QED Radiative Corrections for Precision Measurements of Nucleon Form Factors

1
QED Radiative Corrections for Precision
Measurements of Nucleon Form Factors

• Andrei Afanasev
• Jefferson Lab
• Nucleon 2005
• INFN, Frascati, October 12, 2005

2
Main problem

• Uncertainties in QED radiative corrections limit
  interpretability of precision experiments on
  electron-hadron scattering

3
Plan of talk

• Radiative corrections for electron scattering
• Model-independent and model-dependent soft and
  hard photons
• Two-photon exchange effects in the process
  ep?ep
• Models for two-photon exchange
• Cross sections
• Polarization transfer
• Single-spin asymmetries
• Parity-violating asymmetry
• Refined bremsstrahlung calculations

4
Elastic Nucleon Form Factors

• Based on one-photon exchange approximation

• Two techniques to measure

Latter due to Akhiezer, Rekalo Arnold, Carlson,
Gross
5
Do the techniques agree?
SLAC/Rosenbluth
5 difference in cross-section x5 difference in
polarization
JLab/Polarization

• Both early SLAC and Recent JLab experiments on
  (super)Rosenbluth separations followed
  Ge/Gmconst
• JLab measurements using polarization transfer
  technique give different results (Jones00,
  Gayou02)
• Radiative corrections, in particular, a
  short-range part of 2-photon
• exchange is a likely origin of the discrepancy

6
Basics of QED radiative corrections
(First) Born approximation
Initial-state radiation
Final-state radiation
Cross section d?/? gt integral diverges
logarithmically IR catastrophe
Vertex correction gt cancels divergent terms
Schwinger (1949)
Multiple soft-photon emission solved by
exponentiation, Yennie-Frautschi-Suura (YFS),
1961
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Complete radiative correction in O(aem )

• Radiative Corrections
• Electron vertex correction (a)
• Vacuum polarization (b)
• Electron bremsstrahlung (c,d)
• Two-photon exchange (e,f)
• Proton vertex and VCS (g,h)
• Corrections (e-h) depend on the nucleon
  structure
• MoTsai MeisterYennie formalism
• Further work by BardinShumeiko MaximonTjon
  AA, Akushevich, Merenkov
• GuichonVanderhaeghen03
• Can (e-f) account for the Rosenbluth vs.
  polarization experimental discrepancy? Look for
  3 ...

• Main issue Corrections dependent on nucleon
  structure
• Model calculations
• Blunden, Melnitchouk,Tjon, Phys.Rev.Lett.91142304
  ,2003
• Chen, AA, Brodsky, Carlson, Vanderhaeghen,
  Phys.Rev.Lett.93122301,2004

8
Separating soft 2-photon exchange

• Tsai Maximon Tjon (k?0)
• Grammer Yennie prescription PRD 8, 4332 (1973)
  (also applied in QCD calculations)
• Shown is the resulting (soft) QED correction to
  cross section
• Already included in experimental data analysis
• NB Corresponding effect to polarization transfer
  and/or asymmetry is zero

e
dSoft
Q2 6 GeV2
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Bethe-Heitler corrections to polarization
transfer and cross sections
AA, Akushevich, Merenkov Phys.Rev.D64113009,2001
AA, Akushevich, Ilychev, Merenkov, PL B514, 269
(2001)
Pion threshold ummp2
In kinematics of elastic ep-scattering
measurements, cross sections are more sensitive
to RC
10
Lorentz Structure of 2-? amplitude
Generalized form factors are functions of two
Mandelstam invariants Specific dependence is
determined by nucleon structure
11
New Expressions for Observables
We can formally define ep-scattering observables
in terms of the new form factors
For the target asymmetries AxPx, AyPy, Az-Pz
12
Calculations using Generalized Parton
Distributions

• Model schematics
• Hard eq-interaction
• GPDs describe quark emission/absorption
• Soft/hard separation
• Use Grammer-Yennie prescription

Hard interaction with a quark
AA, Brodsky, Carlson, Chen, Vanderhaeghen,
Phys.Rev.Lett.93122301,2004 hep-ph/0502013
13
Short-range effects on-mass-shell quark(AA,
Brodsky, Carlson, Chen,Vanderhaeghen)
Two-photon probe directly interacts with a
(massless) quark Emission/reabsorption of the
quark is described by GPDs
Note the additional effective (axial-vector)2
interaction absence of mass terms
14
Hard contributions to generalizedform factors
GPD integrals
Two-photon-exchange form factors from GPDs
15
Two-Photon Effect for Rosenbluth Cross Sections

