Transverse Momentum Distributions Research Articles

Scaling of factorial moments in cumulative variables

A search for power-law fluctuations within the framework of the intermittency method is ongoing to locate the critical point of the strongly interacting matter. In particular, experimental data on proton and pion production in heavy-ion collisions are analyzed in transverse-momentum, pT, space.In this regard, we have studied the dependence of the second scaled factorial moment F2 of particle multiplicity distribution on the number of subdivisions of transverse momentum-interval used in the analysis. The study is performed using a simple model with a power-law two-particle correlation function in pT. We observe that F2 values depend on the size and position of the pT interval. However, when we convert the non-uniform transverse-momentum distribution to uniform one using cumulative transformation, F2 calculated in subdivisions of the cumulative pT becomes independent of the cumulative-pT interval. The scaling behaviour of F2 for the cumulative variable is observed. Moreover, F2 follows a power law with the number of subdivisions of the cumulative-pT interval with the intermittency index close to the correlation function's exponent.

Non-extensive transverse momentum distribution for identified particles at SNN = 7.7, 11.5, 19.6, 27, 39GeV

The transverse momentum distribution of charged particles formed in Au–Au collisions at Beam Energy Scan (BES) ([Formula: see text][Formula: see text]GeV) is investigated. In addition, [Formula: see text] spectra of [Formula: see text] particle at [Formula: see text][Formula: see text]GeV were examined. Tsallis distribution is used to extract the temperature, volume and the entropic index from the experimental results at mid-rapidity and zero chemical potential. We measure some particle ratios like [Formula: see text] and [Formula: see text] which are puzzling horn in the experiment and in the thermal model. We conclude that the horn vanished when we used Tsallis distribution, but this does not confirm a solution to the puzzle, which is primarily visible in the experimental results.

Threshold resummation of transverse momentum distributions beyond next-to-leading log

We derive a general expression for the threshold resummation of transverse momentum distributions for processes with a colorless final state, by suitably generalizing the renormalization-group based approach to threshold resummation previously pursued by two of us. The ensuing expression holds to all logarithmic orders, and it can be used to extend available results in the literature, which only hold up to the next-to-leading log (NLL) level. We check agreement of our result with the existing NLL result, as well as against the known fixed next-to-leading order results for the Higgs transverse momentum distribution in gluon fusion, and we provide explicit expressions at the next-to-next-to-leading log level.

Study of transverse momentum and nuclear modification factors distribution of charged particles produced in pp and Pb–Pb collisions at s NN = 2.76TeV and 5.02TeV

We have studied transverse momentum distributions of charged particles produced in pp and Pb–Pb collisions at [Formula: see text] TeV and 5.02 TeV in the pseudorapidity interval [Formula: see text] and transverse momentum range [Formula: see text][Formula: see text]GeV/[Formula: see text]. We simulated data using EPOS-LHC, EPOS-1.99 and QGSJETII-04 models. The simulation data is compared with the ALICE experimental data values at [Formula: see text] TeV and 5.02 TeV for pp and most central Pb–Pb collisions. It has been observed that, EPOS-LHC and QGSJETII-04 models explain the experimental results for pp collision at [Formula: see text] TeV and 5.02 TeV. The behavior of nuclear modification factors has been studied. The simulation codes of all three models EPOS-LHC, EPOS-1.99 and QGSJETII-04 overestimate the experimental results at low transverse momentum interval: [Formula: see text] GeV/[Formula: see text], for Pb–Pb collisions at [Formula: see text] TeV and 5.02 TeV. However, only EPOS-LHC model can explain the experimental data at high transverse momentum in the range: [Formula: see text] GeV/[Formula: see text]. EPOS-1.99 and QGSJETII-04 underestimate in the region of Cronin effect and cannot give satisfactory estimates for the [Formula: see text] values for which [Formula: see text] demonstrates stronger suppression because of the collective parton effect. It can be inferred that these effects are not taken into account in EPOS-1.99 and QGSJETII-04 models. These models, however, satisfactorily explain the ALICE experimental data in the ranges of [Formula: see text] for which nuclear modification factor [Formula: see text] shows rising trend.

