Andrei Afanasev, Trento, 6/13/07 Higher-Order Electromagnetic Corrections in SIDIS Andrei Afanasev...

Andrei Afanasev, Trento, 6/13/07

Higher-Order Electromagnetic Corrections

in SIDIS

Andrei Afanasev

Hampton University/Jefferson Lab

Talk Presented at ECT Workshop Transverse momentum, spin, and position distributions of partons in hadrons


Plan of Talk

. QED radiative corrections overview

. Bremsstrahlung corrections for SIDIS

. Cross section

. Moments <cos(nφ)>

. SSA from two-photon exchange in inclusive DIS

. Role of transversity

. Interplay of non-partonic and partonic mechanisms for two-photon exchange; Cancellation of divergences

. Outlook


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)

)}(2

1

36

17)1)(ln

12

13{(ln

2,)1( 2

2

exp f

m

Q

E

E

eBorn

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

e )1(


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.


Electron Structure Functions. For polarized ep scattering, AA et al, JETP 98, 403 (2004)

. Resummation technique

xB= 0.5; V= 10 GeV2


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 (EXCLURAD code)

. Can be used for any exclusive electroproduction of 2 hadrons, e.g., d(e,e’p)n

See http://www.jlab.org/RC for other codesUsed in data analysis at JLab (and MIT, HERMES, MAMI,…)


HAPRAD

. Fortran code for rad.corrections in SIDIS

. O(α) correction

. Uses Bardin-Shumeiko covariant technique for IR cancellation

. Available from www.jlab.org/RC

. See description in I. Akushevich et al, Eur.Phys.J.C10:681-687, 1999.


HAPRAD results[Akushevich et al.’99]

δ=σobs/σBorn


Azimuthal angular dependence of rad.correction

. Rad.correction is a function of kinematic invariants k1·ph, k2·ph, …,

. Which are functions of cos(φ) leading to nonzero cos(φ), cos(2φ), cos(3φ),… moments

. Sin(nφ) dependence does not appear (for unpolarized particles) due to parity


<cos(2φ)> moment from photon radiation

. Assume <cos(2φ)>=0 for Born cross section

xB=0.2 xB=0.3

z=0.60 0.18E-2

z=0.7 0.12E-2 0.35E-2

z=0.8 0.08E-2 0.22E-2

<cos(2φ)> for E=5.7 GeV, pT=0.4 GeV,Q2=2 GeV2


Rad.correction to Cahn effectJLAB kinematics

<cos(φ)>obs/ <cos(φ)>Born for E=5.7 GeV, pT=0.4 GeV,Q2=2 GeV2

xB=0.2 xB=0.3

z=0.6 0.91

z=0.7 0.92 0.96

z=0.8 0.94 0.98


Summary on brem correction

. Rad.correction for Cahn effect evaluated at 10% level

. Correction depends on a model used for pT-dependence

. Generate <cos(2φ)>=0.001-0.002

. Conclude: Iteration procedure required for data analysis

. Further improvements:

. Radiative tail from exclusive process N(e,e’π)N

. Contribution of nucleon resonance region


Single-Spin Asymmetries in DIS

from 2-photon exchangeAA, M. Strikman, and C.Weiss


Motivation

. Motivated by experimental+theoretical two-photon exchange studies at JLab

. Implications for SIDIS: Measured SSA in (e,e’h) are of the order of a few per cent

. What if higher-order electromagnetic correction is also a few per cent?

=> Then EM-generated SSA would become a major problem

. Recent calculation of normal target asymmetry from two-photon exchange in a parton model obtained a divergent result, see

. A. Metz, M. Schlegel, K. Goeke Phys.Lett.B643:319-324,2006; e-Print Archive: hep-ph/0610112


Transverse target spin dependence in eN→e’X


Spin dependence with two-photon exchange


Example: Point-like spin-1/2 targetBarut, Fronsdal, 1960;…


Composite nucleon approximation

Within reach of experiment polarized He3 X.Jiang et al JLAB PR-07-013


Divergence cancellation

. Divergence: terms of the type ln(Q2/λ2), where λ is a cut-off parameter (`photon mass’); final results should be independent of λ

. Two kinds of divergence appear at intermediate steps:

. Infra-red: exchanged photon momentum 0. Such divergent terms result in a spin-independent common factor appearing in front of one-photon exchange amplitude; the factors cancel in the result for asymmetry (difference σn+ -σn- )

. Collinear: intermediate photon is collinear to the parent electron, while carrying substantial energy: Divergence cancels at the amplitude level; electromagnetic current conservation for the Compton tensor is essential (see AA,Merenkov’04 proof for elastic ep-scattering)


Normal Asymmetry: Elastic ep→ep(AA, Merenkov)

0

ˆ

)ˆ1)(ˆ()ˆ(4

1

)ˆ()ˆ1)(ˆ()ˆ(4

1

2Im

),(

1212

512

512

22

210

3

22

2,

qHqHqHqLqLqL

aa

TMpMpTrH

mkmkmkTrL

QQ

HL

k

kd

QsD

QA

p

eeee

Pen

EM gauge invariance important for cancellation of collinear singularity for unpolarized beam

00// 22

2121 HLthenqorandqifqorandqL

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.

Also calculations by Vanderhaeghen, Pasquini (2004); Gorchtein (2005);Borisyuk&Kobushkin (2005) confirm quasi-real photon exchange enhancement of inelastic intermediate excitations

2

2

2

222

22

1 log,log~0/e

e

e

eem

Qm

m

QmAQorandQifconstmHL


Model example

. Collinear divergence ~ln(Q2/λ2) from diagram (a) precisely cancels the divergence of the diagram (b)

. Divergence disappeared before integration over p2 => no enhancement of the effect in SIDIS and inclusive

. To obtain sensible results for the single-spin asymmetry from two-photon exchange, need to work with models that exactly satisfy electromagnetic current conservation for the (inelastic) virtual Compton amplitude


Summary

. Bremsstahlung rad.correction to SIDIS cross section is tens of per cent

. Azimuthal dependence of rad.corrections not negligible, leading to ≈10% (relative) correction to Cahn asymmetry, and (absolute) <cos(2φ)>≈0.001÷0.002

. Model dependence →Iteration procedure necessary for data analysis

. Target SSA from two-photon exchange in DIS estimated in a model at 10-4

. Neglecting electromagnetic current conservation results in (unphysical) collinear divergence in SSA induced by two-photon exchange; divergence absent for gauge-invariant Compton tensor

. Expect log-enhanced ~log(Q2/me2) higher-twist effects for beam SSA

(measurable in parity-violating DIS setup at JLab)


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Andrei Afanasev, Trento, 6/13/07 Higher-Order Electromagnetic Corrections in SIDIS Andrei Afanasev...

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