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Nucleon Electromagnetic and Weak Form Factors Theory Overview

Nucleon Electromagnetic and Weak Form Factors Theory Overview. Andrei Afanasev Jefferson Lab JLab Users Workshop Jefferson Lab June 20, 2005. Elastic lepton scattering and nucleon structure. How does the nucleon respond to the electromagnetic or weak probe?.

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Nucleon Electromagnetic and Weak Form Factors Theory Overview

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  1. Nucleon Electromagnetic and Weak Form FactorsTheory Overview Andrei Afanasev Jefferson Lab JLab Users Workshop Jefferson Lab June 20, 2005

  2. Elastic lepton scattering and nucleon structure How does the nucleon respond to the electromagnetic or weak probe? • Study Form Factors at high Q2: • QCD, GPDs; Helicity Flip; OAM; Ji’s sum rule; Lattice QCD • Status of nucleon form factor measurements : • See review C.Hyde-Wright, K. de Jager, Annu.Rev.Nucl.Part.Sci. 54, 217 (2004)

  3. GPDs, DIS, and Elastic Form Factors Link to form factors (sum rules) ] [ 1 å ò x = q dx H ( x , , t ) F1 ( t ) Dirac FF ~ ~ q x q q q q H , E , H , E ( x , , t ) ] [ 1 å ò x = q dx E ( x , , t ) F2 ( t ) Pauli FF q 1 1 ~ ~ ò ò x = x = q q dx H ( x , , t ) G ( t ) , dx E ( x , , t ) G ( t ) , , A q P q - - 1 1 Access to quark angular momentum (X. Ji’s sum rule) [ ] 1 1 1 ò = - JG = x + x q q q J xdx H ( x , , 0 ) E ( x , , 0 ) 2 2 - 1 x Link to DIS at =t=0 = - - q H ( x , 0 , 0 ) q ( x ), q ( x ) ~ = D D - q ( x , 0 , 0 ) q ( x ), q ( x ) H

  4. Global Analysis P. Bosted et al. PRC 51, 409 (1995) Three form factors very similar GEn zero within errors -> accurate data on GEn early goal of JLab Madey et al.; Day et al. (polarization methods)

  5. Neutron Form Factors For Q2 > 1 GeV2 data indicate that GEn has similar Q2-behaviour as GEp GMn follows dipole dependence

  6. Elastic Nucleon Form Factors • Based on one-photon exchange approximation • Two techniques to measure Latter due to: Akhiezer, Rekalo; Arnold, Carlson, Gross

  7. 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 ~5% difference in cross-section JLab/Polarization

  8. Q2 dependence of Dirac vs. Pauli form factors • JLab polarization transfer data favored Earlier SLAC+recent JLab spin-unpolarized data Belitsky, Ji and Yuan suggested thet pQCD picture Holds, but with double-log corrections:

  9. Log-corrected scaling • Consistency with polarization data

  10. From fitting Form Factors to fitting GPDs • Radyushkin’98, Afanasev’98,99, Stoler’02 • New generation of fits: Diehl et al., Eur.Phys.J.C39:1-39,2005, Guidal et al., hep-ph/041025.

  11. Matching CBM and Lattice QCD • Matevosyan, Miller, Thomas’05

  12. Electron Scattering: LO and NLO in 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 • 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, Melnitchuk,Tjon, Phys.Rev.Lett.91:142304,2003 • Chen, AA, Brodsky, Carlson, Vanderhaeghen, Phys.Rev.Lett.93:122301,2004

  13. Separating soft photon exchange • Tsai; Maximon & Tjon • We used Grammer &Yennie prescription PRD 8, 4332 (1973) (also applied in QCD calculations) • Shown is the resulting (soft) QED correction to cross section • NB: Corresponding effect to polarization transfer is zero ε δSoft Q2= 6 GeV2

  14. 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

  15. Updated Ge/Gm plot AA, Brodsky, Carlson, Chen, Vanderhaeghen, Phys.Rev.Lett.93:122301,2004; hep-ph/0502013

  16. Two-Photon Effect for Rosenbluth Cross Sections • Blunden, Melnitchouk, Tjon, Phys.Rev.Lett.91:142304,2003; nucl-th/0506039

  17. Polarization transfer from GPDs • Also corrected by two-photon exchange, but with little impact on Gep/Gmp extracted ratio

  18. 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.

