We compute the differential cross-section for inclusive prompt photon$+$quark production in deeply inelastic scattering of electrons off nuclei at small $x$ ($e+A$ DIS) in the framework of the Color Glass Condensate effective field theory. The result is expressed as a convolution of the leading order (in the strong coupling $α_{\mathrm{s}}$) impact factor for the process and universal dipole matrix elements, in the limit of hard photon transverse momentum relative to the nuclear saturation scale $Q_{s,A}(x)$. We perform a numerical study of this process for the kinematics of the Electron-Ion Collider (EIC), exploring in particular the azimuthal angle correlations between the final state photon and quark. We observe a systematic suppression and broadening pattern of the back-to-back peak in the relative azimuthal angle distribution, as the saturation scale is increased by replacing proton targets with gold nuclei. Our results suggest that photon+jet final states in inclusive $e+A$ DIS at high energies are in general a promising channel for exploring gluon saturation that is complementary to inclusive and diffractive dijet production. They also provide a sensitive empirical test of the universality of dipole matrix elements when compared to identical measurements in proton-nucleus collisions. However because photon+jet correlations at small $x$ in EIC kinematics require jet reconstruction at small $k_\perp$, it will be important to study their feasibility relative to photon-hadron correlations.
Exploiting recently obtained analytic solutions of classical Yang-Mills equations for higher order perturbations in the field of the dilute object (proton), we derive the complete first saturation correction to the single inclusive semi-hard gluon production in high energy proton-nucleus collisions by applying the Lehmann-Symanzik-Zimmermann reduction formula. We thus finalize the program started by Balitsky (see Ref.~\cite{Balitsky:2004rr}) and independently by Chirilli, Kovchegov and Wertepny (see Ref.~\cite{Chirilli:2015tea}) albeit using a very different approach to carry out our calculati…
In this letter we suggest the generalization of $k_T$-factorization formula for inclusive gluon production for the dense-dense parton system scattering. It turnes out that the soft gluon production with transverse momentum $p_T$ is suppressed by additional Sudakov-like factor that depends on $p^2_T/Q^2_s$ ratio in a good agreement with the first numerical calculation in Colour Glass Condensate approach by J.P. Blaizot, T. Lappi and Y. Mehtar-Tan.
Yoichiro Nambu put a great foot print in nuclear physics in the era of its fundamental developments including his pioneering insight into essential ingredients of repulsive core of nuclear force and its relation to the saturation of nuclear matter. The present review article focuses onto recent developments of the interaction models between colliding nuclei in terms of Brueckner's G-matrix theory staring from realistic nuclear forces and the saturation property of symmetric nuclear matter as well as neutron-star matter. A recently proposed unique scenario of extracting the saturation property …
We demonstrate the QCD factorization for inclusive hadron production in $pA$ collisions in the saturation formalism at one-loop order, with explicit calculation of both real and virtual gluon radiation diagrams. The collinear divergences associated with the incoming parton distribution of the nucleon and the outgoing fragmentation function of the final state hadron, as well as the rapidity divergence with small-$x$ dipole gluon distribution of the nucleus are factorized into the splittings of the associated parton distribution and fragmentation functions and the energy evolution of the dipole …
Geometric scaling is well confirmed for transverse momentum distributions observed in proton-proton collisions at LHC energies. We introduced multiplicity dependence on a saturation momentum of the geometrical scaling, assuming the scaling holds for semi-inclusive distributions as well as for inclusive distributions. The saturation momentum is usually given by Bjorken's $x$ variable, but redefinition of the scaling variable can make the saturation momentum a function of collision energy $W$. We treat the energy as a free parameter (denoted $W^*$ to distinguish it from $W$) and associate the en…
In high energy proton-nucleus collisions, the gluon saturation effects from the nucleus are fully incorporated into the light-like Wilson lines. The gluon saturation effects from the proton, which are anticipated to be important either in the extreme high energy limit or towards the dense-dense (nucleus-nucleus) collision regimes, have been studied perturbatively within the Color Glass Condensate effective theory in previous papers of this series. A configuration-by-configuration expression for the single inclusive semi-hard gluon production including the first saturation correction was obtain…
Single and double inclusive cross-sections in nucleus-nucleus collisions are derived in the perturbative QCD with interacting BFKL pomerons in the quasi-classical approximation.
