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Cross Sections and Spin Asymmetries in Hadronic Scattering

Cross Sections and Spin Asymmetries in Hadronic Scattering. Werner Vogelsang BNL Nuclear Theory KEK, 03/10/2007 Dedicated to Jiro. Outline:. QCD perturbation theory in hadronic collisions Some NLO phenomenology at RHIC Phenomenology of resummation in hadronic collisions Conclusions.

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Cross Sections and Spin Asymmetries in Hadronic Scattering

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  1. Cross Sections and Spin Asymmetries in Hadronic Scattering Werner Vogelsang BNL Nuclear Theory KEK, 03/10/2007 Dedicated to Jiro

  2. Outline: • QCD perturbation theory in hadronic collisions • Some NLO phenomenology at RHIC • Phenomenology of resummation in hadronic collisions • Conclusions

  3. Jiro’s work has had a big impact on the development of this area: QCD spin physics: • some of the early seminal papers of the field  polarized-DIS & RHIC programs • proposals and studies for processes at RHIC • brought young people into field QCD resummation: • open the door to beyond-LL resummation

  4. I. Introduction

  5. pp  jet X pp   X pp   X, … Polarized and unpolarized protons

  6. One prime example: at RHIC to measure Such reactions : • short-distance interaction  perturbation theory • important tests of our understanding of QCD, need for higher orders, resummations, power corrections, … • important insights into proton structure • baseline for heavy-ion collisions, New Physics searches, …

  7. short-distance: perturbation theory universal pdf’s : factorization/ren. scale (good up to corrections suppressed as )

  8. II. Some NLO phenomenology Example: pp at RHIC

  9. K (Aversa et al.; de Florian) RHIC

  10. Scales varied between pT/2 <  < 2 pT

  11. STAR (NLO calculation assumes “narrow” jet cone) Jäger, Stratmann, WV

  12. Aurenche et al.; Baer et al.; Gordon, WV

  13. “axial anomaly” Altarelli et al. The gluon distribution g Not much information until recently:

  14. Ultimately: “global analysis” to really extract g and its integral

  15. III. Phenomenology of resummation in hadronic scattering

  16.  A long-standing problem : Aurenche et al.; Bourrely, Soffer …well described by NLO at RHIC …but data much higher than NLO at fixed-target energies !

  17. “threshold” logarithms Real emission inhibted Only soft/collinear gluons allowed (without rapidity integration: ) • higher-order corrections beyond NLO ?

  18. • convolution with PDFs : emphasized, in particular as

  19. • work began in the late ‘70s Dokshitzer et al.; Parisi Petronzio; Collins, Soper, Sterman; Kodaira, Trentadue  qTresummation  threshold resummation Sterman; Catani, Trentadue; … Kidonakis, Sterman; Bonciani et al.; Catani, Mangano, Nason; Laenen, Oderda, Sterman; Catani, Grazzini, de Florian; Moch, Vogt, Vermaseren; Aybat, Dixon, Sterman; • today : high level of sophistication  many other reactions in QCD  towards NNLL  “joint resummations” Li; Laenen, Sterman, WV  other formalisms Becher, Neubert; Ji, Ma, Yuan • will spoil perturbative series - unless taken into account to all orders = Resummation

  20. Resummation usually done in “transform space”:  Exponentiation In our case, Mellin moments in

  21. •  : soft-collinear emission off “observed” partons. LL+… • J : collinear (soft/hard) emission off “unobserved” recoiling “jet” LL+… • (int) : large-angle soft emission (matrix problem) NLL+… Kidonakis, Sterman; Bonciani, Catani, Mangano, Nason; Aybat, Dixon, Sterman

  22. Kodaira, Trentadue

  23. Jet function: • expect large enhancement ! de Florian, WV

  24. de Florian, WV E706 (use “Minimal Prescription” of ) Catani, Mangano, Nason, Trentadue

  25. WA70

  26.  subleading terms important at collider energies resummation effects much smaller

  27. Application to prompt photons: “direct” contributions: Relatively small resum. effects (Catani et al.; Sterman, WV; Kidonakis, Owens) “fragmentation” contributions: de Florian, WV a bit like 0 production, but less gggg (because Dg is smaller)

  28. de Florian, WV

  29. de Florian, WV

  30. Application to jet production: de Florian, WV Jet cone •“unobserved” jet: becomes massless at threshold •“ observed” jet: involves integration over jet mass  no double logs Kidonakis, Sterman •can be explicitly verified by comparison to “analytical” NLO calculation in small-cone approximation Jäger, Stratmann,WV

  31. Tevatron 1800 GeV RHIC 200 GeV de Florian, WV

  32. Drell-Yan @ J-PARC Yokoya, WV

  33. Conclusions • good understanding of high-p cross sections at colliders  • gives confidence for analysis of spin asymmetries at RHIC • progress in fixed-target regime through soft-gluon resummation • generally, resummation techniques important with regard to hadron colliders: J-PARC to RHIC to Tevatron to LHC • Jiro’s contributions crucial throughout this physics

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