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Hadron Form Factors : theory

Hadron Form Factors : theory. Marc Vanderhaeghen College of William & Mary / JLab. EINN 2005, Milos (Greece), September 20-24, 2005. Outline. Nucleon electromagnetic form factors : theoretical approaches  N Δ form factors two-photon exchange effects

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Hadron Form Factors : theory

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  1. Hadron Form Factors : theory MarcVanderhaeghen College of William & Mary / JLab EINN 2005, Milos (Greece), September 20-24, 2005

  2. Outline • Nucleonelectromagnetic form factors : theoretical approaches • NΔform factors • two-photon exchange effects nucleon FF : Rosenbluth vs polarization data extension to N -> Δ FF • For weak form factors/parity violation : see talks -> D. L’Huillier, K. Paschke Recent review on “electromagnetic form factors of the nucleon and Compton scattering” Ch. Hyde-Wright and K. de Jager : Ann. Rev. Nucl. Part. Sci. 2004, 54

  3. Nucleonelectromagnetic form factors : theoretical approaches i) Dispersion theory ii)Mapping outpion cloud, chiral perturbation theory iii) lattice QCD : recent results & chiral extrapolation iv) link to Generalized Parton Distributions : nucleon “tomography” v) other disclaimer: v) will not be discussed in this talk

  4. nucleon FF : dispersion theory * q2 > 0 : timelike Hoehler et al. (1976) q Mergell, Meißner, Drechsel (1995) q2 = - Q2 < 0 : spacelike Hammer, Meißner, Drechsel (1996) V N N Hammer, Meißner (2004) general principles : analyticity in q2 , unitarity FF -> dispersion relation in q2 branch cuts for q2 > 4 mπ2 : vector meson poles + continua (ππ,… ) basic dipole behavior : explained by 2 nearby poles with residua of equal size but opposite sign analysis of Hammer & Meißner (2004) isovector channel : 2π continuum + 4 poles : ρ, ρ’(1050), ρ’’(1465), ρ’’’(1700) isoscalar channel : 4 poles : ω, φ(1019), S’(1650) S’’(1680) masses & 16 residua (V, T) fitted + PQCD scaling behavior parametrized

  5. nucleon FF : dispersion theory Hammer, Meißner (2004) Hammer, Meißner, Drechsel (1996) phenomenological fit by Friedrich, Walcher (2003) DR : good description, except for GEp / GMp

  6. nucleon form factors : pion cloud Friedrich, Walcher (2003) phenomenological fit : “smooth” part (sum of 2 dipoles) + “bump” (gaussian) 6 parameter fit for each FF pion cloud extending out to  2 fm pronounced structure in all FF around Q  0.5 GeV/c

  7. nucleon FF : Chiral Perturbation Theory Kubis, Meißner (2001) Goldstone boson -Baryon loops (relativistic ChPT, 4th order, IR reg.) + vector mesons SU(3) SU(2) : πN DR see also Schindler et al. (2005) (EOM renorm. scheme)

  8. nucleon FF : lattice QCD QCDSF Coll. : Goeckeler et al. (2003) Lattice results fitted by dipoles -> for isovector channel : masses MeV , MmV lattice lattice Expt. Expt. quenched approximation : qq loops neglected Expt. linear extrapolation in mπ reasonable good description of GEp / GMp at larger Q2 (where role of pion cloud is diminished) lattice

  9. nucleon FF : lattice & chiral extrapolation Leinweber, Lu, Thomas (1999) lattice : QCDSF Hemmert and Weise (2002) + … (r1V )2 lattice : QCDSF κV 4 LEC fit 3 LEC fit lattice : QCDSF (r2V )2 Hemmert : chiral extrapolation using SSE at O(ε3) -> fit LEC to available lattice points qualitative description obtained, not clear for (r1V )2

