高能物理学会第八届全国会员代表大会暨学术年会 Azimuthal Asymmetry in Semi-Inclusive Deep-Inelastic Lepton-Nucleon Scattering 梁作堂 (Liang Zuo-tang) 山东大学物理学院 (School of Physics, Shandong University) 南昌, 2010年4月18日 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

山东大学(Shandong University) Contents Introduction Collinear expansion in Semi-inclusive deeply inelastic eN scattering (SIDIS) Azimuthal asymmetry in SIDIS Nuclear dependence of the azimuthal asymmetry in SIDIS Summary and outlook 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

山东大学(Shandong University) Introduction High energy reactions Structure of Nucleon Inclusive Deep-Inelastic Scattering (DIS) Parton Distribution Functions Semi-Inclusive Deep-Inelastic Scattering (SIDIS) Parton Correlation Functions e.g. Sivers function ... ... ... ... 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

山东大学(Shandong University) Introduction Tasks: (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 correlation functions. For inclusive DIS (1) (2) Global fit PDF parametrizations (3) Simple probability interpretaion of the PDF’s azimuthal asymmetries are examples of the sensitive measurable quantities. For SIDIS 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

Azimuthal asymmetry in unpolarized SIDIS 1977: Georgi & Politzer, “Clean test to pQCD”, Phys. Rev. Lett. 40,3 (77). lepton plane 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

Azimuthal asymmetry in unpolarized SIDIS 1978: Cahn, Intrinsic momentum 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) 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

Azimuthal asymmetry in polarized SIDIS lepton plane defined w.r.t. the lepton plane defined w.r.t. the polarization direction History: triggered by single-spin asymmetry in p()+p+X 1993, Collins: Proof of non-existence using the definition of p.d.f. 2002, 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: 1993’s proof is wrong because forgot gauge link. 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

Azimuthal asymmetry in SIDIS Lessons: intrinsic transverse momentum (higher twist) and gauge link are important in studying azimuthal 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? 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

高能物理学会第八届全国会员代表大会暨学术年会 Gauge link in p.d.f. and Collinear expansion in DIS and SIDIS 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

Inclusive DIS: where does the gauge link come from? DIS without QCD interaction The hard part: contracted with the leptonic tensor The matrix element: parton distributions No QCD interactions. Not (color) gauge invariant. 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

Inclusive DIS with QCD interaction … Parton distribution/correlation: Not gauge invariant! 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

Inclusive DIS with QCD interaction Ellis, Furmanski, Petronzio, (82) Qiu, Sterman (90,91) Collinear expansion:  Expanding the hard parts around k =xp:  Decomposition of the gluon field:  Using the identities such as, to replace the derivatives etc. 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

Inclusive DIS with QCD interaction Contain QCD interactions. (Color) gauge invariant ! 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

Semi-Inclusive DIS with QCD interaction Consider first e +p e + q + X, i.e., NO fragmentation We successfully showed that, the same collinear expansion technique applies, and it leads to Liang & Wang, PRD (2007). 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

高能物理学会第八届全国会员代表大会暨学术年会 Some of the consequences: (1) SIDIS e+pe+q+X upto twist-3 Liang 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: 1001.3146 [hep-ph] . (4) Twist-4 contributions and cos2 Song, Gao, Liang and Wang, in preparation. 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

SIDIS with (leading twist): Direct consequence I Consider the contribution from Cross section for e+pe+q+X Parton distributions = Cross section for eqeq without  (without transverse momentum)  (with transverse momentum) 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

SIDIS with (twist 3): Direct consequence II A simplification of left cut independent of x2! right cut independent of x1! 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

SIDIS with (twist 3): Direct consequence II This leads to Only is relevant in semi-inclusive deep-inelastic lepton-nucleon scattering. 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

SIDIS with (twist 3): differential cross-section to 1/Q Unpolarized SIDIS:  Expanding the matrices ’s in terms of ’s:  The general Lorentz-structure of the coefficient functions are: un-integrated parton distriution/correlation functions  Equation of motion 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

SIDIS with (twist 3): differential cross-section to 1/Q Unpolarized SIDIS: Differential cross section: Azimuthal asymmetry: which reduces to Cahn’s result if we set g=0 so that Transverse momentum dependent (TMD) quark distribution: A practical way to study the parton correlation function 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

Transverse momentum broadening in nucleus Transverse momentum dependent (TMD) quark distribution: Gauge link comes from: + +…+ … +… Replace N by A, the gluons can connect to different nucleons in A. Nuclear enhancement or transverse momentum broadening Transverse momentum broadening should be obtained from the gauge link. 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

Transverse momentum dependent PDF in nucleus With “maximal two gluon approximation”, i.e., only maximal two gluons are connected to one nucleon transverse momentum broadening squared nucleon density in nucleus A gluon distribution function in nucleon N 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

Nuclear dependence of the azimuthal asymmetry Azimuthal asymmetry in Azimuthal asymmetry in Nuclear dependence of TMD parton distribution/correlation functions 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

Nuclear dependence of the azimuthal asymmetry An example: take a Gaussian for the transverse momentum dependence for the case that suppressed! Integrated over : 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

SIDIS with (twist 4): differential cross-section to 1/Q2 Unpolarized SIDIS: Differential cross section (up to twist 4): The asymmetry: Another parton correlation function: 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

山东大学(Shandong University) Summary Progresses have been made in finding the correct relation between measurable quantities in SIDIS and parton correlation functions. Collinear expansion has been extended to SIDIS e+pe+q+X. Naïve 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 carried out. In “maximal two gluon approximation”, Azimuthal asymmetry in eA is suppressed, e.g. 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌

Thank you for your attention! Outlook Liang Zuo-tang et al (Shandong University) ........... Ma Bo-qiang et al (Peking University) ................ Chen Xiang-song et al (Hua-zhong University of Science and Technology) ................ Joint efforts in (1) A complete calculation including fragmentation, both in unpolarized and polarized case, also to other reactions; (2) Phenomenology of the related parton correlation functions; (3) Physical interpretation of the related parton correlation functions. Thank you for your attention! 山东大学(Shandong University) 2010年4月　高能物理学会学术年会 南昌