Quark Helicity Distribution at large-x Collaborators: H. Avakian, S. Brodsky, A. Deur,...
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![Page 1: Quark Helicity Distribution at large-x Collaborators: H. Avakian, S. Brodsky, A. Deur, arXiv:0705.1553 [hep-ph] Feng Yuan Lawrence Berkeley National Laboratory.](https://reader034.fdocuments.net/reader034/viewer/2022051620/56649ede5503460f94bee9ed/html5/thumbnails/1.jpg)
Quark Helicity Distribution at large-x
Collaborators: H. Avakian, S. Brodsky, A. Deur, arXiv:0705.1553 [hep-ph]
Feng Yuan Lawrence Berkeley National Laboratory
RBRC, Brookhaven National Laboratory
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Outline
Introduction Issues at large-x Quark orbital angular momentum
contribution Outlook
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Physics Motivation for large-x Global fit for the PDFs New Physics at Tevatron and LHC Precision Test of EW physics at Colliders … Itself is very interesting to study QCD
effects, such as resummation; and nucleon structure, such as quark orbital angular momentum,…
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Importance of high x in global fit
Djouadi and Ferrag, hep-ph/0310209
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New physics or PDF uncertainty?
Inclusive Jet production at Tevatron, hep-ex/0506038
High x Partons relevant
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Theoretical Issues at High x
Resummation Power counting, pQCD predictions
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Why Perturbative calculable
• All propagators are far off-shell: ~ kT2/(1-x)>>QCD
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• Spectator power counting
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Power counting of Large x structure Drell-Yan-West (1970)
Farrar-Jackson (1975)
Brodsky-Lepage (1979)
Brodsky-Burkardt-Shmidt (1995)fit the polarized structure functions.
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Power counting from LZ=0
Eight propagators (1-x)8, (1-x)-4 from the scattering, (1-x)-1 from the phase space integral (1-x)3
Spectator two quarks with spin-1 configuration will be suppressed by (1-x)2 relative to spin-0 q- ~(1-x)2q+
q+~
q-~
Spin-0
Spin-1
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Quark polarization at large-x
Power counting rule: q+~ (1-x)3, q-~(1-x)5
The ratio of q/q will approach 1 in the limit of x->1 Brodsky-Burkardt-Shmidt
(1995)
JLab Hall A, PRL04
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Light-front wave function decomposition:
Total quark spin
Lz=0
Lz=1 Lz=1
Quark orbital angular momentum of proton
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OAM relevance to nucleon structure Finite orbital angular momentum is essential for
Anomalous magnetic moment of nucleons Helicity-flip Pauli form factor F2
g2 structure function Asymmetric momentum-dependent parton
distribution in a transversely polarized nucleon, Sivers function
Large-x quark helicity distribution …
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For example, the Sivers functions Quark Orbital Angular
Momentum e.g, Sivers function ~ the wave
function amplitude with nonzero orbital angular momentum!
Vanishes if quarks only in s-state!Ji-Ma-Yuan, NPB03Brodsky-Yuan, PRD06
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Lz=1 contributions to q-
No suppression from the partonic scattering part Intrinsic pt expansion will lead to power
suppression
Total suppression factor will be
Spin-0
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Orbital angular momentum contribution It does not change the power counting
q-~ (1-x)5
It introduces double logarithms to q-
q-~(1-x)5 log2(1-x)Coming from additional factor 1/y3y3’ in
the intrinsic pt expansionq-/q+~(1-x)2 log2(1-x) at x->1
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1604/20/23 Large-x Partons
OAM contribution to the Pauli form factor F2
Belitsky-Ji-Yuan, PRL, 2003
Lz=1
It predicts that F2 goes like (ln2Q2)/Q6 and henceF2/F1 ~ (ln2Q2)/Q2
Lz=0
Expansion~1/x3y3
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Quark orbital angular momentum contribution at large-x Power counting rule
Brodsky-Burkardt-Schmidt 95Leader-Sidorov-Stamenov 98q-/q+~ (1-x)2
Quark-orbital-angularMomentum contributionAvakian-Brodsky-Deur-Yuan,07q-/q+~(1-x)2 log2(1-x)
It will be interested to see how this compares withthe future data from JLab
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12GeV JLab Upgrade
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Outlook Soft divergence factorization
1/kt4 for Pion distribution
Quantitative connections to the quark orbital angular momentumModel building, light-cone wave functions
of nucleon Large logarithms resummation
Log2(1-x) terms should be resummed consistently
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Applications to GPDs: GPD for Pion
Gauge Link
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Where is the t-dependence
• In the leading order, there is no t-dependence• Any t-dependence is suppressed by a factor (1-x)2
(See also, Burkardt, hep-ph/0401159)
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Power counting results for pion GPD in the limit of x->1,
We can approximate the GPD with forward PDF at large x,
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GPDs for nucleon
Helicity nonflip
Helicity flip
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Helicity non-flip amplitude
The propagator
Power behavior
Forward PDF
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Helicity flip amplitude• Since hard scattering conserves quark helicity, to get the helicity flip amplitude, one needs to consider the hadron wave function with one-unit of orbital angular momentum
• In the expansion of the amplitude at small transverse momentum l, additional suppression of (1-x)2 will arise
Lz=1 Lz=0
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• Two kinds of expansionsPropagator:
Wave function:
• The power behavior for the helicity flip amplitude
• GPD EE
• GPD HHForward PDF
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Summary for the GPDs’ power prediction No t-dependence at leading order Power behavior at large x
Forward PDF
~(1-x)2
~ (1-x)3
=
Log(1-x) should also show up
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Conclusion
Quark orbital angular momentum contribution changes significantly power counting results for the quark helicity distribution at large-x
More precise determination of these contributions requires a model building and/or a NLO global fit with all experimental data
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Factorization (II)
Leading region
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Factorization (III)
Factorization formula
The power behavior of q(x) is entirely determined by the eikonal cross section
Ji,Ma,Yuan,PLB610(2005)
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Power Counting for GPDs No t-dependence at leading order Power behavior at large x
Forward PDF
~ (1-x)2
~ (1-x)3
= ~ (1-x)5
Yuan, PRD69(2004)
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Why Resummation is Relevant Additional scale, Q2>> (1-x)Q2>>QCD
2
Real and Virtual contributions are “imbalanced” IR cancellation leaves large logarithms (implicit)
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Example INet Enhancement for the DIS Structure functions
A. Vogt
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34Large-x Partons
Example II: Spin Asymmetry Resummation effects cancel exactly
in moment space, and “almost” in x-space
W. Vogelsang