Inclusive diffractive heavy quarkonium photoproduction including quark subprocesses

The inclusive $J/\Psi$, $\Psi(2S)$ and $\Upsilon(1S)$ direct and resolved photoproduction are investigated by including the quark subprocesses in the framework of non-relativistic quantum chromodynamics (NRQCD). We find that the theoretical total cross section of heavy quarkonium productions are in good agreement with the data available at HERA, once the $\gamma q$, $qg$ and $qq$ subprocesses in the heavy quark pair productions are taken into account. The inclusive diffractive rapidity and transverse momentum distributions of $J/\Psi$, $\Psi(2S)$ and $\Upsilon(1S)$ in $pp$, $pPb$ and $PbPb$ collisions at LHC are also studied by our quark improved NRQCD model combined with the resolved pomeron model. We find that the contributions from the quark involved subprocesses can reach to $8\%$ in the rapidity distribution and $6\%$ in the transverse momentum distribution. The numerical results show that the contributions from quark involved subprocesses are significant in heavy quarkonium photoprodution.

New findings in gluon TMD physics

We revisit the model-independent decomposition of the gluon correlator, producing T-even and T-odd gluon transverse momentum distributions (TMDs), at leading twist. We propose an expansion of the gluon correlator, using a basis of four tensors (one antisymmetric and three symmetric), which are expressed through generators of the $U(2)$ group acting in the two-dimensional transverse plane. One can do clear interpretations of the two transversity T-odd TMDs with linear polarization of gluons: symmetric and asymmetric under permutation of the transverse spin of the nucleon and the transverse momentum of the gluon. Using light-front wave function (LFWF) representation, we also derive T-even and T-odd gluon TMDs in the nucleon at leading twist. The gluon-three-quark Fock component in the nucleon is considered as bound state of gluon and three-quark core (spectator). The TMDs are constructed as factorized product of two LFWFs and gluonic matrix encoding information about both T-even and T-odd TMDs. In particular, T-odd TMDs arise due to gluon rescattering between the gluon and three-quark spectator. Gluon rescattering effects are parametrized by unknown scalar functions depending on the $x$ and ${\bf k}_{\perp}$ variables. Our gluon TDMs obey the model-independent Mulders-Rodrigues inequalities. We also derive new sum rules (SRs) involving T-even TMDs. One of the SRs states that the square of the unpolarized TMD is equal to a sum of the squares of three polarized TMDs. Based on the SR derived for T-even gluon TMDs, we make a conjecture that there should two additional SRs involving T-odd gluon TMDs, valid at orders $\alpha_s$ and $\alpha_s^2$. Then, we check these SRs at small and large values of $x$. We think that our study could serve as useful input for future phenomenological studies of TMDs.

The multiple-charm hierarchy in the statistical hadronization model

In relativistic nuclear collisions the production of hadrons with light (u,d,s) quarks is quantitatively described in the framework of the Statistical Hadronization Model (SHM). Charm quarks are dominantly produced in initial hard collisions but interact strongly in the hot fireball and thermalize. Therefore charmed hadrons can be incorporated into the SHM by treating charm quarks as ‘impurities’ with thermal distributions, while the total charm content of the fireball is fixed by the measured open charm cross section. We call this model SHMc and demonstrate that with SHMc the measured multiplicities of single charm hadrons in lead-lead collisions at LHC energies can be well described with the same thermal parameters as for (u,d,s) hadrons. Furthermore, transverse momentum distributions are computed in a blast-wave model, which includes the resonance decay kinematics. SHMc is extended to lighter collision systems down to oxygen-oxygen and includes doubly- and triply-charmed hadrons. We show predictions for production probabilities of such states exhibiting a characteristic and quite spectacular enhancement hierarchy.