  10. nucleon FF : lattice & chiral extrapolation Pascalutsa, Holstein, Vdh (2004) For κ : resummation of higher order terms by using a new sum rule(SR) (linearized version of GDH) -> analyticity is built in Relativistic chiral loops (SR) give smoother behavior than the heavy-baryon expansion (HB) or Infrared-Regularized ChPT (IR) lattice : Adelaide group (Zanotti) red curve is the 2-parameter fit to lattice data based on sum rule (SR) result chiral loops

  11. nucleon FF : lattice prospects LHP Collaboration (R. Edwards) F1V state of art : employ full QCD lattices (e.g. MILC Coll.) using “staggered” fermions for sea quarks employ domain wall fermions for valence quarks Pion masses down to less than 300 MeV As the pion mass approaches the physical value, the calculated nucleon size approaches the correct value √(r2)1V next step : fully consistent treatment of chiral symmetry for both valence & sea quarks

  12. FF : link to Generalized Parton Distributions * Q2 large t = Δ2 low –t process : -t << Q2 Ji , Radyushkin (1996) x + ξ x - ξ P - Δ/2 P + Δ/2 GPD (x, ξ ,t) (x + ξ) and (x - ξ): longitudinal momentum fractions of quarks at large Q2 : QCD factorizationtheorem hard exclusive process can be described by 4 transitions(GPDs) : ~ Vector :H (x, ξ ,t) Tensor :E (x, ξ ,t) Axial-Vector :H (x, ξ ,t) Pseudoscalar :E (x, ξ ,t) ~ see talks -> Diehl, Camacho, Hadjidakis

  13. Δ P - Δ/2 P + Δ/2 known information on GPDs forward limit : ordinaryparton distributions unpolarized quark distr polarized quark distr : do NOT appear in DIS new information first moments : nucleonelectroweak form factors Dirac Pauli axial ξ independence : Lorentz invariance pseudo-scalar

  14. GPDs : 3D quark/gluon imaging of nucleon Fourier transform of GPDs : simultaneous distributions of quarks w.r.t. longitudinal momentum x P and transverse positionb theoretical parametrization needed

  15. GPDs : t dependence modified Regge parametrization : Guidal, Polyakov, Radyushkin, Vdh (2004) Input : forward parton distributions atm2 = 1 GeV2 (MRST2002 NNLO) Drell-Yan-West relation : exp(- α΄ t ) -> exp(- α΄ (1 – x) t) : Burkardt (2001) parameters : regge slopes : α’1 = α’2 determined from rms radii determined from F2 / F1 at large -t future constraints : moments from lattice QCD

  16. electromagnetic form factors PROTON NEUTRON modified Regge parametrization Regge parametrization

  17. GPDs : transverse image of the nucleon (tomography) Hu(x, b? ) x b?(GeV-1)

  18. proton Dirac & Pauli form factors modified Regge model Regge model PQCD Belitsky, Ji, Yuan (2003)

  19. timelike proton FF :GM = F1 + F2 PQCD Fermilab p p -> e+ e- q2 timelike (q2 > 0) spacelike (q2 < 0) analytic function in q2 (Phragmen-Lindelöf theorem) around |q2|= 10 GeV2 timelike FF twice as large as spacelike FF HESR@GSI can measure timelike FF up to q2 ≈ 25 GeV2

  20. JLab 12 GeV JLab (2005) 4 M2 timelike proton FF :F2 / F1 VMD Iachello et al. (1973, 2004) q2 PQCD Belitsky, Ji, Yuan (2003) VMD PQCD REAL part REAL part IMAG part IMAG part

  21. e+ p p e- measurement of timelike F2 / F1 Brodsky et al. (2003) Polarization Pynormal to elastic scattering plane (polarized beam OR target) VMD PQCD

  22. N -> Δtransition form factors in large Nc limit modified Regge model Regge model

  23. Sphere: Prolate: Q20=0 Q20/R2 > 0 Oblate: Q20/R2 < 0 electromagnetic N -> Δ(1232) transition in chiral effective field theory J P=3/2+ (P33), M' 1232 MeV,  ' 115 MeV N ! transition:  N !  (99%),  N !  (<1%) non-zero values for E2 and C2 : measure of non-spherical distribution of charges spin 3/2 Role of quark core (quark spin flip) versus pion cloud

