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Calculations of single-inclusive cross sections and spin asymmetries in pp scattering

This talk focuses on the general status and progress of calculations for single-inclusive cross sections and spin asymmetries in pp scattering. It discusses topics such as next-to-leading order, resummation, power corrections, and their implications for understanding proton structure and hadronic final states.

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Calculations of single-inclusive cross sections and spin asymmetries in pp scattering

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  1. Calculations of single-inclusive cross sections and spin asymmetries in pp scattering Werner Vogelsang RBRC & BNL Nuclear Theory Spin2004, Trieste Oct. 11

  2. Outline: Talk will focus on general status & progress of calculations, rather than on specific predictions for spin asymmetries etc. • Introduction • Next-to-leading order • Resummation • Power corrections • Conclusions

  3. I. Introduction

  4. High- single-inclusive reactions : • the “next-simplest” observables in pp scattering, after Drell-Yan • short-distance interaction  perturbation theory • important tests of QCD hard scattering, need for higher orders, resummations, power corrections • important insights into proton structure, and into formation of hadronic final states One prime example: at RHIC, to measure

  5. (for pions, additional fragmentation functions)

  6. Ingredients for theoretical framework: • parton distributions / fragmentation functions • higher order QCD corrections  may be particularly sizable in hadronic collisions  reduction in scale dependence  NLO = state of the art  in some cases, all-order resummations of dominant terms • idea about power corrections, e.g., if not so high

  7. II. NLO - successes and failures

  8. NLO calculations for single-inclusive processes : Aurenche et al. ; Baer, Ohnemus, Owens ; Contogouris et al. ; Gordon, WV ; Mukherjee, Stratmann, WV Ellis, Kunszt, Soper; Furman ; Guillet ; … De Florian, Frixione, Signer, WV ; Jäger. Stratmann, WV Aversa et al.; de Florian; Jäger, Schäfer, Stratmann, WV

  9. at RHIC

  10. Spin asymmetries at RHIC (Stratmann, Jäger,WV)

  11. (Stratmann, Jäger,WV) (L = 7/pb, P = 0.4)

  12. at lower energies Apanasevich et al. (see also Aurenche et al.; Bourrely, Soffer)

  13. at lower energies Aurenche et al.

  14.  Why problems in fixed-target regime ? Why “near perfect” at colliders ?  • higher-order corrections beyond NLO ? • power corrections ? (e.g., “intrinsic” as a model. Actually tries to mimic higher orders and power corrections. There is no unique way of implementing it. See Murgia’s talk)

  15. III. Resummation

  16. Threshold resummation Example: prompt photons “threshold” logarithms, associated with soft/coll. gluons

  17. Are these terms relevant ? “parton luminosity”

  18. How dominant are they ?

  19. Sterman; Catani, Trentadue; • exponentiation occurs when Mellin moments in are taken Large terms may be resummed to all orders in

  20. Leading logarithms : • these exponents are positive  enhancement (NLL far more complicated, known: Laenen, Oderda, Sterman; Catani. Mangano, Nason)

  21. Same for inclusive hadrons • expect much larger enhancement ! • important techniques for NLL color exchange : Sen; Kidonakis, Sterman; Bonciani et al. • also, use NLO calculation by Jäger, Schäfer, Stratmann, WV

  22. LO NLO NNLO · · · · · · · · · · · · k N LO LL NLL NNLL • What is the general structure ? Fixed order Resummation

  23. E706 Sterman, WV  Significant reduction in scale dependence ! • resummation compensates soft part of DGLAP evolution  Effects negligible at collider energies

  24. E706 de Florian, WV (note, the resummation is for rapidity-integrated cross section)

  25. WA70

  26. discrepancies for pion production are strongly reduced • colliders: much smaller effects (but watch out for subleading terms) • curious situation: bigger problems between data and NLO for prompt  however, resummation effects larger for pions ! • experimental issues ? • how about power corrections ?

  27. IV. Power Corrections

  28. • singularity in reflected in factorial growth of PT series DY: • ill-defined because of strong-coupling regime •  structure of power corrections from resummation ? • resummed logarithms not associated with factorial growth • regime of very low : • overall powers all even, exponentiating ! Sterman, WV

  29. • closer analysis shows that there are also effects from transverse-momentum resummation connects and to values from analysis ? • for single-inclusive cross sections : • then, • qualitatively, for inclusive hadrons, replace

  30. V. Conclusions

  31. tremendous success of NLO at collider energies • at lower energies: resummation appears crucial large effects for inclusive hadrons reduction of scale dependence will be relevant in many situations ! • beginnings of analysis of power corrections implied by resummation : energy dependence  smaller effects at colliders • a lot of work remains ! resummation: rapidity dependence subleading terms recoil effects at smaller effects on spin asymmetries power corrections: full analysis, global fit ?

  32.  subleading terms important at collider energies

  33. • singular at • Mellin contour chosen as • PT series defined in this way has no factorial growth

  34. Sterman, WV

  35. Sterman, WV

  36. Jäger, Stratmann, WV

  37. Perturbative series :

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