Unintegrated Gluon Distribution Research Articles

On the mechanism of T4c(6900) tetraquark production

We discuss the production mechanism of a new state, a putative fully charm tetraquark, observed recently by the LHCb at M=6.9 GeV in the J/ψJ/ψ channel. Both single parton scattering (SPS) and double parton scattering (DPS) mechanisms are considered. We calculate the distribution in the invariant mass of the four-quark system M4c for SPS and DPS production of ccc¯c¯ in the kT-factorization approach with modern unintegrated gluon distribution functions (UGDFs). The so-calculated contribution of DPS is almost two orders of magnitude larger than the SPS one, but the tetraquark formation mechanism is unknown at present. Imposing a mass window around the resonance position we calculate the corresponding distribution in pt,4c – the potential tetraquark transverse momentum. The cross section for the J/ψJ/ψ continuum is calculated in addition, again including SPS (box diagrams) and DPS contributions which are of similar size. The formation probability is estimated trying to reproduce the LHCb signal-to-background ratio. The calculation of the SPS gg→T4c(6900) fusion mechanism is performed in the kT-factorization approach assuming different spin scenarios (0+ and 0−). The 0+ assignment is preferred over the 0− one by the comparison of the transverse momentum distribution of signal and background with the LHCb preliminary data assuming the SPS mechanism dominance. There is no reliable approach for the DPS formation mechanism of tetraquarks at present as this is a complicated multi-body problem.

Dilepton production through timelike Compton scattering within the kT -factorization approach

In this work we consider the dilepton production via timelike Compton scattering (TCS) in electron-proton and proton-proton collisions. In particular, the differential cross section in terms of the dilepton invariant mass and rapidity is computed within the $k_T$-factorization approach. Besides, we utilize distinct unintegrated gluon distributions (UGD) in order to compare their impact on the differential cross section of TCS in $pp$ ($ep$) collisions evaluated at the LHC (LHeC), HL-LHC (LHeC), HE-LHC (LHeC) and FCC-hh (eh) center-of-mass energies.

Intrinsic charm in the nucleon and charm production at large rapidities in collinear, hybrid and kT-factorization approaches

We discuss the role of intrinsic charm (IC) in the nucleon for forward production of c-quark (or overline{c} -antiquark) in proton-proton collisions for low and high energies. The calculations are performed in collinear-factorization approach with on-shell partons, kT-factorization approach with off-shell partons as well as in a hybrid approach using collinear charm distributions and unintegrated (transverse momentum dependent) gluon distributions. For the collinear-factorization approach we use matrix elements for both massless and massive charm quarks/antiquarks. The distributions in rapidity and transverse momentum of charm quark/antiquark are shown for a few different models of IC. Forward charm production is dominated by gc-fusion processes. The IC contribution dominates over the standard pQCD (extrinsic) gg-fusion mechanism of coverline{c} -pair production at large rapidities or Feynman-xF. We perform similar calculations within leading-order and next-to-leading order kT-factorization approach. The kT-factorization approach leads to much larger cross sections than the LO collinear approach. At high energies and large rapidities of c-quark or overline{c} -antiquark one tests gluon distributions at extremely small x. The IC contribution has important consequences for high-energy neutrino production in the Ice-Cube experiment and can be, to some extent, tested at the LHC by the SHIP and FASER experiments by studies of the ντ neutrino production.

Production of f2(1270) meson in pp collisions at the LHC via gluon-gluon fusion in the kt-factorization approach

We calculate inclusive cross section for f2(1270) tensor meson production via color singlet gluon-gluon fusion in the kt-factorization approach with unintegrated gluon distribution functions (UGDFs). The process may be potentially interesting in the context of searches for saturation effects. The energy-momentum tensor, equivalent to helicity-2 coupling, and helicity-0 coupling are used for the g⁎g⁎→f2(1270) vertex. Two somewhat different parametrizations of helicity-2 and helicity-0 tensorial structure from the literature are used in our calculations. Some parameters are extracted from γγ→f2(1270)→ππ reactions. Different modern UGDFs from the literature are used. The results strongly depend on the parametrization of the g⁎g⁎→f2(1270) form factor. Our results for transverse momentum distributions of f2 are compared to preliminary ALICE data. We can obtain agreement with the data only at larger f2(1270) transverse momenta only for some parametrizations of the g⁎g⁎→f2(1270) form factor. No obvious sign of the onset of saturation is possible. At low transverse momenta one needs to include also the ππ final-state rescattering. The agreement with the ALICE data can be obtained by adjusting probability of formation and survival of f2(1270) in a harsh quark-gluon and multipion environment. The pomeron-pomeron fusion mechanism is discussed in addition and results are quantified.

