Unintegrated Gluon Distribution Functions 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.

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.

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.

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.

Unintegrated dipole gluon distribution at small transverse momentum

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.

Charm quark and meson production in association with single-jet at the LHC

We discuss charm quark/antiquark and charmed meson production in association with one extra jet (gluon, quark, antiquark) at the LHC. The calculations are performed both in collinear and $k_T$-factorization approaches. Different unintegrated gluon distribution functions are used in the $k_T$-factorization approach. Several predictions for the LHC are presented. We show distributions in rapidity and transverse momenta of $c$/$\bar c$ (or charmed mesons) and the associated jet as well as some two-dimensional observables. Interesting correlation effects are predicted, \textit{e.g.} in azimuthal angles $\varphi_{c\bar{c}}$ and $\varphi_{c\mathrm{\textit{-jet}}}$. We have also discussed a relation of the $2 \to 2$ and $2 \to 3$ partonic calculations in the region of large transverse momenta of charm quarks/antiquarks as well as the similarity of the next-to-leading order collinear approach and the $k_T$-factorization approach with the KMR unintegrated parton distribution functions. Integrated cross sections for $D^{0}$ + jet production for ATLAS detector acceptance and for different cuts on jet transverse momenta are also presented.

B-meson production at Tevatron and the LHC in the Regge limit of quantum chromodynamics

We study the inclusive hadroproduction of B0, B+, and Bs0 mesons in the leading order in the parton Reggeization approach. We have described B-meson transverse momentumdistributionsmeasured in the central region of rapidity by the CDF Collaboration at Fermilab Tevatron and CMS Collaboration at LHC within uncertainties and without free parameters, applying Kimber–Martin–Ryskin unintegrated gluon distribution function in a proton.

Open charm production in the parton Reggeization approach: Tevatron and the LHC

We study the inclusive hadroproduction of D^0, D^+, D^star+, and D_s^+ mesons at leading order in the parton Reggeization approach endowed with universal fragmentation functions fitted to $e^+e^-$ annihilation data from CERN LEP1. We have described $D$-meson transverse momentum distributions measured in the central region of rapidity by the CDF Collaboration at Tevatron (|y|<1) and ALICE Collaboration at LHC (|y|<0.5) within uncertainties and without free parameters, using Kimber-Martin-Ryskin unintegrated gluon distribution function in a proton. The forward D-meson production (|y|>2.0) measured by the LHCb Collaboration also has been studied and expected disagreement between our theoretical predictions and data has been obtained.

B-meson production in the Parton Reggeization Approach at Tevatron and the LHC

We study the inclusive hadroproduction of B0, B+and [Formula: see text] mesons at leading order in the Parton Reggeization Approach using the universal fragmentation functions extracted from the combined e+e-annihilation data from CERN LEP1 and SLAC SLC colliders. We have described B-meson transverse momentum distributions measured in the central region of rapidity by the CDF Collaboration at Fermilab Tevatron and CMS Collaboration at LHC within uncertainties and without free parameters, applying Kimber–Martin–Ryskin unintegrated gluon distribution function in a proton. The forward B-meson production (2.0&lt;y&lt;4.5) measured by the LHCb Collaboration also has been studied and expected disagreement between our theoretical predictions and data has been obtained.

Рождение $D$-мезонов на Большом адронном коллайдере в реджевском пределе КХД

В работе рассматривается инклюзивное рождение очарованных $D^{0}$, $D^{+}$, $D^{\star+}$ и $D_{s}^{+}$ мезонов в протон-антипротонных соударениях на коллайдере Тэватрон и протон-протонных соударениях на Большом адронном коллайдере (БАК). Теоретические расчeты проведены в лидирующем порядке теории реджезованных партонов (ТРП), основанной на эффективной квантовой теории поля Л. Н. Липатова и подходе $k_{T}$-факторизации при высоких энергиях. В работе были использованы универсальные функции фрагментации (ФФ), полученные фитированием данных рождения $D$-мезонов на линейном электрон-позитронном коллайдере LEP1. Нами описаны распределения $D$-мезонов по поперечному импульсу, измеренные в центральной области быстрот коллаборациями CDF на Тэватроне ($|y|&lt;1$) и ALICE на БАК ($|y|&lt;0.5$) в пределах ошибок измерений и без привлечения свободных параметров. На стадии численных расчeтов нами использовались неинтегрированные глюонные функции распределения (ФР) Кимбера, Мартина и Рыскина (КМР).