• Data shown are from Andivahis et al, PRD 50, 5491
  (1994)
• Included GPD calculation of two-photon-exchange
  effect
• Qualitative agreement with data
• Discrepancy likely reconciled

16
Updated Ge/Gm plot
AA, Brodsky, Carlson, Chen, Vanderhaeghen,
Phys.Rev.Lett.93122301,2004 hep-ph/0502013
17
Full Calculation of Bethe-Heitler Contribution
Additional work by AA et al., using MASCARAD
(Phys.Rev.D64113009,2001) Full calculation
including soft and hard bremsstrahlung
Radiative leptonic tensor in full form AA et al,
PLB 514, 269 (2001)
Additional effect of full softhard brem ? 1.2
correction to e-slope Resolves additional 25 of
Rosenbluth/polarization discrepancy!
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Polarization transfer

• Also corrected by two-photon exchange, but with
  little impact on Gep/Gmp extracted ratio

19
Charge asymmetry

• Cross sections of electron-proton scattering and
  positron-proton scattering are equal in
  one-photon exchange approximation
• Different for two- or more photon exchange

To be measured in JLab Experiment 04-116,
Spokepersons W. Brooks et al.
20
Single-Spin Asymmetries in Elastic Scattering

• Parity-conserving
• Observed spin-momentum correlation of the type
• where k1,2 are initial and final electron
  momenta, s is a polarization vector
• of a target OR beam
• For elastic scattering asymmetries are due to
  absorptive part of 2-photon exchange amplitude
• Parity-Violating

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QuarkNucleon Contributions to An

• Single-spin asymmetry or polarization normal to
  the scattering plane
• Handbag mechanism prediction for single-spin
  asymmetry/polarization of elastic ep-scattering
  on a polarized proton target

Only minor role of quark mass
22
Radiative Corrections for Weak Processes

• Semi-Leptonic processes involving nucleons
• Neutrino-nucleon scattering
• Per cent level reached by NuTeV. Radiative
  corrections for DIS calculated at a partonic
  level (D. Bardin et al.)
• Neutron beta-decay Important for Vud
  measurements axial-vector coupling gA
• Marciano, Sirlin, PRL 56, 22 (1986) Ando et
  al., Phys.Lett.B595250-259,2004 Hardy, Towner,
  PRL94092502,2005
• Parity-violating DIS Bardin, Fedorenko,
  Shumeiko, Sov.J.Nucl.Phys.32403,1980
  J.Phys.G71331,1981, up to 10 effect from
  rad.corrections
• Parity-violating elastic ep (strange quark
  effects, weak mixing angle)

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Parity Violating elastic e-N scattering
Longitudinally polarized electrons, unpolarized
target
t Q2/4M2 e 12(1t)tan2(q /2)-1 e
t(t1)(1-e2)1/2
Neutral weak form factors contain explicit
contributions from strange sea
GZA(0) 1.2673 0.0035 (from b decay)
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Born and Box diagrams for elastic ep-scattering

• (d) Computed by Marciano,Sirlin,
  Phys.Rev.D2975,1984, Erratum-ibid.D31213,1985
  for atomic PV
• (c) Presumed small, e.g., M. Ramsey-Musolf,
  Phys.Rev. C60 (1999) 015501

25
New Expressions for PV asymmetry
PV-asymmetry, Born Approximation

• PV asymmetry in terms of generalized form factors
  including multi-photon exchange

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2?-exchange Correction to Parity-ViolatingElectro
n Scattering
x
Z0
?
?
Electromagnetic
Neutral Weak

• New parity violating terms due to (2gamma)x(Z0)
  interference should be added

27
GPD Calculation of 2?Z-interference

• Can be used at higher Q2, but points at a problem
  of additional systematic corrections for
  parity-violating electron scattering. The effect
  evaluated in GPD formalism is the largest for
  backward angles

