High Energy QCD Research Articles

Energy evolution ofJ/ψproduction in DIS on nuclei

In this paper we show, that the $J/\psi$ production in DIS, is the main source of information about the events with two parton shower production. We attempt to develop our theoretical acumen of this process, to a level compatible with the theoretical description of inclusive DIS. We revisit the problem of the linear evolution equation for the double gluon densities, and include Bose-Einstein enhancement to these equations. We find that the Bose-Einstein correlations lead to an increase of the anomalous dimension, which turns out to be suppressed as $1/(N^2_c -1)^2$, in agreement with the estimates for the twist four anomalous dimension. We believe that understanding what happens to these contributions at ultra high energies, is a key question for an effective theory, based on high energy QCD. We derive the evolution equation for the scattering amplitude of two dipoles with a nucleus, taking into account the shadowing corrections, and investigate the analytical solutions in two distinct kinematic regions: deep in the saturation region, and in the vicinity of the saturation scale. The suggested non-linear evolution equation is a direct generalization of the Balitsky-Kovchegov equation, which has to be solved with the initial condition that depends on the saturation scale $Q_s(Y=Y_0,b)$. With the goal of finding a new small parameter, it is instructive to compare the solution of the non-linear equation with the qusi-classical approximation, in which in the initial condition we replace $Q_s(Y=Y_0,b)$ by $Q_s(Y,b)$. Our final result is that the shadowing corrections in the elastic amplitude generate the survival probability, which suppresses the growth of the amplitude with energy, caused by the Bose-Einstein enhancement.

S-matrix and productions amplitudes in high energy QCD

In this note we discuss a generalization of the Lipatov's effective action approach, [1,2], for the case of description of gluon and quark production amplitudes in the quasi-multi-Regge kinematics. Following to [3], we define the S-matrix elements of high energy QCD processes in this kinematics and discuss applications of the obtained results.

CGC/saturation approach: Soft interaction at the LHC energies

In this paper we demonstrate that our model which is based on the CGC/saturation approach, is able to describe the soft interaction collisions including the new TOTEM preliminary data at 13 TeV. We believe that this strengthens the argument that the CGC/saturation approach is the only viable candidate for an effective theory for high energy QCD.

Predictions on three-particle azimuthal correlations in proton--proton collisions

The ridge signal, which is long-ranged in rapidity, in the di-hadron correlations in high-multiplicity p-p and p-A collisions opened up a whole new research area in high-energy QCD. Although the ridge had been observed in A-A collisions and interpreted as a result of the radial flow of quark-gluon plasma, it had not appeared until recently in the data of small collision systems such as p-p and p-A, nor had it been predicted theoretically or seen in the event generators. There are two competing approaches that attempt to explain the systematics of the di-hadron ridge signal; hydrodynamics and gluon saturation physics (color glass condensate/glasma). In this work, we present predictions for the transverse momentum and rapidity dependence of the three-particle correlation function within the gluon saturation physics. Tri-hadron correlations can be measured, and the data can possibly rule out one of the two alternative approaches.

Fluctuations of the gluon distribution from the small- x effective action

The computation of observables in high energy QCD involves an average over stochastic semiclassical small-x gluon fields. The weight of various configurations is determined by the effective action. We introduce a method to study fluctuations of observables, functionals of the small-x fields, which does not explicitly involve dipoles. We integrate out those fluctuations of the gluon field under which a given observable is invariant. Thereby we obtain the effective potential for that observable describing its fluctuations about the saddle point. We determine explicitly the effective potential for the covariant gauge gluon distribution both for the McLerran-Venugopalan (MV) model and for a (non-local) Gaussian approximation for the small-x effective action. This provides insight into the correlation of fluctuations of the number of hard gluons versus their typical transverse momentum. We find that the spectral shape of the fluctuations of the gluon distribution is fundamentally different in the MV model, where there is a pile-up of gluons near the saturation scale, versus the solution of the small-x JIMWLK renormalization group, which generates essentially scale invariant fluctuations above the absorptive boundary set by the saturation scale.

