Using the dipole picture for electron-nucleus deep inelastic scattering at small Bjorken $x$, we study the effects of gluon saturation in the nuclear target on the cross-section for SIDIS (single inclusive hadron, or jet, production). We argue that the sensitivity of this process to gluon saturation can be enhanced by tagging on a hadron (or jet) which carries a large fraction $z \simeq 1$ of the longitudinal momentum of the virtual photon. This opens the possibility to study gluon saturation in relatively hard processes, where the virtuality $Q^2$ is (much) larger than the target saturation momentum $Q_s^2$, but such that $z(1-z)Q^2\lesssim Q_s^2$. Working in the limit $z(1-z)Q^2\ll Q_s^2$, we predict new phenomena which would signal saturation in the SIDIS cross-section. For sufficiently low transverse momenta $k_\perp\ll Q_s$ of the produced particle, the dominant contribution comes from elastic scattering in the black disk limit, which exposes the unintegrated quark distribution in the virtual photon. For larger momenta $k_\perp\gtrsim Q_s$, inelastic collisions take the leading role. They explore gluon saturation via multiple scattering, leading to a Gaussian distribution in $k_\perp$ centred around $Q_s$. When $z(1-z)Q^2\ll Q^2$, this results in a Cronin peak in the nuclear modification factor (the $R_{pA}$ ratio) at moderate values of $x$. With decreasing $x$, this peak is washed out by the high-energy evolution and replaced by nuclear suppression ($R_{pA}<1$) up to large momenta $k_\perp\gg Q_s$. Still for $z(1-z)Q^2\ll Q_s^2$, we also compute SIDIS cross-sections integrated over $k_\perp$. We find that both elastic and inelastic scattering are controlled by the black disk limit, so they yield similar contributions, of zeroth order in the QCD coupling.
We investigate hadrons and direct photon production in pp collisions at the LHC energy within the color-dipole approach. We show that greatest sensitivity to gluon saturation effects is reached at very forward rapidities in pp collisions at LHC (\sqrt{s}=14 TeV). The discrepancies among various saturation models (fitted to HERA data) results can be about a factor of 2-3 at forward rapidities. We found that the ratio of direct-photon to pion production can be about 20-10 at forward rapidities η=7-8. Therefore, direct photon production at forward rapidities should provide a rather clean probe as…
Constraining the Dipole Amplitude at NLO with HERA Data and Probing Gluon Saturation in SIDIS
Department of Physics, University of Jyv\"askyl\"a, P.O. Box 35, 40014 University of Jyv\"askyl\"a, Finland；Helsinki Institute of Physics, P.O. Box 64, 00014 University of Helsinki, Finland
We investigate direct photon production in pp collisions at the energies of RHIC, CDF and LHC, at different rapidities employing various color-dipole models. The cross section peaks at forward rapidities due to the abelian dynamics of photon radiation. This opens new opportunities for measurement of direct photons at forward rapidities, where the background from radiative hadronic decays is strongly suppressed. Our model calculations show that photon production is sensitive to the gluon saturation effects, and strongly depends on the value of the anomalous dimension.
We compute the cross section for photons emitted from sea quarks in proton-nucleus collisions at collider energies. The computation is performed within the dilute-dense kinematics of the Color Glass Condensate (CGC) effective field theory. Albeit the result obtained is formally at next-to-leading order in the CGC power counting, it provides the dominant contribution for central rapidities. We observe that the inclusive photon cross section is proportional to all-twist Wilson line correlators in the nucleus. These correlators also appear in quark-pair production; unlike the latter, photon produ…
We investigate hadrons and direct photon production in pp and pA collisions at the energies of RHIC and LHC within the color-dipole approach employing various saturation models. We show that greatest sensitivity to saturation effects is reached at very forward rapidities for pp collisions at LHC (\sqrt{s}=14 TeV). The ratio of direct-photon to pion production can be about 20-10 (at η=7-8). Therefore, direct photon production at forward rapidities should provide a rather clean probe. We calculate the rapidity dependence of the invariant cross-section and find some peculiar enhancement at forwar…
Higher order corrections to the Balitsky-Kovchegov equation have been estimated by introducing a rapidity veto which forbids subsequent emissions to be very close in rapidity and is known to mimic higher order corrections to the linear BFKL equation. The rapidity veto constraint has been first introduced using analytical arguments obtaining a power growth with energy, Q_s (Y) ~ exp(lambda Y), of the saturation scale of lambda ~ 0.45. Then a numerical analysis for the non-linear Balitsky-Kovchegov equation has been carried out for phenomenological rapidities: when a veto of about two units of r…
Different kinematical regimes of semi-inclusive deeply inelastic scattering (SIDIS) processes correspond to different underlying partonic pictures, and it is important to understand the transition between them. This is particularly the case when there is sensitivity to intrinsic transverse momentum, in which case kinematical details can become especially important. We address the question of how to identify the current fragmentation region --- the kinematical regime where a factorization picture with fragmentation functions is appropriate. We distinguish this from soft and target fragmentation…
The description of the hadron production at very forward rapidities and low transverse momentum is usually made using phenomenological models based on nonperturbative physics. However, at high energies and large rapidities the wave function of one of the projectiles is probed at very small Bjorken $x$, being characterized by a large number of gluons. In this kinematical regime, a new state of matter - the Color Glass Condensate (CGC) - is expected to be formed. One the main characteristics of such system is the presence of a new dynamical momentum scale, the saturation scale $Q_s$, which can a…
