Small Small xx QCD: QCD: from from pa/aa pa/aa at at RHIC/LHC RHIC/LHC to to the the eic eic Adrian Dumitru RIKEN-BNL and Baruch College/CUNY AA: dn/dy, det/dy, eccentricity ε pa: forward dn/dpt2 2-point function pp, pa, AA: - forward dijets - near-side long-range rapidity correlations higher n-point functions, B-JIMWLK
Single-inclusive production [ N(k,x;b,A), Φ(k,x;b,A) ] (forward) pa: testing small-x QCD / CGC AA: provide initial conditions for hydro / thermalization models
Let's start with AA : centrality and energy dependence of multiplicities RHIC, s=200 GeV LHC, s=2.75 TeV MV model + rcbk (J. Albacete, 2010) provides constraints on entropy production due to final-state interactions (arxiv0706.2203)
Shen, Heinz, Huovinen, Song: arxiv:1010.1856 Hydro predicts elliptic flow Viscosity effects seen in v2! precise value of η/s depends (also) on initial condition!
Pressure gradients and elliptic flow Target Spectators Coordinate space y 2 x 2 = 2 2 x y Y Momentum space v2 = p 2x p2y p 2x p2y Projectile Spectators Initial X Participants Later Idea : Pressure gradients convert spatial anisotropy to momentum anisotropy
Glauber model for the initial transverse density profile Geometry: wounded nucleon model: number of participants scaling part r, b = Apart r, b Bpart r, b B = T A r b / 2 1 1 inel T r b/2 / B NN B A T B r b/ 2 1 1 inel T r b/ 2 / A NN A T A x = dz A x, z 0 A r = 1 exp[ r R 0 / a ]
... vs QCD dynamics Kt-factorization: Y X
Eccentricity nucl-th/0605012 Kt-factorization: Glauber (part.)
Scaling properties: dn g 2 d r dy = 4 Nc N ~ Q A 2 2 c 1 2 s min log d pt p Q Q B d 2 t 2 s max 2 s min 2 2 t 2 k t s x 1, k x 2, pt k t e.g. Kharzeev, Levin, PLB523 (2001) CGC: dn A B ~ min, part part 2 d r dy Glauber: dn ~ 2 d r dy A part CGC Glauber 2 B part
T. Hirano at al., Phys. Lett. B636 (2006) 299 Hydro with CGC vs. Glauber initial conditions Different predictions for eq. of state & viscosity!
forward forward p+a p+a collisions collisions suppression of forward single-inclusive production forward back-to-back dijet correlations
Single inclusive hadron production in pa 2-point function only: same as in DIS UNIVERSALITY anom. dim. γ<1 modifies pt distributions
Single inclusive hadron production proton-proton BDH PRD74 (2006) 074018 deuteron-gold DHJ NPA770 (2006) 57
rcbk dipole J. Albacete + C. Marquet, PLB 687, 2010
BUT: xp~0.4 (gg g kinematics) How about cold matter energy loss? B. Kopeliovich, L.Frankfurt+M.Strikman (PLB 2007) I. Vitev (2010)
Bottom line: - there is still some quantitative uncertainty for two-point function (especially for ions) - eic could settle its dependence on x (at x«1), r and A (or b) cleanly, once and for all inclusive Also, single q, q production g production: adj. dipole Kovchegov, Tuchin: PRD 2002
Double inclusive hadron production in pa E. Braidot [STAR]: arxiv:1005.2378 ATTN: back to back partons with the same rapidity! (both forward)
Albacete & Marquet: PRL 2010
BUT: Marquet: NPA 2007 Kovchegov & JJM: PRD 2004 Correlations probe higher n-point fcs, beyond ugd / dipole scatt. amplitude
Dipole + large Nc approximation: used in Albacete & Marquet: PRL 2010 This O6 misses many terms though, even at leading order in Nc 2 (plus dozens of O(1/Nc ) contributions)
Evolution of O6 from JIMWLK: A.D. & Jalilian-Marian: PRD 2010
Two hadron correlations: DIS FG-JJM, PRD67 (2003) JJM-YK, PRD70 (2004) Kovner-Lublinsky, JHEP (2006) two-particle production in DIS probes higher-point functions
F. Dominguez et al., 2010 large Nc, high pt (but low tr. mom. imbalance) while ordinary ugd for F2, single production:
F. Dominguez et al., 2010
near-side near-side two-particle two-particle correlations correlations aka the ridge discovered at STAR, seen also in high-mult. pp at CMS
Near-side correlations, ΔΦ«π (the ridge ) STAR (arxiv:0909.0191) PYTHIA pp@rhic, pttrig > 2.5 GeV
Independent production of two gluons: PYTHIA: independent multi-parton interactions Correlated two-gluon production: A.D., Gelis, McLerran, Venugopalan: 0804.3858
PHOBOS Au+Au, 0-30% Amplitude: fitting ridge amplitude in AA requires radial hydro boost ~γb! Dusling, Gelis, Lappi,Venug.: 0911.2720
CMS: 1009.4122 Ridge!
CMS: arxiv:1009.4122 sees a Qs-ish scale! arxiv:1009.5295
one single loop momentum k! Assumes factorization of 4-point function into two ugd!
however, we should rather compute THIS diagram:
however, subleading-nc piece contributes at the same order to C(p,q) Complete Balitsky/JIMWLK four-point function: (in Gaussian approximation) A.D.+JJM: arxiv:1001.4820 Projectile Target [Note: independent/uncorrel. production ]
gg production: energy ΔΦ«π, Δy>1 (high energy!) dense target + quantum evolution required at classical level highly suppressed: Jalilian-Marian + Kovchegov, PRD70 (2004)
Bottom line: - very little is known about higher n-point fcts such as,... - eic could measure those via semi-excl. final states, investigate B-JIMWLK vs. dipole model (and again: we're not talking just about 1/N c corrections!)
interesting observables for eic (at small x) : F2(x,Q2;A) (T and L photon) single particle production [diffr. F2; ρ, J/ψ production] 2-point function two, three,... particle production: B-JIMWLK hierarchy of n-point functions
Backup Slides
Di-hadron production kinematics final state : k1, y1 k 2, y2 k1 e y1 + k 2 e y2 xp = s k1 e y1 + k 2 e y2 xa = s scanning the wave-functions central rapidities probe moderate x central-forward xp increases xa ~ unchanged forward-forward correlations probe small xa xp ~ unchanged xa decreases
Fluctuations of nucleons ( light-cone sources ) important for central / peripheral Au+Au smaller systems (Cu+Cu) fluctuations of v2 PHOBOS