  19. Backward-angle double-logarithm resummationof multi-photon exchange • Electron-muon scattering at backward angles; calculations by Gorshkov, Gribov, Lipatov, Frolov, Sov.J.Nucl.Phys.6, 95 (1968): • Double-logarithmic contributions coming from • Hard-photon exchange with highly-virtual spinor states • Resummation via recurrence relations (Bethe-Salpeter ladder resummation gives an equivalent result) For opposite-charge particles, Rad. Correction omitted in Mo-Tsai approach is negative and log-enhanced at backward scattering angles (small ε); zero at forward angles => Positive correction to Rosenbluth slope

  20. (Previously Neglected) Effect from Hard Brem • Additional work in progress: • Role of spin-dependent terms in conventional (hard) bremsstrahlung (1-2% effect) Radiative leptonic tensor in full form AA et al, PLB 514, 269 (2001) Size of hard brem correction

  21. 2γ-exchange Correction to Parity-ViolatingElectron Scattering • New parity violating terms due to (2gamma)x(Z0) interference should be added: x Z0 γ γ Electromagnetic Neutral Weak

  22. 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 & C. Carlson, PRL 94, 212301 (2005): measurements of strange-quark content of the nucleon are affected, Δs may shift by ~10%

  23. Two-photon exchange for electron-proton scattering • 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 Generalized Parton Distributions bring into agreement the results of polarization transfer and Rosenbluth techniques for Gep measurements • Collinear photon exchange dominance for beam asymmetry • Experimental tests of multi-photon exchange • Comparison between electron and positron elastic scattering • Measurement of nonlinearity of Rosenbluth plot • Search for deviation of angular dependence of polarization and/or asymmetries from Born behavior at fixed Q2 • Elastic single-spin asymmetry or induced polarization • All above tests are now approved JLab experiments => Through active theoretical support emerged=> JLab program of double-virtual VCS studies with two spacelike photons

  24. Weak processes • Measurements of fundamental constants of EW interactions • Learning the structure of nucleon • Weak decays • Neutrino scattering • Weak capture

  25. Neutrino Scattering • Experiments with accelerator neutrinos: • Long history: Fanorakis et al PRD 21, 62 (1980); Ahrens et al., PRD 35, 78 (1987); PLB 202, 284 (1988); Barish et al., PRD 16, 3103 (1977), Miller et al., PRD D26, 537 (1982); Mann et al., PRL 31, 844 (1973); Baker et al., PRD 23, 2499; Kitagaki et al. PRD 28, 436 (1983); D42, 1331 (1990). • Anticipated experiments with neutrino beams at Fermilab (see hep-ex/0405002 by Minerva Collab.) • Need to study JLAB opportunities on weak electron capture

  26. Probe neutral weak current of a nucleon • Measurements of νp→νp are free of rad. corrections uncertainties for GA(Q2) relevant to ep→ep (Musolf & Holstein) • Available measurements from BNL Ahrens et al’87

  27. Electroproduction of pions • Electroproduction of pions near threshold can be used to obtain GA through measurement of Kroll-Ruderman in E0+ amplitudes • See review by Bernard, Elouadrhiri, Meissner, J. Phys. G: Nucl.Part.Phys. 28 (2002) R1

  28. Weak transition form factors • Nucleon beta-decay: CKM matrix Vud • Kl3 decays (timelike regime) are a source of information of a) Vsu CKM matrix element b) low-energy QCD • Space-like regime is inaccessible in decays, but can be probed in either neutrino scattering (e.g., at Fermilab) or weak capture at JLab AA, Buck, PRD’97

  29. Summary • Substantial progress in the theory of form factors for the recent years, stimulated by JLab data on electromagnetic form factors • GPD and Lattice QCD in particular • Both electromagnetic and weak form factors need to be included • JLab potential on weak form factor measurements beyond PV-scattering needs to be explored

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