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We have updated theoretical studies of heavy vector quarkonium production, including J / Ψ , Ψ ′ and ϒ , in the exclusive W-boson decays. Particularly, in the standard model the branching fraction of W − → J / Ψ ℓ − ν ̄ ℓ (ℓ = e or μ) has been predicted to be about 8. 5 × 1 0 − 7 , which is substantially larger than those of two-body hadronic radiative W decays. Thus in the future high-luminosity experimental facilities, this rare channel could be very useful to search for the exclusive W-boson decays containing the hadronic final state. Furthermore, the surprisingly large decay rate can be explained by an electromagnetic fragmentation formalism. We have analyzed the lepton fragmentation and the photon fragmentation processes, and calculated their contributions to the differential decay rate of W − → J / Ψ ℓ − ν ̄ ℓ in the fragmentation limit. It is found that the fragmentation contribution agrees well with the result from the full calculation. [ABSTRACT FROM AUTHOR]

A generalized fractional derivative of the analytical exact iteration method is used, in which the two-body potential in strongly coupled quark–gluon plasma is devoted to solve the N-dimensional radial Schrödinger equation. The energy eigenvalues for any state (n, l) and mass spectra in the N-dimensional space have been investigated. The dissociation temperatures were computed in the N-dimensional space for different states of quarkonia. The effect of fractional-order parameter is investigated on the dissociation temperatures of heavy quarkonium masses such as charmonium and bottomonium and thermodynamic properties such as entropy, free energy, internal energy, and specific heat in the 3D and the higher-dimensional space. Also, the effect of dimensionality number on dissociation temperatures is discussed. A comparison with other recent works is displayed. We deduce that the fractional-order plays an essential role in 3D and higher-dimensional space. [ABSTRACT FROM AUTHOR]

[Display omitted] Jet quenching has long been regarded as one of the key signatures for the formation of quark-gluon plasma in heavy-ion collisions. Despite significant efforts, the separate identification of quark and gluon jet quenching has remained as a challenge. Here we show that J / ψ in high transverse momentum ( p T ) region provides a uniquely sensitive probe of in-medium gluon energy loss since its production at high p T is particularly dominated by gluon fragmentation. Such gluon-dominance is first demonstrated for the baseline of proton-proton collisions within the framework of leading power non-relativistic quantum chromodynamics factorization formalism. We then use the linear Boltzmann transport model combined with hydrodynamics for the simulation of jet-medium interaction in nucleus-nucleus collisions. The satisfactory description of experimental data on both nuclear modification factor R AA and elliptic flow v 2 reveals, for the first time, that the gluon jet quenching is the driving force for high p T J / ψ suppression. This novel finding is further confirmed by the data-driven Bayesian analyses of relevant experimental measurements, from which we also obtain the first quantitative extraction of the gluon energy loss distribution in the quark-gluon plasma. [ABSTRACT FROM AUTHOR]

We review recent studies about anisotropic flows ( v 1 , v 2 , v 3 ) of charmonium in the quark-gluon plasma produced in relativistic heavy-ion collisions. Collective flows of the bulk medium are developed due to the anisotropic pressure gradient of the medium. Strongly coupled with the bulk medium, charm quarks carry collective flows from the expanding medium, which will be inherited by the regenerated charmonium via the coalescence process. In event-by-event collisions where nucleon positions fluctuate from the smooth distribution, there is triangularity in the medium initial energy density. Triangular flows of the bulk medium and heavy flavor particles can be developed due to the initial fluctuations. In the longitudinal direction, the rapidity-odd distribution of the initial energy density is induced by the rotation of the medium in non-central heavy-ion collisions. Charmonium suffers biased dissociation along positive and negative x-directions in forward (backward) rapidity. The directed flow of charmonium becomes non-zero. The directed, elliptic and triangular flows ( v 1 , v 2 , v 3 ) of charmonium come from the anisotropic initial distributions of the medium energy density in the transverse and longitudinal directions. [ABSTRACT FROM AUTHOR]

