Some thoughts on the helicity-dependence of “jet kT”

Werner VogelsangRBRC and BNL Nuclear Theory

OAM workshop, UNM, 02/24/2006

(aka the “Fields Effect”)

• Introduction

• A simple model

• Sudakov effects

• Conclusions

Outline:

with Feng Yuan

I. Introduction

• 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

(1) can describe process by partonic hard scattering

Let’s assume :

()

(?)

(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

(5) gluons are “broader” than quarks :

(the “2” really is CA/CF = 9/4)

(has probably some truth …)

(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.

(6) now assume that kT-widths are spin-independent:

(supported by pert. theory)

Then :

Note :

• a relatively small effect :

GRV, GRSV, KKP

fragm., 0.25 GeV2

III. Sudakov effects

• example : Drell-Yan cross section

mass Q, transv. momentum qT

• LO partonic cross section :

• first-order correction :

• higher orders :

...

Z bosons

qT distribution is measurable :

• perturbation theory appears in distress

• phenomenon (and solution) well understood

For qT0 real radiation is inhibited, only soft emission is allowed: affects IR cancellations

real emission

qT≠0R

virtual corrections qT=0V

• same phenomenon in back-to-back hadrons :

J. Owens

= Resummation !

• work began in the ‘80s with Drell-YanDokshitzer et al.; Parisi Petronzio;Collins, Soper, Sterman; …

qT resummation

• , … can be taken into account to all orders

• large log. terms exponentiate after suitable integral transform is taken :

Leading logs :

Full exponent :

Resummed cross section really is: Collins, Soper, Sterman

To NLL, need

Note, for ggHiggs :

(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

Z bosonspert.resummed@ NLL

pert.resummed@ NLL

resummed, w/ non-pert. term

Kulesza, Sterman, WV

• phenomenologically observed x-dependence in non-pert. piece would expect difference in and

• Sudakov factor spin-independent Ji, Ma, Yuan; …

• 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

one expects a difference between

and

IV. Conclusions

for pp X

not related to “intrinsic” properties

on the other hand, effect is probably relatively small

Refinement of observable ? Other final states?