We revisit the "`hybrid formalism"' for particle production used recently to study saturation effects in single hadron multiplicities at forward rapidities at RHIC and LHC. We point out that at leading twist there is an extra contribution to the formulae used so far, which corresponds to particle production via inelastic scattering of the projectile partons on the target fields. This contribution is expected to be small due to kinematics at very forward rapidities/very high transverse momenta, but should be significant at high momenta and very high energies. This contribution is expected to be…
We discuss the Drell-Yan production of dileptons at high energies in the forward rapidity region of proton-proton collisions in a hybrid high-energy approach. This approach uses unintegrated gluon distributions in one proton and collinear quark/antiquark distributions in the second proton. We compute various distributions for the case of low-mass dilepton production and compare to the LHCb and ATLAS experimental data on dilepton mass distributions. In distinction to dipole approaches, we include four Drell-Yan structure functions as well as cuts at the level of lepton kinematics. The impact of…
We study a strong suppression of the relative production rate (d-Au)/(p-p) for inclusive high-pT hadrons of different species at large forward rapidities (large Feynman xF). The model predictions calculated in the light-cone dipole approach are in a good agreement with the recent measurements by the BRAHMS and STAR Collaborations at the BNL Relativistic Heavy Ion Collider. We predict a similar suppression at large pT and large xF also at lower energies, where no effect of coherence is possible. It allows to exclude the saturation models or the models based on Color Glass Condensate from interp…
The Color Glass Condensate picture of the nuclear wave function at small-x successfully predicted the suppressed production of high-pT particles at forward rapidities in deuteron-gold collisions at RHIC. This triggered more efforts which resulted in theoretical improvements and predictions for different observables which will provide further phenomenological tests. I review recent theoretical developments and discuss the resulting predictions.
We investigate the effects of the saturation boundary on small-x evolution at the next-to-leading order accuracy and beyond. We demonstrate that the instabilities of the next-to-leading order BFKL evolution are not cured by the presence of the nonlinear saturation effects, and a resummation of the higher order corrections is therefore needed for the nonlinear evolution. The renormalization group improved resummed equation in the presence of the saturation boundary is investigated, and the corresponding saturation scale is extracted. A significant reduction of the saturation scale is found, and…
We consider the J/Psi production in proton (deuteron) -- nucleus collisions at high energies. We argue that the production mechanism in this case is different from that in pp collisions due to gluon saturation in the nucleus and formation of the Color Glass Condensate. At forward rapidities (in the proton fragmentation region), the production of J/Psi is increasingly suppressed both as a function of rapidity and centrality. On the other hand, at backward rapidities at RHIC (in the fragmentation region of the nucleus) the coherent effects lead to a modest enhancement of the production cross sec…
Phenomenological models of the dipole cross section that enters in the description of for instance deep inelastic scattering at very high energies have had considerable success in describing the available small-x data in both the saturation region and the so-called extended geometric scaling (EGS) region. We investigate to what extent such models are compatible with the numerical solutions of the Balitsky-Kovchegov (BK) equation which is expected to describe the nonlinear evolution in x of the dipole cross section in these momentum regions. We find that in the EGS region the BK equation yields…
The predictions for the atmospheric neutrino flux at high energies strongly depend on the contribution of prompt neutrinos, which are determined by the production of charmed meson in the atmosphere at very forward rapidities. In this paper we estimate the related cross sections taking into account the presence of an intrinsic charm (IC) component in the proton wave function and the QCD dynamics modified by the onset of saturation effects. The impact on the predictions for the prompt neutrino flux is investigated assuming different values for the probability to find the IC in the nucleon. Compa…
The study of azimuthal correlations in particle production at forward rapidities in proton-nucleus collisions provides direct information about high gluon density effects, like gluon saturation, in the nuclear wavefunction. In the kinematical conditions for proton-lead collisions at the LHC, the forward di-hadron production is dominated by partonic processes in which a gluon from the proton splits into a pair of gluons, while undergoing multiple scattering off the dense gluon system in the nucleus. We compute the corresponding cross-section using the Colour Glass Condensate effective theory, w…
We apply the Color Glass Condensate formalism to photon $+$ hadron production cross section in high energy deuteron (proton)-gold collisions at RHIC. We investigate the dependence of the production cross section on the angle between the produced hadron and photon for various rapidities and transverse momenta. It is shown that the angular correlation between the produced hadron and photon is a sensitive probe of the saturation dynamics.
