Institute of Particle Physics, Central China Normal University

Transcription

1 in Institute of Particle Physics, Central China Normal University / 6

2 Deep into lowx region in Partons in the lowx region is dominated by gluons. See HERA data. BFKL equation Resummation of the α s ln x. When too many gluons squeezed in a confined hadron, gluons start to overlap and recombine Nonlinear dynamics BK (JIMWLK) equation Use Q s(x) to separate the saturated dense regime from the dilute regime. Core ingredients: Multiple interactions + Smallx (high energy) evolution / 6

3 e+a and p+a provide excellent information on properties of gluons in the nuclear wave functions Both are complementary and offer the opportunity to perform stringent checks of factorization/universality Issues: p+a combines initial and final state effects multiple colour interactions in p+a p+a lacks the direct access to x, Q in physics (Color Glass Condensate) Scattering of protons on protons is like colliding physics Swiss describes watches to high find out density how they parton are distributions at high energy limit. built. R. Feynman p x correlation in p+p is an inevitable consequence of QCD dynamics at high energy. Operation Hard Probes : macl@bnl.gov in and R. Feynman used to say: Scattering protons on protons is like banging two fine Swiss watches to find out how they are built. future operations. Using AA collisions to search for saturation is too hard due to factorization issues: Finding a needle in a haystack he search for parton saturation is much easier in dilutedense scatterings.. single hadron ( and ea);. dijet (dihadron) correlation ( and ea). / 6

4 in of some phenomenological predictions to LHC data for the particle multiplicities in both protonproton and leadlead collisions factorizations was presented by the ALICE collaboration k t factorization vs DiluteDense [].) he k factorization formula used in this area is (see, k t factorization for single inclusive e.g., Ref. [8, gluon Eq. productions ()]): in hadronhadron collision: dσ d p dy = α s C F p d k A, f A (x A,k A, ) f B (x B,p k A, ). () Here f A and f B are MD densities of gluons in their ization and NLO parent correction? hadrons, Only and the proved two gluons for DYcombine and Higgs to give! an For dijet processes inoutgoing pp, AA gluon collisions, of transverse no k t factorization[collins, momentum p whichqiu, gives rise to an observed jet in the final state. In the formula, 8],[Rogers, Mulders; ]. C F = (Nc )/N c with N c = for QCD, y is the Observation at high energy s DiluteDense factorizations rapidity of the finalstate jet, and x A,B =(p / s)e ±y. he incoming hadrons A and B can be protons or nuclei. Questions that now naturally arise are: Where does projectile: x p e +y this formula originate from? Where can s valence a proper derivation be found, and under target: what x conditions p e y and gluon to what accuracy is the derivation valid? What s are the explicit definitions of the unintegrated distributions f A,B,anddo! Protons he spin and asymmetry virtual photons these becomes definitions are dilute the largest overcome probes at forward of the the subtleties dense rapidity target that region, are hadrons. found corresponding to in constructing definitions of MD distributions in QCD For dijet productionsin inthe forward nonsmallx collisions, regime [, effective Chs. k! & t factorization: he partons in the projectile (the polarized proton) have very large ]? momentum In an ideal fraction x: dominated world, by the we valence couldquarks say that (spin ineffects orderare forvalence the requirements effects) dσ() () ggx to be fulfilled, it is absolutely necessary that! he partons in the target (the unpolarized =x proton or nucleus) have very small momentum fraction these x: dominated questions by be pg(x the answered, p, µ)x Ag(x smallx gluons and A, q d P d that ) dˆσ q dy dy a person π dˆt. who reads a paper which makes use of this formula can, if needed,! hus spin asymmetry go in back the toforward the original region source could and probe himself/herself both repro / 6 normal alone e demons ization pendice the nor here a cal issu fully sa issues g the exi is a dia sympto criterio explicit tion fac At th chosen [8 ] t highly exist a (), so indicat is given whethe hat approx dipole lations here structu