AA Carlson, hep-ph/0502128, Phys. Rev. Lett.
94, 212301 (2005) measurements of strange-quark
content of the nucleon are affected, ?s may shift
by 10
Important note (nonsoft) 2?-exchange amplitude
has no 1/Q2 singularity 1?-exchange is 1/Q2
singular gt At low Q2, 2?-corrections is
suppressed as Q2 P. Blunden used this formalism
and evaluated correction of 0.16 for Qweak
28
Two-photon exchange for PV electron-proton
scattering

• Quark-level short-range contributions are
  substantial (2-3)
• 2?-correction to parity-violating asymmetry does
  not cancel. May reach a few per cent for GeV
  momentum transfers
• Corrections are angular-dependent, not reducible
  to re-definition of coupling constants
• Revision of ?Z-box contribution and extension of
  model calculations to lower Q2 is necessary
• Experimentally measurable directly by comparing
  electrons vs positrons on a spin-0 target- it is
  difficult gt in the meantime need to rely on the
  studies of 2?-effect for parity-conserving
  observables

29
Parity-Conserving Single-Spin Asymmetries in
Scattering Processes(early history)

• N. F. Mott, Proc. R. Soc. (London), A124, 425
  (1929), noticed that polarization and/or
  asymmetry is due to spin-orbit coupling in the
  Coulomb scattering of electrons (Extended to high
  energy ep-scattering by AA et al., 2002).
• Julian Schwinger, Phys. Rev. 69, 681 (1946)
  ibid., 73, 407 (1948), suggested a method to
  polarize fast neutrons via spin-orbit interaction
  in the scattering off nuclei
• Lincoln Wolfeinstein, Phys. Rev. 75, 1664 (1949)
  A. Simon, T.A.Welton, Phys. Rev. 90, 1036 (1953),
  formalism of polarization effects in nuclear
  reactions

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Proton Mott Asymmetry at Higher Energies
Spin-orbit interaction of electron moving in a
Coulomb field N.F. Mott, Proc. Roy. Soc. London,
Set. A 135, 429 (1932) BNSA for electron-muon
scattering Barut, Fronsdal, Phys.Rev.120, 1871
(1960) BNSA for electron-proton scattering
Afanasev, Akushevich, Merenkov, hep-ph/0208260
Transverse beam SSA, units are parts per million
Figures from AA et al, hep-ph/0208260

• Due to absorptive part of two-photon exchange
  amplitude shown is elastic contribution
• Nonzero effect observed by SAMPLE Collaboration
  (S.Wells et al., PRC63064001,2001) for 200 MeV
  electrons
• Calculations of Diaconescu, Ramsey-Musolf (2004)
  low-energy expansion version of hep-ph/0208260

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Phase Space Contributing to the absorptivepart
of 2?-exchange amplitude

• 2-dimensional integration (Q12, Q22) for the
  elastic intermediate state
• 3-dimensional integration (Q12, Q22,W2) for
  inelastic excitations

Examples MAMI A4 E 855 MeV Tcm 57 deg SAMPLE,
E200 MeV
Soft intermediate electron Both photons are
hard collinear
One photon is Hard collinear
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MAMI data on Mott Asymmetry

• F. Maas et al., Phys.Rev.Lett.94082001, 2005
• Pasquini, Vanderhaeghen
• Surprising result Dominance of inelastic
  intermediate excitations

Elastic intermediate state
Inelastic excitations dominate
33
Beam Normal Asymmetry(AA, Merenkov)
Gauge invariance essential in cancellation of
infra-red singularity for target asymmetry
Feature of the normal beam asymmetry After me is
factored out, the remaining expression is
singular when virtuality of the photons reach
zero in the loop integral! But why are the
expressions regular for the target SSA?!
Also calculations by Vanderhaeghen, Pasquini
(2004) Gorschtein, hep-ph/0505022 Confirm
quasi-real photon exchange enhancement
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Peaking Approximation

• Dominance of collinear-photon exchange gt
• Can replace 3-dimensional integral over
  (Q12,Q22,W) with one-dimensional integral
  along the line (Q120 Q22Q2(s-W2)/(s-M2))
• Save computing time
• Avoid uncertainties associated with (unknown)
  double-virtual Compton amplitude
• Provides more direct connection to VCS and RCS
  observables

35
Special property of normal beam asymmetry
AA, Merenkov, Phys.Lett.B59948,2004,
Phys.Rev.D70073002,2004 Erratum (2005)

• Reason for the unexpected behavior hard
  collinear quasi-real photons
• Intermediate photon is collinear to the parent
  electron
• It generates a dynamical pole and logarithmic
  enhancement of inelastic excitations of the
  intermediate hadronic state
• For sgtgt-t and above the resonance region, the
  asymmetry is given by

