1. 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

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
• 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 ?

5. II. A simple model

6. 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. :
(?)

7. (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

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:
(supported by
pert. theory)
Then :
Note :

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

11. III. Sudakov effects

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

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

15. qT distribution is measurable :
Z bosons

16. 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

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

18. • , … 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 :

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

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

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

22. 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

23. Brock, Landry, Nadolsky, Yuan

24. @ 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

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

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

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

28. 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?