Probing small-x gluons in hadrons and nuclei Kazuhiro Watanabe Old Dominion University Jan 4, 2017 Jefferson Lab Kazuhiro Watanabe (ODU) Probing gluon saturation dynamics at small-x Jan 4, 2017 1 / 16
Introduction Biography Educational Background 2009, B.S. at Tokyo University of Science Charmonium spectroscopy 2014, Ph.D at University of Tokyo (supervisors: T. Matsui and H. Fujii) Color Singlet Model for quarkonium production in hadronic collisions Study of heavy quark pair production in high energy pa collisions in the Color Glass Condensate framework Professional background 2014 2016: Postdoc researcher in Nuclear Theory Group at Central China Normal University. Small-x factorization, saturation physics, TMD physics 2016 Present: Postdoctoral researcher in ODU Nuclear Theory Group. Small-x and TMD physics Kazuhiro Watanabe (ODU) Probing gluon saturation dynamics at small-x Jan 4, 2017 2 / 16
Introduction My work Research interests Gluon saturation dynamics at small value of Bjorken variable x. Transverse momentum dependent gluon distribution in hadron/nucleus xf 1 H1 and ZEUS 2 Q 2 = 10 GeV 0.8 HERAPDF1.0 exp. uncert. 0.6 xg ( 0.05) model uncert. parametrization uncert. xu v 0.4 xs ( 0.05) xd v 0.2-4 10-3 10-2 10-1 10 1 x One large scale Q and dilute : collinear factorization. (At least) Two large scales Q Q Λ QCD and dilute : TMD factorization. Small-x and dense : Small-x saturation/color-glass-condensate (CGC). Unintegrated (Transverse momentum dependent) PDFs are important. Kazuhiro Watanabe (ODU) Probing gluon saturation dynamics at small-x Jan 4, 2017 3 / 16
Introduction My work Q. Is there any clear evidence of the gluon saturation? Not clear. Q. How to find out a smoking gun evidence of the gluon saturation? High energy ea collision provides clean tests. Future EIC and LHeC are promising, although we need to wait and prepare a lot of things. High energy pa collision is more or less complicated. However, we should learn invaluable lessons from pa and also pp collisions. Q. What kinds of measurements should we consider? Inclusive hadron Heavy quark pair (c c, b b) p + p/a h + X p + p/a J/ψ, Υ, D, D D, etc. + X Kazuhiro Watanabe (ODU) Probing gluon saturation dynamics at small-x Jan 4, 2017 4 / 16
Highlights Talk Plan 1 Introduction 2 Highlights J/ψ and Open charm productions : Phenomenology One loop factorization in the small-x formalism Sudakov effect in the small-x formalism 3 Future research plans Kazuhiro Watanabe (ODU) Probing gluon saturation dynamics at small-x Jan 4, 2017 5 / 16
Highlights J /ψ and Open charm productions : Phenomenology J/ψ and Open charm productions : Phenomenology KW, arxiv:1611.00700 [hep-ph]; H. Fujii and KW, Nucl. Phys. A 951, 45 (2016); Nucl. Phys. A 920, 78 (2013); Nucl. Phys. A 915, 1 (2013). p k1 pq p q k2 k k2 k A LO k t -factorization framework [Blaizot,Gelis,Venugopalan (2004)] [Kovchegov,Tuchin (2005)] dσ q q = Ξ LO Hard ϕ p,x 1 (k 1 ) φ A,x2 (k 2, k ) Unintegrated dipole gluon distribution function and multipoint Wilson line correlator (Large-N c ): ϕ p,x1 (k 1 ) = S p N c k 2 1 4α s F A x 1 (k 1 ). φ A,x2 (k 2, k ) = S A N c k 2 2 4α s F F x 2 (k 2 k )F F x 2 (k ) Small-x evolution for F x rcbk evolution equation. [Balitsky (2007)] Kazuhiro Watanabe (ODU) Probing gluon saturation dynamics at small-x Jan 4, 2017 6 / 16