We calculate the classical single-gluon production amplitude in nucleus-nucleus collisions including the first saturation correction in one of the nuclei (the projectile) while keeping multiple-rescattering (saturation) corrections to all orders in the other nucleus (the target). In our approximation only two nucleons interact in the projectile nucleus: the single-gluon production amplitude we calculate is order-g^3 and is leading-order in the atomic number of the projectile, while resumming all order-one saturation corrections in the target nucleus. Our result is the first step towards obtain…
We study single inclusive hadron production in proton-proton and proton-nucleus collisions in the CGC framework. The parameters in the calculation are determined solely by standard nuclear geometry and by electron-proton deep inelastic scattering data, which is fit using the running coupling BK equation. We show that it is possible to obtain a good fit of the HERA inclusive cross section also without an anomalous dimension in the initial condition. We argue that one must consistently use the proton transverse area as measured by a high virtuality probe in DIS also for the single inclusive cros…
A parton picture of inclusive quasi-elastic electron-nucleus scattering, where individual nucleons are treated as (non point-like) partons of the nucleus, is presented. All the necessary target-mass corrections to asymptotic scaling are evaluated and a new scaling variable is obtained. Recent inclusive data from Jefferson Lab are analyzed and shown to scale in terms of the new variable. The new approach allows to extract in a model-independent way the nucleon light-cone momentum distribution in the nucleus.
We present a complete comparison of semi-inclusive $ν_μ$-$^{12}$C cross-section measurements by T2K and MINER$ν$A collaborations with the predictions from the SuSAv2-MEC model implemented in the neutrino-nucleus event generator GENIE and an unfactorized approach based on the relativistic distorted wave impulse approximation (RDWIA). Results, that include cross sections as function of the final muon and proton kinematics and correlations between both, show that the agreement with data obtained by the RDWIA approach, that accounts for final-state interactions, matches or improves GENIE-SuSAv2 pr…
We compare the results of the relativistic Green's function model with the experimental data of the charged-current inclusive differential neutrino-nucleus cross sections published by the T2K Collaboration. The model, which is able to describe both MINER$ν$A and MiniBooNE charged-current quasielastic scattering data, underpredicts the inclusive T2K cross sections.
In this letter we demonstrate that our dipole model is successful in describing the inclusive production within the same framework as diffractive physics. We believe that this achievement stems from the fact that our approach incorporates the positive features of the Reggeon approach and CGC/saturation effective theory, for high energy QC
We present a full kinematic analysis of neutrino-nucleus charged current quasielastic interactions based on the Local Fermi Gas model and the Random PhaseApproximation. The model was implemented in the NEUT Monte Carlo framework, which allows us to investigate potentially measurable observables, including hadron distributions. We compare the predictions simultaneously to the most recent T2K and MINERvA charged current (CC) inclusive, CC0$π$ and transverse kinematic-imbalance variable results. We pursuit a microscopic interpretation of the relevant reaction mechanisms, with the aim of achieving…
We show that gluon saturation gives rise to a strong modification of the scaling in both the nuclear mass number $A$ and the virtuality $Q^2$ of the vector meson production cross-section in exclusive deep-inelastic scattering off nuclei. We present qualitative analytic expressions for how the scaling exponents are modified as well as quantitative predictions that can be tested at an Electron-Ion Collider.
