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Evolution of GPDs at NLO. Laurent Schoeffel (CEA/Saclay) : June 05. GPDs and skeewing [R=GPDs/PDFs] important for quarks DVCS R² > 4 impact on cross sections… We have a large Q² range of measurements : Q² evolution (GPDs) ?
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Evolution of GPDs at NLO Laurent Schoeffel (CEA/Saclay) : June 05 GPDs and skeewing [R=GPDs/PDFs] important for quarks DVCS R² > 4 impact on cross sections… We have a large Q² range of measurements : Q² evolution (GPDs) ? GPDs of gluons => large effect for DVCS AND for VMs : R²>1.5 impact on J/ cross sections… Here also, large Q² range! => Intesrest for an evolution code of GPDs at NLO : Basis : Freund routines for splitting functions. THEN
Skeewing for Quarks 1. The skeewing of the GPD is important already at 1.5/2 2. x< belongs to the ERBL domain => another regime of QCD evol In particular, we can check the symmetry at /2 conserved by the QCD evolution! see Martin et al. ’99 3. Above Q²> 5 GeV², the Q² evol for GPDs is quite low / DGLAP evol alone… (<= matching with the ERBL domain) 4. R= [A] / [B] ~ 2 (at 5 GeV²) Note :R ~ 2.5/3 at < 0.01 =0.2 [A] GPD 5 GeV² GPD 21 GeV² [B] u+ubar (MRS/CTEQ) Standard PDF (5 GeV²) Matching (continuity) of FDGLAP and FERBL/ not trivial… (sum rules)
Q² evolution and skeewing 1 ; 5 ; 21 GeV² Q² and are « mixed » in the evolution + matching at x=…. Q² evol Q² evol =0.5 =0.2 Initial param of the GPD Q0² = 1 GeV² Influence of the D-term
Skeewing for Gluons =10-4 Important skeewing of the complete distribution Results in agreement with Martin et al. (Shuvaev) ‘99 Symmetry in the ERBL domain =0.01 21 GeV² Large Q² evolution… 5 GeV² RG~ 1.3/1.4 5 GeV² MRS/CTEQ
Conclusions Possibility to implement directly the Gluon GPDs in Martin et al. calculations => Examine the differences with the « effective » approximation GPD=RG xG ! => A way to solve the problems arising with the RG derivations / Fit group… Short/Mid Term : DVCS amplitudes at NLO from the GPDs : at LO, very simple, ADVCS ~ -i GPD(x=,,Q²) + « Re » Then, we would have the complete chain for MC MILOU : the present version is using files of amplitudes produced by Freund => impossible to change the param. in the MC… In the future : Combined DVCS/ VMs QCD Fit => GPDs But only after analysis of 03-05 data + charge asymmetry !
Skeewing for Quarks (appendix) X [0,1] LO DVCS graph p+(x-) x p+ (x-) p+ Fq+qbar(x,,…) GPD Low xBj => ~ xBj ADVCS ~ dx 1/ (x- +i)Fq+qbar(x,,…) +… -i FS(,,…) + “Re” R = FS(,,…)/Q(,...) ~2 => factor R²~4 on DVCS Freund et al. ‘99
