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Some thoughts on the helicity-dependence of “jet k T ”

Some thoughts on the helicity-dependence of “jet k T ”. (aka the “Fields Effect”). Werner Vogelsang RBRC and BNL Nuclear Theory OAM workshop, UNM, 02/24/2006. Outline:. Introduction A simple model Sudakov effects Conclusions. with Feng Yuan. I. Introduction. . _. _. +,. +,.

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Some thoughts on the helicity-dependence of “jet k T ”

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  1. Some thoughts on the helicity-dependence of “jet kT” (aka the “Fields Effect”) Werner Vogelsang RBRC and BNL Nuclear Theory OAM workshop, UNM, 02/24/2006

  2. Outline: • Introduction • A simple model • Sudakov effects • Conclusions with Feng Yuan

  3. I. Introduction

  4. _ _ +, +,  • it is hoped that any difference has to do with OAM (won’t be discussed in this talk…) Meng et al. • The observable : measure vs • what can we say (in pQCD) about this observable ?

  5. II. A simple model

  6. (2)can use factorization in terms of kT-dependent parton distributions and fragmentation fcts. : Let’s assume : (1)can describe process by partonic hard scattering () (?)

  7. then : for one part. channel ab  cd (3)dependence of distrib. on kT is entirely non-perturbative, Gaussian, and factorizes from x-dependence : (none of these will be true …) usual pdf

  8. (4)if all quarks and antiquarks have same widths, obtain after sum over all partonic channels : contain all partonic cross secs. pdf’s & fragm. fcts. (5)gluons are “broader” than quarks : (the “2” really is CA/CF = 9/4) (has probably some truth …)

  9. (6)now assume that kT-widths are spin-independent: Then : Note : (supported by pert. theory)

  10. • a relatively small effect : fragm., 0.25 GeV2 GRV, GRSV, KKP

  11. III. Sudakov effects

  12. • example : Drell-Yan cross section mass Q, transv. momentum qT • LO partonic cross section :

  13. . . . • higher orders : • first-order correction :

  14. Z bosons qT distribution is measurable :

  15. virtual corrections V qT=0 real emission R qT≠0 • perturbation theory appears in distress • phenomenon (and solution) well understood For qT0 real radiation is inhibited, only soft emission is allowed: affects IR cancellations

  16. • same phenomenon in back-to-back hadrons : J. Owens

  17. • , …can be taken into account to all orders • large log. terms exponentiate after suitable integral transform is taken : = Resummation ! • work began in the ‘80s with Drell-Yan Dokshitzer et al.; Parisi Petronzio; Collins, Soper, Sterman; …  qTresummation

  18. Resummed cross section really is: Collins, Soper, Sterman Full exponent : Leading logs :

  19. Note, for ggHiggs : (different though for B terms) (gluons are “broader”) To NLL, need

  20. Logarithms are contained in • need prescription for treating b integral Laenen, Sterman, WV “complex-b” Collins, Soper, Sterman

  21. • suggests Gaussian non-pert. contribution with logarithmic Q dependence •“global” fits see log(Q) dependence Davies, Webber, Stirling; Brock et al., Ladinsky, Yuan; Qiu, Zhang Nadolsky, Konychev; Kulesza, Stirling Contribution from very low k

  22. Brock, Landry, Nadolsky, Yuan

  23. pert. resummed @ NLL pert. resummed @ NLL Z bosons resummed, w/ non-pert. term Kulesza, Sterman, WV

  24. • Sudakov factor spin-independent Ji, Ma, Yuan; … • phenomenologically observed x-dependence in non-pert. piece  would expect difference in and

  25. • Back to the pp  X case : for each leg. Different for each partonic channel. • Beyond LL, spin-dependence from color-interplay w/ hard parts

  26. • LL resummation in unpol. case : Boer, WV • NLL hasn’t been done. Neither has long. pol. case

  27. IV. Conclusions • one expects a difference between and for pp  X • not related to “intrinsic” properties • on the other hand, effect is probably relatively small • Refinement of observable ? Other final states?

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