kT-factorization Approach Research Articles

Production mechanism of fully heavy tetraquarks in proton-proton collisions

We discuss the production mechanism of fully charm tetraquark, observed last year 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. We present transverse momentum distribution in pt,4c for ccc¯ c¯ system in a mass window around tetraquark mass. The calculation of the SPS g ∗ g ∗ → T4c(6900) fusion mechanism is performed in the kT -factorization approach assuming different spin scenarios (0 + and 0 −).

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.

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.

Two-Jet Correlations in Multijet Events in the Regge Limit of QCD

A new method for matching calculations in the leading approximation in the kT-factorization approach with the higher-order contributions of perturbation theory, which appear due to the emission of additional hard partons, is proposed. In the proposed method, azimuthal correlations between the leading and subleading jets in a multijet event are considered. The calculations are carried out within the parton Reggeization approach (PRA) that is based on kT-factorization of hard processes in multi-Regge kinematics, the Kimber–Martin–Ryskin model for nonintegrated parton distribution functions (nPDF), and the effective field theory of Reggeized gluons and quarks proposed by L.N. Lipatov. Theoretical predictions are compared with the CMS collaboration data collected at the Large Hadron Collider at energy $$\sqrt S = 13$$ TeV.

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.

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.

Inclusive Higgs Boson Production at the LHC within the QCD kt-Factorization Approach

Inclusive Higgs Boson Production at the LHC within the QCD kt-Factorization Approach

Quarkonium Production and Polarization in an Improved Color Evaporation Model

An improved version of the color evaporation model (ICEM) has been introduced to describe heavy quarkonium production. In contrast to the traditional color evaporation model, the constraint was imposed that the invariant mass of the intermediate heavy quark-antiquark pair must be larger than the mass of produced quarkonium. A momentum shift between heavy quark-antiquark pair and the quarkonium was also introduced. Calculations show that the model can describe the charmonium yields as well as ratio of ψ′ over J/ψ better than the traditional color evaporation model. The ICEM has been extended to calculate the polarization of prompt J/ψ and ϒ(1S) production for the first time in the color evaporation approach. The first calculations were made at leading order. The polarization parameter λϑ was calculated as a function of center of mass energy and rapidity in p + p collisions. The xF dependence of the polarization was also calculated and compred to experimental results in p+Cu and π+W collisions. The next step of calculating the pT dependence of the polarization has been taken, with a calculation in the kT-factorization approach. We compare the unpolarized pT distributions for the J/ψ and ψ′, as well as the ψ′ to J/ψ ratio, in p + p collisions at RHIC and the LHC for several energies. We also present the polarization results and make comparison to polarization data.

The EMC ratios of 4He, 3He and 3H nuclei in the kt factorization framework using the Kimber–Martin–Ryskin unintegrated parton distribution functions

The unintegrated parton distribution functions (UPDFs) of 3H, 3He and 4He nuclei are generated to calculate their structure functions (SFs) in the kt-factorization approach. The Kimber–Martin–Ryskin (KMR) formalism is applied to evaluate the double-scale UPDFs of these nuclei from their single-scale parton distribution functions (PDFs), which can be obtained from the constituent quark exchange model (CQEM). Afterwards, these SFs are used to calculate the European Muon Collaboration (EMC) ratios of these nuclei. The resulting EMC ratios are then compared with the available experimental data and good agreement with data is achieved. In comparison with our previous EMC ratios, in which the conventional PDFs were used in the calculations, the accord of the present outcomes with experiment at the small x region becomes impressive. Therefore, it can be concluded that the kt dependence of partons can reproduce the general form of the shadowing effect at the small x values in above nuclei.

Can the triple-parton scattering be observed in open charm meson production at the LHC?

We investigate whether the triple-parton scattering effects can be observed in open charm production in proton–proton collisions at the LHC. We use so-called factorized Ansatz for calculations of hard multiple-parton interactions. The numerical results for each parton interaction are obtained within the kT-factorization approach. Predictions for one, two and three cc¯ pairs production are given for s=7 TeV and s=13 TeV. Quite large cross sections, of the order of milibarns, for the triple-parton scattering mechanism are obtained. We suggest a measurement of three D0 or three D0¯ mesons by the LHCb Collaboration. Confronting our results with recent LHCb experimental data for single and double D0 (or D0¯) meson production we present our predictions for triple meson final state: D0D0D0 or D0¯D0¯D0¯. We present cross sections for the LHCb fiducial volume as well as distributions for D0 meson transverse momentum and three-D0 meson invariant mass. The predicted visible cross sections, including the detector acceptance, hadronization effects and c→D0 branching fraction, is of the order of a few nanobarns. The counting rates including D0→K−π+ branching fractions are given for known or expected integrated luminosities.

