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Deep Virtual Meson Production: Insights from Data to Generalized Parton Distributions

This lecture explores the production of deep virtual mesons and the transition from experimental data to generalized parton distributions (GPDs). Emphasizing the non-linear interactions of quarks and gluons, we discuss Regge theory, the role of meson exchange in reactions, and how QCD dynamics manifests in hard processes. Our focus on kinematics is substantiated by recent data from experiments like HERMES and CLAS, illustrating the behavior of gluonts and the evolution of GPDs. The findings indicate that the hard regime can be well-represented by handbag approaches and provide insights on forward particle production dynamics.

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Deep Virtual Meson Production: Insights from Data to Generalized Parton Distributions

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  1. Varenna, 06/07/2011 Lecture 2: Deep Virtual Meson Production: From data to GPDs ? M. Guidal, IPN Orsay

  2. q=qV+qseaq=qseaso: total sea (q+q): qsea= 2 q Kresimir Kumericki, Dieter Mueller,Nucl.Phys.B841:1-58,2010.

  3. Belitsky A V, Mueller D and Kirchner A 2002 Nucl. Phys. B629 323–392

  4. HIm HRe JLab (Hall A) xB=0.36,Q2=2.3 HIm HRe HERMES xB=0.09,Q2=2.5 t (GeV2)

  5. y Hu(x,b ) z x x (GeV-1) b

  6. t-dependence at fixedxB ~ of HIm& HIm Axial charge more concentrated than electromagnetic charge ? Fit with 7 CFFs (boundaries 3xVGG CFFs) Fit with 7 CFFs (boundaries 5xVGG CFFs) ~ Fit with ONLYH and H VGG prediction

  7. In the non-perturbativeregime the interaction of quarks and gluons is highly non-linear

  8. One example: g*p->p L.O calculation with running as calculation with kperpeffects (more data existing)

  9. ,

  10. Reggetheory: Exchange of families of mesons in the t-channel

  11. Reggetheory: Exchange of families of mesons in the t-channel M(s,t) ~ sa(t) wherea(t) (trajectory) is the relation between the spin and the (squared) mass of a family of particles stot~1/s x Im(M(s,t=0))->sa(0)-1 [optical theorem] M->sa(t) ds/dt~1/s2 x |M(s,t)|2->s2a(t)-2 ->[ea(t)lns(s)] stot ds/dt t s

  12. However, when a reaction proceeds via the exchange of vacuumquantum numbers, the cross section doesn’t decrease (even slightly increases). Each time a reaction proceeds via the exchange of a charged (meson) in the t-channel, the cross-section decreases (a(0)~0.5)

  13. However, when a reaction proceeds via the exchange of vaccuum quantum numbers, the cross section doesn’t decrease (even slightly increases). Each time a reaction proceeds via the exchange of a charged (meson) in the t-channel, the cross-section decreases (a(0)~0.5) =>Introduction of a trajectory with intercept a(0) ~1 : the Pomeron [a(0) ~1.08] However, in contrast with meson trajectories, there is no physical particles which has been identified very Conclusively for such trajectory. [QCD:glueballs]

  14. The theory of Reggepoles has been very popular a few decades ago because it could describe the main characteristics of numerous processes with a limited number of parameters However, relative loss of interest after: describe with precision the data and refine the theory means to go beyond the basic hypothesis and becomes very quickly complicated. For instance, other singularities than simple poles (cuts…) =>first approximation Difficulty to connect Reggewith quantum field theory (QCD) and the fundamental degrees of freedom (quarks, gluons)=> hadronic theory.

  15. ,

  16. ,

  17. , Q2>>

  18. , Q2>> Q2>>

  19. Some signatures of the (asymptotic) « hard » processes: Q2dependence: sL~1/Q6 sT~1/Q8 sL/sT~Q2 Wdependence: s~|xG(x)|2 (for gluon handbag) r/w/f/(J/Y)~9/1/2/8 (for gluon handbag) Ratioofyields: Saturationwith hard scale of aP(0), b, … SCHC : checkswithSDMEs

  20. LO (w/o kperp effect) LO (with kperp effect) Handbag diagram calculation needs kperp effects to account for preasymptotic effects Same thing for 2-gluon exchange process

  21. H1, ZEUS , Q2>> Q2>>

  22. HERMES H1, ZEUS H1, ZEUS CLAS COMPASS , Q2>> Q2>>

  23. HERMES H1, ZEUS H1, ZEUS CLAS COMPASS , + « older » data from: E665, NMC, Cornell,… Q2>> Q2>>

  24. HERMES H1, ZEUS H1, ZEUS CLAS COMPASS , + « older » data from: E665, NMC, Cornell,… Q2>> Q2>>

  25. W dependence SteepeningWslope as a function of Q2 indicates« hard » regime (reflects gluon distribution in the proton)

