高能物理學會第八屆全國會員代表大會暨學術年會

1、高能物理學會第八屆全國會員代表大會暨學術年會 Azimuthal Asymmetry in Semi-Inclusive Deep-Inelastic Lepton-Nucleon Scattering梁作堂 (Liang Zuo-tang)南昌, 2010年4月18日山東大學物理學院(School of Physics, Shandong University)2010年4月高能物理學會學術年會 南昌1山東大學(Shandong University)ContentsIntroductionCollinear expansion in Semi-inclusive deeply inelas

2、tic eN scattering (SIDIS)Azimuthal asymmetry in SIDISNuclear dependence of the azimuthal asymmetry in SIDISSummary and outlook2010年4月高能物理學會學術年會 南昌2山東大學(Shandong University)IntroductionHigh energy reactionsParton Distribution FunctionsParton Correlation Functionse.g. Sivers function . . . .Semi-Inclu

3、sive Deep-InelasticScattering (SIDIS)Inclusive Deep-Inelastic Scattering (DIS)Structure of Nucleon2010年4月高能物理學會學術年會 南昌3山東大學(Shandong University)IntroductionTasks:For inclusive DIS(1)(2) Global fitPDF parametrizations(3) Simple probability interpretaion of the PDFsFor SIDISazimuthal asymmetries are e

4、xamples of the sensitive measurable quantities.(1) Establish the relation between the measurable quantities and the parton distribution and/or correlation functions;(2) Phenomenology of the parton distribution and correlation functions;(3) Physical interpretation of the parton distribution and corre

5、lation functions.2010年4月高能物理學會學術年會 南昌4山東大學(Shandong University)Azimuthal asymmetry in unpolarized SIDIS1977: Georgi & Politzer, “Clean test to pQCD”, Phys. Rev. Lett. 40,3 (77).lepton plane2010年4月高能物理學會學術年會 南昌5山東大學(Shandong University)Azimuthal asymmetry in unpolarized SIDIS1978: Cahn, Intrinsic mom

6、entum effects. Phys. Lett. B78B, 269 (1978).Generalized parton model to include an intrinsic transverse momentum but no gluon radiation in the final state:(higher twist, power suppressed)2010年4月高能物理學會學術年會 南昌6山東大學(Shandong University)Azimuthal asymmetry in polarized SIDISHistory: triggered by single-

7、spin asymmetry in p()+p+X2002, Brodsky, Hwang, Schmidt: an explicit example of the existence of the asymmetry by taking quark orbital angular momentum & “final state interaction” (multi-parton scattering) into account.Collins: 1993s proof is wrong because forgot gauge link. lepton planedefined w.r.t

8、. the lepton planedefined w.r.t. the polarization direction1993, Collins: Proof of non-existence using the definition of p.d.f. 2010年4月高能物理學會學術年會 南昌7山東大學(Shandong University)Azimuthal asymmetry in SIDISLessons:intrinsic transverse momentum (higher twist) and gauge link are important in studying azim

9、uthal asymmetries in SIDIS. Questions:What is gauge link? where does it come from?What is the relation between the asymmetries and higher twist parton correlation functions?2010年4月高能物理學會學術年會 南昌8山東大學(Shandong University)高能物理學會第八屆全國會員代表大會暨學術年會Gauge link in p.d.f. andCollinear expansion in DIS and SIDI

10、S2010年4月高能物理學會學術年會 南昌9山東大學(Shandong University)Inclusive DIS: where does the gauge link come from?DIS without QCD interactionNo QCD interactions.Not (color) gauge invariant.contracted with the leptonic tensorparton distributionsThe hard part:The matrix element:2010年4月高能物理學會學術年會 南昌10山東大學(Shandong Uni

11、versity)Inclusive DIS with QCD interactionNot gauge invariant!Parton distribution/correlation:2010年4月高能物理學會學術年會 南昌11山東大學(Shandong University)Inclusive DIS with QCD interactionCollinear expansion: Decomposition of the gluon field:Ellis, Furmanski, Petronzio, (82) Qiu, Sterman (90,91) Expanding the ha