5 A 68, USA O) on the forward rmed in the large Inclusive hadron production in smallx formalism ons together with he available RHIC! At forward rapidity, the hadron is produced as follows (at LO) HC. his analysis[dumitru, JalilianMarian, ] Inclusive forward hadronpproduction = z q in collisions can reveal the parton satucs imental observables which ut also reduces the dσ K dz = d b xf (x)f (x, q )D (z) Physics in A q/p h/q ncertainties. he phenomenon, dyd p (π) xf z d ration the forward single inclusive hadron Z q hx cs beyond leading X dσlo dz d r iq r collisions is unique x. inf= protonnucleus () gnals of productions the gluon (xa, q ) = (r ) x )D e xnpcqfr(xup()u, µ)f(k A h/q (z, µ) + xp g(xp, µ)f (k )Dh/g (z, µ). (π) d pof h simplicity dy τ z n in terms its and accuracy. f follows! Dipole gluon distribution BK evolution equation, which can be solved hadron production in collisions Protonnucleus collisions single inclusive hadron production in production collision numerically i single inclusive hadron in colcomparison with RHIC data e lisions p + A h(y, p ) + X can be viewed as follows: can reveal the parton satu or a collinear parton from theh proton projectile scatters off rward single inclusive phadron in Results () collisions is unique eeus the dense nuclear target A and subsequently fragments nd accuracy. CRONIN EFFEC: d into a measured forward hadron at rapidity y with transhadron production in colux momentum p. Measuring the produced hadron can verse be viewed as Afollows: Results projectile scatters off eproton at forward rapidity yinclusive is particularly since the CRONIN EFFEC: Single forward particle productioninteresting in p(d)a collisions and subsequently fragments y. projectile with large x is always dilute measured large relatively rapidity y: dron at proton rapidity y with trans at asuring the produced hadron g while the projectile nuclearprobed target with Proton at large x small xg is dense in this Caveats: arbitrary choice of the renormalization scale µ and K factor. ticularly interesting since the Nucleusregion. target probed at smallpx Qs (xg ) # ΛQCD, one ikinematic When tively large x is always dilute NLO correction? [Dumitru, Hayashigaki, JalilianMarian, 6; Altinoluk, xg is dense in this msith smallshould expect that gluon saturation plays an important effects in the nucleus could be important Kovner ] [Chirilli, Xiao and Yuan, ] p Qs (xg ) # ΛQCD, one Collinear factorization not expected to work h role, while the traditional collinear factorization, which aturation plays an important rcollineardoes factorization, which not include multiple scatterings and smallx evoand smallx evoyscatterings lutions, breaks down. his observable is also relatively s observable is also relatively o in depends the large Nc limit since it only then depends it since simple it only then nich has been studied most ex! AlbaeteMarquet, J. L. Albacete Enhancement in the production of intermediate collisions respect to pp collisions due to multiple scattering h ++h!= particles in pa BRAHMS PRL9, h ++h!= h! =. h! =. J. L. Albacete kt Enhancement in the production of intermediate particles in pa Jan 8, Zhongbo Kang, LANL collisions pp collisions scattering p [GeV/c] respect p to [GeV/c] p [GeV/c]due to pmultiple [GeV/c] BRAHMS PRL9,... 6 LBL Feb p.6 8 BRAHMS data h ++h!= %/68% CGC: suppression originates in QSAu = GeV the dynamical shadowing generated by the QSd =. GeV Braun, PLB76 (). quantum nonlinear BKJIMWLK evolution Running slows down the supprestowards smallx running "s coupling sion Y= fixed "s= Albacete, Armesto, Kovner, Salgado, Wiedemann, hepph/779, PRL to appear. NonLinear Evolution of Cronin Enhancement x.6. Albacete, Armesto, Kovner, Salgado, Wiedemann, hepph/779, PRL to appear. Braun, PLB76 (). running αs fixed αs= Y=.. p [GeV/c] h! =. 7 p [GeV/c] p [GeV/c] Alternative: Energy loss arising from induced gluon bremstahlung (stronger in nucleus than in proton) factor Nuclear modification Suppression of Cronin effect is rooted in small evolution and in the behaviour of the gluon QSAu = GeV QSd =. GeV Y= x Y= Y=.6. h! =. Nuclear modification factor p t (GeV/c) h ++h!= NonLinear Evolution of Cronin Enhancement.6 Y=. Y=.6 %/68% Suppression of Cronin effect is rooted in small evolution and in the behaviour p [GeV/c] of the gluon RdAu RdAu Y= x QSd =. GeV running "s fixed "s=.8 Braun, PLB76 ().. kt RdAu. QSAu = GeV Albacete, Armesto, Kovner, Salgado, Wiedemann, hepph/779, PRL to appear. NonLinear Evolution of Cronin Enhancement uesday, January 8,.6 %/68% %/68% Probability of not losing energy: Y= Running coupling slows down the suppression P ( y) e ng ( y) ( xf )# / 6

