We provide a semi-classical description of the inclusive gluon induced Deep Inelastic Scattering cross section in a way that accounts for the leading powers in both the Regge and Bjorken limits. Our approach thus allows a systematic matching of small and moderate $x_{\rm Bj}$ regimes of gluon proton structure functions. We find a new unintegrated gluon distribution with an explicit dependence on the longitudinal momentum fraction $x$ which entirely spans both the dipole operator and the gluonic Parton Distribution Function. Computing this gauge invariant gluon operator on the lattice could allow to probe the energy dependence of the saturation scale from first principles.
In this talk, we revisit inclusive DIS in the small $x$ limit and derive a new factorization formula that accounts for leading powers in both Bjorken and Regge limits. In this semi-classical description, we obtain a new unintegrated gluon distribution which encompasses both the dipole operator and the gluon Parton Distribution Function with an explicit dependence on the longitudinal momentum fraction $x$.
We systematically study dijet production in various processes in the small-$x$ limit and establish an effective $k_t$-factorization for hard processes in a system with dilute probes scattering on a dense target. We find that the well-known Weizsäcker-Williams gluon distribution can be directly probed in the quark-antiquark jet correlation in deep inelastic scattering and the dipole gluon distribution can be directly measured in the direct photon-jet correlation in $pA$ collisions. In the large-$N_c$ limit, the unintegrated gluon distributions involved in other different dijet channels in pA co…
We present detailed numerical analysis of the unintegrated double gluon distribution which includes the dependence on the transverse momenta of partons. The unintegrated double gluon distribution was obtained following the Kimber-Martin-Ryskin method as a convolution of the perturbative gluon splitting function with the collinear integrated double gluon distribution and the Sudakov form factors. We analyze the dependence on the transverse momenta, longitudinal momentum fractions and hard scales. We find that the unintegrated gluon distribution factorizes into a product of two single unintegrat…
An impact parameter dependent unintegrated gluon distribution is constructed as a solution of a nonlinear evolution equation with realistic Glauber--Gribov input. Photon--jet correlations in the proton fragmentation region of pA collisions are proposed as a direct probe of the nuclear unintegrated glue.
We test several BFKL-like evolution equations for unintegrated gluon distributions against forward-central dijet production at LHC. Our study is based on fitting the evolution scenarios to the LHC data using the high energy factorization approach. Thus, as a by-product, we obtain a set of LHC-motivated unintegrated gluon distributions ready to use. We utilize this application by calculating azimuthal decorrelations for forward-central dijet production and compare with existing data.
We derive analytical results for unintegrated color dipole gluon distribution function at small transverse momentum. By Fourier transforming the $S$-matrix for large dipoles we derive the results in the form of a series of Bells polynomials. Interestingly, when resumming the series in leading log accuracy, the results showing up striking similarity with the Sudakov form factor with role play of coupling is being done by a constant that stems from the saddle point condition along the saturation line.
This note is a physics manual for a recent numerical implementation of k_t-factorization with running-coupling BK unintegrated gluon distributions. We also compile some results for Pb+Pb collisions at \sqrt{s} = 2.75 TeV, such as predictions for the centrality dependence of the charged particle multiplicity and transverse energy. The model can further be used to obtain initial conditions for hydrodynamic simulations of A+A collisions at the LHC.
The solution of non-linear evolution equations for dense nuclear gluon density has been suggested as one of the relevant mechanisms of pA and AA collisions at collider energies. Here we study a simple parameterization for the unintegrated gluon distribution using the knowledge of asymptotic solutions of the Balitsky-Kovchegov equation, describing high-energy QCD in the presence of saturation effects. A satisfactory description of nuclear shadowing at small-x is obtained and it allows us to understand the qualitative behavior shown by data.
We present here some arguments to support our suggestion that data on the helicity structure for the hard exclusive electroproduction of $ρ$ mesons at HERA (and in possible future high-energy electron-proton colliders) provide useful information to constrain the $κ$-shape of the unintegrated gluon distribution in the proton.
We evaluate the unintegrated gluon distribution of the proton starting from a parametrization of the color dipole cross section including DGLAP evolution and saturation effects. To this end, we perform the Fourier-Bessel transform of $σ(x,r)/α(r)$. At large transverse momentum of gluons we match the so-obtained distribution to the logarithmic derivative of the collinear gluon distribution. We check our approach by calculating the proton structure function $F_L(x,Q^2)$ finding good agreement with HERA data.
Feynman diagrams with two real partons contributing to the next-to-leading-order singlet gluon-quark DGLAP kernel are analysed. The infra-red singularities of unintegrated distributions are examined numerically. The analytical formulae are also given in some cases. The role of the colour coherence effects is found to be crucial for cancellations of the double- and single-logarithmic infra-red singularities.
We propose an evolution equation for unintegrated gluon densities that is valid for large values of the QCD coupling constant $\barα _s$. Our approach is based on the linear resummation model introduced by Staśto. We generalize the model including a non-linear term in the diffusive regime. The validity of the diffusive evolution at strong coupling is supported by the AdS/CFT consideration, as well as perturbative arguments. We solve the evolution equation numerically and extract the saturation scale, which we compare with the weak coupling counterpart.
