RBRC and BNL Nuclear Theory 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

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

I. Introduction

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

II. A simple model

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

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

(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 …)

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

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

III. Sudakov effects

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

• first-order correction : • higher orders : .

qT distribution is measurable : Z bosons

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

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

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

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

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

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

Contribution from very low k • 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

Brock, Landry, Nadolsky, Yuan

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

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

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

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

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