We consider the influence of parton saturation in the Color Glass Condensate on the back-to-back azimuthal correlations of high $p_T$ hadrons in $pA$ (or $dA$) collisions. When both near--side and away--side hadrons are detected at mid-rapidity at RHIC energy, the effects of parton saturation are constrained to transverse momenta below the saturation scale $p_T \leq Q_s$; in this case the back-to-back correlations do not disappear but exhibit broadening. However when near-side and away-side hadrons are separated by several units of rapidity, quantum evolution effects lead to the depletion of b…
Photon-jet azimuthal correlations in proton-nucleus collisions are a promising tool for gaining information on the gluon distribution of the nucleus in the regime of non-linear color fields. We compute such correlations from the process $g+A\to q \bar{q} γ$ in the rapidity regime where both the projectile and target light-cone momentum fractions are small. By integrating over the phase space of the quark which emits the photon, subject to the restriction that the photon picks up most of the transverse momentum (to pass an isolation cut), we effectively obtain a $g+A\to q γ$ process. For nearly…
Deep inelastic scattering at small x can be described very effectively using saturation inspired dipole models. We investigate whether such models are compatible with the numerical solutions of the Balitsky-Kovchegov (BK) equation which is expected to describe the nonlinear evolution in x of the dipole cross section. We find that the BK equation yields results that are qualitatively different from those of phenomenological studies. Geometric scaling is recovered only towards asymptotic rapidities. In this limit the value of the anomalous dimension gamma(r,x) at the saturation scale approaches …
We study single lepton production from semileptonic decays of heavy flavor hadrons ($D,B\rightarrow~l$) in pp and p$A$ collisions at RHIC and the LHC within the saturation/Color-Glass-Condensate (CGC) framework. Using the gluon distribution function obtained with the dipole amplitude, whose energy dependence is described by the Balitsky-Kovchegov equation with running coupling effect, we compute the transverse-momentum ($p_\perp$) spectra of the lepton yields at mid and forward rapidities. We find that a large fraction of leptons at low $p_\perp$ stems from the saturation regime of the incomin…
We discuss new physical phenomena expected in particle production in hadron-hadron collisions at high energy, as a consequence of Pomeron loop effects in the evolution equations for the Color Glass Condensate. We focus on gluon production in asymmetric, `dilute-dense', collisions : a dilute projectile scatters off a dense hadronic target, whose gluon distribution is highly evolved. This situation is representative for particle production in proton-proton collisions at forward rapidities (say, at LHC) and admits a dipole factorization similar to that of deep inelastic scattering (DIS). We show …
We calculate the triple- and quadruple-gluon inclusive distributions with arbitrary rapidity and azimuthal angle dependences in the gluon saturation regime by using glasma diagrams. Also, we predict higher-dimensional ridges in triple- and quadruple-hadron correlations for p-p and p-Pb collisions at LHC, which have yet to be measured. In p-p and p-Pb collisions at the top LHC energies, gluon saturation is expected to occur since smaller Bjorken-$x$ values are being probed. Glasma diagrams, which are enhanced at small-$x$, include the gluon saturation effects, and they are used for calculating …
Unintegrated gluon densities in nuclei, dipole-nucleus cross-sections and quark densities are numerically investigated in the high-colour limit, with the scattering on a heavy nucleus exactly described by the sum of fan diagrams of BFKL pomerons. The initial condition for the evolution in rapidity is quickly forgotten, and the gluon density presents a "supersaturation" pattern, as previous studies indicated. Both dipole-nucleus cross-sections and quark densities present the expected saturation features. Identifying the position in transverse momentum $l$ of the maximum of the gluon distributio…
