Kees de Jager Hall A Workshop December 14, 2011

Hall A, December 14, 2011, 1

Kees de JagerHall A WorkshopDecember 14, 2011

Nucleon Electromagnetic Form Factors:An Overview

•Introduction•Experimental Status of EMFF•Two-photon exchange effects•Proton charge radius•Flavor separation

•Analysis and Interpretation•Outlook•Summary

Thomas Jefferson National Accelerator Facility


Historical Overview➙ 1910s - Rutherford discovers the

positively charged core of atoms➙ 1932 – James Chadwick

discovers the neutron➙ 1933 - Stern observes

anomalous magnetic moment of the proton by deflecting a beam of hydrogen molecules in an inhomogeneous magnetic field

➙ 1955 - Hofstadter et al. at Stanford discover, through elastic electron scattering, that protons have a size, quote an RMS charge radius of 0.74 ± 0.24 fm

➙ 1968 – nucleon constituents were established from scaling in deep inelastic scattering


where

Definitions of the EMFFs

+

The Sachs FFs:


Visualizing charge and magnetic distributions

Fourier transforms of nucleon FFs (the neutron pictured above) have provided important insight, but suffer in that the momentum transfers are too large to ignore relativistic effects

Vanderhaeghen and Walcher, Nucl. Phys. News 21 (2011) 14

Interpreted as pion cloud

neutron charge density

While referred to as “charge densities”, these cannot be directly related to our usual lab-frame concept of charge density

neutronproton

transversely polarized

rest frame

light-front frame


Impact of EMFF on GPDs

2. Describes correlations of quarks/gluons

4. EMFFs are essential to determine the high-Q2 contributions to the GPDs in order to allow access to the quark angular momentum (in model-dependent way)

1. GPDs allow for a unified description of form factors and parton distributions

x < 0.1 x ~ 0.3 x ~ 0.8

3. Allows for Transverse Imaging

eqq∑ dxH q(x,x =0,Q2 )

−1

1

∫ =F1(Q2 ); κ q

q∑ dxEq(x,x =0,Q2 )

−1

1

∫ =F2(Q2 )


World Data Set on GEp by mid 1990s

σ R Q2 ,ε( ) = ε 1 +1τ

⎛⎝⎜

⎞⎠⎟

EE '

σ E,θ( )σ Mott

= (GMp )2 Q2( ) +

ετ

(GEp )2 Q2( ) ε =

11+ 2(1+ τ ) tan2 (θ / 2)

➙ Relied on Rosenbluth separation

➙ General assumption that GE

p/GMp ≈ 1

➙ Although data showed large scatter

τ =Q2

4M 2 =EE 'sin2 (θ / 2)

M 2Rosenbluth separation (cross-section measurement at constant Q2)


Alternative: Spin Transfer Reaction 1H(e,e’p)

€

r

€

r

€

Pn = 0

±hPt = mh2 τ (1+ τ )GEpGM

p tanθe

2 ⎛ ⎝

⎞ ⎠/ I0

±hPl = ±h Ee + Ee'( ) GMp

( )2

τ (1+ τ )tan2 θe

2 ⎛ ⎝

⎞ ⎠ / M / I0

I0 = GEp Q2( ){ }

2+ τ GM

p Q2( ){ }2

1+ 2(1+ τ )tan2 θ e

2 ⎛ ⎝

⎞ ⎠

⎡ ⎣ ⎢

⎤ ⎦ ⎥

€

GEp

GMp = −

Pt

Pl

Ee + Ee'

2Mtan

θ e

2 ⎛ ⎝

⎞ ⎠ No error contributions from

• analyzing power• beam polarimetryAkhiezer et al., Sov. Phys. JETP 6, 588 (1958)


World Data Set on GEp more than ten years later

• Detailed reanalysis of SLAC data resulted in acceptable scatter of data• JLab Rosenbluth data (open red symbols in top) in agreement with SLAC

data• No reason to doubt quality of either Rosenbluth or polarization transfer

data• Investigate possible theoretical sources for discrepancy

➙ Large new data set based on polarization transfer show a close to linear decrease of GE

p/GMp with

Q2

➙ In contrast with Rosenbluth dataA. Puckett et al., arXiv: 1102.5737


Two-photon Exchange (TPE) Contributions

Guichon and Vanderhaeghen (PRL 91, 142303 (2003)) introduced a general formalism for two-photon exchange effects in elastic electron-nucleon scattering

• The 2γ/1γ interference term δ2γ has opposite sign for e+p and e-p scattering, is expected to vary from 1 to 10%, but no data with significant accuracy exist. Experiments are ongoing at VEPP-III, CLAS and DORIS.