A phenomenological study on the production of Higgs bosons in the cSMCS model at the LHC

In the present work, we intend to predict the production rates of the Higgs bosons in the simplest extension of the Standard Model (SM) by a neutral complex singlet (cSMCS). This model has an additional source of CP violation and provides strong enough first-order electroweak phase transition to generate the baryon asymmetry of universe (BAU). The scalar spectrum of the cSMCS includes three neutral Higgs particles with the lightest one considered to be the 125 GeV Higgs boson found at LHC. The SM-like Higgs boson comes mostly from the SM-like SU(2) doublet, with a small correction from the singlet. To predict the production rates of the Higgs bosons, we use a conventional effective LO QCD framework and the unintegrated parton distribution functions (UPDF) of Kimber–Martin–Ryskin (KMR). We first compute the SM Higgs production cross-section and compare the results to the existing theoretical calculations from different frameworks as well as the experimental data from the CMS and ATLAS collaborations. It is shown that our framework is capable of producing sound predictions for these high-energy QCD events in the SM. Afterwards we present our predictions for the Higgs boson production in the cSMCS.

LHC production of forward-center and forward-forward di-jets in the kt-factorization and transverse dependent unintegrated parton distribution frameworks

The present work is devoted to study the high-energy QCD events, such as the di-jet productions from proton–proton inelastic collisions at the LHC in the forward-center and the forward-forward configurations. This provides us with much valuable case study, since such phenomena can provide a direct glimpse into the partonic behavior of a hadron in a dominant gluonic region. We use the unintegrated parton distribution functions (UPDF) in the kt-factorization framework. The UPDF of Kimber et al. (KMR) and Martin et al. (MRW) are generated in the leading order (LO) and next-to-leading order (NLO), using the Harland-Lang et al. (MMHT2014) PDF libraries. While working in the forward-center and the forward-forward rapidity sectors, one can probe the parton densities at very low longitudinal momentum fractions (x). Such a model computation can provide simpler analytic description of data with respect to existing formalisms such as perturbative QCD. The differential cross-section calculations are performed at the center of mass energy of 7 TeV corresponding to CMS collaboration measurement. It is shown that the gluonic jet productions are dominant and a good description of data as well as other theoretical attempts (i.e. KS-linear, KS-nonlinear and rcBK) is obtained. The uncertainty of the calculations is derived by manipulating the hard scale of the processes by a factor of two. This conclusion is achieved, due to the particular visualization of the angular ordering constraint (AOC), that is incorporated in the definition of these UPDF.

High energy QCD at NLO: from light-cone wave function to JIMWLK evolution

Soft components of the light cone wave-function of a fast moving projectile hadron is computed in perturbation theory to the third order in QCD coupling constant. At this order, the Fock space of the soft modes consists of one-gluon, two-gluon, and a quark-antiquark states. The hard component of the wave-function acts as a non-Abelian background field for the soft modes and is represented by a valence charge distribution that accounts for non-linear density effects in the projectile. When scattered off a dense target, the diagonal element of the S-matrix reveals the Hamiltonian of high energy evolution, the JIMWLK Hamiltonian. This way we provide a new direct derivation of the JIMWLK Hamiltonian at the Next-to-Leading Order.

Forward hadron productions in proton-proton collisions in small-xformalism

Employing the so-called hybrid formalism, we calculate the cross section of inclusive hadron production in proton-proton collisions at forward rapidity in small-$x$ formalism at one-loop order. For the case of hadron production at forward rapidity, we can uses collinear parton distributions for projectile proton and $k_\perp$ dependent gluon distribution for target proton. We show that collinear divergences associated with initial and final state parton radiations are renormalized into parton distributions and fragmentation functions in terms of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equation, respectively. Furthermore, rapidity divergence can be absorbed into the wave function of target proton which gives rise to the well-known Balitsky-Fadin-Kuraev-Lipatov equation. These divergences are completely separated from the short distance partonic hard parts, which is now finite at the next-to-leading order accuracy. The result presented in this paper can be reckoned as a baseline calculation without any non-linear QCD effects in small-$x$ formalism. As a consistency check, we compare our results with the previous calculation for non-linear proton-nucleus collisions in the small-$x$ formalism and find complete agreement in the dilute and large $N_c$ limit. In phenomenology, the direct comparison of the above two separate calculations can reveal the role and strength of the non-linear dynamics in high energy QCD, and thus help us reliably study the onset of gluon saturation when genuine non-linear interactions become important.