Single-diffractive production of charmed mesons at the LHC within the kt-factorization approach

We discuss the single-diffractive production of cc pairs and charmed mesons at the LHC. For a first time we propose a kt-factorization approach to the diffractive processes. The transverse momentum dependent diffractive parton distributions are obtained from standard (collinear) diffractive parton distributions used in the literature. In this calculation the transverse momentum of the pomeron is neglected with respect to transverse momentum of partons entering the hard process. We also perform a first evaluation of the cross sections at the LHC using the diffractive transverse momentum dependent parton distributions. The results of the new approach are compared with those of the standard collinear one. Significantly larger cross sections are obtained in the kt-factorization approach in which some parts of higher-order effects is effectively included. The differences between corresponding differential distributions are discussed. Finally, we present a feasibility study of the process at the LHC using proton tagging technique. The analysis suggests that the measurement of single-diffractive charm production is possible using ATLAS and CMS/TOTEM detectors.

Prompt charmonia production and polarization at LHC in the NRQCD withkT-factorization. II.χcmesons

In the framework of kt-factorization approach,the production of prompt $\chi_c$ mesons in pp collisions at the LHC energies is studied. Our consideration is based on the off-shell amplitudes for hard partonic subprocesses $g^*g^*\to\chi_{cJ}$ and non-relativistic QCD formalism for bound states. The transverse momentum dependent (unintegrated) gluon densities in a proton were derived from Ciafaloni-Catani-Fiorani-Marchesini evolution equation or, alternatively, were chosen in accordance with Kimber-Martin-Ryskin prescription. Taking into account both color singlet and color octet contributions, we deduce the corresponding non-perturbative long-distance matrix elements from the fits to the latest ATLAS data on $\chi_{c1}$ and $\chi_{c2}$ transverse momentum distributions at $\sqrt s = 7$ TeV. We find that these distributions at small and moderate pt are formed mainly by the color singlet components. We successfully described the data on the differential cross sections and relative production rates $\sigma(\chi_{c2})/\sigma(\chi_{c1})$ presented by the ATLAS, CMS and LHCb Collaborations. We find that the fit points to unequal wave functions of $\chi_{c1}$ and $\chi_{c2}$ states.

Light Vector Mesons Production in Ultrarelativistic Heavy Ion Collisions from the Color Glass Condensate**Supported by the National Natural Science Foundation of China under Grant Nos. 11465021 and 11065010

We calculate inclusive light vector mesons (ρ, ω, and ϕ) production in relativistic heavy ion collisions based on the idea of gluon saturation in the color glass condensate (CGC) framework. At high energies, the value of saturation momentum becomes larger than the Quantum Chromodynamics (QCD) confinement scale ΛQCD, which implies that αs(Qs) ≪ 1. Using the relativistic kinetic theory, we derive the production rate for the light vector mesons produced by gluon-gluon fusion in the kT-factorization approach. The numerical results indicate that the light vector mesons from the color glass condensate become prominent in p-p, p-Pb, and Pb-Pb collisions at Large Hadron Collider (LHC) energies.

Prompt charmonia production and polarization at LHC in the NRQCD with $$k_T$$ k T -factorization. Part I: $$\psi (2S)$$ ψ ( 2 S ) meson

In the framework of kt-factorization approach, the production and polarization of prompt psi(2S) mesons in pp collisions at the LHC energies is studied. Our consideration is based on the non-relativistic QCD formalism for bound states and off-shell amplitudes for hard partonic subprocesses. The transverse momentum dependent (unintegrated) gluon densities in a proton were derived from Ciafaloni-Catani-Fiorani-Marchesini evolution equation or, alternatively, were chosen in accordance with Kimber-Martin-Ryskin prescription. The non-perturbative color-octet matrix elements were first deduced from the fits to the latest CMS data on psi(2S) transverse momentum distributions and then applied to describe the ATLAS and LHCb data on psi(2S) production and polarization at 7 TeV. We perform the estimation of polarization parameters $\lambda_\theta$, $\lambda_\phi$ and $\lambda_{\theta \phi}$ which determine psi(2S) spin density matrix and demonstrate that taking into account the off-shellness of initial gluons in the color-octet contributions leads to unpolarized psi(2S) production at high transverse momenta, that is in qualitative agreement with the LHC data.

