8 pages, 2 figures, plenary talk given at the XXVIIIth International Conference on Ultrarelativistic Nucleus-Nucleus Collisions (Quark Matter 2019), November 3rd-9th 2019, Wuhan, PRC
Heavy quarkonium theory has seen significant progress over the past years. Not only has the community steadily improved the understanding of fully equilibrated quarkonium using first principles lattice QCD studies, but it has taken major steps towards developing a genuine dynamical understanding of quark-antiquark pairs immersed in a hot medium by embracing the paradigm of open quantum systems. We review recent developments, placing an emphasis on quarkonium real-time dynamics.
The nuclear suppression of heavy quarkonium production at low transverse momentum in pA collisions in high energy scatterings is investigated in the small-x factorization formalism. A universal suppression is found in the large Nc limit between the two formalisms to describe the heavy quarkonium production: the non-relativistic QCD (NRQCD) and the color-evaporation model (CEM). This provides an important probe to the saturation momentum at small-x in big nucleus. We also comment on the phenomenological applications of our results.
A dense parton system is expected to be formed in the early stage of relativistic heavy-ion collisions at RHIC energies and above. The probability of a quark gluon plasma production and the resulting strength of its signatures depends strongly on the initial conditions associated to the distributions of partons in the nuclear wave functions. At very high energies, the growth of parton distributions should saturate, possibly forming a Color Glass Condensate, which is characterized by a bulk momentum scale $Q_s$. As a direct consequence, the possible signatures of the QGP should be $Q_s$-depende…
I discuss quarkonium suppression in equilibriated strongly interacting matter. After a brief review of basic features of quarkonium production I discuss the application of recent lattice data on the heavy quark potential to the problem of quarkonium dissociation as well as the problem of direct lattice determination of quarkonium properties in finite temperature lattice QCD.
We use recent lattice data on the heavy quark potential in order to determine the dissociation temperatures of different quarkonium states in hot strongly interacting matter. Our analysis shows in particular that certain quarkonium states dissociate below the deconfinement point.
Quarkonium suppression in relativistic heavy ion collisions has been studied experimentally for decades to probe the properties of the quark-gluon plasma. For this purpose, complete theoretical understanding of the time evolution of quarkonium inside the quark-gluon plasma is needed but challenging. Here I review recent progress in applying the open quantum system framework to describe the real-time dynamics of quarkonium, with a focus on the gauge-invariant chromoelectric field correlators of the plasma that control the dynamics.
About 40-50 % of the quarkonium ground states J/psi(1S) and Upsilon(1S) produced in hadronic collisions originate from the decay of higher excitations. In a hot medium, these higher states are dissociated at lower temperatures than the more tightly bound ground states, leading to a sequential suppression pattern. Using new finite temperature lattice results, we specify the in-medium potential between heavy quarks and determine the dissociation points of different quarkonium states. On the basis of recent CDF data on bottomonium production, we then obtain first predictions for sequential Upsilo…
The quarkonium data suggest a qualitatively new production mechanism, enhancing the rate of the quarkonia produced in the fragmentation region of an incoming coloured particle.
The conventional color-singlet model was challenged by the recent data on quarkonium production. Discrepancies in production rates were observed at the Tevatron, at LEP, and in fixed-target experiments. The newly advocated color-octet mechanism provides a plausible solution to the anomalous quarkonium production observed at the Tevatron. The color-octet mechanism should also affect other quarkonium production channels. In this paper we will summarize the studies of quarkonium production in $Z^0$ and $Υ$ decays.
In this talk, I briefly review several models of the heavy quarkonium production at collider energies, and discuss the status of QCD factorization for these production models.
We explore polarized heavy quarkonium production using the color evaporation model at leading order. We present the polarized to total yield ratio as a function of center of mass energy and rapidity in $p+p$ collisions. At energies far above the $Q \overline Q$ production threshold, we find charmonium and bottomonium production to be longitudinally polarized ($J_z=0$). The quarkonium states are also longitudinally polarized at central rapidity, becoming transversely polarized ($J_z=\pm1$) at the most forward rapidities.
We compute the third-order correction to electromagnetic S-wave quarkonium production and annihilation rates due to the emission and absorption of an ultrasoft gluon. Our result completes the analysis of the non-relativistic quarkonium bound-state dynamics in the next-to-next-to-next-to-leading order. The impact of the ultrasoft correction on the Upsilon(1S) leptonic width and the top quark-antiquark threshold production cross section is estimated.