We review recent studies about anisotropic flows (v1,v2,v3) of charmonium in the quark-gluon plasma produced in relativistic heavy-ion collisions. Collective flows of the bulk medium are developed due to the anisotropic pressure gradient of the medium. Strongly coupled with the bulk medium, charm quarks carry collective flows from the expanding medium, which will be inherited by the regenerated charmonium via the coalescence process. In event-by-event collisions where nucleon positions fluctuate from the smooth distribution, there is triangularity in the medium initial energy density. Triangular flows of the bulk medium and heavy flavor particles can be developed due to the initial fluctuations. In the longitudinal direction, the rapidity-odd distribution of the initial energy density is induced by the rotation of the medium in non-central heavy-ion collisions. Charmonium suffers biased dissociation along positive and negative x-directions in forward (backward) rapidity. The directed flow of charmonium becomes non-zero. The directed, elliptic and triangular flows (v1,v2,v3) of charmonium come from the anisotropic initial distributions of the medium energy density in the transverse and longitudinal directions.

We present a next-to-leading order (NLO) relativistic correction to B c → J / ψ tensor form factors within nonrelativistic QCD (NRQCD). We also consider complete Dirac bilinears c ̄ Γ b with 4 × 4 matrices Γ = 1 , γ 5 , γ μ , γ μ γ 5 , σ μ ν in the b → c transition. The relation among different current form factors is given and it shows that symmetries emerge in the heavy bottom quark limit. For a phenomenological extension, we propose to extract the long-distance matrix elements (LDMEs) for B c meson from the recent HPQCD lattice data and the NLO form factors at large momentum recoil. [ABSTRACT FROM AUTHOR]

In this paper, we give a brief review of recent theoretical studies of double prompt J / ψ production at the FNAL Tevatron and the CERN LHC, to which both single- and double-parton-scattering processes contribute. In single parton scattering, we mainly present the results computed within the framework of non-relativistic quantum chromodynamics factorization combined with one of the two approaches to describe the parton inside the (anti)proton, the collinear parton model and the parton Reggeization approach. The contributions from double parton scattering calculated with different values of σ eff are also discussed. We conclude that, in double prompt J / ψ hadroproduction, there remain some differences between theoretical predictions and experimental measurements. [ABSTRACT FROM AUTHOR]

Using the charmonium light-front wavefunctions obtained by diagonalizing an effective Hamiltonian with the one-gluon exchange interaction and a confining potential inspired by light-front holography in the basis light-front quantization formalism, we compute production of charmonium states in diffractive deep inelastic scattering and ultra-peripheral heavy ion collisions within the dipole picture. Our method allows us to predict yields of all vector charmonium states below the open flavor thresholds in high-energy deep inelastic scattering, proton–nucleus and ultra-peripheral heavy ion collisions, without introducing any new parameters in the light-front wavefunctions. The obtained charmonium cross section is in reasonable agreement with experimental data at HERA, RHIC and LHC. We observe that the cross-section ratio σΨ(2s)/σJ/Ψ reveals significant independence of model parameters.

The inclusive J / Ψ production by direct and resolved photoproduction in the γp scattering is calculated based on the nonrelativistic quantum chromodynamics (NRQCD) factorization formalism, which is in good agreement with the experimental data of total cross section distribution of heavy quarkonium production at HERA. Then we extend the formalism including the direct and resolved photoproduction processes to resolved pomeron model to study the heavy quarkonium photoproduction at the LHC energies. We present the predictions of rapidity and transverse momentum distributions of the inclusive diffractive J / Ψ , Ψ (2 S) and ϒ photoproduction in pp , pPb and P b P b collisions at the LHC energies. Our numerical results indicate that the resolved photoproduction processes play an important role in the heavy quarkonium production. Especially for pp collisions, the contribution of resolved photoproduction processes is the largest, which can reach to 28%, 13% and 44% for the rapidity distributions of J / Ψ , Ψ (2 S) and ϒ inclusive diffractive photoproduction, respectively. [ABSTRACT FROM AUTHOR]

Within the framework of the instanton Liquid Model (ILM) we evaluate the heavy quark Q Q ̄ potential at finite temperature. The potential in the ILM has two components: direct instantons contribution and the ILM modified one-gluon exchange contribution. The dynamical "electric" mass M e l (q , T) , which was generated by rescattering of the gluons from the ILM instantons, was taken into account. [ABSTRACT FROM AUTHOR]

We study the heavy quarkonium within the basis light-front quantization approach. We implement the one-gluon exchange interaction and a confining potential inspired by light-front holography. We adopt the holographic light-front wavefunction (LFWF) as our basis function and solve the non-perturbative dynamics by diagonalizing the Hamiltonian matrix. We obtain the mass spectrum for charmonium and bottomonium. With the obtained LFWFs, we also compute the decay constants and the charge form factors for selected eigenstates. The results are compared with the experimental measurements and with other established methods.