Production of two charm quark–antiquark pairs in single-parton scattering within the [formula omitted]-factorization approach

We present first results for the 2→4 single-parton scattering gg→cc¯cc¯ subprocess for the first time fully within the kt-factorization approach. In this calculation we have used the Kimber–Martin–Ryskin unintegrated gluon distribution which effectively includes some class of higher-order gluon emissions, and an off-shell matrix element squared calculated using recently developed techniques. The results are compared with our earlier result obtained within the collinear-factorization approach. Only slightly larger cross sections are obtained than in the case of the collinear approach. Inclusion of transverse momenta of gluons entering the hard process leads to a much stronger azimuthal decorrelation between cc and c¯c¯ than in the collinear-factorization approach. A comparison to predictions of double parton scattering (DPS) results and the LHCb data strongly suggests that the assumption of two fully independent DPS (gg→cc¯⊗gg→cc¯) may be too approximate.

Associated [formula omitted] production at the LHC and prospects to observe double parton interactions

Associated production of charged gauge bosons and charged charmed mesons at the LHC is considered in the framework of kt-factorization approach. Theoretical predictions are compared with ATLAS data, and reasonably good agreement is found. Predictions on the same-sign W±D± configurations are presented including single parton scattering and double parton scattering contributions. The latter are shown to dominate over the former, thus giving evidence that the proposed process can serve as another indicator of double parton interactions.

Exclusive photoproduction of charmonia in γp → V p and pp → pV p reactions within kt-factorization approach

The amplitude for $\gamma p \to J/\psi p$ ($\gamma p \to \psi' p$) is calculated in a pQCD $k_{T}$-factorization approach. The total cross section for this process is calculated for different unintegrated gluon distributions and compared with the HERA data and the data extracted recently by the LHCb collaboration. The amplitude for $\gamma p \to J/\psi p$ ($\gamma p \to \psi' p$) is used to predict the cross section for exclusive photoproduction of $J/\psi$ ($\psi'$) meson in proton-proton collisions. Compared to earlier calculations we include both Dirac and Pauli electromagnetic form factors. The effect of Pauli form factor is quantified. Absorption effects are taken into account and their role is discussed in detail. Different differential distributions e.g. in $J/\psi$ ($\psi'$) rapidity and transverse momentum are presented and compared with existing experimental data. The UGDF with nonlinear effects built in better describe recent experimental data of the LHCb collaboration but no definite conclusion on onset of saturation can be drawn. We present our results also for the Tevatron. A good agreement with the CDF experimental data points at the midrapidity for both $J/\psi$ and $\psi'$ is achieved.

Measurement of the differential [formula omitted]-jet cross section and the ratio [formula omitted] in [formula omitted] collisions at [formula omitted

We present the first measurements of the differential cross section dσ/dpTγ for the production of an isolated photon in association with at least two b-quark jets. The measurements consider photons with rapidities |yγ|<1.0 and transverse momenta 30<pTγ<200 GeV. The b-quark jets are required to have pTjet>15 GeV and |yjet|<1.5. The ratio of differential production cross sections for γ+2b-jets to γ+b-jet as a function of pTγ is also presented. The results are based on the proton–antiproton collision data at s=1.96 TeV collected with the D0 detector at the Fermilab Tevatron Collider. The measured cross sections and their ratios are compared to the next-to-leading order perturbative QCD calculations as well as predictions based on the kT-factorization approach and those from the sherpa and pythia Monte Carlo event generators.

Exclusive photoproduction ofJ/Ψ and Ψ′ mesons in proton-proton collisions

We present results based on our new paper (1). The amplitude for the γp → Vp reaction is calculated in a pQCD kt-factorization approach. The corresponding total cross section for different unintegrated gluon distributions is calculated and compared with new HERA data for photon-proton collisions. We also compare the total cross section for γp → Vpreaction with recent data extracted by the LHCb collaboration. The amplitude for γp → Vpis used to predict cross section for exclusive photoproduction of J/ψ and ψ � mesons in proton-proton collisions. Both Dirac and Pauli electromagnetic form factors are included in the calculation and results are compared with results when only Dirac form factor is included. The effect of Pauli form factor is quantified. Absorption effects are included and their uncertainties are discussed. Different differential distributions e.g. in J/ψ(ψ � ) rapidity and transverse momentum are presented and compared with existing experimental data for the Tevatron and LHC energy.