Highlights J /ψ and Open charm productions : Phenomenology J/ψ and Open charm productions : Phenomenology KW, arxiv:1611.00700 [hep-ph]; H. Fujii and KW, Nucl. Phys. A 951, 45 (2016); Nucl. Phys. A 920, 78 (2013); Nucl. Phys. A 915, 1 (2013). Selected Results J/ψ: Color Evaporation Model Open charm: Functional form Fragmentation Function Key measurements: R pa = dσ p A Adσ p p, Two particle correlation 1.2 1 0.8 J/Ψ ALICE 1.2 s = 5.02 TeV, 2.5 < y < 4.0 1 0.8 0.25 0.2 (a) s = 7 TeV, 2 < y < 4 MV g1118 LHCb pp 3 < p D, p D - < 12 GeV/c R pa 0.6 0.4 LHC pa ( s = 5.02 TeV) forward (2.035 < y < 3.535) 0.2 Solid line; k -factorized formula Dotted line; Hybrid formula 0 0 1 2 3 4 5 6 p [GeV/c] RpA 0.6 0.4 Q 2 sa = 3Q2 sp 0.2 Prompt D 0 Q 2 sa = 4Q2 sp LHCb (Prelim) 0 0 1 2 3 4 5 6 p [GeV] Q 2 sa = 2Q2 sp 1/σ dσ/d Φ 0.15 0.1 0.05 0 0 0.2 0.4 0.6 0.8 1 Φ /π These results are first numerical implementations. Cold Nuclear Matter effect is a hot issue. Many things to do! NLO calculation is strongly desired. Kazuhiro Watanabe (ODU) Probing gluon saturation dynamics at small-x Jan 4, 2017 7 / 16
Highlights One loop factorization in the small-x formalism One loop factorization in the small-x formalism KW and B.-W. Xiao, Phys. Rev. D 92, no. 11, 111502 (2015): KW, B.-W. Xiao, F. Yuan and D. Zaslavsky, Phys. Rev. D 92, no. 3, 034026 (2015) Inclusive hadron production: p + p/a h + X First NLO calculations in pa are done by [Chirilli, Xiao, Yuan (2011)] x y + + + Full NLO calculations in pa [KW, Yuan, Xiao, Zaslavsky (2015)], in pp [KW, Xiao (2016)]: Exact light cone energy conservation: x P = l 2 l 2 2(1 ξ)xp + + k2 2ξ xp + P leads to the constraint ξ 1 l2 xs. xs provides double logarithmic power corrections in coordinate space. (Similar to Sudakov double logs.) ((1 ξ)xpp +, l ) (xpp +, 0 ) (ξxpp +, k ) x g P Kazuhiro Watanabe (ODU) Probing gluon saturation dynamics at small-x Jan 4, 2017 8 / 16
Highlights One loop factorization in the small-x formalism One loop factorization in the small-x formalism KW and B.-W. Xiao, Phys. Rev. D 92, no. 11, 111502 (2015): KW, B.-W. Xiao, F. Yuan and D. Zaslavsky, Phys. Rev. D 92, no. 3, 034026 (2015) Numerical Results: LO+NLO+Double logs in Hybrid formalism Beyond Hybrid formalism k -factorization for projectile proton. Kazuhiro Watanabe (ODU) Probing gluon saturation dynamics at small-x Jan 4, 2017 9 / 16
Highlights Sudakov effect in the small-x formalism Sudakov effect in the small-x formalism KW and B.-W. Xiao, Phys. Rev. D 92, no. 11, 111502 (2015) Indeed, for heavy quarkonium production, two kinds of resummation parameters involve in the small-x formalism: [Mueller, Xiao, Yuan (2013)] [Qiu, Sun, Xiao, Yuan (2013)] α s N c ln x 1 = O(1) BK equation α s N c ln 2 M2 = O(1) CSS equation p 2 We improved heavy quark pair production cross section in the b -space to include both the saturation effect and the Sudakov effect. [KW, Xiao (2015)] dσ q q d 2 x d 2 y (2π) 4 ( e ik x e i(k 2 k ) y S Y (x )S Y (y )x 1 G µ = c ) 0 v e S Sud(M,v ) } {{ } W term x v k2 k k y + Kazuhiro Watanabe (ODU) Probing gluon saturation dynamics at small-x Jan 4, 2017 10 / 16