Rapidity profile of the initial energy density in heavy-ion collisions

The rapidity dependence of the initial energy density in heavy-ion collisions is calculated from a three-dimensional McLerran-Venugopalan model (3dMVn) introduced by Lam and Mahlon. This model is infrared safe since global color neutrality is enforced. In this non-boost-invariant framework, the nuclei have non-zero thickness in the longitudinal direction. This results in Bjorken-x dependent unintegrated gluon distribution functions which lead to a rapidity-dependent initial energy density after the collision. The initial energy density and its rapidity dependence are important initial conditions for the quark gluon plasma and its hydrodynamic evolution.

PromptΥ(nS)production at the LHC in the Regge limit of QCD

We study prompt $\ensuremath{\Upsilon}(nS)$ hadroproduction ($n=1$, 2, 3) invoking the hypothesis of gluon Reggeization in $t$-channel exchanges at high energy and the factorization formalism of nonrelativistic quantum chromodynamics at leading order in the strong-coupling constant ${\ensuremath{\alpha}}_{s}$ and the relative velocity $v$ of the bound quarks. The transverse-momentum distributions of prompt $\ensuremath{\Upsilon}(nS)$-meson production measured by the ATLAS Collaboration at the CERN LHC are fitted to obtain the color-octet nonperturbative long-distance matrix elements, which are used to predict prompt $\ensuremath{\Upsilon}(nS)$ production spectra measured by the CMS and LHCb Collaborations. At the numerical calculation, we adopt the Kimber-Martin-Ryskin prescription to derive unintegrated gluon distribution function of the proton from its collinear counterpart, for which we use the Martin-Roberts-Stirling-Thorne set. We find good agreement with measurements by the ATLAS, CMS, and LHCb Collaborations at the LHC at the hadronic c.m. energy $\sqrt{S}=7\text{ }\text{ }\mathrm{TeV}$ as well as with measurements by the CDF Collaboration at the Fermilab Tevatron.

Inclusiveb-jet andbb¯-dijet production at the LHC via Reggeized gluons

We study inclusive $b$-jet and $b\bar b$-dijet production at the CERN LHC invoking the hypothesis of gluon Reggeization in $t$-channel exchanges at high energy. The $b$-jet cross section includes contributions from open $b$-quark production and from $b$-quark production via gluon-to-bottom-pair fragmentation. The transverse-momentum distributions of inclusive $b$-jet production measured with the ATLAS detector at the CERN LHC in different rapidity ranges are calculated both within multi-Regge kinematics and quasi-multi-Regge kinematics. The $b\bar b$-dijet cross-section is calculated within quasi-multi-Regge kinematics as a function of the dijet invariant mass $M_{jj}$, the azimuthal angle between the two jets $\Delta\phi$ and the angular variable $\chi$. At the numerical calculation, we adopt the Kimber-Martin-Ryskin and Bl\"umlein prescriptions to derive unintegrated gluon distribution function of the proton from its collinear counterpart, for which we use the Martin-Roberts-Stirling-Thorne set. We find good agreement with measurements by the ATLAS and CMS Collaborations at the LHC at the hadronic c.m.\ energy of $\sqrt S=7$ TeV.

PromptJ/ψproduction in the Regge limit of QCD: From the Tevatron to the LHC

We study prompt J/psi-meson hadroproduction invoking the hypothesis of gluon Reggeization in t-channel exchanges at high energy and the factorization formalism of nonrelativistic quantum chromodynamics at the leading order in the strong-coupling constant alpha_s and the relative velocity of quarks v. The transverse-momentum distribution of direct and prompt J/psi-meson production measured at the Fermilab Tevatron fitted to obtain the nonperturbative long-distance matrix elements, which are used to predict prompt J/psi production spectra at the CERN LHC. At the numerical calculation, we adopt the Kimber-Martin-Ryskin and Blumlein prescriptions to derive unintegrated gluon distribution function of the proton from their collinear counterpart, for which we use the Martin-Roberts-Stirling-Thorne set. Without adjusting any free parameters, we find good agreement with measurements by the ATLAS, CMS and LHCb Collaborations at the LHC at the hadronic c.m. energy sqrt S=7 TeV.