6 Fill in the steps to show this) Both the renormalization and factorization scale dependen the order calculated, although there is still residual scal QCD explains observed scaling violation due to higher order corrections he following plot shows the type of behavior which is t and NLO calculations Why do we need NLO calculations? Large x: valence quarks Small x: Gluons, sea quarks p p > jet + X s = 8 GeV E = 7 GeV < y < LO NLO in dσ/dyde (pb/gev). µ/e Q F for fixed x Q F for fixed x Due to quantum evolution, PDF and FF changes with scale. his introduces large theoretical uncertainties in xf (x) and D(z). Choice of the scale at LO requires information at NLO. Scaling violation is one of the clearest manifestation of radiative effect predicted by QCD. LO cross section is always a monotonic function of µ, thus it is just order of magnitude estimate. Quantitative NLO calculation description significantly of scaling reduces violation the scale dependence. More reliable. K = σ LO+σ NLO is not a good approximation. Quark Parton Model σ LO NLO Q is vital in establishing the QCD factorization in saturation physics. x M F ( x) x ei qi ( ) ( x ) d x ei qi ( x) i i 6 / 6

7 NLO Calculation and ization in ization is about separation of short distant physics (perturbatively calculable hard factor) from large distant physics (Non perturbative). σ xf (x) H D h(z) F(k ) NLO (loop) calculation always contains various kinds of divergences. Some divergences can be absorbed into the corresponding evolution equations. he rest of divergences should be cancelled. Hard factor H = H () LO + αs π H() NLO + should always be finite and free of divergence of any kind. NLO vs NLL Naive α s expansion sometimes is not sufficient! LO NLO NNLO LL α sl (α sl) NLL α s α s (α sl) Evolution Resummation of large logs. LO evolution resums LL; NLO NLL. 7 / 6

8 Approximation and Relavent Diagrams in Large N c approximation. In the high energy limit s, one can assume that medium size L is much less than the typical coherence time. hree possible real diagrams: (a) In the shock wave approximation, only (a) and (b) are taken into account. As to jet quenching related calculation, if one assumes L, (c) diagram must be included. Also Virtual diagrams must be included. By integrating over the gluon phase space, we encounter several types of divergences. (b) (c) 8 / 6

9 Chirilli, Xiao, Yuan ctions performed according to the normalization ization group equations for single inclusive hadron productions Cf H R in X Systematic factorization for the p + A H + X process [G. Chirilli, ization BX and F. Yuan, formula Phys. in coordinate Rev. Lett. 8, space at one ()] loop Ph d σ p+a h+x dyd p = a dz dx z x ξxfa(x, µ)d h/c(z,µ) [dx ]Sa,c Y ([x])ha c(αs, ξ, [x]µ) Collinear divergence: pdfs Collinear divergence: fragmentation functs P p Rapidity divergence: BK evolution Finite hard factor k + P + A Rapidity Divergence Collinear Divergence (P) Collinear Divergence (F) Subtracting off divergence the NLO correction. By invoking the NLO evolutions, we promote the NLO calculation up to NLL. All different channels are included. q q, q g, g q( q) and g g. 9 / 6