Dipole models based on various saturation scenarios provide reasonable fits to small-x DIS inclusive, diffractive and exclusive data from HERA. Proton un-integrated gluon distributions extracted from such fits are employed in a $k_\bot$-factorization framework to calculate inclusive gluon distributions at various energies. The n-particle multiplicity distribution predicted in the Glasma flux tube approach shows good agreement with data over a wide range of energies. Hadron inclusive transverse momentum distributions expressed in terms of the saturation scale demonstrate universal behavior over…
In high density QCD the hadron production stems from decay of mini-jets that have the transverse momenta of the order of the saturation scale. It is shown in this paper that this idea is able to describe in a unique fashion both the inclusive hadron production for \sqrt{s} \geq 546 GeV including the first data from LHC and the deep inelastic scattering at HERA. Recently reported data from ALICE, CMS and ATLAS including inclusive charged-hadron transverse-momentum and multiplicity distribution in pp collisions are well described in our approach. We provide predictions for the upcoming LHC measu…
We discuss the saturation of the parton density in heavy ion collisions at RHIC energiesusing a Pomeron approach. Our predictions for the particle density in ion-ion collisions at RHIC energies can be utilized as the background for the observation of possible quark-gluon plasma production.
The contribution of the different terms of the running-coupling Balistky-Kovchegov (rcBK) equation to the description of inclusive HERA data is discussed. Within this framework an alternative definition of the saturation scale is presented. The definition is based on the ratio of the term corresponding to the recombination of two dipoles to the term corresponding to a dipole splitting. A similar ratio is used to study the contribution of the recombination term to the evolution of inclusive HERA data with rapidity. It is found that, although the data are well described, the behaviour of the dif…
We study the quasi--elastic contribution to the inclusive $(ν_l,ν_l N)$, $(ν_l,l^- N)$, $({\bar ν}_l,{\bar ν}_l N)$ and $({\bar ν}_l,l^+ N)$ reactions in nuclei using a Monte Carlo simulation method to account for the rescattering of the outgoing nucleon. As input, we take the reaction probability from the microscopical many body framework developed in Phys. Rev. {\bf C70} (2004) 055503 for charged-current induced reactions, while for neutral currents we use results from a natural extension of the model described in that reference. The nucleon emission process studied here is a clear signal fo…
The Quasi-Elastic (QE) contribution of the nuclear inclusive electron scattering model developed in Nucl. Phys. A627 (1997) 543 is extended to the study of electroweak Charged Current (CC) induced nuclear reactions, at intermediate energies of interest for future neutrino oscillation experiments. The model accounts for, among other nuclear effects, long range nuclear (RPA) correlations, Final State Interaction (FSI) and Coulomb corrections. Predictions for the inclusive muon capture in $^{12}$C and the reaction $^{12}$C $(ν_μ,μ^-)X$ near threshold are also given. RPA correlations are shown to …
We review recent progress on the calculations on the inclusive forward hadron production within the saturation formalism. After introducing the concept of perturbative parton saturation and nonlinear evolution we discuss the formalism for the forward hadron production at high energy in the leading and next-to-leading order. Numerical results are presented and compared with the experimental data on forward hadron production in $dA$ and $pA$. We discuss the problem of the negativity of the NLO cross section at high transverse momenta, study its origin in detail and present possible improvements …
We make quantitative predictions for the rapidity and centrality dependencies of hadron multiplicities in dA collisions at RHIC basing on the ideas of parton saturation in the Color Glass Condensate.
Saturation models -- colour glass condensate and string percolation -- impose a strict relation between the average transverse momentum, <P_T>, and the rapidity particle densities, dn/dy. By combining this relation with an appropriate evolution equation for dn/dy, and imposing energy-momentum conservation, we obtain a fair description of data, for generic AB collisions (hadron-hadron, hadron-nucleus and nucleus-nucleus) at all rapidities and (high) energies. Predictions are given for the LHC.