Single jet and prompt-photon inclusive production with multi-Regge kinematics: From Tevatron to LHC

We study single jet and prompt-photon inclusive hadroproduction with multi-Regge kinematics invoking the hypothesis of parton Reggeization in t-channel exchanges at high energy. In this approach, the leading contributions are due to the fusion of two Reggeized gluons into a Yang-Mills gluon and the annihilation of a Reggeized quark-antiquark pair into a photon, respectively. Adopting the Kimber-Martin-Ryskin and Bluemlein prescription to derive unintegrated gluon and quark distribution functions of the proton from their collinear counterparts, for which we use the Martin-Roberts-Stirling-Thorne set, we evaluate cross section distributions in transverse momentum (p_T) and rapidity. Without adjusting any free parameters, we find good agreement with measurements by the CDF and D0 Collaborations at the Tevatron and by the ATLAS Collaboration at the LHC in the region 2p_T/sqrt{S} < 0.1, where sqrt{S} is the hadronic c.m. energy.

Exclusive production of [formula omitted] meson and its measurement in the [formula omitted] channel

We report on the results of a theoretical study of the central exclusive production of scalar χc(0+) meson via χc0→π+π− decay in high-energy hadron collisions at the RHIC, Tevatron and LHC. The corresponding amplitude for exclusive double-diffractive χc0 meson production was obtained within the kt-factorization approach including virtualities of active gluons and the cross section is calculated with unintegrated gluon distribution functions (UGDFs) known from the literature. The four-body pp→ppπ+π− reaction constitutes an irreducible background to the exclusive χc0 meson production. We include the absorption effects due to proton-proton interaction and pion-pion rescattering. Several differential distributions for pp(p¯)→pp(p¯)χc0 process, including the absorptive corrections, were calculated. The influence of kinematical cuts on the signal-to-background ratio is investigated.

Measurement of exclusive production of scalar [formula omitted] meson in proton–(anti)proton collisions via [formula omitted] decay

We consider a measurement of exclusive production of scalar χc(0++) meson in the proton–proton collisions at LHC and RHIC and in the proton–antiproton collisions at the Tevatron via χc0→π+π− decay. The corresponding amplitude for exclusive double-diffractive χc0 meson production was obtained within the kt-factorization approach including virtualities of active gluons and the corresponding cross section is calculated with unintegrated gluon distribution functions (UGDFs) known from the literature. The four-body pp→ppπ+π− reaction constitutes an irreducible background to the exclusive χc0 meson production. We include absorption effects due to proton–proton interaction and pion–pion rescattering. We calculate several differential distributions for pp(p¯)→pp(p¯)χc0 process including the absorptive corrections. The influence of kinematical cuts on the signal-to-background ratio is investigated. Corresponding experimental consequences are discussed.

Inclusivebandbb¯production with quasi-multi-Regge kinematics at the Tevatron

We consider $b$-jet hadroproduction in the quasi-multi-Regge-kinematics approach based on the hypothesis of gluon and quark Reggeization in $t$-channel exchanges at high energies. The preliminary data on inclusive $b$-jet and $b\overline{b}$-dijet production taken by the CDF Collaboration at the Fermilab Tevatron are well described without adjusting parameters. We find the main contribution to inclusive $b$-jet production to be the scattering of a Reggeized gluon and a Reggeized $b$ quark to a $b$ quark, which is described by the effective Reggeon-Reggeon-quark vertex. The main contribution to $b\overline{b}$-pair production arises from the scattering of two Reggeized gluons to a $b\overline{b}$ pair, which is described by the effective Reggeon-Reggeon-quark-quark vertex. Our analysis is based on the Kimber-Martin-Ryskin prescription for unintegrated gluon and quark distribution functions using as input the Martin-Roberts-Stirling-Thorne collinear parton distribution functions of the proton.