Investigating the inclusive transverse spectra in high-energy pp collisions in the context of geometric scaling framework

The presence of geometric scaling within the $p_T$ spectra of produced hadrons at high energy $pp$ collisions using small-$x$ $k_T$-factorization is investigated. It is proposed a phenomenological parameterization for the unintegrated gluon distribution in the scaling range which reproduces the features of the differential cross section both in the saturated and dilute perturbative QCD regimes. As the saturation scale acts as an effective regulator of the infrared region (IR), the extension of the model to quantities usually associated to soft physics is studied. The approach is applied to compute the average $p_T$ and the rapidity distribution of produced gluons at high energies.

Photoproduction of three jets in the CGC: gluon TMDs and dilute limit

We study the process γA → qoverline{q}g + X in the Color Glass Condensate (CGC) effective theory. After obtaining the cross section, we consider two kinematic limits which are encompassed in our result. In the so-called correlation limit, the vector sum of the transverse momenta of the three outgoing particles is small with respect to the individual transverse momenta; the cross section then simplifies considerably and can be written in a factorized form, sensitive to both the unpolarized and linearly-polarized Weizsäcker-Williams transverse momentum dependent gluon distribution function (gluon TMD). The second limit of the CGC cross section that we consider is the dilute limit, which we obtain after performing a weak-field expansion; we recover a typical linear-regime expression, involving a single unintegrated gluon distribution function. Using numerical simulations of the small-x QCD evolution of the TMDs, we investigate the rapidity dependence of the cross section in the correlation limit.

Central exclusive χc,b production at high energy colliders and gluon saturation approach

The central exclusive production of χc and χb at the LHC, RHIC and Tevatron energies is analyzed, using the recent unintegrated parton distribution (UGDs) functions available in the package TMDlib. Comparison with data is performed, which tests the underlying assumptions basing the theoretical approach and it can constrain the unintegrated gluon distribution function at the small-x region. Predictions for LHC energies using recent UGDs based in CCFM formalism are provided. It is explored the underlying uncertainties on this production as the choice for the unintegrated gluon distribution and factorization scale is done. Moreover, based on the parton saturation model for the gluon distribution, analytical expressions for the rapidity distributions are proposed. The prompt production of J/ψ+γ and ϒ+γ is computed for the first time for LHC energies within the very same formalism used for χ production.

Production of f0(980) meson at the LHC: Color evaporation versus color-singlet gluon-gluon fusion

The production of the f0(980) meson at high energies is not well understood. We investigate two different potential mechanisms for inclusive scalar meson production in the kt-factorization approach: color-singlet gluon-gluon fusion and color evaporation model. The γ⁎γ⁎→f0(980) form factor(s) can be constraint from the f0(980) radiative decay width. The g⁎g⁎→f0(980) form factors are obtained by a replacement of αem electromagnetic coupling constant by αs strong coupling constant and appropriate color factors. The form factors for the two couplings are parametrized with a function motivated by recent results for scalar quarkonia. The differential cross sections are calculated in the kt-factorization approach with modern unintegrated gluon distributions. Unlike for quarkonia it seems rather difficult to describe a preliminary ALICE data for inclusive production of f0(980) exclusively by the color singlet gluon-gluon fusion mechanism. Two different scenarios for flavor structure of f0(980) are considered in this context. We consider also mechanism of fusion of quark-antiquark associated with soft gluon emission in a phenomenological color evaporation model (CEM) used sometimes for quarkonium production. Here we use kt-factorization version of CEM to include higher-order contributions. In addition, for comparison we consider also NLO collinear approach with qq¯q and qq¯g color octet partonic final states. Both approaches lead to a similar result. However, very large probabilities are required to describe the preliminary ALICE data. The pomeron-pomeron fusion mechanism is also discussed and results are quantified.

Exclusive production of ϕ meson in the γ*p→ϕp reaction at large photon virtualities within kT -factorization approach

We apply the $k_T$-factorization approach to the production of $\phi$ meson in deep-inelastic scattering. The helicity-conserving $\gamma^*(T,L) \to \phi$ impact factor is calculated for longitudinal and transverse photon polarization using $\phi$ meson distribution amplitudes. Different unintegrated gluon distributions are used in the calculations. The formalism for massless quarks/antiquarks gives too large transverse and longitudinal cross sections for photon virtualities below $Q^2\sim 8 \, \rm{GeV}^2$. We suggest how to improve the description of the HERA data by introducing effective strange quark masses into the formalism. We derive the corresponding massive impact factor by comparing to the light-cone wave function representation used in previous $k_T$-factorization calculations and the color-dipole approaches. As a byproduct we present expressions for higher twist-amplitudes as weighted integrals over the light-cone wave function. The quark mass $m_q \approx 0.5$ GeV allows to improve the description of both longitudinal and transverse cross section down to $Q^2 \sim$ 4 GeV$^2$. We present also the polarized cross section ratio $\sigma_L/\sigma_T$ and the behavior of the total cross section $\sigma_{tot} = \sigma_{L} + \sigma_{T}$ as a function of photon virtuality.