The gluon content of the proton is embodied by the unintegrated gluon distribution (UGD), which has universal validity. In literature many models of UGD have been proposed so far. The polarized $ρ$-meson leptoproduction at HERA offers a nowadays unexplored testfield to discriminate among existing models of UGD, via the comparison with theoretical predictions formulated in the $κ$-factorization approach.
Sufficiently inclusive processes, like the deep inelastic scattering (DIS), are described in terms of scale-dependent parton distributions, which correspond to the density of partons with a given longitudinal momentum fraction, integrated over the parton transverse momentum. For less inclusive processes, one needs to consider densities unintegrated over the transverse momentum. This work focuses on the unintegrated gluon distribution (UGD), describing the probability that a gluon can be emitted by a colliding proton, with definite longitudinal fraction and transverse momentum. Through the lept…
The gluon content of the proton, in the high-energy regime, is embodied by the unintegrated gluon distribution (UGD), which describes the gluon emission probability, with a given longitudinal momentum fraction and transverse momentum. The UGD, formulated within the $κ$-factorization approach, has universal validity and several models for it have been proposed so far. We will show that the polarized $ρ$-meson leptoproduction at HERA is a not trivial testfield for discriminating among existing models of UGD.
We found the parameterization of the unintegrated gluon distribution from the best description of the LHC data on the inclusive spectra of hadrons produced in $pp$ collisions at the mid-rapidity region and small transverse momenta. It is different from the one obtained within perturbative QCD only at low intrinsic transverse momenta $k_t$. The application of this distribution to analysis of the $e-p$ DIS allows us to get the results which do not contradict the H1 and ZEUS data on the structure functions at low $x$. So, the connection between the soft processes at LHC and low-$x$ physics at HER…
We review and discuss the use of TMD, or "unintegrated", gluon distributions in the domain of small-x physics. The definitions employed, and the hazards of the naive applications of the TMD factorization and the associated gluon distributions are discussed.
Exclusive emissions of vector mesons in forward directions of rapidity offer us a faultless chance to probe the proton structure at small-$x$. A high-energy factorization formula is established within BFKL, given as the convolution of an impact factor depicting the forward-meson emission and of an unintegrated gluon distribution (UGD) driving the gluon evolution at small-$x$. As a nonperturbative quantity, the UGD is not well known and several models for it exist. We present recent progresses on the study of the exclusive forward $ρ$-meson leptoproduction at HERA and EIC energies, showing how …
We compute the leading order (LO) $qg\to q γ$ and next-to-leading order (NLO) $gg\to q{\bar q} γ$ contributions to inclusive photon production in proton-proton (p+p) collisions at the LHC. These channels provide the dominant contribution at LO and NLO for photon transverse momenta $k_{γ\perp}$ corresponding to momentum fractions of $x\leq 0.01$ in the colliding protons. Our computations, performed in the dilute-dense framework of the Color Glass Condensate effective field theory (CGC EFT), show that the NLO contribution dominates at small-$x$ because it is sensitive to $k_\perp$-dependent unin…
A method for tuning parameters in Monte Carlo generators is described and applied to a specific case. The method works in the following way: each observable is generated several times using different values of the parameters to be tuned. The output is then approximated by some analytic form to describe the dependence of the observables on the parameters. This approximation is used to find the values of the parameter that give the best description of the experimental data. This results in significantly faster fitting compared to an approach in which the generator is called iteratively. As an ap…
Inclusive as well as exclusive emissions in forward and central directions of rapidity are widely recognized as excellent channels to access the proton structure at small-x. In this regime, to describe nucleons structure, it is necessary to use kT-unintegrated distributions. In particular, at large transverse momenta, the x-evolution of the so-called unintegrated gluon distribution is driven by the Balitsky-Fadin-Kuraev-Lipatov equation, within the framework of the high-energy factorization (HEF). Recent analyses on the diffractive electroproduction of ρmesons have corroborated the underlying …
Quarkonium production in high-energy proton (deuteron)-nucleus collisions is investigated in the color glass condensate framework. We employ the color evaporation model assuming that the quark pair produced from dense small-x gluons in the nuclear target bounds into a quarkonium outside the target. The unintegrated gluon distribution at small Bjorken x in the nuclear target is treated with the Balitsky-Kovchegov equation with running coupling corrections. For the gluons in the proton, we examine two possible descriptions, unintegrated gluon distribution and ordinary collinear gluon distributio…
We present differential cross sections for Higgs boson and/or two-photon production from intermediate (virtual) Higgs boson within the formalism of $k_t$-factorization. Resulting distributions for two photons from the Higgs boson are compared with recent ATLAS collaboration data. In contrast to a recent calculation the leading order $g g \to H$ contribution is rather small compared to the ATLAS experimental data ($γγ$ transverse momentum and rapidity distributions). We include also higher-order contribution $g g \to H (\to γγ) g$, $g g \to g H g$ and the contribution of the $W^+ W^-$ and $Z^0 …