The Production of Gauge Bosons Pairs $${{W}^{ + }}{{W}^{ - }}$$ Associated with 0, 1, and 2 Jets in Proton–Proton Collisions at LHC

We report in this work the production of $W^+W^-$ pairs gauge bosons associated with 0, 1 and 2 jets in proton-proton collisions at LHC with an energy of 14 TeV in the center of mass. These processes are produced at leading-order (LO) and next-to-leading-order (NLO) with QCD corrections in the standard model, using MadGraph5@aMC. For a realistic description of the processes, we match the hard scattering processes with Pythia8 parton showering and hadronization. The obtained events are run through the fast detector simulation, Delphes, which serves to accurately model the ATLAS and CMS detectors and the final state reconstructions that are performed. We analyze the total cross sections according on two cuts in jet transverse momentum p T,j > 20 GeV and p T,j > 100 GeV. We describe the important numerical aspects of our calculations by presenting transverse momentum and rapidity distributions at partonic fixed order and at parton shower for both W and the $W^+W^-$ pair.

Small-pT and large-x regions for Higgs transverse momentum distributions

It was shown recently that standard resummation of logarithms of Q/pT can be supplemented with the resummation of logarithmic contributions at large x = Q2/s in the case of a colourless final state such as Higgs produced via gluon fusion or the production of a lepton pair via Drell–Yan mechanism. Such an improved transverse momentum resummation takes into account soft emissions that are emitted at very small angles. We report on recent phenomenological studies of a combined threshold-improved pT and threshold resummation formalism to the Higgs boson produced at the LHC where small-pT and threshold logarithms are resummed up to NNLL and NNLL* respectively. We show that the effect of the modified pT resummation yields a faster perturbative convergence in the small-pT region while the effect of the threshold one improves the agreement with fixed-order calculations in the medium and large-pT regions.

Fluid velocity from transverse momentum spectra

We parametrize the transverse momentum distribution of outgoing hadrons in ultrarelativistic nucleus-nucleus collisions as a superposition of boosted thermal distributions. In this approach, which generalizes the conventional blast wave, the momentum distribution is determined by the distribution of the fluid velocity. We analyze the difference between this generalized blast-wave parametrization and a full hydrodynamic calculation. We then apply the generalized blast-wave fit to experimental data on Pb+Pb collisions at $\sqrt{s_{\rm NN}}=2.76\ \mathrm{TeV}$. The fit is reasonable up to $p_t\sim 6\ \mathrm{GeV}$, much beyond the range where hydrodynamics is usually applied, but not perfect. Based on the differences between the fit and the data, we argue that an ideal hydrodynamic calculation cannot fit simultaneously all identified particle spectra, irrespective of the specific implementation. In particular, data display a significant excess of pions at low $p_t$, whose physical interpretation is discussed. Data also show that the distribution of the fluid velocity becomes broader as the collision becomes less central. This broadening is explained by event-by-event hydrodynamic calculations, where it results from the centrality dependence of initial-state fluctuations.

Estimating the impact of mixed QCD-electroweak corrections on the W -mass determination at the LHC

We study the impact of the recently computed mixed QCD-electroweak corrections to the production of $W$ and $Z$ bosons at the LHC on the value of the $W$ mass extracted from the transverse momentum distribution of charged leptons from $W$ decays. Using the average lepton transverse momenta in $W$ and $Z$ decays as simplified observables for the determination of the $W$ mass, we estimate that mixed QCD-electroweak corrections can shift the extracted value of the $W$ mass by up to $\mathcal{O}(20)\text{ }\text{ }\mathrm{MeV}$, depending on the kinematic cuts employed to define fiducial cross sections for $Z$ and $W$ production. Since the target precision of the $W$-mass measurement at the LHC is $\mathcal{O}(10)\text{ }\text{ }\mathrm{MeV}$, our results emphasize the need for fully differential computations of mixed QCD-electroweak corrections and a careful analysis of their potential impact on the determination of the $W$ mass.

Two-gluon production of ϕ and η′ mesons in proton-proton collisions at high energies

