1 probing the nucleon structure with azimuthal asymmetries --cos2φ distribution & boer-mulders...
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Probing the Nucleon Structure with Azimuthal Asymmetries
--cos2φ distribution & Boer-Mulders F. Lingyan Zhu
University of Illinois at Urbana-Champaign
FNAL E866/Nusea Collaboration
Nov 21, 2006 at Jefferson Lab
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Sea Asymmetry from Drell-Yan Processes
Towell et al., Phys.Rev. D64 (2001) 052002
Drell-Yan enables us to measured dbar/ubar asymmetry precisely.
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Angular Distribution in the Drell-Yan Process
In the simple parton model: ( for massless quarks and measured
relative to the annihilation axis)
=1 and ==0
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Conway et al., PRD39,92(1989)
First-order QCD Corrections to Drell-Yan
• Increase the overall cross section by a K-factor~2.
•The Lam-Tung relation still hold (in any reference frame for massless quarks), reflecting the spin-1/2 nature of the quarks. Lam & Tung, PRD21,2712(1980)
(Analog to Callan-Gross relation in DIS)
•The NLO correction at O(s2) to the
angular distribution is small. Mirkes & Ohnemus, PRD51,,4891(1995)With QCD corrections, the calculated cross section agrees with data.
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Conway et al., PRD39,92(1989)
E615 at Fermilab: 252 GeV π- + W
Violation of the Lam-Tung Relation
Also see NA10 results: 140/194 GeV π- + W, 286 GeV π- + W/d
Z. Phys. C37, 545 (1988)
•The deviations from 1+cos2due to the soft-gluon resummation are less than 5%.Chiappatta & Bellac,ZPC32,521 (1986)
•The correction due to the intrinsic transverse momenta is estimated to be less than 0.05Cleymans & Kuroda, PLB105,68(1981)
•Lam-Tung relation not affected by lowest order QCD correction even at small QT. Boer & Wogelsang, hep-ph/0604177
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Conway et al., PRD39,92(1989) E615 at Fermilab: 252 GeV π- + W
Angular Distribution in the W Drell-Yan Process
Also see NA10 results: 140/194 GeV π- + W, 286 GeV π- + W/d Z. Phys. C31, 513 (1986); Z. Phys. C37, 545 (1988)
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Conway et al., PRD39,92(1989) E615 at Fermilab: 252 GeV π- + W
Azimuthal cos2φ Distribution in the W Drell-Yan
NA10 at CERN: 140/194/286 GeV π- + W Z. Phys. C37, 545 (1988)
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Possible Explanations for the cos2φ Asymmetry
The high twist effect.Brandenburg, Brodsky, Khoze & Muller, PRL73,939(1994).
The nuclear distortion of hadronic projectile wavefunction, typically a spin-orbit effect occurring on the nuclear surface.
Bianconi & Radici, JPG31,645(2005).
The spin correlation due to nontrival QCD vacuum.Brandenburg, Nachtmann & Mirkes, Z. Phy. C60,697(1993); …
The hadronic effect due to non-zero Boer-Mulders function h1┴ .
Boer, PRD60,014012(1999); …
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Higher Twist Effect?Higher twist effect leads to =-1 for low mass as x 1.
Berger & Brodsky, PRL42, 940 (1979); Berger, ZPC4,289(1980)
Higher twist effect in terms of pion bound state effect: Brandenburg, Brodsky, Khoze & Muller, PRL73,939(1994)
High twist in terms of pion bound state effect is not enough.
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Nuclear Effect?
NA10 Z. Phys. C37, 545 (1988)Open: DeuteriumSolid: Tungsten
Nuclear effect should not be the dominant contribution.
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The factorization-breaking spin correlation due to nontrivial QCD vacuum may fit the NA10 data at 194 GeVBrandenburg, Nachtmann & Mirkes, Z. Phy. C60,697(1993)
The helicity flip in the instanton-induced contribution may lead to nontrivial vacuum and violation of the Lam-Tung relation.Boer,Brandenburg,Nachtmann&Utermann, EPC40,55(2005).Brandenburg,Ringwald&Uermann, hep-ph/0605234
This vacuum effect should be flavor blind.
QCD Vacuum Effect
0=0.17mT=1.5
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Leading-Twist Quark Distributions
1ˆ
Tf T TS (p×k )
1( ) Lh T T Lk s S
1ˆ h T Ts (p×k )
Survive k┴ integration
k┴ - dependent, T-odd
k┴ - dependent, T-even
1Lg L LS s
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Boer-Mulders Function h1┴
An spin-correlation approach in terms of h1┴ can fit the NA10 data
at 194 GeV. Boer, PRD60,014012(1999)
On the base of quite general arguments, for |qT|<<Q(=m ),Salvo,hep-ph/0407208.