Highlights Sudakov effect in the small-x formalism Sudakov effect in the small-x formalism KW and B.-W. Xiao, Phys. Rev. D 92, no. 11, 111502 (2015) Numerical Results: Sudakov + Saturation effects dσ / dp dy (nb / (GeV/c)) 10 4 10 3 10 2 J/Ψ w/o Sudakov: µ = 2-30 GeV w/ Sudakov: b max = 0.5 GeV -1 LHCb s = 7 TeV, Y = 4.25 Br dσ / dp dy (pb / (GeV/c)) 10 2 Υ(1S) w/o Sudakov: µ = 5-30 GeV w/ Sudakov: b max = 0.5 GeV -1 LHCb s = 7 TeV, Y = 4.25 10 1 0 1 2 3 4 5 6 7 8 P (GeV/c) 10 1 0 1 2 3 4 5 6 7 8 P (GeV/c) - Sudakov factor is essential to interpret the data (large P broadening). - This framework breaks down around P M. We need to add Y-term". We must obtain the Sudakov factor in the NLO saturation formalism. We need to investigate other observables for which both Sudakov & Saturation effects are important. Kazuhiro Watanabe (ODU) Probing gluon saturation dynamics at small-x Jan 4, 2017 11 / 16
Highlights Sudakov effect in the small-x formalism One more thing: CSS evolution & Small-x evolution Mueller-Navelet jets (forward-backward dijets) production in pp collisions a(p 1 ) + b(p 2 ) c(k 1 ) + d(k 2 ). dσ d 2 k 1 d 2 k 2 dy 1 dy 2 = σ 0 ab d 2 b (2π) 2 e iq b W (b ) with W ab cd (b ) = x 1 f a (x 1, µ)x 1 f b (x 2, µ)h ab cd (ŝ, ˆt)e S ab c d (P J,b ) S NN = 7 TeV, 35 GeV < P J < 1000 GeV S NN = 7 TeV, 35 GeV < P J < 1000 GeV S NN = 7 TeV, 35 GeV < P J < 1000 GeV 10 1 0 < Y < 3 10 1 3 < Y < 6 10 1 6 < Y < 9.4 CMS CMS CMS 10 0 w/o x-resummation 10 0 w/o x-resummation 10 0 w/o x-resummation 1/σ dσ/dφ 10-1 1/σ dσ/dφ 10-1 1/σ dσ/dφ 10-1 10-2 10-2 10-2 10-3 0 0.5 1 1.5 2 2.5 3 10-3 0 0.5 1 1.5 2 2.5 3 10-3 0 0.5 1 1.5 2 2.5 3 Φ Φ Φ Clearly, BFKL evolution is required on top of CSS evolution to interpret data. Sudakov + BFKL is underway with Mueller, Szymanowski, Wallon, Xiao, Yuan. Kazuhiro Watanabe (ODU) Probing gluon saturation dynamics at small-x Jan 4, 2017 12 / 16
Future research plans Talk Plan 1 Introduction 2 Highlights J/ψ and Open charm productions : Phenomenology One loop factorization in the small-x formalism Sudakov effect in the small-x formalism 3 Future research plans Kazuhiro Watanabe (ODU) Probing gluon saturation dynamics at small-x Jan 4, 2017 13 / 16
Future research plans Future research plans (I) Saturation effect as a CNM effect for quarkonium, open flavor productions Calculate NLO contributions to quarkonium production with use of various models of bound state formation (CEM, NRQCD). Verify that Sudakov double logarithms appeared systematically in the small-x formalism. Reduce uncertainties of higher order corrections. More clean process than pa collision DIS, SIDIS, Dijet, Quarkonium, D D productions in ep/ea scatterings. Various hard scales: Q, p, M dijet, Q s, Verify that Sudakov double logs and Small-x logs are involved. Powerful tools: Operator Product Expansion and Lightcone Perturbation Theory. Kazuhiro Watanabe (ODU) Probing gluon saturation dynamics at small-x Jan 4, 2017 14 / 16