Following the original idea of Debye, we define and extract a gauge-invariant screening mass from the complex static in-medium heavy-quark potential VQQ¯, recently obtained from lattice QCD. To this end we derive a formula using concepts from both effective- and classical field theories that faithfully reproduces both the screened real- and the imaginary part of the lattice potential with a single temperature dependent fit parameter mD(T). Using values of the real part of VQQ¯ in a gluonic medium, we obtain Debye masses compatible with HTL perturbation theory.

Abstract Using the chromo-electric dipole coupling Hamiltonian from QCD multipole expansion, we derive the dissociation cross sections of heavy quarkonia by thermal gluons at next-to-leading order (NLO, also known as inelastic parton scattering dissociation) in the Quark–Gluon Plasma (QGP) in the framework of second order quantum mechanical perturbation theory. While suffering divergence (infrared and soft-collinear divergences) in vacuum, the cross sections thus derived become finite in the QGP as rendered by the finite thermal gluon masses. In contrast to the leading order (LO, also known as gluo-dissociation) counterparts rapidly dropping off with increasing incident gluon energy, the NLO cross sections exhibits finite value toward high energies because of new phase space being opened up. We then carry out a full calculation of the dissociation rates for various charmonia and bottomonia within a non-relativistic in-medium potential model. The NLO process is shown to dominate the dissociation rate toward high temperatures when the binding energies of heavy quarkonia become smaller relative to the Debye screening mass. [ABSTRACT FROM AUTHOR]

Recently we have proved the factorization of NRQCD S-wave heavy quarkonium production at all orders in coupling constant. In this paper we extend this to prove the factorization of infrared divergences in χcJ production from color singlet cc¯ pair in non-equilibrium QCD at RHIC and LHC at all orders in coupling constant. This can be relevant to study the quark-gluon plasma at RHIC and LHC. [ABSTRACT FROM AUTHOR]

Many measurements of quarkonium suppression at the LHC, e.g. the nuclear modification factor R AA of J / Ψ , are well described by a multitude of different models. Thus pinpointing the underlying physics aspects is difficult and guidance based on first principles is needed. Here we present the current status of our ongoing high precision study of in-medium spectral properties of both bottomonium and charmonium based on NRQCD on the lattice. This effective field theory allows us to capture the physics of quarkonium without modeling assumptions in a thermal QCD medium. In our study a first principles and realistic description of the QCD medium is provided by state-of-the-art lattices of the HotQCD collaboration at almost physical pion mass. Our updated results corroborate a picture of sequential modification of states with respect to their vacuum binding energy. Using a novel low-gain variant of the Bayesian BR method for reconstructing spectral functions we find that remnant features of the Upsilon may survive up to T ∼ 400MeV, while the χ b signal disappears around T ∼ 270MeV. The c c ‾ analysis hints at melting of χ c below T ∼ 190MeV while some J / Ψ remnant feature might survive up to T ∼ 245MeV. An improved understanding of the numerical artifacts in the Bayesian approach and the availability of increased statistics have made possible a first quantitative study of the in-medium ground state masses, which tend to lower values as T increases, consistent with lattice potential based studies. [ABSTRACT FROM AUTHOR]

Using the charmonium light-front wavefunctions obtained by diagonalizing an effective Hamiltonian with the one-gluon exchange interaction and a confining potential inspired by light-front holography in the basis light-front quantization formalism, we compute production of charmonium states in diffractive deep inelastic scattering and ultra-peripheral heavy ion collisions within the dipole picture. Our method allows us to predict yields of all vector charmonium states below the open flavor thresholds in high-energy deep inelastic scattering, proton–nucleus and ultra-peripheral heavy ion collisions, without introducing any new parameters in the light-front wavefunctions. The obtained charmonium cross section is in reasonable agreement with experimental data at HERA, RHIC and LHC. We observe that the cross-section ratio σ Ψ ( 2 s ) / σ J / Ψ reveals significant independence of model parameters. [ABSTRACT FROM AUTHOR]