In high energy proton-nucleus collisions, the single- and double-inclusive soft gluon productions at the leading order have been calculated and phenomenologically studied in various approaches for many years. These studies do not take into account the saturation and multiple rescatterings in the field of the proton. The first saturation correction to these leading order results (the terms that are enhanced by the combination $α_s^2 μ^2$, where $μ^2$ is the proton's color charge squared per unit transverse area) has not been completely derived despite recent attempts using a diagrammatic approa…
In this paper, we discuss the inclusive production of hadrons in the framework of CGC/saturation approach. We argue, that the gluon jet inclusive production stems from the vicinity of the saturation momentum, even for small values of the transverse momenta $p_T$. Since in this region, theoretically, we know the scattering amplitude, we claim that we can provide reliable estimates for this process. We demonstrate, that in a widely accepted model for confinement, to describe the experimental data, we require a thermal radiation term. In this model the parton (quark or gluon) with the transverse …
We present a model for weak CC induced nuclear reactions at energies of interest for current and future neutrino oscillation experiments. This model is a natural extension of the work of Refs.[1,2], where the QE contribution to the inclusive electron and neutrino scattering on nuclei was analyzed. The model is based on a systematic many body expansion of the gauge boson absorption modes that includes one, two and even three body mechanisms, as well as the excitation of Delta isobars. The whole scheme has no free parameters, besides those previously adjusted to the weak pion production off the …
In this paper we solve the equation for nucleus-nucleus scattering in the BFKL Pomeron calculus, suggested by Braun. We find these solutions analytically at high energies as well as numerically in the entire region of energies inside the saturation region. The semi-classical approximation is used to select out the infinite set of the parasite solutions. The nucleus-nucleus cross sections at high energy are estimated and compared with the Glauber-Gribov approach. It turns out that the exact formula gives the estimates that are very close to the ones based on Glauber-Gribov formula which is impo…
Inclusive cross-sections for gluon jet production are studied numerically in the perturbative QCD pomeron model for central collisions of identical nuclei at high energies. Two forms for the inclusive cross-sections, with and without emission from the triple pomeron vertex, are compared. The difference was found to reduce to a numerical factor 0.8$÷$ 09 for momenta $k$ below the saturation momentum $Q_s$. Above $Q_s$ no difference was found at all. The gluon spectrum was found to be $\sim A$ for $k<Q_s$ and $\sim A^{1.1}$ for $k>Q_s$. At large $k$ the spectrum falls as $1/k^{2.7÷3.3}$ flatteni…
The leading order single inclusive soft gluon production in high energy proton-nucleus (pA) collisions has been studied by various approaches for more than two decades. The first correction due to the gluon saturation in proton was analytically attempted recently through a diagrammatic approach in which only partial results were obtained. An important feature of the first saturation correction is that it includes both initial state and final state interactions. In this paper, we present the complete result derived from the Color Glass Condensate framework. Our approach is to analytically solve…
It is shown that in semi-inclusive deep inelastic scattering (DIS) of electrons off a complex nucleus A, the detection, in coincidence with the scattered electron, of a nucleus (A-1) in the ground state, as well as of a nucleon and a nucleus (A-2), also in the ground state, may provide unique information on several long standing problems, such as : i) the nature and the relevance of the final state interaction in DIS; ii) validity of the spectator mechanism in DIS; iii) the medium induced modifications of the nucleon structure function; iv) the origin of the EMC effect.
Using the recently found hA amplitude, single and double inclusive jet production rates on the nucleus are studied in the perturbative QCD with $N_c\to\infty$. Jet multiplicities are found to grow with $A$ and energy as $A^{2/9}s^Δ$ where $Δ$ is the BFKL intercept. Long range correlations are found to behave as $A^{4/9}s^{2Δ}$ and change from negative to positive at a certain high energy.
We reconsider the perturbative next-to-leading calculation of the single inclusive hadron production in the framework of the hybrid formalism, applied to hadron production in proton-nucleus collisions. Our analysis, performed in the wave function approach, differs from the previous works in three points. First, we are careful to specify unambiguously the rapidity interval that has to be included in the evolution of the leading-order eikonal scattering amplitude. This is important, since varying this interval by a number of order unity changes the next-to-leading order correction that the calcu…
We analize semi-inclusive electron-nucleus processes e+A->e'+h+X at moderate Q**2 and energy transfer nu. Our results show that nucleons bound in the nuclear medium are distributed according to a function f_A that reduces to the standard light-cone distribution in the Bjorken limit and exhibits a sizeable Q**2-dependence at lower Q**2, particular Q**2 is order of nu**2.