Double inclusive small- x gluon production and their azimuthal correlations in a biased ensemble

We consider double $gg\rightarrow g$ production in the presence of a bias on the unintegrated gluon distribution of the colliding hadron or nuclei. Such bias could be due to the selection of configurations with a greater number of gluons or higher mean transverse momentum squared or, more generally, due to a modified spectral shape of the gluon distribution in the hadrons. Hence, we consider reweighted functional averages over the stochastic ensemble of small-x gluons. We evaluate explicitly the double inclusive gluon transverse momentum spectrum in high-energy collisions, and their azimuthal correlations, for a few simple examples of biases.

Small x phenomenology on gluon evolution through the BFKL equation in light of a constraint in multi-Regge kinematics

We investigate the impact of so-called kinematic constraint on gluon evolution at small x. Implanting the constraint on the real emission term of the gluon ladder diagram, we obtain an integro-differential form of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation. Later we solve the equation analytically using the method of characteristics. We sketch the Bjorken x and transverse momentum dependence of our solution of unintegrated gluon distributions in the kinematic constraint supplemented BFKL equation and contrasted the same with the original BFKL equation. Then we extract the integrated gluon density xg(x, Q2) from unintegrated gluon distributions and compared our theoretical prediction with that of global data fits, namely NNPDF3.1sx and CT14. Finally we illustrate the phenomenological implication of our solution for unintegrated gluon distribution towards exploring high precision HERA DIS data by the theoretical prediction of proton structure functions (F2 and FL).

Prompt hadroproduction of \u03b7c(1S, 2S) in the kT-factorization approach

In this work, we present a thorough analysis of ηc(1S, 2S) quarkonia hadroproduction in k⊥-factorisation in the framework of the light-front potential approach for the quarkonium wave function. The off-shell matrix elements for the g*g*ηc(1S, 2S) vertices are derived. We discuss the importance of taking into account the gluon virtualities. We present the transverse momentum distributions of ηc for several models of the unintegrated gluon distributions. Our calculations are performed for four distinct parameterisations for the coverline{c} interaction potential consistent with the meson spectra. We compare our results for ηc(1S) to measurements by the LHCb collaboration and present predictions for ηc(2S) production.

From Transition Electromagnetic Form Factors \(\gamma ^* \gamma ^* \eta _c(1S,2S)\) to the Production of \(\eta _c(1S,2S)\) at the LHC

We review our recent results for production of $\eta_c(1S)$ and $\eta_c(2S)$ in the $\gamma^* \gamma^* \to \eta_c(1S,2S)$ fusion and in proton-proton collisions via gluon-gluon fusion. The quarkonium wave functions are calculated by solving Schr\"odinger equation for different $c \bar c$ potentials. Using Terentev prescription the light-cone wave functions are obtained. The light-cone wave functions are used then to calculate $\gamma^* \gamma^* \to \eta_c$ transition form factors. The theoretical results are compared to the Belle experimental data for $\eta_c(1S)$. In addition we discuss our results for two-photon decay width. We present also results of our calculations for proton-proton collisions obtained within $k_T$-factorization approach for different unintegrated gluon distributions. The results for hadroproduction of $\eta_c(1S)$ are compared to the LHCb experimental data.

Study of small x behaviour of unintegrated gluon distribution constraining gluon evolution in MD-BFKL equation

In this work we have proposed a modified form of MD-BFKL nonlinear evolution equation imposing a kinematic constraint on the gluon evolution in multi-Regge kinematics. Later we have suggested an analytical solution to our KC imposed MD-BFKL equation and studied nonlinear effect of the transverse momentum dependent (TMD) gluon distribution function at small x (10−6 ≤ x ≤ 10−2). Our results have been compared to various TMDlibuPDF datasets viz. PB-NLO-HERA I+II 2018, ccfm set A0.

QCD evolution based evidence for the onset of gluon saturation in exclusive photo-production of vector mesons

We investigate photo-production of vector mesons J/Ψ and ϒ measured both at HERA and LHC, using 2 particular fits of inclusive unintegrated gluon distributions, based on non-linear Balitsky-Kovchegov evolution (Kutak-Sapeta gluon; KS) and next-to-leading order Balitsky-Fadin-Kuraev-Lipatov evolution (Hentschinski-Sabio Vera-Salas gluon; HSS). We find that linear next-to-leading order evolution can only describe production at highest energies, if perturbative corrections are increased to unnaturally large values; rendering these corrections to a perturbative size, the growth with energy is too strong and the description fails. At the same time, the KS gluon, which we explore both with and without non-linear corrections, requires the latter to achieve an accurate description of the energy dependence of data. We interpret this observation as a clear signal for the presence of high gluon densities in the proton, characteristic for the onset of gluon saturation.