1=0.5mC=2.3T=CH=1
221 12 2
( , ) ( )T TkC HTT H
T C
M Mh x k c e f x
k M
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Models for Boer-Mulders Function h1┴
Initial-state gluon interaction can produce nonzero h1┴ for the
proton in the quark-scalar diquark model. In this model, h1
┴ =f1T┴.
Boer,Brodsky&Hwang, PRD67,054003(2003).Twist 2 (as well as the kinematic twist 4) contribution in a
parton-spectator framework Gamberg&Goldstein, hep-ph/0506127.
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Pion Boer-Mulders Function
Final-state interaction with one gluon exchange can produce nonzero h1
┴ for the pion in the quark-spectator-antiquark model with constant coupling g.
Lu&Ma, PRD70,094044(2004).The quark-spectator-antiquark model with effective pion-quark-
antiquark coupling as a dipole form factor Lu & Ma, hep-ph/0504184
The only model that can fit the NA10 data at different beam energy.
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On the basis of time reversal arguments: f1T
┴(x,pT2)=0
Collins, NPB396, 161(1993) Final-state interaction from gluon exchange
between the quark and the spectator lead to nonzero Sivers function.Brodsky, Hwang & Schmidt, PLB530, 99(2002).
Final-state interaction can be reproduced by a prescription of the light-cone singularities or an extra gauge link at the spatial infinity for the parton distributions.Ji & Yuan, PLB543,66(2002).
Add final state interaction to the time reversal arguments:
f1T┴(x,pT
2)SIDIS=-f1T┴(x,pT
2)DY
Collins, PLB536, 43(2002)
Sivers Function
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Models for Sivers Function f1T┴
•Calculation fit with MIT bag model in the presence of final state interaction through one gluon exchange
Yuan, PLB575, 45(2003)[hep-ph/0308157].•Calculation in a spectator model with axial-vector diquarks in the presence of gluon rescattering
Bacchetta, Schaefer & Yang, PLB578,109(2004)[hep-ph/0309246]•Calculation in a light-cone SU(6) quark-diquark modelLu & Ma, NPA741,200 (2004).
- -
These calculations are before HERMES’ transverse data .
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An Intuitive Explanation of Sivers Asymmetry
M. Burkardt, Phys. Rev. D66(2002)114005[hep-ph/0209179].
Кu=1.67Кd=-2.03
Attractive FSIf1T┴,q Кq <0 f1T
┴,u f1T┴,d <0
Attractive FSI
The quark distribution in transverse polarized nucleon is deformed because the superposition of translational and orbital motion
misleads the photons in the x.
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Sivers Function Extraction from HERMES Data
Fits to the Hermes data “Prediction” of the Compass data
, ,1 1Assuming ( ) (1 ) ( ); ( ) (1 ) ( )
0.81 0.07, 1.86 0.28
u dT u T d
u dS
f x S x x u x f x S x x u x
S
Vogelsang and Yuan, Phys.Rev.D72(2005)054028 [hep-ph/0507266]
Striking flavor dependence of the Sivers function
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Comparing Sivers Functions from HERMES
Ref.[20] M.Anselmino et al, Phys.Rev.D72(2005)094007[hep-ph/0507181] Ref.[21] W.Vogelsang & F.Yuan, Phys.Rev.D72(2005)054028[hep-ph/0507266]Ref.[23] J.C.Collins et al, hep-ph/0510342
Satisfactory qualitative agreement between different models.
M.Anselmino et al, hep-ph/0511017
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Comparing Boer-Mulders Functions from Models
(a)MIT bag model: F. Yuan, Phys. Lett. B575,45(2003).
(b)Spectator model with axial-vector diquark: Bacchetta, Schaefer & Yang, Phys. Lett. B578,109(2004).
(c)Large-NC limit, P.V. Pobylitsa, hep-ph/0301236
Knowledge of the Boer-Mulders functions is very poor.
Z. Lu, B.Q. Ma and I. schmidt, Phys. Lett. B639(2006)494.
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Unpolarized Semi-Inclusive DIS
TWIST-2
Cahn Effect QED Modulation of f1D1 term due to intrinsic transverse momentum. Anselmino et al., PRD71(2005) 074006
[hep-ph/0501196].Add to 2(1-y+y2/2):
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Prediction of cos2φ in SIDISBarone, Lu and Ma, Phys. Lett. B632(2006)277[hep-ph/0512145].
The LT curve is proportional to h1┴, estimated from πN Drell-Yan.