Two-gluon emission and interference in a thin QCD medium: insights into jet formation

In heavy-ion collisions, an abundant production of high-energy QCD jets allows to study how these multiparticle sprays are modified as they pass through the quark-gluon plasma. In order to shed new light on this process, we compute the inclusive two-gluon rate off a hard quark propagating through a color deconfined medium at first order in medium opacity. We explicitly impose an energy ordering of the two emitted gluons, such that the “hard” gluon can be thought of as belonging to the jet substructure while the other is a “soft” emission (which can be collinear or medium-induced). Our analysis focusses on two specific limits that clarify the modification of the additional angle- and formation time-ordering of splittings. In one limit, the formation time of the “hard” gluon is short compared to the “soft” gluon formation time, leading to a probabilistic formula for production of and subsequent radiation off a quark-gluon antenna. In the other limit, the ordering of formation is reverted, which automatically leads to the fact that the jet substructure is resolved by the medium. We observe in this case a characteristic delay: the jet radiates as one color current (quark) up to the formation of the “hard” gluon, at which point we observe the onset of radiation of the new color current (gluon). Within our kinematic constraints, our computation supports a picture in which the in-medium jet dynamics are described as a collection of subsequent antennas which are resolved by the medium according to their transverse extent.

Color fluctuations in high energy hadron- and photon-nucleus collisions

We explain that coherence of high energy QED and QCD processes implies existence of new kind of phenomena which are beyond a framework based on Regge poles (cuts). New phenomena emerge as the consequence of compositeness of the bound states and the Lorentz slowing down of interaction. We focus on the color fluctuations phenomena predicted earlier for [Formula: see text] collisions within QCD and recent evidence for this phenomenon from [Formula: see text] LHC run, significant modification of nuclear shadowing phenomenon in the diffractive photoproduction of vector mesons observed recently in the ultra peripheral collisions at LHC. We outlined briefly general properties of color fluctuations phenomena and perspectives of future studies of this phenomenon in electron (photon) collisions with nuclei.

Cos(4φ)azimuthal anisotropy in small-xDIS dijet production beyond the leading power TMD limit

We determine the first correction to the quadrupole operator in high-energy QCD beyond the TMD limit of Weizsaecker-Williams and linearly polarized gluon distributions. These functions give rise to isotropic resp. ~ cos 2 phi angular distributions in DIS dijet production. On the other hand, the correction produces a ~ cos 4 phi angular dependence which is suppressed by one additional power of the dijet transverse momentum scale (squared) P^2.

Axial-vector dominance predictions in quasielastic neutrino-nucleus scattering

The axial form factor plays a crucial role in quasielastic neutrino-nucleus scattering, but the error of the theoretical cross section due to uncertainties of $G_A$ remains to be established. Reversely, the extraction of $G_A$ from the neutrino nucleus cross section suffers from large systematic errors due to nuclear model dependencies, while the use of single parameter dipole fits underestimates the errors and prevents an identification of the relevant kinematics for this determination. We propose to use a generalized axial-vector-meson-dominance (AVMD) in conjunction with large-$N_c$ and high energy QCD constrains to model the nucleon axial form factor, as well as the half width rule as an a priori uncertainty estimate. The minimal hadronic ansatz comprises the sum of two monopoles corresponding to the lightest axial-vector mesons being coupled to the axial current. The parameters of the resulting axial form factor are the masses and widths of the two axial mesons as obtained from the averaged PDG values. By applying the half width rule in a Monte Carlo simulation, a distribution of theoretical predictions can then be generated for the neutrino-nucleus quasielastic cross section. We test the model by applying it to the $(\nu_\mu,\mu)$ quasielastic cross section from $^{12}$C for the kinematics of the MiniBooNE experiment. The resulting predictions have no free parameters. We find that the relativistic Fermi gas model globally reproduces the experimental data, giving $\chi^2/ \# bins = 0.81$. A $Q^2$-dependent error analysis of the neutrino data shows that the uncertainties in the axial form factor $G_A(Q^2)$ are comparable to the ones induced by the a priori half width rule. We identify the most sensitive region to be in the range $0.2 \lesssim Q^2 \lesssim 0.6 \,{\rm GeV}^2$.