We review the current status of heavy quarkonium production phenomenology based on nonrelativistic effective field theories, focusing on spin-triplet $S$-wave states such as $J/ψ$, $ψ(2S)$, and $Υ$. We present some representative examples for heavy quarkonium production mechanisms proposed in the literature, which vary significantly depending on the choice of data employed in analyses. We then discuss the rôle of polarization in discriminating between the different possible scenarios for quarkonium production. Other observables that may be useful in pinpointing the production mechanism are als…
I describe the NRQCD factorization approach to the inclusive production of heavy quarkonium, contrasting it with the color-singlet and color evaporation models. These approaches differ dramatically in their assumptions about the roles played by color and spin in the production process. They also differ dramatically in their predictions for the production of charmonium at large transverse momentum.
Quarkonium production at low transverse momentum in hadron collisions can be used to extract Transverse-Momentum-Dependent(TMD) gluon distribution functions, if TMD factorization holds there. We show that TMD factorization for the case of P-wave quarkonium with $J^{PC}=0^{++}, 2^{++}$ holds at one-loop level, but is violated beyond one-loop level. TMD factorization for other P-wave quarkonium is also violated already at one-loop.
We present hadron-level predictions from the Monte-Carlo generator CASCADE and numerical calculations of beauty quark and quarkonium production in the framework of the kt-factorization approach for LHC energies. Our predictions are compared with the CMS experimental data.
By employing the differential equations, we compute analytically the elliptic sectors of two-loop master integrals appearing in the NNLO QCD corrections to CP-even heavy quarkonium exclusive production and decays, which turns out to be the last and toughest part in the relevant calculation. The integrals are found can be expressed as Goncharov polylogarithms and iterative integrals over elliptic functions. The master integrals may be applied to some other NNLO QCD calculations about heavy quarkonium exclusive production, like $γ^*γ\rightarrow Q\bar{Q}$, $e^+e^-\rightarrow γ+ Q\bar{Q}$,~and~$H/…
We calculate the heavy quarkonium production in double pomeron exchange processes in perturbative QCD by using two-gluon exchange model. For the $P$-wave $χ_J$ productions, we find $χ_1$ and $χ_2$ production amplitudes which vanish in the forward scattering limit. We also calculate direct $J/ψ(Υ)+γ$ production in the same approach, and these direct contributions are much smaller than the feeddown contributions from the $P$-wave states.
Heavy quarkonium production in the framework of the nonrelativistic quantum chromodynamics and leading order of the parton Reggeization approach at the Tevatron and LHC Colliders is discussed. The new results, which are reviewed in this report, include the comparison with recent data on chi_{c1,c2} production from ATLAS Collaboration and special discussion of heavy quarkonium polarization issues in the considered framework.
Production cross sections of heavy quarkonia are considered as useful tools to study various aspects of QCD. We have entered a new era of quarkonium production phenomenology, with the help of new measurements from the LHC giving access to more varieties of observables, and recent theoretical developments that provided us a better understanding of the short-distance process in which quarkonia are produced. With a more concrete understanding of perturbative corrections and a prolific collection of data, a satisfactory description of the quarkonium production mechanism might now be within reach. …
We present the study of accessing unpolarized and linearly polarized gluon TMDs in J/ψ and Υ(1S) production in unpolarized proton-proton collision at LHC, RHIC and AFTER energies. Non- relativistic QCD based color octet model (COM) is used for estimating quarkonium production rates within transverse momentum dependent factorization formalism. A comparison is drawn between the experimental data and the transverse momentum distribution of quarkonium obtained in COM and color evaporation model.
We summarize the theoretical description of charmonium and bottonium production in hadronic collisions and compare it to the available data from hadron-nucleon interactions. With the parameters of the theory established by these data, we obtain predictions for quarkonium production at RHIC and LHC energies.