We discuss gluon-gluon mechanisms for production of mesons with hidden strangeness, such as $\eta'$ and $\phi$ meson, in proton-proton collisions at large energies. The $g^* g^* \to \eta'$ and $g^* g^* \to \phi g$ mechanisms are considered only and the corresponding cross sections are calculated in the $k_t$-factorization approach. The $F_{\gamma^* \gamma^* \to \eta'}$ and $F_{g^* g^* \to \eta'}$ form factors are calculated from quark-antiquark $\eta'$ light-cone wave function including quark/antiquark transverse momenta. The result for two-photon transition form factor demonstrates that higher twists may survive even to large photon virtualities. The result is compared with the result of a recent leading-twist NLO analysis which uses phenomenological distribution amplitudes fitted to exclusive production of $\eta'$ in $e^+ e^- \to e^+ e^- \eta'$ reaction. We calculate transverse momentum distributions of both $\eta'$ and $\phi$ mesons in proton-proton collisions for RHIC and LHC energies. The results are compared to experimental data whenever available. The results of the Lund string model are shown for comparison for $\eta'$ production at LHC energies. It seems that the two-gluon fusion is not the dominant mechanism for both $\phi$ and $\eta'$ production, although the situation for $\eta'$, especially at larger energies, is less clear due to lack of experimental data.

Infrared renormalons in kinematic distributions for hadron collider processes

Infrared renormalons in Quantum Chromodynamics are associated with non-perturbative corrections to short distance observables. Linear renormalons, i.e. such that the associated non-perturbative corrections scale like one inverse power of the hard scale, can affect at a non-negligible level even the very high-energy phenomena studied at the Large Hadron Collider. Using an Abelian model, we study the presence of linear renormalons in the transverse momentum distribution of a neutral vector boson Z produced in hadronic collisions. We consider a process where the Z transverse momentum is balanced by a sizable recoil against a coloured final state particle. One may worry that such a colour configuration, not being azimuthally symmetric, could generate unbalanced soft radiation, associated in turn with linear infrared renormalons affecting the transverse momentum distribution of the vector boson. We performed a numerical calculation of the renormalon effects for this process in the so-called large b0 limit. We found no evidence of linear renormalons in the transverse momentum distribution of the Z in the large transverse-momentum region, irrespective of rapidity cuts.

A weakly-interacting many-body system of Rydberg polaritons based on electromagnetically induced transparency

The combination of Rydberg atoms and electromagnetically induced transparency (EIT) has been extensively studied in the strong-interaction regime. Here we proposed utilizing an EIT medium with a high optical depth (OD) and a Rydberg state of low principal quantum number to create a many-body system of Rydberg polaritons in the weak-interaction regime. The phase shift and attenuation induced by the dipole–dipole interaction (DDI) were still significant, and can be viewed as the consequences of elastic and inelastic collisions among Rydberg polaritons. We further observed that the width of the transverse momentum distribution of Rydberg polaritons at the exit of the system became notably smaller as compared with that at the entrance. The observation demonstrates the cooling effect in this system. The μs-long interaction time due to the high-OD EIT medium plus the μm2-size collision cross section due to the DDI suggests a feasible platform of polariton Bose–Einstein condensation.

Gluon parton densities in soft-wall AdS/QCD

We study the gluon parton densities [parton distribution functions (PDFs), transverse momentum distributions (TMDs), generalized parton distributions (GPDs)] and form factors in soft-wall AdS/QCD. We show that the power behavior of gluon parton distributions and form factors at large values of the light-cone variable and large values of square momentum is consistent with quark counting rules. We also show that the transverse momentum distributions derived in our approach obey the model-independent Mulders-Rodrigues inequalities without referring to specific model parameters. All gluon parton distributions are defined in terms of the unpolarized and polarized gluon PDFs and profile functions. The latter are related to gluon PDFs via differential equations.

Higher-order corrections for tW production at high-energy hadron colliders

We discuss cross sections for tW production in proton-proton collisions at the LHC and at higher-energy colliders with energies of up to 100 TeV. We find that, remarkably, the soft-gluon corrections are numerically dominant even at very high collider energies. We present results with soft-gluon corrections at approximate NNLO and approximate N3LO matched to complete NLO results. These higher-order corrections are large and need to be included for better theoretical accuracy and smaller scale dependence. Total cross sections as well as top-quark and W-boson transverse-momentum and rapidity distributions are presented using various recent sets of parton distribution functions.

