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Setting the Scale for DIS at Large Bjorken x

Setting the Scale for DIS at Large Bjorken x. Simonetta Liuti University of Virginia INT Workshop, “The Jefferson Laboratory Upgrade to 12 GeV” October 7th, 2009 , USA. Outline. Review DGLAP evolution at large Bjorken x

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Setting the Scale for DIS at Large Bjorken x

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  1. Setting the Scale for DIS at Large Bjorken x Simonetta Liuti University of Virginia INT Workshop, “The Jefferson Laboratory Upgrade to 12 GeV” October 7th, 2009, USA

  2. Outline Review DGLAP evolution at large Bjorken x z-dependent scale gives rise to “large Bjorken x evolution” Interplay of TMCs, Large Bjorken x evolution,HigherTwists (A. Fantoni) Nuclear corrections at large Bjorken x Conclusions/Outlook for the 12 GeV program and beyond…

  3. Interest in Large x Studies • Precise determination of PDFs(Jlab + CTEQ studies): extend the domain of validity of PDF global analyses (importance of large x gluons, …) • QCD predictions at xBj=1 (Ratio F2n/F2p,…) • Parton-Hadron Duality in DIS at large xBj monitors the transition in QCD between the “perturbative” region, where factorization applies to the “non-perturbative” region: consequence of factorization theorems in QCD? (L. Frankfurt, J. Collins) • Possibility of extracting sat low scale (complementary to GDH sum rule analysis by J.P. Chen and A. Deur)

  4. Large xBj at fixed Q2 impliesthe continuation of the pQCD curve into the resonance region Main question: how to continue pQCD curve? What defines the pQCD curve? Suggested approach (S.L., R. Ent, C.Keppel, I. Niculescu, PRL 2000) TMC Fix the order of the analysis, e.g. NLO and extend curve  corrections arise that are more important than at low xBj and that point at interesting physics (duality) Large x structure of PQCD evolution equations NNLO and higher… Higher Twists Nuclear corrections (for neutron)

  5. All effects need to be taken into account simultaneuosly. Some results from Bianchi, Fantoni, S.L. (PRD, 2003) and Fantoni, S.L. (2006) n=2 Precise pQCD prediction  Mn  lnQ2 + NLOrders… n=4 n=6 n=8 In and Mn calculated using CTEQ

  6. Unpolarized Jlab+SLAC data (I. Niculescu) Polarized HERMES+Jlab+SLAC data TMC Large x Res.

  7. New polarized data? (O. Rondon et al.) O.Rondon

  8. Large xBj evolution (S. Brodsky, SLAC lectures (1979), D. Amati et al., NPB(1980), R. Roberts, “Structure of the Proton”) S  g2/4=S (k2) at each vertex

  9. k’ *q  q’ g q k * l g Invariant mass! In terms of LC variables k (k+=zP+,,k-=P-- l-, kT)  Next, write amplitude for *P  (final quark) + g + X 

  10. |Amplitude|2 for *P  (final quark) + g + X  k’+q q k’ l k P’ P If z-dependence in kT integration limit is disregarded

  11. kT2=Q2=10 GeV2 z-dependent limit It matters at large x!

  12. As a consequence… This takes care of the large log term in the Wilson coefficient f. (NLO, MS-bar) { The scale that allows one to annihilate the effect of the large ln(1-z) terms at large x at NLO is the invariant mass, W2 Equivalent to a resummation of these terms up to NLO

  13. Work in progress based on recent analysis by A.Accardi, J.Qiu, JHEP (2008) that extends range of validity of TMCs approach without introducing mismatches between the x andranges (see Alberto’s talk) Instead of 1 Join large x evoluion with new treatment of TMCs A.Accardi, S.L., W.Melnitchouk

  14. Once PQCD is taken into account, extract HTs additive form F2exp=FPQCD(1+C(x)/Q2)

  15. Nuclei (S. Malace’s talk)  Are HTs isospin dependent? Deviations from PQCD effects Cp-Cn NMC data Alekhin, Kulagin and S.L., PRD (2003)

  16. In addition …. Sneeds to be continued at very low Q2 J.P. Chen and A. Deur GDH analysis S.L. work in progress Use this “positively” to extract S at low scale

  17. Towards the Jlab 12 GeV program….The very large and accurate Jlab Hall C set of data has shown that parton hadron duality can be studied in detail: Q2,W2 and longitudinal variables dependences have been analyzed thouroughly Observation of similarity between “high” and “low” energy cross sections at the core of strong interaction theory Theoretical background: starts from Finite Energy Sum Rules (FESR) Dolen, Horn and Schmid, PR166(1968) Is there an interpretation within QCD? Shifman (2005), Bigi and Uraltsev (2004) Is there a more general implication from factorization theorems of QCD? Interplay of ISI and FSI Frankfurt (this workshop)

  18. All experimental measurements should be compared….

  19. Conclusions and Outlook • Parton-hadron duality is interesting theoretically: low to high energy connection… • Quantitative studies of parton-hadron duality are important in “Global Analyses” but… all aspects including TMCs, LxR, and dynamical HTs need to be included\ • Interesting to compare unpolarized and polarized results Thank you!

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