By employing the method of differential equations, we compute the various types of two-loop master integrals involved in CP-even heavy quarkonium exclusive production and decays. All the integrals presented in this paper can be casted into canonical forms and expressed in terms of Goncharov polylogarithms and Harmonic polylogarithms. These master integrals are frequently used in the calculation of NNLO corrections of the heavy quarkonium production processes, as $γ^*γ\rightarrow Q\bar{Q}$, $e^+e^-\rightarrow γ+ Q\bar{Q}$, and $H/Z^0\rightarrow γ+ Q\bar{Q}$, and decay processes. They are also a…
Quarkonium production in hadron collisions at low transverse momentum $q_\perp \ll M$ with $M$ as the quarkonium mass can be used for probing transverse momentum dependent (TMD) gluon distributions. For this purpose, one needs to establish the TMD factorization for the process. We examine the factorization at the one-loop level for the production of $η_c$ or $η_b$. The perturbative coefficient in the factorization is determined at one-loop accuracy. Comparing the factorization derived at tree level and that beyond the tree level, a soft factor is, in general, needed to completely cancel soft d…
I discuss NRQCD and, in particular, the NRQCD factorization formalism for quarkonium production and decay. I also summarize the current status of the comparison between the predictions of NRQCD factorization and experimental measurements.
In this paper, we study the application of the recently proposed soft gluon factorization (SGF) to exclusive quarkonium production or decay. We find that in the nonrelativistic QCD factorization framework there are too many nonperturbative parameters. Thanks to the factorization of kinematical physics from dynamical physics, the SGF significantly reduces the number of nonperturbative parameters. Therefore, the SGF can improve our predictive power of exclusive quarkonium production or decay. By applying to $η_c+γ$ production at B-factories, our result is the closest one to data among all theore…
We review the physics of quarkonium production at high energy colliders, with a specific emphasis on production $via$ fragmentation. We discuss the fragmentation picture for the production of quarkonia at large-$p_T$ at the Tevatron and emphasise the importance of the colour-octet components of the quarkonium wave function which are included in the fragmentation functions. Applications of these theoretical ideas to other processes, both at the Tevatron and at other experiments like LEP, HERA and the LHC are important as they will provide stringent tests of these ideas.
I summarize the current status of the comparison between experiment and the predictions of the NRQCD factorization approach to quarkonium decay and production. I also present the results of some recent calculations and theoretical developments in the NRQCD factorization approach.
The theoretical description of heavy quarkonium production at high-energy p-pbar and e-p colliders is reviewed. Predictions based on non-relativistic QCD factorisation are confronted with recent charmonium and bottomonium data from the Tevatron and HERA. Potential shortcomings of the present theoretical analyses are discussed, and the prospects for quarkonium physics at the upgraded Tevatron and HERA colliders and at the LHC are summarised.
Quarkonium production in high-energy reactions is found to exhibit a behaviour more universal than that expected from velocity scaling. Total rates of quarkonia produced in hadronic interactions as well as Feynman-x and transverse momentum distributions can be described over the full range of accessible energies (15 < sqrt{s} < 1800 GeV) by two-stage processes. The quarkonium production cross section factors into a process-dependent short-distance part and a single long-distance matrix element. The first part describing the production of a free quark--antiquark pair is the perturbatively calcu…
We review recent progress in the description of heavy-quarkonium production in 2->2 processes at next-to-leading order in the factorization framework of nonrelativistic quantum chromodynamics. Specifically, we consider the production of prompt charmonium in association with a hadron jet or a prompt photon in two-photon collisions and exclusive double-charmonium production in e^+e^- annihilation.
We report on recent theory progress in understanding the production of heavy quarkonium in heavy-ion collisions based on the in-medium heavy-quark potential extracted from lattice QCD simulations. On the one hand, the proper in-medium potential allows us to study the spectral properties of heavy quarkonium in thermal equilibrium, from which we estimate the $ψ^\prime$ to $J/ψ$ ratio in heavy-ion collisions. On the other hand, the potential provides a central ingredient in the description of the real-time evolution of heavy-quarkonium formulated in the open-quantum-systems framework.
We present a recent calculation of $J/ψ$ and $Υ$ production in unpolarized $pp$ collision and show that this can be used to probe the unpolarized gluon as well as the linearly polarized gluon transverse momentum dependent parton distributions (TMDs). We use the color evaporation model for the heavy quarkonium production and use a generalized factorized form of the cross section. We compare the results with experimental data.
