p ? dependence of ssa -- from nonpert. to pert
DESCRIPTION
P ? Dependence of SSA -- from nonpert. to pert. Feng Yuan RBRC , Brookhaven National Laboratory. References: Ji, Ma, Yuan, Phys. Rev. D70, 074021; Phys. Lett. B597, 299; hep-ph/0503015; to be published;. Outline. Introduction - PowerPoint PPT PresentationTRANSCRIPT
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May 18-20, 2005 SIR05 JLab 1
PP?? Dependence of Dependence of SSASSA
-- from nonpert. to pert.-- from nonpert. to pert.Feng Yuan
RBRC , , Brookhaven National Laboratory
References: Ji, Ma, Yuan, Phys. Rev. D70, 074021; Phys. Lett. B597, 299; hep-ph/0503015; to be published;
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May 18-20, 2005 2SIR05 JLab
OutlineOutline Introduction Introduction Low PLow PTT region: TMD parton region: TMD parton
distributions and QCD distributions and QCD factorizationfactorization
High PHigh PTT region: quark-gluon- region: quark-gluon-quark correlation (ETQS quark correlation (ETQS mechanism)mechanism)
SummarySummary
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May 18-20, 2005 3SIR05 JLab
Inclusive and Inclusive and Semi-inclusive DISSemi-inclusive DIS
Inclusive DIS:Partonic Distribution depending on the longitudinal momentum fraction
Semi-inclusive DIS:Probe additional information for partons’transverse distribution in nucleon
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May 18-20, 2005 4SIR05 JLab
Different Different PPTT Region Region
Integrate out PT
-- similar to inclusive DIS, probe int. PDF Large PT (>>QCD)
-- hard gluon radiation, can be calculated from perturbative QCD,
Polarized ->q-g-q correlations Low PT (~QCD)
-- nonperturbative information (TMD): new factorization formula
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May 18-20, 2005 5SIR05 JLab
TMD PhysicsTMD Physics
A way to measure Transversity A way to measure Transversity Distribution, the last Distribution, the last unkownunkown leading leading twisttwist distribution distribution
Collins 1993Collins 1993 The Novel Single Spin AsymmetriesThe Novel Single Spin Asymmetries Connections with GPDs, and Quantum Connections with GPDs, and Quantum
Phase Space Wigner distributionsPhase Space Wigner distributions Quark Orbital Angular Momentum andQuark Orbital Angular Momentum and
Many others …Many others …
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May 18-20, 2005 6SIR05 JLab
TMD Distribution: the TMD Distribution: the definitiondefinition
Gauge Invariance requires the Gauge Link
Brodsky,Hwang,Schmidt 02’Collins 02’Belitsky,Ji,Yuan 02’
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May 18-20, 2005 SIR05 JLab 7
This definition is This definition is also consistent also consistent
with the with the QCD factorizationQCD factorization
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May 18-20, 2005 8SIR05 JLab
Illustrate the FactorizationIllustrate the Factorization(one-loop order)(one-loop order)
Take an on-shell quark targetTake an on-shell quark target Calculate the TMD Dis. and F.F. Calculate the TMD Dis. and F.F. Separate the cross section into different Separate the cross section into different
piecespieces Show the soft divergence is cancelled outShow the soft divergence is cancelled out
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May 18-20, 2005 9SIR05 JLab
TMD Dis. At One-loopTMD Dis. At One-loop
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May 18-20, 2005 10SIR05 JLab
No soft divergenceNo soft divergence
Collinear divergence : Collinear divergence : ln(mln(m22))
Double Logarithms: Double Logarithms: lnln22((22 b b22) ) --- Collins-Soper equation--- Collins-Soper equation
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May 18-20, 2005 11SIR05 JLab
FactorizationFactorization
Soft Factor
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May 18-20, 2005 12SIR05 JLab
The Factorization Applies The Factorization Applies toto
Semi-inclusive DIS (polarized and Semi-inclusive DIS (polarized and unpolarized)unpolarized)
Drell-Yan at Low transverse momentumDrell-Yan at Low transverse momentum Di-hadron production in e+e- Di-hadron production in e+e-
annihilation (extract the Collins annihilation (extract the Collins function)function)
Di-jet and/or di-hadron correlation at Di-jet and/or di-hadron correlation at hadron collider (work in progress)hadron collider (work in progress)
Many others, …Many others, …
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May 18-20, 2005 13SIR05 JLab
Large Logarithms Large Logarithms ResummationResummation
At low At low PT, , PT<< Q, we must resum the , we must resum the large logarithms large logarithms ss
nnln2n-1(Q2/PT2)
-- Dokshitzer, Diakonov, Troian, 1978-- Dokshitzer, Diakonov, Troian, 1978
-- Parisi, Petronzio, 1979-- Parisi, Petronzio, 1979 These large logarithms can be These large logarithms can be
resummed by solving the energy resummed by solving the energy evolution equation for the TMD parton evolution equation for the TMD parton dis.dis.
-- Collins-Soper 1981 -- Collins-Soper 1981
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May 18-20, 2005 14SIR05 JLab
TMD: the Energy TMD: the Energy DependenceDependence
The TMD distributions depend on the The TMD distributions depend on the energy of the hadron! (or Q in DIS)energy of the hadron! (or Q in DIS)
One can write down an evolution One can write down an evolution equation in equation in ζζ==2(P2(P++))22vv--/v/v++
K and G obey an RG equation, K and G obey an RG equation,
Collins and Soper (81’)
μ independent!