We show that the quasielastic (QE) response calculated with the SuSAv2 (superscaling approach) model, that relies on the scaling phenomenon observed in the analysis of (e,e') data and on the relativistic mean-field theory, is very similar to that from a relativistic distorted wave impulse approximation model when only the real part of the optical potentials is employed. The coincidence between the results from these two completely independent approaches, which satisfactorily agree with the inclusive data, reinforces the reliability of the quasielastic predictions stemming from both models and …
We calculate the photon production cross-section in $pA$ collisions under the assumption that the nucleus has reached the saturation regime, while the proton can be described by the standard parton distribution functions. We show that due to the strong classical field $O(1/g)$ of the nucleus, bremsstrahlung diagrams become dominant over the direct photon diagrams. In particular, we show that $γ-$jet transverse momentum spectrum and correlations are very sensitive to gluon saturation effects in the nucleus.
We compute the differential cross-section for inclusive prompt photon production in deeply inelastic scattering (DIS) of electrons on nuclei at small $x$ in the framework of the Color Glass Condensate (CGC) effective theory. The leading order (LO) computation in this framework resums leading logarithms in $x$ as well as power corrections to all orders in $Q_{s,A}^2/Q^2$, where $Q_{s,A}(x)$ is the nuclear saturation scale. This LO result is proportional to universal dipole and quadrupole Wilson line correlators in the nucleus. In the soft photon limit, the Low-Burnett-Kroll theorem allows us to…
We discuss the inclusive dilepton cross section for proton (quark)-nucleus collisions at high energies in the very forward rapidity region. Starting from the calculation in the quasi-classical approximation, we include low-x evolution effects in the nucleus and predict leading twist shadowing together with anomalous scaling behaviour.
In this paper we solve the equations that describe nucleus nucleus scattering, in high density QCD,in the framework of the BFKL Pomeron calculus. We found that (i) the contribution of short distances to the opacity for nucleus-nucleus scattering dies at high energies, (ii) the opacity tends to unity at high energy, and (iii) the main contribution that survives comes from soft (long distance) processes for large values of the impact parameter. The corrections to the opacity $Ω\Lb Y,b\Rb = 1$ were calculated and it turns out that they have a completely different form, namely($1 - Ω\to \exp\Lb - …
We study the effects of gluon saturation on pion production in high energy proton-nucleus collisions using the color glass condensate model. At high p_perp, we show that the p_perp-distribution of gluons behaves as ~ 1/(p_perp^7) in accordance with both conventional perturbative QCD calculations and experiment. Fragmentation of gluons into pions leads to a rapidity dependent depletion of pions relative to the conventional perturbative QCD predictions. We argue that these clear and systematic differences provide a signal for the onset of gluon saturation which is accessible in upcoming experime…
In the perturbative QCD approach single and double inclusive cross-sections for gluon production off the nucleus are studied from the relevant reggeized gluon diagrams. Various terms corresponding to emission of gluons from the triple Pomeron vertex are found. Among them the term derived by Kovchegov and Tuchin emerges as a result of transition from the diffractive to effective high-energy vertex. However it does not exhaust all the vertex contributions to the inclusive cross-section. In the double inclusive cross-section a contribution violating naive AGK rules is found, in which one gluon is…
We analyze the experimental data on the inclusive double differential cross section by neutrinos charged current, measured by T2K, with the same model which was successful for the MiniBooNE quasielastic cross sections. As in our previous analysis the multinucleon component is needed in order to reproduce the data. For the total cross section our evaluation is smaller than the SciBooNE data above 1 GeV. This indicates the opening of a new channel not included in our evaluation, presumably the two pion emission channel. We also check that our description holds for the exclusive single pion produ…
We compute single inclusive hadron production in proton-proton and proton-nucleus collisions consistently within the CGC framework. The parameters in the calculations are obtained from electron-proton DIS and standard nuclear geometry. We obtain a good description of the DIS data without an anomalous dimension in the initial condition of the BK evolution and get a good agreement with the available single inclusive proton-proton and proton-nucleus data.
