Exploring the Proton Spin

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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
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Outline

• Introduction
• A simple model
• Sudakov effects
• Conclusions

with Feng Yuan
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I. Introduction
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The observable
measure
vs
what can we say (in pQCD) about this
observable ?
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II. A simple model
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Lets assume
(1) can describe process by partonic hard
scattering
(?)
(?)
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(3) dependence of distrib. on kT is entirely
non-perturbative, Gaussian, and
factorizes from x-dependence
(none of these will be true )
usual pdf
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(has probably some truth )
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(supported by pert. theory)
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a relatively small effect
fragm., 0.25 GeV2
GRV, GRSV, KKP
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III. Sudakov effects
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first-order correction
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qT distribution is measurable
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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
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same phenomenon in back-to-back hadrons
J. Owens
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Resummation !
work began in the 80s with Drell-Yan
Dokshitzer et al. Parisi Petronzio Collins,
Soper, Sterman
? qT resummation
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Leading logs
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To NLL, need
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Contribution from very low k?
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Brock, Landry, Nadolsky, Yuan
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Kulesza, Sterman, WV
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Sudakov factor spin-independent
Ji, Ma, Yuan
phenomenologically observed x-dependence in
non-pert. piece ? would expect difference in
and
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Back to the pp ? ??X case
for each leg. Different for each partonic channel.
Beyond LL, spin-dependence from
color-interplay w/ hard parts
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LL resummation in unpol. case
Boer, WV
NLL hasnt been done. Neither has long. pol.
case
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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?