  26. W dependence SteepeningWslope as a function of Q2 indicates« hard » regime (reflects gluon distribution in the proton) Twoways to set a « hard » scale: *large Q2 *mass of produced VM Universality : r, f at large Q2+M2similar to J/y

  27. aP(0) increases from “soft” (~1.1) to “hard” (~1.3) as a function of scalem2=(Q2+MV2)/4. Hardening of W distributions withm2

  28. Q2 dependence sL~1/Q6=>Fit with s~1/(Q2+MV2)n Q2 >0 GeV2=>n=2+/- 0.01 r: J/y: Q2 >0 GeV2=>n=2.486 +/- 0.08 +/-0.068 Q2 >10 GeV2=>n=2.5+/- 0.02 (S. Kananov) Q2dependenceisdampedatlow Q2and steepensat large Q2 Approachinghandbagprediction of n=6 (Q2 not asymptotic, fixedW vs fixedxB, stot vs sL, Q2evolution of G(x)…)

  29. t dependence b decreases from “soft” (~10 GeV-2) to “hard”(~4-5 GeV-2) as a function of scalem2=(Q2+MV2)/4

  30. Ratios r/w/f/(J/Y) ~ 9/1/2/8 (SU(4) universality) |r0>=1/sqrt(2){|uu>-|dd>} ~{2/3-(-1/3)} Ratio r/w=9 |w>=1/sqrt(2){|uu>+|dd>} ~{2/3+(-1/3)}

  31. sL/sT (almost) compatible withhandbagprediction (dampingat large Q2)

  32. SDMEs HERMES H1 (almost) no SCHC violation

  33. At high energy (W>5 GeV), the general features of the kinematics dependences and of the SDMEs are relatively/qualitatively well understood Good indications that the “hard”/pQCD regime is dominant for m2=(Q2+MV2)/4 ~ 3-5 GeV2. Data are relatively well described by GPD/handbag approaches

  34. HERMES H1, ZEUS H1, ZEUS CLAS COMPASS , Q2>> Q2>>

  35. Exclusive r0, w, f & r+ electroproduction on the proton @ CLAS6 } e1-b (1999) K. Lukashin et al., Phys.Rev.C63:065205,2001 (f@4.2 GeV) C. Hadjidakis et al., Phys.Lett.B605:256-264,2005 (r0@4.2 GeV) } L. Morand et al., Eur.Phys.J.A24:445-458,2005 (w@5.75GeV) e1-6 (2001-2002) J. Santoro et al., Phys.Rev.C78:025210,2008 (f@5.75GeV) S. Morrow et al., Eur.Phys.J.A39:5-31,2009(r0@5.75GeV) } e1-dvcs (2005) A. Fradi, Orsay Univ. PhD thesis (r+@5.75 GeV)

  36. e1-6 experiment (Ee =5.75 GeV) (October 2001 – January 2002)

  37. Mm(epp+ X) Mm(epX) ep  ep p+(p-) p+ e (p-) p

  38. BackgroundSubtraction • 1) Ross-Stodolsky B-W forr0(770),f0(980)andf2(1270) • with variable skewedness parameter, • 2)D++(1232) p+p-inv.mass spectrumandp+p- phase space.

  39. sr(g*p  pr0) vs W

  40. r+ r0 w f C. Hadjidakis et al., Phys.Lett.B605:256-264,2005 (r0@4.2 GeV) S. Morrow et al., Eur.Phys.J.A39:5-31,2009(r0@5.75GeV) L. Morand et al., Eur.Phys.J.A24:445-458,2005 (w@5.75GeV) J. Santoro et al., Phys.Rev.C78:025210,2008 (f@5.75GeV) K. Lukashin, Phys.Rev.C63:065205,2001 (f@4.2 GeV) A. Fradi, Orsay Univ. PhD thesis, 2009 (r+@5.75GeV)

  41. ep->epf ( K+[K-]) GK sL fL

  42. GPDs parametrization based on DDs (VGG/GK model) Strong power corrections… but seems to work at large W…

  43. + VGG GPD model

  44. VGG GPD model GK GPD model

  45. t ERBL DGLAP x +1 -1 -ξ 0 ξ Quark distribution W~1/x γ, π, ρ, ω… -2ξ x+ξ x-ξ ~ ~ H, H, E, E (x,ξ,t) “ERBL” region “DGLAP” region Antiquark distribution q q Distributionamplitude

  46. DDs + “meson exchange” DDs w/o “meson exchange” (VGG) “meson exchange”

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