Bose-Einstein condensation of pions in proton–proton collisions at the Large Hadron Collider using non-extensive Tsallis statistics

The possibility of formation of Bose-Einstein Condensation (BEC) is studied in pp collisions at $$\sqrt{s} = 7$$ TeV at the Large Hadron Collider. A thermodynamically consistent non-extensive formulation of the identified hadron transverse momentum distributions is used to estimate the critical temperature required to form BEC of charged pions, which are the most abundant species in a multi-particle production process in hadronic and nuclear collisions. The obtained results have been contrasted with the systems produced in Pb-Pb collisions to have a better understanding. We observe an explicit dependency of BEC critical temperature and number of particles in the pion condensates on the non-extensive parameter q, which is a measure of degree of non-equilibrium – as q decreases, the critical temperature increases and approaches to the critical temperature obtained from Bose-Einstein statistics without non-extensivity. Studies are performed on the final state multiplicity dependence of number of particles in the pion condensates in a wide range of multiplicity covering hadronic and heavy-ion collisions, using the inputs from experimental transverse momentum spectra.

Measurement of b jet shapes in proton-proton collisions at sqrt{s} = 5.02 TeV

We present the first study of charged-hadron production associated with jets originating from b quarks in proton-proton collisions at a center-of-mass energy of 5.02 TeV. The data sample used in this study was collected with the CMS detector at the CERN LHC and corresponds to an integrated luminosity of 27.4 pb−1. To characterize the jet substructure, the differential jet shapes, defined as the normalized transverse momentum distribution of charged hadrons as a function of angular distance from the jet axis, are measured for b jets. In addition to the jet shapes, the per-jet yields of charged particles associated with b jets are also quantified, again as a function of the angular distance with respect to the jet axis. Extracted jet shape and particle yield distributions for b jets are compared with results for inclusive jets, as well as with the predictions from the pythia and herwig++ event generators.

The role of the threshold variable in soft-gluon resummation of the toverline{t}h production process

We study the role of the scale of the threshold variable in soft-gluon threshold resummation. We focus on the computation of the resummed total cross section, the final-state invariant-mass distribution, and transverse-momentum distribution of the Higgs boson when produced in association with a top-anti-top quark pair for the Large Hadron Collider operating at 13 TeV. We show that different choices for the scale of the threshold variable result in differences at next-to-leading power, i.e. contributions that are down by one power of the threshold variable. These contributions are noticeable numerically, although their effect on the resummed observables lies within the scale uncertainty of those observables. The average central results, obtained after combining several central- scale choices, agree remarkably well for different choices of the threshold variable. However, different threshold choices do affect the resulting scale uncertainty. To compute our results, we introduce a novel numerical method that we call the deformation method, which aids the stabilization of the inverse Mellin transform in cases where the analytical Mellin transform of the partonic cross section is unknown. We show that this method leads to a factor of 10 less function evaluations, while gaining a factor of 4 − 5 in numerical precision when compared to the standard method.

Hawking radiation from acoustic black holes in relativistic heavy ion collisions

We propose a new analogue model of gravity - the evolving quark gluon plasma (QGP) produced in relativistic heavy ion collisions. This quark gluon plasma is the “most inviscid” fluid known. Such low kinematic viscosity is believed to reflect strongly correlated nature for QGP in these experiments. Hence, it may provide a good example of a quantum fluid naturally suited to studies of acoustic Hawking radiation. Due to rapid longitudinal expansion, presence of a sonic horizon is also naturally guaranteed here, though, in general, this horizon is not static. Using Ultra relativistic quantum molecular dynamics (UrQMD) simulations, we show that, under certain conditions, the longitudinal velocity of the plasma, near the sonic horizon, can become time independent for a short span during the evolution of the system. During this period, we can have a conformally static acoustic metric with a (conformal) Killing horizon coinciding with the apparent horizon. An asymptotic observer will then see a thermal flux of phonons, constituting the Hawking radiation, coming from the horizon. For the relatively low energy collision considered here, where the resulting QCD system is governed by non-relativistic hydrodynamics, we estimate the Hawking temperature to be about 4-5 MeV (with the temperature of the QCD fluid being about 135 MeV). We discuss the experimental signatures of this Hawking radiation in terms of a thermal component in the rapidity dependence of the transverse momentum distribution of detected particles. We also discuss extension to ultra-relativistic case which should lead to a higher Hawking temperature, along with the effects of dynamical horizon leading to blue/red shift of the temperature.