We study single inclusive hadron production in proton-proton and proton-nucleus collisions in the CGC framework. The parameters in the calculation are obtained by fitting electron-proton deep inelastic scattering data. The obtained dipole-proton amplitude is generalized to dipole-nucleus scattering without any additional nuclear parameters other than the Woods-Saxon distribution. We show that it is possible to use an initial condition without an anomalous dimension and still obtain a good description of the HERA inclusive cross section and LHC single particle production measurements. We argue …
The phenomenology of gluon saturation at small parton momentum fraction, Bjorken-x, in the proton and in the nucleus is introduced. The experimentally-accessible kinematic domains at the nucleus-nucleus colliders RHIC and LHC are discussed. Finally, the saturation hints emerging from measurements at RHIC and the perspectives for LHC are described.
In this paper, it is shown that the experimental values of the nonextensive scattering entropies $S_L (p)$ and $S_θ(q)$ for the pion-nucleus ($π^0 He, π^0 C, π^0 O, π^0 Ca$) scatterings, in the energy region corresponding to $Δ(1236)$ resonance in the elementary pion-nucleon interaction, are well described by the entropic optimal resonance predictions $S_L^o1 (p)$ and $S_θ^o1 (q)$ and when the nonextensivities indices are correlated by a Riesz-Thorin-like relation: 1/2p+1/2q=1.
We formulate a generalization of the Glauber formalism for hadron-nucleus and nucleus-nucleus collisions based on the Pomeron approach to high energy interactions. Our treatment is based on two physical assumptions (i.e. two small parameters) : (i) that only sufficiently small distances contribute to the Pomeron structure; and (ii) the triple Pomeron vertex $G_{3P}/g_{P-N} \ll 1$ (where $g_{P-N}$ is the Pomeron-nucleon vertex) is small. A systematic method is developed for calculating the total, elastic and diffractive dissociation cross sections as well as the survival probability of large ra…
Single inclusive particle production at next-to-leading order in proton-nucleus collisions at forward rapidities: hybrid approach meets TMD factorization
The characteristics of the thermal radiation are investigated using a two - component model, with the hard component being described by the Color Glass Condensate formalism. The inclusive transverse momentum spectra of charged hadrons produced in proton - proton and proton - nucleus collisions at LHC energies and large - $p_T$ are estimated using the running coupling $k_T$ - factorization formula and the solution of the Balitsky - Kovchegov equation. Our results indicate that the thermal term is necessary to describe the experimental data and that the effective thermal temperature has an energ…
We present results on rapidity and transverse momentum distributions of inclusive charm quark production in hadronic and heavy-ion collisions at RHIC and LHC energies, including the next-to-leading order, $O(α_s^3)$, radiative corrections and the nuclear shadowing effect. We determine the hadronic and the {\it effective} (in-medium) K-factor for the differential and total inclusive charm cross sections. We find the fraction of central and inelastic events that contain at least one charm quark pair at LHC energies and obtain the effective $A$-dependence of the inclusive charm production in prot…
We show that the cross section for inclusive charm production exhibits geometric scaling in a large range of photon virtualities. In the HERA kinematic domain the saturation momentum $Q_{sat}^2(x)$ stays below the hard scale $μ_c^2=4m_c^2$, implying charm production probing mostly the color transparency regime and unitarization effects being almost negligible. We derive our results considering two saturation models which are able to describe the DESY ep collider HERA data for the proton structure function at small values of the Bjorken variable $x$. A striking feature is the scaling on $τ=Q_2^…
We successfully describe the HERA-data on diffractive deep inelastic scattering using a saturation model which has been applied in our earlier analysis of the inclusive $ep$-scattering data. No further parameters are needed. Saturation already turned out to be essential in describing the transition from large to small values of $Q^2$ in inclusive scattering. It is even more important for diffractive processes and naturally leads to a constant ratio of the diffractive versus inclusive cross sections. We present an extensive discussion of our results as well as detailed comparison with data.
Hadron production in lepton-nucleus deep inelastic scattering is studied in a model including quark energy loss and nuclear absorption. The leading-order computations for hadron multiplicity ratios are presented and compared with the selected HERMES experimental data with the quark hadronization occurring inside the nucleus by means of the hadron formation time. It is shown that with increase of the energy fraction carried by the hadron, the nuclear suppression on hadron multiplicity ratio from nuclear absorption gets bigger. It is found that when hadronization occurs inside the nucleus, the n…