Future research plans Future research plans (II) Saturation effect in Spin physics Q. Saturation effect is important for quarkonium production in p p and p A collisions? Yes, it should be important. It is possible to examine so-called Sivers effect at intermediate or small-x in p p or p A collisions by employing polarized TMDs. Q. How about ep and ea collisions? It is possible. Direct probe to access gluon TMD in hadron or nuleus. Model dependence : CEM, NRQCD [see, Yuan (2008)] Kazuhiro Watanabe (ODU) Probing gluon saturation dynamics at small-x Jan 4, 2017 15 / 16
Future research plans My potential contributions to physics at JLab TMD PDFs are the key issues at Theory group. Polarized& Unpolarized TMDs are process dependent and x-evolution of TMD PDFs are not understood well. I can study TMDs from small-x viewpoint by considering SIDIS & Dijet in DIS in terms of Lightcone Perturbation Theory or Operator Product Expansion. Exploring the onset of the gluon saturation in nucleus is the important issue in future Medium energy EIC at JLab. The initial condition for BK equation for nucleus is poorly understood due to lack of precise data of Nuclear DIS. Data analysis of dihadron or dijet production at MEIC could solve this problem. Kazuhiro Watanabe (ODU) Probing gluon saturation dynamics at small-x Jan 4, 2017 16 / 16
Backup slides Backup slides 4 Backup slides Kazuhiro Watanabe (ODU) Probing gluon saturation dynamics at small-x Jan 4, 2017 1 / 4
Backup slides Conventional TMD framework One loop calculations in NRQCD factorization framework [Sun, Yuan, Yuan (2012)] dσ d 2 P dy P M = d 2 b (2π) 2 eip b W (M, b, x 1, x 2 ) + (Y term) with W (M, b, x 1, x 2 ) = e S su d (M,b ) W (M, b, C 1, C 2 ) M 2 dx dx ( W (M, b, C 1, C 2 ) = σ 0 s x x C x1 ) ( x2 ) gg C gg x x G(x 1, µ)g(x 2, µ) TMD factorization [Collins-Soper-Sterman (1985)] [Collins (2011)] Y-term is power suppressed by P /M at low P µ = c 0 b with c 0 = 2e γ E 1 Kazuhiro Watanabe (ODU) Probing gluon saturation dynamics at small-x Jan 4, 2017 2 / 4
Backup slides Collins-Soper-Sterman (CSS) formalism Split the Sudakov factor into two parts S Sud (M, b) = S per p (M, b ) + S NP (M, b) with b = b 1 + (b/bmax ) 2 Perturbative : b b b max S per p (M, b) = M 2 dµ 2 c 0 /b 2 µ 2 [ A ln ( ) M 2 µ 2 ] + B A = i=1 A ( ) (i) α s i, π B = i=1 B ( ) (i) α s i. π A (1) = C A and B (1) = (b 0 + δ 8c /2)N c with b 0 = ( 11 6 N c n ) f 1 3 N c. Non-perturbative : b > b max [Sun, Yuan, Yuan (2012)] ( ( ) )] M S NP (M, b) = exp [b 2 g 1 g 2 ln g 1 g 3 ln(100x 1 x 2 ) 2Q 0 g 1 = 0.03, g 2 = 0.87, g 1 g 3 = 0.17 with Q 0 = 1.6 GeV, b max = 0.5 GeV. Kazuhiro Watanabe (ODU) Probing gluon saturation dynamics at small-x Jan 4, 2017 3 / 4
Backup slides Lesson from conventional TMD calculation [Sun, Yuan, Yuan (2012)] Left fig: J/ψ at LHC forward, RHIC mid and forward. Right fig: Υ at LHC forward. The agreement between theoretical results and experimental data for J/ψ production is not as good as that for Υ production Kazuhiro Watanabe (ODU) Probing gluon saturation dynamics at small-x Jan 4, 2017 4 / 4