We consider modifications of the standard non-linear QCD evolution in an attempt to account for some of the missing ingredients discussed recently, such as correlations, discreteness in gluon emission and Pomeron loops. The evolution is numerically performed using the Balitsky-Kovchegov equation on individual configurations defined by a given initial value of the saturation scale, for reduced rapidities $y=(α_s N_c/π) Y<10$. We consider the effects of averaging over configurations as a way to implement correlations, using three types of Gaussian averaging around a mean saturation scale. Furthe…
I give a pedagogical survey of the nuclear collective effects associated with gluon saturation and their impact on particle production in high-energy proton (or deuteron)-nucleus collisions at RHIC. At central rapidity, the theory predicts a Cronin peak due to independent multiple scattering off the valence quarks in the nucleus. At forward rapidities, the peak flattens out and disappears very fast, because of the correlations induced through quantum evolution in the nuclear gluon distribution at small x. Also, the ratio R_{pA} between the particle yield in proton-nucleus and proton-proton col…
We discuss prompt production of $J/ψ$ mesons in proton-proton collisions at the LHC within NRQCD $k_t$-factorization approach using Kimber-Martin-Ryskin (KMR) unintegrated gluon distributions (UGDF). We include both direct color-singlet production ($g g \to J/ψg$) as well as a feed-down from $χ_c \to J/ψγ$ and $ψ' \to J/ψX$ decays. The production of the decaying mesons ($χ_c$ or $ψ'$) is also calculated within NRQCD $k_t$-factorization approach. The corresponding matrix elements for $g g \to J/ψ$ g, $g g \to ψ'g$ and $g g \to χ_c$ include parameters of the nonrelativistic space wave functions …
We study the disappearance of the away-side peak of the di-hadron correlation function in p+A vs p+p collisions at forward rapidities, when the scaterring process presents a manifest dilute-dense asymmetry. We improve the state-of-the-art description of this phenomenon in the framework of the Color Glass Condensate (CGC), for hadrons produced nearly back-to-back. In that case, the gluon content of the saturated nuclear target can be described with transverse-momentum-dependent gluon distributions, whose small-$x$ evolution we calculate numerically by solving the Balitsky-Kovchegov equation wit…
We demonstrate that strong suppression of the relative production rate (d+Au)/(p+p) of inclusive high-pT hadrons at forward rapidities observed at RHIC is due to parton multiple rescatterings in nuclear matter. The light-cone dipole approach-based calculations are in a good agreement with BRAHMS and STAR data. They also indicate a significant nuclear suppression at midrapidities with a weak onset of the coherence effects. This prediction is supported by the preliminary d+Au data from the PHENIX Collaboration. Moreover, since similar suppression pattern is also expected to show up at lower ener…
Within the framework of a (1+1)-dimensional model which mimics evolution and scattering in QCD at high energy, we study the influence of the running of the coupling on the high-energy dynamics with Pomeron loops. We find that the particle number fluctuations are strongly suppressed by the running of the coupling, by at least one order of magnitude as compared to the case of a fixed coupling, for all the rapidities that we have investigated, up to Y=200. This reflects the slowing down of the evolution by running coupling effects, in particular, the large rapidity evolution which is required for…
We study the effect of nuclear matter in Upsilon production in dAu collisions at RHIC and pPb collisions at the LHC. We find that the nuclear modification factor, R^Upsilon_dAu, measured at RHIC is not satisfactorily reproduced by the conventional effects used in the literature, namely the modification of the gluon distribution in bound nucleons and an --effective-- survival probability for a bound state to escape the nucleus. In particular, we argue that this probability should be close to 1 as opposed to the J/psi case. We note that, at backward rapidities, the unexpected suppression of R^Up…
The Drell-Yan (DY) process of dilepton pair production off nuclei is not affected by final state interactions, energy loss or absorption. A detailed phenomenological study of this process is thus convenient for investigation of the onset of initial-state effects in proton-nucleus ($pA$) collisions. In this paper, we present a comprehensive analysis of the DY process in $pA$ interactions at RHIC and LHC energies in the color dipole framework. We analyse several effects affecting the nuclear suppression, $R_{pA}<1$, of dilepton pairs, such as the saturation effects, restrictions imposed by energ…
