 15 GeV2 with new large acceptance Multi Purpose Spectrometer (MPS), to be built with single dipole and GEM trackers

04-108 (GEp(III)) has just been completed in Hall C; promising data at 5.2, 6.8 and 8.5 GeV2

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04-019 (2-gamma) also just completed in Hall C; very small error bars on GEp/GMp at 2.5 GeV2, 3 values of ε.

GEp/GMp with 12 GeV at JLab

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FPP and BigCal in Hall C

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2001….2008

F. Wesselman, M. Meziane (WM student)

L. Pentchev, A. Puckett (MIT student), W. Luo (Lanzhou U. student)

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From P HMS

σ=0.3o

From θHMS σ=0.56o

Angular resolution from theCalorimeter BigCal

Actual performance of FPP and BC

Azimuthal dependence of asymmetry in FPP at a Q2 of 6.8 GeV2

Q2=6.8 GeV2

Conclusion, Perspective

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Both experimental characterization and phenomenological understanding of the structure of the proton, have changed drastically since 1998, year of the first recoil polarization experiment in Hall A.

Rapid decrease of GEp with Q2 not a surprise: predicted in at least 3 papers: Iachello Jackson and Lande (73) with VMD, Frank, Jennings and Miller (96) withCQM, and Holzwarth (96) with chiral soliton.

Full understanding of implications of the JLab finding not in yet. Where does the pQCD behavior start? are the nucleons spherical in their ground state? Are we “really” seeing the effect of quark orbital angular momentum?

Also under development is a full understanding of two-photon effects, and revision of standard radiative correction calculation codes.

The hope is that lattice QCD predictions will soon catch up with the data!

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The End