12、rd parts around k =xp: Using the identities such as,to replace the derivatives etc.2010年4月高能物理學會學術年會 南昌12山東大學(Shandong University)Inclusive DIS with QCD interactionContain QCD interactions.(Color) gauge invariant !2010年4月高能物理學會學術年會 南昌13山東大學(Shandong University)Semi-Inclusive DIS with QCD interaction

13、Consider first e +p e + q + X, i.e., NO fragmentationLiang & Wang, PRD (2007).We successfully showed that, the same collinear expansion technique applies, and it leads to2010年4月高能物理學會學術年會 南昌14山東大學(Shandong University)高能物理學會第八屆全國會員代表大會暨學術年會Some of the consequences: (1) SIDIS e+pe+q+X upto twist-3 Lia

14、ng and Wang, Phys. Rev. D (2007) (2) Transverse momentum broadening in nucleus Liang, Wang & Zhou, Phys. Rev. D (2008) (3) Nuclear dependence of the azimuthal asymmetry. Gao, Liang and Wang, arXiv: 1001.3146hep-ph . (4) Twist-4 contributions and cos2 Song, Gao, Liang and Wang, in preparation.2010年4月

15、高能物理學會學術年會 南昌15山東大學(Shandong University)SIDIS with (leading twist): Direct consequence IConsider the contribution from Cross section for e+pe+q+XParton distributionsCross section for eqeq without=(with transverse momentum)(without transverse momentum)2010年4月高能物理學會學術年會 南昌16山東大學(Shandong University)SI

16、DIS with (twist 3): Direct consequence IIA simplification of right cutleft cutindependent of x2!independent of x1!2010年4月高能物理學會學術年會 南昌17山東大學(Shandong University)SIDIS with (twist 3): Direct consequence IIThis leads toOnlyis relevant in semi-inclusive deep-inelastic lepton-nucleon scattering.2010年4月高

17、能物理學會學術年會 南昌18山東大學(Shandong University)SIDIS with (twist 3): differential cross-section to 1/QUnpolarized SIDIS: Expanding the matrices s in terms of s: The general Lorentz-structure of the coefficient functions are: Equation of motionun-integrated parton distriution/correlation functions2010年4月高能物理

18、學會學術年會 南昌19山東大學(Shandong University)SIDIS with (twist 3): differential cross-section to 1/QUnpolarized SIDIS: Differential cross section:Azimuthal asymmetry:A practical way to study the parton correlation functionwhich reduces to Cahns result if we set g=0 so that Transverse momentum dependent (TMD)

19、 quark distribution:2010年4月高能物理學會學術年會 南昌20山東大學(Shandong University)Transverse momentum broadening in nucleusReplace N by A, the gluons can connect to different nucleons in A. Gauge link comes from: +Nuclear enhancement or transverse momentum broadeningTransverse momentum broadening should be obtaine

20、d from the gauge link.Transverse momentum dependent (TMD) quark distribution:2010年4月高能物理學會學術年會 南昌21山東大學(Shandong University)Transverse momentum dependent PDF in nucleusWith “maximal two gluon approximation”, i.e., only maximal two gluons are connected to one nucleontransverse momentum broadening squ

21、aredgluon distribution function in nucleon Nnucleon density in nucleus A2010年4月高能物理學會學術年會 南昌22山東大學(Shandong University)Nuclear dependence of the azimuthal asymmetryAzimuthal asymmetry in Azimuthal asymmetry in Nuclear dependence of TMD parton distribution/correlation functions 2010年4月高能物理學會學術年會 南昌23

22、山東大學(Shandong University)Nuclear dependence of the azimuthal asymmetryAn example: take a Gaussian for the transverse momentum dependencefor the case that suppressed! Integrated over :2010年4月高能物理學會學術年會 南昌24山東大學(Shandong University)SIDIS with (twist 4): differential cross-section to 1/Q2Unpolarized SI

23、DIS: Differential cross section (up to twist 4):The asymmetry:Another parton correlation function:2010年4月高能物理學會學術年會 南昌25山東大學(Shandong University)Collinear expansion has been extended to SIDIS e+pe+q+X.Nave extension of TMD parton distributions convoluting with e+q e+q cross section to include intrinsic transverse momentum is incorrect. The existence of the projection operator simplifies the higher twist calculations very much. Calculations up to twist 4 have been