# Presentation: 882420

## Radiative Corrections for Lepton Scattering 

***Andrei Afanasev***
***Hampton University and Jefferson Lab***
***Presentation for PPD/Neutrino Department, Feb.22, 2008***

- Collaborators: I. Akushevich, N. Merenkov, A. Ilyichev, *K. Joo, V. Burkert,*
- S. Brodsky, C. Carlson, M. Vanderhaeghen, *G. Gilfoyle*

## Main problem Accelerated charge radiates

- ...While radiative corrections were the largest corrections to the data, and involved a considerable amount of computation, they were understood to a confidence level of 5% to 10% and did not significantly increase the total error in the measurements.
**Henry W. Kendall**
***Nobel Lecture, December 8, 1990***
**Uncertainties in QED radiative corrections limit interpretability of precision experiments on electron-hadron scattering**

## Plan of talk

**Radiative corrections for electron scattering**
- Model-independent and model-dependent; soft and hard photons
- Refined bremsstrahlung calculations** ****	**
- Two-photon exchange effects in the process *e+p**→e+p*
**Rad. corrections for electroweak processes**

## Example:Measurements of Elastic Nucleon Form Factors

- Based on one-photon exchange approximation

- Two techniques to measure

- Latter due to: Akhiezer, Rekalo; Arnold, Carlson**,** Gross

## Do the techniques agree?

**Both early SLAC and Recent JLab experiments on (super)Rosenbluth separations followed Ge/Gm~const**
**JLab measurements using polarization transfer technique give different results (Jones’00, Gayou’02)**
***Radiative corrections, in particular, a short-range part of 2-photon ***
***exchange is a likely origin of the discrepancy   ***

- SLAC/Rosenbluth

- JLab/Polarization

- ~5% difference in cross-section
- x5 difference in polarization

## Basics of QED radiative corrections

- (First) Born approximation

- Initial-state radiation

- Final-state radiation

- Cross section ~ dω/ω => integral diverges logarithmically: **IR catastrophe**

- Vertex correction => cancels divergent terms; Schwinger (1949)

- Multiple soft-photon emission: solved by exponentiation,
- Yennie-Frautschi-Suura (YFS), 1961

## Complete radiative correction in O(αem )

- _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
- Meister&Yennie; Mo&Tsai
- Further work by Bardin&Shumeiko; Maximon&Tjon; AA, Akushevich, Merenkov;
- Guichon&Vanderhaeghen’03:
*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.**91**:142304,2003
- Chen, AA, Brodsky, Carlson, Vanderhaeghen, Phys.Rev.Lett.**93**:122301,2004

- Log-enhanced but calculable (a,c,d)

## Basic Approaches to QED Corrections

- L.W. Mo, Y.S. Tsai, Rev. Mod. Phys. 41, 205 (1969); Y.S. Tsai, Preprint SLAC-PUB-848 (1971).
- Considered both elastic and inelastic inclusive cases. No polarization.
- D.Yu. Bardin, N.M. Shumeiko, Nucl. Phys. B127, 242 (1977).
- Covariant approach to the IR problem. Later extended to inclusive, semi-exclusive and exclusive reactions with polarization.
- E.A. Kuraev, V.S. Fadin, Yad.Fiz. 41, 7333 (1985); E.A. Kuraev, N.P.Merenkov, V.S. Fadin, Yad. Fiz. 47, 1593 (1988).
- Developed a method of electron structure functions based on Drell-Yan representation; currently widely used at e+e- colliders.

## RC for Electroproduction of Pions

**AA, Akushevich, Burkert, Joo, Phys.Rev.D66, 074004 (2002)**
- Conventional RC, precise treatment of phase space, no peaking approximation, no dependence on hard/soft photon separation
- Can be used for any exclusive electroproduction of 2 hadrons, e.g., d(e,e’p)n (EXCLURAD code)

- See _[http://www.jlab.org/RC](http://www.jlab.org/RC)_ for other codes
- Used in data analysis at JLab
- (and MIT, HERMES, MAMI,...)

## Bethe-Heitler corrections to polarization transfer and cross sections

***AA, Akushevich, Merenkov Phys.Rev.D64:113009,2001;***
***AA, Akushevich, Ilychev, Merenkov, PL B514, 269 (2001)***

- Pion threshold: um=mπ2

- In kinematics of elastic ep-scattering measurements, cross sections are more sensitive to RC

## Electron Structure Functions (Kuraev,Fadin,Merenkov)

- For polarized ep->e’X scattering, AA et al, JETP 98, 403 (2004); elastic ep: AA et al. PRD 64, 113009 (2001).
- Resummation technique for collinear photons (=peaking approx.)
- Difference <0.5% from previous calculation including hard brem

## 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

- ε

- δSoft

- Q2= 6 GeV2

## Calculations using Generalized Parton Distributions

- Hard interaction with a quark

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

- AA, Brodsky, Carlson, Chen, Vanderhaeghen,
- Phys.Rev.Lett.**93**:122301,2004; Phys.Rev.D**72**:013008,2005

## 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

## Updated Ge/Gm plot

- AA, Brodsky, Carlson, Chen, Vanderhaeghen,
- Phys.Rev.Lett.93:122301, 2004; Phys.Rev.D72:013008, 2005