Energy dependence of the ridge in high multiplicity proton-proton collisions

We demonstrate that the recent measurement of azimuthally collimated, long range rapidity ("ridge") correlations in $\sqrt{s}=13$ TeV proton-proton (p+p) collisions by the ATLAS collaboration at the LHC are in agreement with expectations from the color glass condensate effective theory of high energy QCD. The observation that the integrated near side yield as a function of multiplicity is independent of collision energy is a natural consequence of the fact that multiparticle production is driven by a single semi-hard saturation scale in the color glass condensate framework. We argue further that the azimuthal structure of these recent ATLAS ridge measurements strongly constrain hydrodynamic interpretations of such correlations in high multiplicity p+p collisions.

High-energy QCD: Interplay of nonperturbative and perturbative effects

Soft interaction is an unavoidable participant of every hard process at high energies. Although the factorisation theorems allow to separate the hard and soft parts of the interaction, in many instances (not covered by the theorems) factorisation is broken, and the processes are dominated by the interplay between the perturbative and nonperturbative effects. Several examples are overviewed in this note.

Colour Glass Condensate (CGC) versus the BFKL Pomeron calculus: a status report

This talk is the review of the recent activity in prooving the equivalence of two approaches to high energy QCD: the CGC approach and the BFKL Pomeron calculus. It is shown that they are equivalent for rapidities η≤2ηmax=2ΔBFKLln⁡(1ΔBFKL).

CGC/saturation approach for soft interactions at high energy: Inclusive production

In this letter we demonstrate that our dipole model is successful in describing 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 QCD.

Rapidity evolution of Wilson lines at the next-to-leading order: Balitsky–JIMWLK equation at NLO

Abstract Scattering amplitudes of proton–Nucleus or Nucleus–Nucleus collisions at high energy are described by matrix elements of Wilson line operators — infinite gauge factors ordered along the straight line trajectories of the fast moving particles. The energy dependence of such amplitudes is described by the evolution equation of Wilson lines with respect to the rapidity parameter — the Balitsky–JIMWLK evolution equation. Most of the current phenomenology of high-energy and high-density QCD is based on the leading-order evolution equation with only running coupling corrections. I will present the derivation of the Balitsky–JIMWLK evolution equation at the next-to-leading order.

Gluon saturation beyond (naive) leading logs

Abstract An improved version of the Balitsky–Kovchegov equation is presented, with a consistent treatment of kinematics. That improvement allows to resum the most severe of the large higher order corrections which plague the conventional versions of high-energy evolution equations, with approximate kinematics. This result represents a further step towards having high-energy QCD scattering processes under control beyond strict Leading Logarithmic accuracy and with gluon saturation effects.

High-energy QCD evolution from BRST symmetry

We show that the (gauge-fixed) classical action of the Color Glass Condensate is invariant under a suitable Becchi–Rouet–Stora–Tyutin symmetry, which holds after the gluon modes are split into their fast, semi-fast, and soft components, according to the longitudinal momenta they carry. This entails the existence of a corresponding Slavnov–Taylor identity which in turn strongly constrains the effective field theory arising when integrating out the semi-fast modes. Specifically, we prove that this identity guarantees the gauge invariance of the resulting effective theory. In addition, we use it to demonstrate that the integration over the semi-fast modes does not deform the classical Yang–Mills equations of motion, thus validating a key assumption in the usual procedure adopted when deriving the renormalization group equation governing the evolution with energy of the effective theory. As far as the latter are concerned, we finally prove that its functional form is common, and it is determined by symmetry arguments alone. The formal properties of these equations valid in different regimes and/or approximations (e.g., the JIMWLK equation and its BFKL limit) can be therefore derived in a unified setting within this algebraic approach.