We calculate the annihilation decay rates of the and charmonia and bottomonia by using the instantaneous Bethe-Salpeter (BS) method. The wave functions of states with quantum numbers and are constructed. By solving the corresponding instantaneous BS equations, we obtain the mass spectra and wave functions of the quarkonia. The annihilation amplitude is written within Mandelstam formalism and the relativistic corrections are taken into account properly. This is important, especially for high excited states, since their relativistic corrections are large. The results for the channel are as follows: keV, keV, keV and keV. [ABSTRACT FROM AUTHOR]

In order to understand the experimental data on heavy quarkonium production in heavy ion collisions at RHIC and LHC it is necessary (though not sufficient) to pinpoint the properties of heavy Q Q ‾ bound states in the deconfined quark-gluon plasma, including their dissolution. Here we present recent results on the temperature dependence of bottomonium and charmonium correlators, as well as their spectral functions in a lattice QCD based effective field theory called NRQCD, surveying temperatures close to the crossover transition 140 MeV < T < 249 MeV . The spectra are reconstructed based on a novel Bayesian prescription, whose systematic uncertainties are assessed. We present indications for sequential melting of different quarkonium species with respect to their vacuum binding energies and give estimates on the survival of S-wave and P-wave ground states. [ABSTRACT FROM AUTHOR]

We study the heavy quarkonium within the basis light-front quantization approach. We implement the one-gluon exchange interaction and a confining potential inspired by light-front holography. We adopt the holographic light-front wavefunction (LFWF) as our basis function and solve the non-perturbative dynamics by diagonalizing the Hamiltonian matrix. We obtain the mass spectrum for charmonium and bottomonium. With the obtained LFWFs, we also compute the decay constants and the charge form factors for selected eigenstates. The results are compared with the experimental measurements and with other established methods. [ABSTRACT FROM AUTHOR]

Following the original idea of Debye, we define and extract a gauge-invariant screening mass from the complex static in-medium heavy-quark potential V Q Q ¯ , recently obtained from lattice QCD. To this end we derive a formula using concepts from both effective- and classical field theories that faithfully reproduces both the screened real- and the imaginary part of the lattice potential with a single temperature dependent fit parameter m D ( T ) . Using values of the real part of V Q Q ¯ in a gluonic medium, we obtain Debye masses compatible with HTL perturbation theory. [ABSTRACT FROM AUTHOR]

We investigate the effect of space-time noncommutativity on the Cornell potential in heavy-quarkonium systems. It is known that the space-time noncommutativity can create bound states, and we therefore consider the noncommutative geometry of the space-time as a correction in quarkonium models. Furthermore, we take the experimental hyperfine measurements of the bottomium ground state as an upper limit on the noncommutative energy correction and derive the maximum possible value of the noncommutative parameter θ, obtaining θ ≤ 37.94 · 10 m. Finally, we use our model to calculate the maximum value of the noncommutative energy correction for energy levels of charmonium and bottomium in 1S and 2S levels. The energy correction as a binding effect in quarkonium system is smaller for charmonium than for bottomium, as expected. [ABSTRACT FROM AUTHOR]

The calculations of thermal single-gluon exchange potential for heavy quarkonium in Feynman and Coulomb gauges are presented, and the comparisons between them and the hard thermal loop approximation ones which were first calculated by Laine et al. are illustrated. The numerical results show that the hard thermal loop thermal single-gluon exchange potential (especially its imaginary part) which used in many researches make some errors in the practical calculations at the temperature range accessible in the present experiment, and the problem of gauge dependent cannot be avoided when the complete self energy is used in the derivation of potential. [ABSTRACT FROM AUTHOR]

The transverse gluon contributions to the thermal static potentials of heavy quarkonia in isotropic medium are studied. Using the resummation of the damping rates method developed by Hou and Li, the infrared divergence that appeared in the effective potential calculations of transverse gluon is avoided. The comparisons between the transverse and the longitudinal contributions for heavy quarkonia are discussed. The results show that the dissociation scales of quarkonia in thermal medium are decreased by the transverse gluon contributions. [ABSTRACT FROM AUTHOR]

We calculate the mass spectra of heavy quarkonium by using matrix Numerov's method to make the predictions of F and G states for further experiments. The method gives a very reasonable result which is in a good agreement with other methods and with recently published theoretical data. From the yielded wave functions we calculate the root mean square radius rms and ß coefficients of heavy quarkonium [ABSTRACT FROM AUTHOR]