Studies on gluon evolution and geometrical scaling in kinematic constrained unitarized BFKL equation: application to high-precision HERA DIS data

We suggest a modified form of a unitarized BFKL equation imposing the so-called kinematic constraint on the gluon evolution in multi-Regge kinematics. The underlying nonlinear effects on the gluon evolution are investigated by solving the unitarized BFKL equation analytically. We obtain an equation of the critical boundary between dilute and dense partonic system, following a new differential geometric approach and sketch a phenomenological insight on geometrical scaling. Later we illustrate the phenomenological implication of our solution for unintegrated gluon distribution f(x,k_T^2) towards exploring high precision HERA DIS data by theoretical prediction of proton structure functions (F_2 and F_L) as well as double differential reduced cross section (sigma _r). The validity of our theory in the low Q^2 transition region is established by studying virtual photon–proton cross section in light of HERA data.

Associated production of χc pairs with a gluon in the collinear-factorization approach

We calculate cross section for production of $\chi_c$ pairs in proton-proton collisions. The cross section for the $g g \to \chi_{c J_1} \chi_{c J_2}$ is considerably smaller (especially for $\chi_{c 1} \chi_{c 1}$ final state) than that obtained recently in the $k_T$-factorization approach. We calculate therefore next-to-leading order contributions with $\chi_c$ pair and one extra associated (mini-)jet. We find these contributions to be much larger than those for the $2 \to 2$ contribution. Especially the emission of a leading gluon (carrying a large momentum fraction of one of the incoming gluons) are important. These emissions in the $k_T$-factorization approach are absorbed into the initial state unintegrated gluon distributions. A smaller contribution to the cross section comes from the production of central gluons emitted with rapidities between the $\chi_c$-mesons. They do lead, however, to an enhancement of the $\chi_c$-pair production at large rapidity distance between the mesons. Our present study explains the size of the cross section for the $\chi_c$ pair production obtained previously in the $k_T$-factorization approach. Several differential distributions are presented.

J/ψ -meson production within improved color evaporation model with the kT -factorization approach for cc¯ production

We use a new approach to color evaporation model (CEM) for quarkonium production. The production of $c\bar c$ pairs is performed within $k_T$-factorization approach using different unintegrated gluon distribution functions (UGDF) from the literature. We include all recent improvements to color evaporation model. We cannot describe simultaneously mid and forward rapidity data measured at the LHC when using the KMR UGDF with the same normalization parameter. Furthermore we get somewhat too hard distribution in $J/\psi$ transverse momentum. Correcting the standard KMR distributions for saturation effects at small values of $x$ improves $J/\psi$ rapidity distributions, while taking correction for emissions hidden in the KMR UGDF in the evaluation of $x$ values improves a bit $J/\psi$ transverse momentum distributions. The modifications improve also description of the LHCb $D$-meson data.

K_T-factorization approach to the Higgs boson production in ZZ^*rightarrow 4ell channel at the LHC

We calculated a differential cross section of the Higgs boson production in the hrightarrow ZZ^*rightarrow 4ell decay channel within the framework of k_T-factorization. Results are obtained using an off-shell matrix element for the g^*g^*rightarrow hrightarrow ZZ^*rightarrow 4ell process together with Ciafaloni–Catani–Fiorani–Marchesini (CCFM) evolution equations for an unintegrated gluon distribution function. We have presented a comparison of our results with the latest experimental measurements at sqrt{S} = 8hbox { TeV} and sqrt{S} = 13 hbox {TeV} from the ATLAS and CMS collaborations at the LHC. In addition to this, we have compared our results with the results from the collinear factorization formalism calculated up to next-to-next-to-leading order plus next-to-next-to-leading logarithm (NNLO + NNLL) accuracy obtained using the HRes code for the Higgs boson production in the gluon-gluon fusion process. Our estimates are consistently close to NNLO + NNLL results obtained using a collinear factorization formalism and are also in agreement with experimental measurements.

Constraining unintegrated gluon distributions from inclusive photon production in proton–proton collisions at the LHC

We compute the leading order (LO) qg→qγ and next-to-leading order (NLO) gg→qq¯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 kγ⊥ corresponding to momentum fractions of x≤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⊥-dependent unintegrated gluon distributions in both of the protons. We predict a maximal 10% modification of the cross section at low kγ⊥ as a direct consequence of the violation of k⊥-factorization. The coherence effects responsible for this modification are enhanced in nuclei and can be identified from inclusive photon measurements in proton–nucleus collisions. We provide numerical results for the isolated inclusive photon cross section for kγ⊥≤20 GeV in p+p collisions that can be tested in the future at the LHC.