  24. Effective field theory calculation of the e p -> e p π0process in Δ(1232) region Pascalutsa, Vdh ( hep-ph/0508060 ) Power counting : in Δ region, treat parameters δ = (MΔ– MN)/MN and mπon different footing ( mπ~ δ2 ) in threshold region : momentum p ~ mπ/ in Δ region : p ~ MΔ - MN calculation to NLO inδ expansion (powers of δ) LO vertex corrections : unitarity & gauge invariance exactly preserved to NLO

  25. e p -> e p π0in Δ(1232) region : observables W = 1.232 GeV , Q2 = 0.127 GeV2 EFT calculation error bands due to NNLO, estimated as : Δσ ~ |σ| δ2 data : MIT-BATES (2001, 2003, 2005)

  26. Q2 dependence of E2/M1 and C2/M1 ratios data points : REM= E2/M1 MIT-Bates (2005) see talk -> Sparveris MAMI : REM(Beck et al., 2000) RSM (Pospischil et al., 2001; Elsner et al., 2005) RSM= C2/M1 EFT calculation error bands due to NNLO, estimated as : ΔR ~ |R| δ2 + |Rav| Q2/MN2 EFT calculation predicts the Q2 dependence

  27. mπ dependence of E2/M1 and C2/M1 ratios Q2 = 0.1 GeV2 quenched lattice QCD results : at mπ= 0.37, 0.45, 0.51 GeV Alexandrou et al., (2005) linear extrapolation in mq ~ mπ2 see talk -> Tsapalis EFT calculation discrepancy with lattice explained by chiral loops(pion cloud)! Pascalutsa, Vdh (2005) see also talk ->Gail data points : MAMI, MIT-Bates

  28. Two-photon exchange effects Rosenbluth vs polarization transfer measurements of GE/GM of proton SLAC, Jlab Rosenbluth data Jlab/Hall A Polarization data Jones et al. (2000) Gayou et al. (2002) Twomethods, twodifferentresults !

  29. Observables including two-photon exchange Real parts of two-photon amplitudes

  30. Phenomenological analysis Guichon, Vdh (2003) 2-photon exchange corrections can become large on the Rosenbluth extraction,and are of different size for both observables relevance when extracting form factors at large Q2

  31. Two-photon exchange calculation : elastic contribution world Rosenbluth data N Polarization Transfer Blunden, Tjon, Melnitchouk (2003, 2005)

  32. Two-photon exchange : partonic calculation hard scattering amplitude GPD integrals “magnetic” GPD “electric” GPD “axial” GPD

  33. Two-photon exchange : partonic calculation GPDs Chen, Afanasev, Brodsky, Carlson, Vdh (2004)

  34. Two-photon exchange in N -> Δtransition Pascalutsa, Carlson, Vdh ( hep-ph/0509055 ) General formalism for eN -> e Δ has been worked out Model calculation for large Q2 in terms of N -> Δ GPDs N Δ 1 result 1 + 2 result REM little affected < 1 % RSM mainly affected when extracted through Rosenbluth method

  35. Summary • Nucleonelectromagnetic form factors : -> dispersion theory, chiral EFT : map out pion cloud of nucleon -> lattice QCD : state-of-art calculations go down to mπ~ 300 MeV, into the regime where chiral effects are important / ChPT regime -> link with GPD : provide a tomographic view of nucleon • NΔform factors : -> chiral EFT ( δ-expansion) is used in dual role : describe both observables and use in lattice extrapolations, -> resolve a standing discrepancy : strong non-analytic behavior in quark mass due to opening of πN decay channel • difference Rosenbluth vs polarization data -> GEp /GMp : understood as due to two-photon exchange effects -> precision test : new expt. planned -> NΔ transition : effect on RSM when using Rosenbluth method

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