## Full Calculation of Bethe-Heitler Contribution

- Radiative leptonic tensor in full form
- AA et al, ***PLB 514, 269 (2001)***

- Additional effect of full soft+hard brem → +1.2% correction to ε-slope
**Resolves additional ~25% of Rosenbluth/polarization discrepancy!**

*Additional work by AA et al., using MASCARAD (****Phys.Rev.D64:113009,2001)***
*Full calculation including soft and hard bremsstrahlung*

## 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 AA, W. Brooks, L.Weinstein, et al.

## Phase Space Contributing to the absorptivepart of 2γ-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
- Θcm= 57 deg;
- SAMPLE, E=200 MeV

- `Soft’ intermediate electron;
- Both photons are hard collinear

- One photon is
- Hard collinear

## Other theoretical developments

- Blunden et al., Phys.Rev.C72:034612, 2005
- 	Approximate proton Compton amplitude by Born terms
- Kondratyuk et al., nucl-th/0506026
-      Add intermediate Δ-excitation to the above
- Pascalutsa et al., hep-ph/0509055
-      GPD approach extended to N→Δ transition
- Borisyuk, Kobushkin, Phys.Rev.C72:035207,2005
- Future task: Resummation of inelastic excitations at lower Q2

## Quark-level short-range contributions are substantial (3-4%) ; correspond to J=0 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
Experimental tests of two-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)
2γ 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

- Structure-dependent radiative corrections calculated using GPDs bring into agreement the results of polarization transfer and Rosenbluth techniques for Gep measurements
- Experimental tests of two-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)
- 2γ 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***

- Two-photon exchange for electron-proton scattering

## Radiative Corrections for Electro-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.B595:250-259,2004; Hardy, Towner, PRL94:092502,2005
- Extended to νN by Fukugita, Acta Phys.Polon.B35:1687-1732,2004; and νD: Phys.Rev.D72:071301,2005, Erratum-ibid.D74:039906,2006;
- Kurylov,  Phys.Rev. C65 (2002) 055501=> ~4% effect for σtotal
- Parity-violating DIS: Bardin, Fedorenko, Shumeiko, Sov.J.Nucl.Phys.32:403,1980; J.Phys.G7:1331,1981, up to 10% effect from rad.corrections
- Parity-violating elastic ep (strange quark effects, weak mixing angle)

## Implications for Nutev

- Diener, Dittmaier, Hollik, Phys.Rev.D69:073005,2004:
**Rad.Corrections used by NuTeV likely underestimated**,
- “...*we compare results that differ in the input-parameter scheme, treatment of real photon radiation, and factorization scheme. The associated shifts in the theoretical prediction for the ratio of neutral- and charged-current cross sections can be larger than the experimental accuracy of the NuTeV result.* ...”

## Neutrino DIS

- Arbuzov, Bardin, Kalinovskaya, JHEP06(2005)078

- Eν=80GeV

- δuNC(%)

- δdCC(%)

## Parity Violating elastic e-N scattering

- Longitudinally polarized electrons, unpolarized target

- Neutral weak form factors contain explicit contributions from strange sea

- GZA(0) = 1.2673 ± 0.0035 (from  decay)

-  = Q2/4M2
-  = [1+2(1+)tan2(/2)]-1
- ’= [(+1)(1-2)]1/2

## Born and Box diagrams for elastic ep-scattering 

- (d) Computed by Marciano,Sirlin, Phys.Rev.D29:75,1984, Erratum-ibid.D31:213,1985 for atomic PV (i.e., Q2 →0)
-  (c) Presumed small, e.g., M. Ramsey-Musolf, Phys.Rev. C60 (1999) 015501

## GPD Calculation of 2γ×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, ***Phys. Rev. Lett. 94, 212301 (2005):***
- Measurements of strange-quark content of the nucleon are affected, Δs may shift by ~10%

- Important note: (nonsoft) 2γ-exchange amplitude has no 1/Q2 singularity;
- 1γ-exchange is 1/Q2 singular => At low Q2, 2γ-corrections is suppressed as Q2 P. Blunden used this formalism and evaluated correction of 0.16% for Qweak

## 
2γ-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 γZ-box contribution and extension of model calculations to lower Q2 is necessary 
Further developments:
Zhu, Kao, Yang, Phys.Rev.Lett.99:262001,2007: Found essential Q2-dependence of EW box contributions
Tjon, Melnitchouk, arXiv:0711.0143 [nucl-th]: Model calculation of EW box

- 2γ-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 γZ-box contribution and extension of model calculations to lower Q2 is necessary
- Further developments:
- Zhu, Kao, Yang, Phys.Rev.Lett.99:262001,2007: Found essential Q2-dependence of EW box contributions
- Tjon, Melnitchouk, arXiv:0711.0143 [nucl-th]: Model calculation of EW box

- 2γ-correction for ep-scattering via Z-exchange

## RC for Minerva

- For CC cross sections, anticipate 1-5% electromagnetic effects
- Bremsstrahlung calculations model-independent, but need to be matched with experimental cuts and acceptances
- Electroweak box diagrams calculations depend on the used model of hadronic structure; can be constrained by existing (and forthcoming) info on 2γ-exchange for elastic ep-scattering
*Expertise at JLab available to implement Rad.Corrections for data analysis of Minerva*