10 + x + ct to pp collisions due to multiple scattering k t lution of Cronin Enhancement ovner, Salgado, Wiedemann, Q = GeV to appear. SAu ). Q Sd =. GeV g " s s= Y= Y= Y= p p.6 t in 6 8 (GeV/c)! = h +h! = h +h! =. h! =. h Numerical implementation of the NLO result %/68% %/68% Single inclusive forward particle production in p(d)a collisions BRAHMS PRL9, p [GeV/c] p [GeV/c] p [GeV/c] p [GeV/c] Single inclusive hadron production BRAHMS updata to NLO + +! = h +h! = h +h! =. h! =. h Nuclear modification factor dσ = xf a(x) D a(z) F xg a (k ) H () %/68% %/68% Suppression of Cronin effect is rooted in small evolution and in the behaviour p [GeV/c] of the p + αs [GeV/c] p [GeV/c] p [GeV/c] gluon xf a(x) D b(z) F xg CGC: suppression originates in Alternative: Energy loss arising from the dynamical shadowing generated by the π quantum nonlinear BKJIMWLK evolution Running coupling towards slows smallx down the suppression NonLinear Evolution of Cronin Enhancement R dau Albacete, Armesto, Kovner, Salgado, Wiedemann, hepph/779, PRL to appear. Braun, PLB76 (). running α s fixed α s= BRAHMS PRL9, Q SAu = GeV Q Sd =. GeV Y= Y= induced gluon bremstahlung (stronger in nucleus than in proton) Probability of not losing energy:. Y= P ( y) e ng( y) ( xf ) #. Kopeliovich et al, Frankfurt Strikman 6 8 p t (GeV/c) NLO parton distributions. (MSW or CEQ) (N)ab H() ab. Consistent implementation should include all the NLO α s corrections. NLO fragmentation function. (DSS or others.) Use NLO hard factors. Partially by [Albacete, Dumitru, Fujii, Nara, ] Use the oneloop approximation for the running coupling rcbk evolution equation for the dipole gluon distribution [Balitsky, Chirilli, 8; Kovchegov, Weigert, 7]. Full NLO BK evolution not available. physics at One Loop Order (SOLO). [Stasto, Xiao, Zaslavsky, ] / 6

11 Surprise in [ ] d N dηd p GeV BRAHMS η =.,. LO NLO data η =. η =. (.) 7 p[gev] he abrupt drop of the NLO correction when p > Q s was really a surprise! What is going wrong? formalism? Dilutedense factorization? Not necessarily positive definite! Does this indicate that we need NNLO correction? Some hidden large correction in αs π H() NLO? / 6

12 xg Numerical implementation of the NLO result in [Stasto, Xiao, Zaslavsky,, accepted for publication in PRL] [ ] d N dηd p GeV 7 BRAHMS η =.,. [ ] d N dηd p GeV p[gev] LO NLO data η =. η =. (.) [ ] d N dηd p GeV [ ] d N dηd p GeV GBW 7 S () xg = exp [ ( r Q x ) λ] BK 7 LHC η = 6.7 p[gev] LO NLO [ ] d N dηd p GeV S () xg [ = exp r ( Q x ) ( )] λ ln e + xg Λr MV rcbk p[gev] [ ] d N dηd p GeV 6 LO NLO (fixed) NLO (running) LHC at η = 6.7 SAR η = RHIC at η =. p[gev] LO NLO data 6 p[gev] (µ/p) Agree with data for p < Q s(y), and reduced scale dependence, no K factor. For more forward rapidity, the agreement gets better and better. Additional +function resummation? / 6

13 Looking into the high p region in Integration over Ξ What is going on exactly? Perform large p expansion Both the LO and NLO calculation manifest themselves in single hard scattering. σ. p he coefficient of the NLO correction for q q and g g channels are I q(x ) = dξ ( + ξ ) ln( x ) x ( ξ) + [ ] I g(x ) = dξ[ + ξ + ( ξ) ξ ( ξ) ] + + ξ( ξ). x ( ξ) + ξ hreshold resummation, since x is related to the x fraction of produced hadron w.r.t. the proton projectile. Still preliminary! / 6

14 k t ization in Smallx VS MD ization [CollinsSoperSterman,8], [JiMaYuan, ] in (Mueller s dipole model) k t factorization is widely used in smallx physics. MD factorization is widely used in spin physics, etc (large x). he same gauge invariant operator definition! What about evolution? [F. Dominguez, BX and F. Yuan, Phys.Rev.Lett. 6, ().] k t factorization MD factorization? Yes, but more complicated. MD evolution (CSS), however, UGD evolution (smallx). / 6