LT
HT(Cahn Effect)
Predictions
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Azimuthal Asymmetries in SIDIS from CLAS
CLAS 5.7 GeV (preliminary)
M.Osipenko
e+X
Significant cosΦ, cos2Ф observed at large PT with CLAS at 5.7 GeV
V. Barone
H. Avakian, Z.-E.Meziani,K.Joo and B.Seitz, JLab proposal PR12-06-112
Prediction for CLAS
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FNAL E866/NuSea experiment
Completed Data analysis:dbar/ubar sea asymmetryDrell-Yan cross sectionlambda for J/Ψ production lambda for upsilon production
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Drell-Yan Cross Section from E866
J.C.Webb et al., hep-ex/0302019.
The calculation with NLO world PDFs agrees with data.
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Angular Distribution of E866 p-Cu Data
•J/: = 0.069±0.004±0.08•Drell-Yan (M=4~7 GeV): = 0.98±0.04T.H. Chang et al., PRL91, 211801 (2003)
• (1s),(2s+3s): plotted against PT and xP.•Drell-Yan: (M=8.1~8.45,11.1~15.0 GeV) =1.008±0.016±0.020C.N. Brown et al., PRL86, 2529 (2001)
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Dimuon Mass Distribution
Data used for cos2φ analysis:High Mass: dset7-39k (+ polarity)
dset8-85k (+ polarity) dset11-25k (- polarity)
Low Mass: dset5-68k (+ polarity)
Towell et al., Phys.Rev. D64 (2001) 052002
Target: Proton, Deuterium
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Comparison of data and simulation
Blue: simulation
Red: data
(dset8)
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In terms of Boer-Mulders function h1┴:
ν(π-Wµ+µ-X)~ valence h1┴(π) * valence h1
┴(p)
ν(pdµ+µ-X)~ valence h1┴(p) * sea h1
┴(p)
Azimuthal cos2Φ Distribution in pd Drell-YanL.Y. Zhu,J.C. Peng, P. Reimer et al., hep-ex/0609005.
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Full Angular Distribution in pd Drell-Yan
L.Y. Zhu,J.C. Peng, P. Reimer et al., hep-ex/0609005.
No significant violation of Lam-Tung relation in pd Drell-Yan.
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Angular Distribution in E866 pp and pd Drell-Yan
pp and pd Drell-Yan show similar angular distribution.
Preliminary
Prelim
inary
PreliminaryPrelim
inary
PT (GeV/c)
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Modeling Sea Boer-Mulders Functions Group led by Z. Lu, B.Q. Ma and I. Schmidt
Meson-baryon fluctuation model:
Predictions depend on the choice of valence Boer-Mulders functions(I,II).
Group led by L. Gamburg and G. GoldsteinTwo possible contributions to sea from the gauge link.
Preliminary
p(I)d(I)
d(II)p(II)
Probing the sea Boer-Mulders functions may constrain the valence ones.
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Summary
Large cos2 azimuthal asymmetry has been observed in unpolarized -induced Drell-Yan.
The are a few possible explanations including the non-trivial vacuum effect and the non-zero Boer-Mulders function . The latter is related to the Sivers function.
The unpolarized p-induced Drell-Yan data show only percent-level cos2φ azimuthal asymmetry. This may disfavor the flavor blind explanation such as vacuum effect.
More data on unpolarized Drell-Yan will be availble from the future experiments at FNAL, RHIC with proton beam, COMPASS with pion beam and especially GSI, complementary to the SIDIS data at JLab and HERMES.
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Backup Slides
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Hadronic Effect vs. QCD Vacuum Effect
D.Boer, hep-ph/0511025
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The Large-x Behavior of the Quark Distributions
Survive k┴ integration
k┴-dependent, T-odd
Brodsky & Yuan, hep-ph/0610236.
k┴ - dependent, T-
even
Sivers and Boer-Mulders functions are one power of (1-x) suppressed.
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Vacuum Contribution to Sivers Function f1T┴
Sizable instanton-induced QCD vacuum contribution to the Sivers function, adopting MIT bag model for the quark wave functions.Cherednikov, D'Alesio, Kochelev & Murgia Phys.Lett.B642:39-47,2006 [hep-ph/0606238].
thin: instantonthick:one-gluon
thin:HERMESthick:total
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Polarized Drell-Yan
Assuming u-quark dominance
Burkardt Relation
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Unpolarized Semi-Inclusive DIS
Ulrike Elschenbroich, HERMES thesis, 2006.TWIST-2
TWIST-3
Cahn Effect QED Modulation of f1D1 term due to intrinsic transverse momentum. Anselmino et al., PRD71(2005) 074006
[hep-ph/0501196].
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Azimuthal moments in SIDIS (1/Q2)
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DY-experiments
E615 Fermilab 80-GeV -, 252-GeV + (1989) – 36000 muon pairs
NA10(1986) 194-GeV - tungsten target (145000 events)
QT-muon pair transverse momentum