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May 18-20, 2005 15SIR05 JLab
Spin-dep. Collins-Soper Spin-dep. Collins-Soper Eq.Eq.
The evolution kennel is the same for all the leading-twist TMD quark distributionsquark distributions
KKtt-even ones: q(x, k-even ones: q(x, k┴┴), ), ΔΔqqLL, , δδqqTT
KKtt-odd ones: -odd ones: qqTT(x, k(x, k┴┴), ), δδq, q, ΔΔqqTT, , δδqqLL
Idilbi, Ji, Ma, Yuan: PRD70 (2004)
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May 18-20, 2005 16SIR05 JLab
Large Logarithms Large Logarithms Resumm. (II)Resumm. (II)
After resummation, large logarithms After resummation, large logarithms associated with associated with QQ22 can be factorized can be factorized into the into the Sudakov form factors, e.g.form factors, e.g.
And the Sudakov form factorAnd the Sudakov form factor
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Double Logarithmic (DL) Double Logarithmic (DL) Approx.Approx.
If If QQ22 is not too large, DL approx. applies. The is not too large, DL approx. applies. The Sudakov suppression form factor then only Sudakov suppression form factor then only depends on depends on QQ22
The The QQ22 dependence of the structure functions dependence of the structure functions can be factorized outcan be factorized out
We can predict the We can predict the PPTT distribution at higher distribution at higher QQ22 from that of lower from that of lower QQ22
The The PT spectrum of the polarization asymmetry spectrum of the polarization asymmetry will be the same for different Qwill be the same for different Q22 at fixed at fixed B and
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May 18-20, 2005 18SIR05 JLab
Phenomenogical applications of the QCD Phenomenogical applications of the QCD resummation to the Presummation to the PTT spectrum of EW spectrum of EW bosons production have been very bosons production have been very successfulsuccessfulYuan, Nadolsky, Ladinsky, Landry, Yuan, Nadolsky, Ladinsky, Landry, Qiu, Zhang, Berger, Li, Qiu, Zhang, Berger, Li, Laenen, Sterman, Vogelsang, Kulesza,Laenen, Sterman, Vogelsang, Kulesza,Bozzi, Catani, deFlorian,Bozzi, Catani, deFlorian,Kulesza, Stirling, Kulesza, Stirling, and many others, …and many others, …working even at NNLL level for someworking even at NNLL level for some
Our interest however, is in the region of Our interest however, is in the region of not so large Qnot so large Q22, where DLA (LLA) should , where DLA (LLA) should applyapply
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May 18-20, 2005 19SIR05 JLab
Drell-Yan at Fixed TargetDrell-Yan at Fixed TargetQT spectrum from E288, PRD23,604(81)
Normalized to the same spectrum!Consequence of DLA
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May 18-20, 2005 20SIR05 JLab
At very large Q2 (e.g., Z0 and W boson), DL Approx. breaks down
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May 18-20, 2005 21SIR05 JLab
Power Counting at Large Power Counting at Large PPTT
kktt-even distributions have the same -even distributions have the same dependence on kdependence on ktt
kktt-odd distributions are suppressed -odd distributions are suppressed at large kat large ktt
Power Counting RulePower Counting Rule
kktt-even: -even: 1/k1/ktt22
kktt-odd: -odd: 1/k1/ktt33
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May 18-20, 2005 22SIR05 JLab
SIDIS: at Large PSIDIS: at Large PTT
Large Large PPTT SIDIS can be calculated from SIDIS can be calculated from perturbative QCD (same for TMDs)perturbative QCD (same for TMDs)
Polarized scattering depends on the Polarized scattering depends on the quark-gluon correlations in the quark-gluon correlations in the nucleonnucleon
Single Spin Asymmetry (Sivers and Single Spin Asymmetry (Sivers and Collins) at large PCollins) at large P?? is not suppressed is not suppressed by by 1/Q1/Q, but by , but by 1/P1/PTT
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May 18-20, 2005 23SIR05 JLab
An example: SSA at An example: SSA at Large PLarge PTT
ETQS mechanismETQS mechanism
It is suppressed by It is suppressed by 1/P1/PTT
Efremov & Teryaev: 1982 & 1984Qiu & Sterman: 1991 & 1999
Quark-gluon correlations
Ji,Ma,Yuan, work in progress
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May 18-20, 2005 24SIR05 JLab
Transition from Transition from Perturbative region to Perturbative region to
Nonperturbative region?Nonperturbative region? Compare different region of PCompare different region of PTT
Nonperturbative TMD Perturbative region
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May 18-20, 2005 25SIR05 JLab
SummarySummary
QQ22 evolution of the P evolution of the PTT spectrum is spectrum is calculable from perturbative QCD, by calculable from perturbative QCD, by solving the associated Collins-Soper eqssolving the associated Collins-Soper eqs
Large PLarge PTT SSA depends on the quark-gluon- SSA depends on the quark-gluon-quark correlation of nucleon (ETQS), quark correlation of nucleon (ETQS), which is suppressed by 1/Pwhich is suppressed by 1/PTT, not 1/Q, not 1/Q
Detailed study of the PDetailed study of the PTT dependence will dependence will provide us information for the provide us information for the perturbative to nonperturbative transition perturbative to nonperturbative transition of of QQCCDD