Milner

• Other processes sensitive to TPE:➙Non-linearity of ε- dependence in polarization transfer➙Normal Single-Spin Asymmetries

σ e+( )σ e−( )

≈ 1 − 2δ 2γ


NSSA in elastic eN scattering

on-shell intermediate state (MX = W)

spin of beam OR target NORMAL to scattering plane

∝ℑ(A2γ)

Androic et al., PRL 107 (2011) 022501

Good agreement with theory

TPE effects known to exist


Q2=2.64 GeV2 No non-linearity observed in PL/PT, but ε-dependence in PLMeziane et al., PRL 106 (2011) 132501

Searching for non-linear ε-dependence in PT

Interpreted phenomenologically by Guttmann, Kivel and VdH, PRD 83 (2011) 094021


Effect on L-T Extractions

LT + BMT*PT

➙ full reanalysis of data, incorporating hadronic TPE calculations, adding a (small) phenomenological correction for nucleon resonances

~1% at 2 GeV2, 2% at 5 GeV2 • Assign 100% of the extra

correction as an uncertainty (affects GM

p uncertainty)

• Corrections in full agreement with existing data on e+/e- ratio

Arrington, Melnitchouk, TjonPRC 76, 035205 (2007)

Arrington, Blunden, MelnitchoukPPNP 66 (2011) 782


CLAS TPE experimentSchematic e+/e- beamline• In the CLAS experiment

mixed identical e+ and e-

beams were directed onto a LH2 target. The scattered leptons and protons were detected in the CLAS detector.

• Overdetermined kinematics allow clean identification of elastic scattering events

• Results within a few months

CLAS

OlympusNovosibirsk


• Use BLAST detector and internal target at DORIS

• Max. energy 4.45 GeV• Stored current 120 mA• Installation completed• Commissioning started

VEPP-III

OLYMPUS@DESY in DORIS


Proton cross-section data from MAMI• Bernauer et al. (PRL 105, 242001

(2010)) collected a large data set (1400 data at six beam energies), using all three A1 spectrometers

• The ≤1% accuracy allowed an L/T separation in a Q2-range of 0.005 to 0.7 GeV2; error bands shown are of fits to complete data set, not representative of individual errors

<r2>E1/2 = 0.879(8)±5±4±2±4

fm<r2>M

1/2 = 0.777(18)±13±9±5±2 fm

stat;syst;model

CODATA (dominated by electronic Lamb Shift) <r2>E

1/2 = 0.879±7 fm

• Results for GEp/GM

p in reasonable agreement with CODATA, but GM

p data 2-3% larger than world data set (due to neglect of TPEs??)


Polarization Transfer at low Q2-valuesDetailed understanding of Hall A HRS spectrometer optics and availability of BigBite spectrometer has made possible polarization transfer measurements with a ~1% accuracy in a Q2-range from 0.3 – 0.7 GeV2

Results agree with Bernauer et al., but the charge radius is extracted using the magnetic world data

These new data analyzed together with the new data set from MAMI will allow to set sensitive limits onTPE effects at low Q2

X. Zhan et al.,PLB 705, 59 (2011)

<r2>E1/2 =

0.875(10)±8±6fm<r2>M

1/2 = 0.867(20)±9±18 fm


Comparison of world data

➙ Blue: MAMI results➙ Dashed black curve: old fit (w/o MAMI

data) with TPE➙ Open circles: old fit w/o TPE➙ Red: updated Arrington fit (w/o MAMI

data), including TPE corrections➙ Green: slope of fit at Q2 = 0

€

˜ G E,M (k) = GE ,M (Q2) 1+ τ( )2 with k 2 =

Q2

1+ τ and τ =

Q2M ⎛ ⎝

⎞ ⎠

2

Kelly, PRC 66 (2002) 065203

r2

int= r2

εxp−

3λ2Mp

2 ~1% decrease in charge radius

Comparison of open circles and black (dashed) curve gives quantitative indication of TPE effects

Relativistic boost effects:


The proton charge radius

➙ What is reason for this >5σ discrepancy?

