Forward correlations and the ridge - theory Cyrille Marquet Theory Division, CERN

Outline Di-hadron correlations, p+p vs d+Au collisions - central/central rapidities : nuclear effects are small - forward/central rapidities: high-x nuclear effects: pT-broadening - forward/forward rapidities : low-x nuclear effects: saturation Long-range rapidity correlations, A+A vs p+p collisions - A+A collisions: radial flow turns the early-time spacial correlations into a ridge - p+p collisions: in the absence of flow, the ridge reflects the actual momentum correlations of the early times

Di-hadron correlations, p+p vs d+Au collisions

The hadron wavefunction in QCD x : parton longitudinal momentum fraction kT : parton transverse momentum the distribution of partons as a function of x and kT : QCD linear evolutions: DGLAP evolution to larger kT (and a more dilute hadron) BFKL evolution to smaller x (and denser hadron) dilute/dense separation characterized by the saturation scale Qs(x) QCD non-linear evolution: meaning recombination cross-section gluon density per unit area it grows with decreasing x recombinations important when the saturation regime: for with this regime is non-linear yet weakly coupled

Di-hadron final-state kinematics scanning the wave-functions xp ~ xA < 1 central rapidities probe moderate x forward/central doesn’t probe much smaller x xp ~ 1, xA < 1 xp increases xA ~ unchanged forward rapidities probe small x xp ~ 1, xA << 1 xp ~ unchanged xA decreases

Dijets in standard pQCD in pQCD calculations based on collinear factorization, dijets are back-to-back this is supported by Tevatron data with high pT’s transverse view ~p probing QCD/pT <<1 power corrections are negligible peak narrower with higher pT

pT broadening at large x with lower transverse momenta, multiple scatterings become important probing pT not much higher than QCD higher twists are important, especially with nuclei Qiu and Vitev (2006) xA not small > 0.01 a Gaussian model with Away ~ also Kharzeev, Levin, McLerran (2005) q ^

Forward/central data STAR (2006) qualitative agreement with data, but quantitative ? coincidence probability signal Df pp Correlation Function dAu 0-20% 1.0 < pTt < 2.0 GeV/c for all plots <pTa>=0.55 GeV/c <pTa>=0.77 GeV/c <pTa>=1.00 GeV/c

What changes at small x forward dijet production at small x, multiple scatterings are characterized by QS (not QCD anymore) q ^ or intrinsic kT , or whatever is introduced to account for higher twists in the OPE becomes ~ QS in addition, when pT ~ QS and therefore multiple scatterings are important, so is parton saturation the OPE approach is not appropriate at small x, because all twists contribute equally starting from the leading twist result and calculating the next term is not efficient calculations with different levels of approximations Jalilian-Marian and Kovchegov (2005) Baier, Kovner, Nardi and Wiedemann (2005) Nikolaev, Schafer, Zakharov and Zoller (2005) C.M. (2007) forward dijet production when x is large, we don’t know a better way, but when x is small (such that QS >> QCD ), we do the CGC can be used to resum the expansion QS/pT expansion

Evidence of monojets p+p d+Au central ~p Df=0 (near side) Df=p (away side) (rad) ~p transverse view

Monojets in central d+Au in central collisions where QS is the biggest an offset is needed to account for the background there is a very good agreement of the saturation predictions with STAR data Albacete and C.M. (2010) Tuchin (2010) to calculate the near-side peak, one needs di-pion fragmentation functions the focus is on the away-side peak where non-linearities have the biggest effect suppressed away-side peak standard (DGLAP-like) QCD calculations cannot reproduce this

About the CGC calculation in the large-Nc limit, the cross section is obtained from and the 2-point function is fully constrained by e+A DIS and d+Au single hadron data in principle the 4-point function should be obtained from an evolution equation (equivalent to JIMWLK + large Nc) Jalilian-Marian and Kovchegov (2006) Dumitru and Jalilian-Marian (2010) even though the knowledge of S(2) is enough to predict the forward dihadron spectrum, there is no kT factorization: the cross section is a non-linear function of the gluon distribution in practice one uses an approximation that allows to express S(4) as a (non-linear) function of S(2) C.M. (2007) this approximation misses some leading-Nc terms Dominguez, Xiao and Yuan (2010) they may become dominant when pT >> Qs

Long-range rapidity correlations, A+A vs p+p collisions

Collision of two CGCs the initial condition for the time evolution in heavy-ion collisions before the collision: the distributions of ρ contain the small-x evolution of the nuclear wave functions r1 r2 the gluon field is a complicated function of the two classical color sources after the collision the field decays, once it is no longer strong (classical) a particle description is again appropriate hard modes decay faster than soft modes (τ ~ 1/pT)

General strategy solve Yang-Mills equations this is done numerically (it could be done analytically in the p+A case) express observables in terms of the field determine , in general a non-linear function of the sources examples later : single- and double-inclusive gluon production perform the CGC averages rapidity factorization proved recently at leading-order for (multi-)gluon production Gelis, Lappi and Venugopalan (2008)

Probing features of the Glasma features of the Glasma fields in general, the following phases (QGP, …) destroy the information coming from the glasma HIC are not great probes of parton saturation nevertheless, some observables are still sensitive to the physics of the early stages long-range rapidity correlations

Particle production in the glasma single gluon production Krasnitz and Venugopalan (1998) strength of the color charge of the projectile p+A A+A the target is always dense in A+A collisions, disconnected diagrams dominate multi-gluon production strength of the diagrams the exact implementation of the small-x evolution is still not achieved as in the single-particle case Gelis, Lappi and Venugopalan (2008) two-gluon production easily obtained from the single-gluon result

The ridge in A+A collisions the ridge is qualitatively understood within the CGC framework the Δϕ collimation is due to the radial flow if it is very extended in rapidity, the ridge is a manifestation of early-time phenomena: Dusling, Gelis, Lappi and Venugopalan (2009) STAR data (2009) quantitative calculations are underway

The ridge in p+p collisions in the absence of flow, the ridge reflect the actual momentum correlations of the early times Dumitru, Dusling, Gélis, Jalilian-Marian, Lappi and Venugopalan (2010) CMS data (2010) no ridge at low pT, there can’t be much flow ridge with pT ~ Qs diagram which gives the Δϕ dependence at the moment, the agreement is only qualitative (some leading-Nc diagrams are notoriously difficult to include)

Conclusions CGC and forward particle production in d+Au collisions the magnitude of the away-side peak, compared to that of the near-side peak, decreases from p+p to d+Au central this happens at forward rapidities, but at central rapidities, the p+p and d+Au signal are almost identical  the suppression of the away-side peak occurs when QS increases this was predicted, in some cases quantitatively with no parameter adjustments so far all di-hadron correlations measured in d+Au vs. p+p are consistent with saturation CGC and the A+A or p+p ridges the features of the data are qualitatively consistent with the CGC expectations but at the moment, there is nothing quantitative