15 Lesson from the oneloop calculation for Higgs productions in [A. Mueller, BX, F. Yuan, Phys. Rev. Lett., 8 ()] dσ (resum) dyd k M = σ k d x d x e ik R e S sud(m,r ) S WW (π) x pg p(x p, µ = c ) R [ ] + αs π π Nc, Y=ln /x g (x, x ) Four independent (at LL level) renormalization equation. No divergences left. Unified description of the CSS and smallx evolution? the same operator definition. MD and UGD share Define S WW (R, M; x g) = Ce S sud(m,r ) S WW Y=ln /x g (x x ) dσ (resum) dyd k M = σ k d x d x e ik R x pg p(x p, µ = c )S WW (R (π) R, M; x g) Straight forward generalization for dijet processes. Competition between and suppressions. / 6

16 Conclusion dihadron angular correlations in RHIC dau data d N dηd p y, y Quadrupole operator. operator Quadrupole 7 () Sxg = exp r Q x xg h () Sxg = exp r Q λ λ ln e + BK GeV Λr i rcbk CGC calculations Stasto et al AlbaceteMarquet "noncgc" calculations. Kang et al. d N dηd p JIMWLK, Y=.8 p [GeV].6 probability JIMWLK, Y=.8 p [GeV].6!" S6 (r) 6 7 c 6 7 Preliminary results by Lappi and H. Mantysaari Hard Probes. Inclusive forward hadron productions in collisions in the smallx saturation oneloop order. (More interesting). formalism Q(b, b, x, x) =at r U(b)U (b )U(x )U (x) Qs r Qs r JIMWLK, Y= Y= lines where Q is a correlator of Gaussian, Wilson.8 (a) Gaussian.6. JIMWLK, Y=.8 Gaussian, Y=.8 (b) Naive. Lappi et al Nc. JIMWLK, Y=. naive approximation, Y= JIMWLK, Y=.8. naive approximation, Y= /Ntrg dn /( p yd ) x xg S6 (r) SAR Preliminary pt < GeV/c <#t> =. pt > pa > GeV/c <#a>=.. Preliminary numerical results Gaussian, Y=.8 naive approximation, Y=.8 Uncertainties in current phenomenological works: Comparison withcgc full JIMWLK evolution (see talk by. Lappi). Dihadron.production cross section depends on sixpoint function central d + Au, y, y =., GeV < pasc <.7 GeV Need of a better description.of npoint functions... < p <.6. < p <.6 (6)..6 < p <.6 < p <. S (b, x, x, b ) = Q(b, b, x., x)s(x, x ) + O, N S6 (r) in.6 CGC calculation by C. Marquet (Nucl.Phys. A796 (7)):..8 Comparison with full JIMWLK evolution (see talk by. Lappi) d d x d x d b d b ik (x x) iq (b b).6 e e xq(x, µ ) d k dquadrupole q dyq dyk ( ) ( ) ( ) ( ) operator 7 6 Results: Coincidence JIMWLK,q qg. JIMWLK, Y= Y= (x b, x "! S () b ).8 S (6) S () + S () Gaussian, Y= naive approximation, Y=.8 S6 (r) Central dau collisions SAR PRELIMINARY p+p (.) d+au central (.) GeV/c < p,s<p,l. MV GBW p,l> GeV/c. CP(!") "!) CP( GeV...9 owards the test of saturation physics beyond LL (More precise)..8 Gaussian approximation is accurate, Naive LargeNc is. not.. Heikki Ma ntysaari (JYFL) Heikki Ma ntysaari (JYFL) Azimuthal 6 angle correlations Azimuthal angle correlations Qs r /. 8 /.6 Qs r 6 7 Dijet (dihadron) correlation in collisions. (More striking evidence!) (a) Gaussian (b) Naive of central PHENIX data (pedestal from exp. data) Good description Gaussian largenc approximation Oneloop calculation for hard processes in collisions, factor. (More complete MD or UGD). Gaussian approximation understanding is accurate, Naive LargeNof is not.. Lappi et al IC: MV, Qs =. GeV, data: PHENIX [.] Heikki Ma ntysaari (JYFL) Azimuthal angle correlations. / c Heikki Ma ntysaari (JYFL) Azimuthal angle correlations. 8 / Gluon saturation could be the next interesting discovery at the LHC. Of course, this needs a lot of hard work and we are hiring postdocs! 6 / 6