➙ Electron scattering and electronic Lamb shift agree

➙ Also, electron scattering and muonic X-ray agree

➙ Unknown interaction between μ and p?➙ Muonic hydrogen much smaller than

atomic hydrogen, more sensitive to off-shell effects?

➙ Leading theoretical uncertainty in HFS of hydrogen ground state dominated by low-Q2 behaviour in Zemach radius:

PSI (muonic Lamb shift) Nature 466, 213 (2010)<r2>E

1/2 = 0.84184(67) fmCODATA (electronic Lamb shift)<r2>E

1/2 = 0.8768(69) fm

De Rujula, PLB 693, 555 (2010); PLB 697 26 (2010)Bernauer et al. PLB 696, 343 (2011)Cloet & Miller, PRC 83, 012201 (2011)Jentschura, EPJD 61, 7 (2011)Barger et al., arXiv: 1011.3519Tucker-Smith and Yavin, arXiv: 1011.4922 Miller et al., arXiv: 1101.407

rZ =−4p

dQQ2∫ GE Q2( )

GM Q2( )1+κ p

−1⎡

⎣⎢⎢

⎤

⎦⎥⎥

Zhan


Impact of E08-007-II➙ A linear fit to all Mainz data at Q2 <

0.02 GeV2 yields a charge radius close to the PSI value! Clearly, the derivative at Q2 = 0 is not a good measure of the radius

Need independent new data at very low Q2, to be provided coming spring by E08-007-II, in order to resolve this issue

Carl Carlson


ISRFSR

FSR

ISR

Future EMFF Research @MAMI

Use ISR to measure GEp down to very small Q2-values

Goal: obtain a 1% accuracy in the proton charge radius

Simulation of elastic scattering at three beam energies


Measuring GMn

➙A systematic difference of several % between results from JLab and MAMI in Q2-range 0.4 – 1.0 GeV2

➙Will be studied in upcoming experiment at MAMI

• Measure (en)/(ep) ratio• Measure inclusive

quasi-elastic scattering off polarized 3He


GEn from polarized 3He target: 3He(e,e′n)

• New data more than double the Q2-range of the world data set• Roberts’ dressed quark-diquark model using the Dyson-Schwinger and

Faddeev equations in good agreement, better than Miller’s CQM prediction• New data allow a flavor separation of the EMFFs up to 3.4 GeV2

e’

nTarget

polarization ~50%

Beam polarization

84%

S. Riordan et al., PRL 105, 262302 (2010)


Comparison with (Effective) Theory


Status of Lattice QCD

Significant progress in LQCD, but still limited to mπ ≥ 300 MeV and neglect of disconnected diagrams, resulting in large underestimates of e.g. isovector charge radius

Bratt et al., PRD 82 (2010) 094502

DataLQCD

experimental value


(Logarithmic) Scaling➙ Basic pQCD scaling predicts F1 ∝ 1/Q4 ; F2 ∝1/Q6 → F2/F1 ∝ 1/Q2

➙ Data clearly do not follow this trend (yet?)➙The introduction of a quark orbital angular momentum component

results in F2/F1 ∝ 1/Q➙ Belitsky et al. have included logarithmic corrections in pQCD limit

➙ Proton data appear to follow this scaling behaviour to some extent, but new neutron data do not


Flavor separation of F1,2

Note that the corresponding ratio F2p/F1p shows no particular change in behavior for Q2 > ~1 GeV2

This disagrees with a generally accepted expectation that dates to Schwinger in the 1950’s that:F2/F1∝1/

Q2Cates, de Jager, Riordan and Wojtsekhowski, PRL vol. 106, pg 252003 (2010)

u

d

The ratios F2q/F1q become constant for Q2 > ~1 GeV2 !