Also suppressed by a standard diffractive factor
exp(-BQ2), where B3.5-4 GeV-2 Compare with
no-structure asymmetry at small ?
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Input parameters

• Used s?p from parameterization by N. Bianchi at
  al., Phys.Rev.C54 (1996)1688 (resonance region)
  and BlockHalzen, Phys.Rev. D70 (2004) 091901

37
Predictions for normal beam asymmetry

• Use fit to experimental data on s?p and exact
  3-dimensional integration over phase space of
  intermediate 2 photons

Data from HAPPEX More to come from G0
2?-exchange is in diffractive regime
HAPPEX
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No suppression for beam asymmetry with energyat
fixed Q2
x10-9
x10-6
SLAC E158 kinematics
Parts-per-million vs. parts-per billion scales a
consequence of soft Pomeron exchange, and hard
collinear photon exchange
39
Beam SSA in the resonance region
40
Normal Beam Asymmetry on Nuclei

• Important systematic correction for
  parity-violation experiments (HAPPEX on 4He, PREX
  on Pb)
• For diffractive 2?-exchange, scales as A/Z2

Five orders of magnitude enhancement for (HAPPEX)
due to excitation of inelastic intermediate
states in 2?-exchange (AA, Merenkov, to be
published)
41
Trouble with Handbag for beam normal asymmetry

• Model schematics
• Hard eq-interaction
• GPDs describe quark emission/absorption
• Soft/hard photon separation
• Use Grammer-Yennie prescription
• Hard interaction with a quark
• Applied for BSSA by Gorshtein, Guichon,
  Vanderhaeghen, NP A741, 234 (2004)

• Exchange of hard collinear photons is
  kinematically forbidden if one assumes
• a handbag approximation (placing quarks on mass
  shell) , BUT
• Collinear-photon-exchange enhancement (up to two
  orders of magnitude) is
• allowed for off-mass-shell quarks (higher twists)
  and Regge-like contributions
• gt If the handbag approximation is violated at
  0.5 level,
• It would result in (0.5)log2(Q2/me2) 100 level
  correction to beam asymmetry
• But target asymmetry, TPE corrections to
  Rosenbluth and polarization transfer
• predictions will be violated at the same 0.5
  level

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Summary on SSA in Elastic ep-Scattering

• Collinear photon exchange present in (light
  particle) beam SSA
• (Electromagnetic) gauge invariance of is
  essential for cancellation of collinear-photon
  exchange contribution for a (heavy) target SSA
• Unitarity is crucial in reducing model dependence
  of calculations at small scattering angles, in
  particular for beam asymmetry
• Strong-interaction dynamics for BNSA small-angle
  ep-scattering above the resonance region is soft
  diffraction
• For the diffractive mechanism An is a) not
  supressed with beam energy and b) does not grow
  with Z
• If confirmed experimentally ? first observation
  of diffractive component in elastic
  electron-hadron scattering

43
Two-photon exchange for electron-proton scattering

• Quark-level short-range contributions are
  substantial (3-4) correspond to J0 fixed pole
  (Brodsky-Close-Gunion, PRD 5, 1384 (1972)).
• Structure-dependent radiative corrections
  calculated using GPDs bring into agreement the
  results of polarization transfer and Rosenbluth
  techniques for Gep measurements
• Full treatment of brem corrections removed 25
  of R/P discrepancy in addition to 2?
• Collinear photon exchange inelastic excitations
  dominance for beam asymmetry
• Experimental tests of multi-photon exchange
• Comparison between electron and positron elastic
  scattering (JLab E04-116)
• Measurement of nonlinearity of Rosenbluth plot
  (JLab E05-017)
• Search for deviation of angular dependence of
  polarization and/or asymmetries from Born
  behavior at fixed Q2 (JLab E04-019)
• Elastic single-spin asymmetry or induced
  polarization (JLab E05-015)
• 2? additions for parity-violating measurements
  (HAPPEX, G0)
• Through active theoretical support emerged a
  research program of
• Testing precision of the electromagnetic probe
• Double-virtual VCS studies with two space-like
  photons