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M. Guidal, IPN Orsay

Varenna , 06/07/2011. Lecture 2: Deep Virtual Meson Production: From data to GPDs ?. M. Guidal, IPN Orsay. q=q V +q sea q=q sea so : total sea (q+q): q sea = 2 q. Kresimir Kumericki , Dieter Mueller, Nucl.Phys. B841:1-58,2010.

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M. Guidal, IPN Orsay

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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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