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TMD Evolution Feng Yuan Lawrence Berkeley National Laboratory 8/3/2017 1 TMDs: center piece of nucleon structure QCD: Factorization, Universality, Evolution, Lattice, … Long. Momentum distributions Nucleon Spin 3D imaging Transverse-momentum-dependent and Generalized PDFs 2 TMDs at small-x kt-dependence crucial to the saturation 3 TMDs in valence region Alex Prokudin @EIC-Whitepaper Quark Sivers function leads to an azimuthal asymmetric distribution of quark in the transverse plane 8/3/2017 4 Evolution is crucial to strength the TMD probes Two particle correlations from pp to dAu Evolution? Saturation? 5 Sign change of Sivers asymmetry Drell-Yan, π- (190GeV)p COMPASS Q2~3-6GeV2 8/3/2017 Q2~16-30GeV2 6 Outlines General theory background Applying to single spin asymmetries Consistent resummation in high enegy BFKL vs Sudakov 8/3/2017 7 Collinear vs TMD factorization TMD factorization is an extension and simplification to the collinear factorization Extends to the region where collinear fails Simplifies the kinematics Power counting, correction 1/Q neglected (PT,Q)=H(Q) f1(k1T,Q) f2(k2T, Q) S(T) There is no x- and kt-dependence in the hard factor 8/3/2017 8 DGLAP vs CSS DGLAP for integrated parton distributions One hard scale (Q)=H(Q/) f1()… Collins-Soper-Sterman for TMDs Two scales, large double logs 8/3/2017 9 Evolution vs resummation Any evolution is to resum large logarithms DGLPA resum single large logarithms CSS evolution resum double logarithms 8/3/2017 10 Sudakov Large Double Logarithms Sudakov, 1956 Differential cross section depends on Q1, where Q2>>Q12>>2QCD We have to resum these large logs to make reliable predictions QT: Dokshitzer, Diakonov, Troian, 78; Parisi Petronzio, 79; Collins, Soper, Sterman, 85 Threshold: Sterman 87; Catani and Trentadue 89 11 How Large of the Resummation effects Resum NLO Kulesza, Sterman, Vogelsang, 02 12 Collins-Soper-Sterman Resummation Introduce a new concept, the Transverse Momentum Dependent PDF Prove the Factorization in terms of the TMDs (PT,Q)=H(Q) f1(k1T,Q) f2(k2T, Q) S(T) Large Logs are resummed by solving the energy evolution equation of the TMDs (Collins-Soper 81, Collins-Soper-Ste 13 CSS Formalism (II) K and G obey the renormalization group eq. The large logs will be resummed into the exponential form factor A,B,C functions are perturbative calculable. (Collins-Soper-Sterman 85) 14 Two Large Scales Processes Very success in applications, DIS and Drell-Yan at small PT (QT Resum) DIS and Drell-Yan at large x (Threshold Resum) Higgs production at small PT or large x Thrust distribution Jet shape function … ResBos: Nadolsky, et al., PRD 2003 CSS resummation built in 15 Single Transverse Spin Asymmetry Separate the singular and regular parts TMD factorization in b-space 8/3/2017 Kang, Xiao, Yuan, PRL 11; Rogers et al., PRD, 2012 16 Evolution equations Idilbi-Ji-Ma-Yuan, PRD04 Boer, NPB, 2002 8/3/2017 17 Final resum form Sudakov the same 8/3/2017 18 Coefficients at one-loop order 8/3/2017 19 Constraints from SIDIS Sun, Yuan, 1308.5003 8/3/2017 20 DIS and Drell-Yan Initial state vs. final state interactions * * Drell-Yan DIS HERMES/C OMPASS “Universality”: QCD prediction 21 Predictions for COMPASS Drell-Yan, π- (190GeV)p COMPASS Q2~3-6GeV2 8/3/2017 Q2~16-30GeV2 22 Fermilab Drell-Yan 120GeV proton beam 8/3/2017 23 Few words on Drell-Yan at RHIC Never been measured before at a collider Fixed target W/Z at Tevatron/LHC Understand the x-evolution of the TMDs, saturation? Compared to that from HERA 8/3/2017 24 Drell-Yan at Fixed Target QT spectrum from E288, PRD23,604(81) Valence region 25 At very large Q2 (e.g., Z0 and W boson), No longer a Gaussian 26 Predictions at RHIC √S = 500GeV Drell-Yan Q=6GeV Additional theory uncertainties: x-dependence of the TMDs comes from a fit to fixed target drell-yan and w/z production at Tevatron ---Nadolsky et al. Sun, Yuan, 1308.5003 8/3/2017 27 y=0 Pt(GeV) y=0 √S = 510GeV Pt(GeV) -0.06 -0.06 Rapidity of8/3/2017 W Rapidity of W 28 QCD evolution reduces the asymmetries about a factor of 3 for W/Z as compared to Drell-Yan 29 Uniqueness of forward RHIC physics Investigate the sign change of Sivers asymmetries and the associated QCD evolution effects in Drell-Yan and W SSAs Mapping out the saturation physics in dihadron and single-hadron production in forward pA collisions Complementary to the EIC Missions!! 8/3/2017 30 Kt-dependent observables PJ>>KT KT CSS 8/3/2017 Hard processes probe the kt-dependent gluon distributions directly Saturation phenomena manifest in the observables Xiao,Yuan, et al, PRL106, 022301 (2011) 31 PRL105, 062001 (2010) Resummation: Sudakov vs BFKL Sudakov double logs can be re-summed in the small-x saturation formalism Radiated gluon momentum Soft gluon, α~β<<1 Collinear gluon, α~1, β<<1 Small-x collinear gluon, 1-β<<1, α0 Rapidity divergence Mueller, Xiao, Yuan, PRL110,082301 (2013); 8/3/2017 arXiv:1308.2993 32 Final result Double logs at one-loop order Collins-Soper-Sterman resummation 8/3/2017 33 Comments Sudakov double logs can be re-summed consistently in the small-x formalism Kinematics of double logs and small-x evolution are well separated Soft vs collinear gluons If Qs is small, back to dilute region If Qs is large (~Q), we can safely neglect the Sudakov effects 8/3/2017 34 Sudakov leading double logs: general hard processes Each incoming parton contributes to a half of the associated color factor Initial gluon radiation, aka, TMDs Soft gluon radiation in collinear calculation also demonstrates this rule Sterman, et al Sub-leading logs will be much complicated, usually a matrix form Mueller, Xiao, Yuan, PRL110,082301 (2013); 8/3/2017 arXiv:1308.2993 35 all order factorization 8/3/2017 Similar calculations for pp collisions: 36 Zhu HX, et al., PRL110 (2013) 082001 Dijet azimuthal correlation at colliders preliminary LO NLLresummation Peng Sun, et al. will be extended to di-hadrons, PRL 94, 221801 (2005) 8/3/2017 37 Two particle correlations in Central dAu collisions η1~η2~3.2 Q2sA~0.85A(1/3) Qsp2 Stasto,Xiao,Yuan,PLB716,430(2012) 38 Conclusions TMDs are important tool to investigate the partonic structure of nucleon/nucleus, and the associated QCD dynamics Although complicated, the evolution effects have been well understood Provide solid ground for phen. Applications Unique place to study QCD 8/3/2017 39