F1,2u =2F1,2

p + F1,2n ; F1,2

d =2F1,2n + F1,2

p

aσσum ing iσoσpin σym m ετry: F1,2u, p =F1,2

d,n and F1,2d, p =F1,2

u,n

Assuming that the s-quark contribution is negligible (based on the PVe results)


Scaling of the up and down quarks

Cates, de Jager, Riordan and Wojtsekhowski, PRL vol. 106, pg 252003 (2010)

Fd seems to scale like 1/Q4 whereas Fu seems to scale more like 1/Q2


Scaling difference caused by diquarks

u-quark scattering amplitude is dominated by scattering from the lone “outside” quark.Two constituents implies 1/Q2

While at present this idea is at a conceptual stage, it is an intriguingly simple interpretation for the very different behaviors (and in agreement with the DSE calculation of Cloët, Roberts and Wilson).

d-quark scattering amplitude is necessarily probing inside the diquark. Two gluons need to be exchanged (or the diquark would fall apart), so scaling goes like1/Q4

Suggested by Jerry Miller


Impact parameter b is defined relative to the transverse center of the quark’s longitudinal momentum fractions

Mapping of nucleon constituents (in the proton)

in proton

➙ Why is the d-quark so much wider?Miller, Strikman, Weiss, arXiv: 1105.6364

• ρd/ρu → -1 for b → ∞ due to dominance of chiral 2π exchange near threshold

• ρd/ρu ≈ 0.5 for 0.2 < b < 1.6 fm (mean-field value of number of quarks)

• ρd/ρu ≈ 0.3 for b → 0 due to large x-behavior

• need accurate GEn data at small Q2


• The Super Bigbite program:➙large dipole magnet ➙GEM trackers (~100,000 channels)➙hadron and EM calorimeter➙Trigger and DAQ

• operating in open geometry at a luminosity of 1038 cm-2s-1

• will extend measurements of EMFFs to double the existing Q2-range• included in the JLab long-term capital funding

GEMs

The SuperBigbite program

PIs: Gordon CatesBogdan Wojtsekhowski


Projected EMFF data with SBS @ 12 GeV


Further neutron FF measurements at lower Q2-values

➙ MAMI will implement a new large neutron detector, to be used to improve data set on GM

n (through (e,n)/(e,p) ratio) and on GE

n through polarization transfer, both on LD2 target

MAMISBS in Hall A

Complementary data set of high accuracy

➙ Large acceptance of BigBite and high neutron efficiency of hadron calorimeter yield large FOM for (n,n’) polarimeter with SBS


Time-Like Region• Can be probed through e+e- -> NN or inverse reaction• Large influx of data through analysis of ISR channel at

BABAR

_

•Effective proton FF (GE = GM)•Increase of FF towards threshold•Agreement with pQCD at high Q2

➙ Measure GE/GM by fitting distribution of helicity angle

➙ Significant disagreement between new BABAR results and those from LEAR

➙ GE ≈ GM at Q2 > 6 GeV2


Time-like Region Prospects

•Expect large expansion of data, especially for the neutron FF at BES-III

Simulation:BABAR: √s = 10.6 GeV, 230 fb-1

BES-III: √s = 3.77 GeV, 10 fb-1

3-4 times higher statistics at BES-III !protons

neutrons


Summary and Outlook• In the decade since the first observation of the surprising GE

p/GMp

ratio important developments in the study of EMFFs have yielded:➙ an extension of the data to much higher Q2-values ➙ surprising insights in the constituent behavior from a flavor

decomposition of the FFs➙ a broad ongoing program to obtain quantitative information on

TPE, but looking forward to the data from CLAS-2γ and OLYMPUS

➙ accurate data on the proton FFs at low Q2, waiting for a combined analysis• However, a broad effort is required to resolve the strong

discrepancy with the muonic result on the proton charge radius• The JLab 12 GeV upgrade will extend the space-like EMFFs to double

the present Q2-range, with an equally impressive improvement in the time-like region from BES-III. Highly accurate data are also needed at low to intermediate Q2-values• It is imperative that this experimental program is accompanied by a

similar progress in our theoretical understanding of the nucleon


THANK YOU !

acknowledging detailed discussions with John Arrington, Carl Carlson, Gordon Cates, Achim Denig, Wally Melnitchouk, Harald Merkel, Seamus Riordan and Bogdan Wojtsekhowski

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Kees de Jager Hall A Workshop December 14, 2011