Some thoughts on the helicity-dependence of “jet k T ” Werner Vogelsang RBRC and BNL Nuclear Theory OAM workshop, UNM, 02/24/2006 (aka the “Fields Effect”)
Jan 25, 2016
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?