The effects of parton energy loss in cold nuclear matter on heavy-quarkonium suppression in p-A collisions are studied. It is shown from first principles that at large quarkonium energy E and small production angle in the nucleus rest frame, the medium-induced energy loss scales as E. Using this result, a phenomenological model depending on a single free parameter is able to reproduce J/psi and Upsilon suppression data in a broad xF-range and at various center-of-mass energies. These results strongly support energy loss as the dominant effect in heavy-quarkonium suppression in p-A collisions. …
Recent data from the Tevatron have revealed that the production rate of prompt charmonium is more than an order of magnitude larger than the best theoretical predictions of a few years ago. This surprising result can be understood by taking into account new production mechanisms that include fragmentation and the formation of charmonium from color-octet $c \bar c$ pairs.
Most recent calculations of quarkonium production are based on the NRQCD factorization formalism. This formalism is reviewed. To make predictions about specific cross section, universal NRQCD matrix elements need to be extracted from experiments. Extractions from different experimental situations are compared, with some emphasis on the extraction from LEP.
The sensitivity of proton-induced $J/ψ$ and $Υ$ production to the possible $\bar u/\bar d$ asymmetry in the nucleon is studied. The ratio of the quarkonium production cross sections at large $x_F$ on hydrogen over deuterium targets, $σ(p+p) / σ(p+d)$, is shown to be sensitive to this asymmetry. Predictions of various theoretical models for this ratio are presented.
As a stringent test of the nonrelativistic QCD factorization approach for inclusive heavy-quarkonium production in high-energy hadron collision, the polarized heavy-quarkonium production at the Tevatron is discussed. The polarization of prompt J/psi at the Tevatron is predicted within the nonrelativistic QCD factorization framework. The contribution from radiative decays of P-wave charmonium states decreases, but does not eliminate, the transverse polarization at large transverse momentum. The prediction agrees with measurements from the CDF collaboration at intermediate values of p_T, but dis…
The photoproduction of quarkonium in coherent hadron-hadron (pp/pA/AA$) interactions for LHC energies is an important tool to investigate the QCD dynamics at high energies. In this paper we estimate the integrated cross section and rapidity distribution for J/Psi and Upsilon production using the Color Glass Condensate (CGC) formalism. We predict large rates, implying that the experimental identification could be feasible at the LHC.
The rates for diffractive quarkonium plus prompt-photon associated production at the LHC are estimated. The theoretical framework considered in the J/Psi (or Upsilon) production associated with a direct photon at the hadron collider is the non-relativistic QCD (NRQCD) factorization formalism. The corresponding single diffractive cross section is computed based on the hard diffractive scattering factorization supplemented by absorptive corrections. Such processes are sensitive to the gluon content of the Pomeron at small Bjorken-x and they may also be a good place to test the different availabl…
The hadronic production of $D$-wave states of $\bar b c$ is studied. The relative yield of such states is estimated for kinematic conditions of LHC experiments.
Quarkonium data suggest an enhancement of the hadroproduction rate from interactions of the heavy quark pair with a comoving color field generated in the hard gg -> Q\bar{Q} subprocess. We review the motivations and principal consequences of this comover enhancement scenario (CES).
The effect of parton energy loss in cold nuclear matter on the suppression of quarkonia (J/psi, Upsilon) in heavy-ion collisions is investigated, by extrapolating a model based on coherent radiative energy loss recently shown to describe successfully J/psi and Upsilon suppression in proton-nucleus collisions. Model predictions in heavy-ion collisions at RHIC (Au-Au, Cu-Cu, and Cu-Au) and LHC (Pb-Pb) show a sizable suppression arising from the sole effect of energy loss in cold matter. This effect should thus be considered in order to get a reliable baseline for cold nuclear matter effects in q…
In this talk I review NRQCD predictions for the production of charmonium at the Tevatron. After a quick presentation of the NRQCD factorization formalism for production and decay I review some old results and discuss how they compare to recent data. Following this I discuss some recent work done with Adam Leibovich and Ira Rothstein.
A model for the production of quarkonium states in the midrapidity region at RHIC and LHC energy range is presented which explores well understood properties of QCD only. An increase of the quarkonium hadronisation time with the initial energy leads to a gradual change of the most important phenomena from fixed target- to collider-energies. We evaluate nuclear effects in the quarkonium production due to medium modification of the momentum distribution of the heavy quarks produced in the hard interactions, i.e. due to the broadening of the transverse momentum distribution. Other nuclear effects…
The pseudoscalar quarkonium state, eta_4 1^S_0, formed by the Standard Model (SM) fourth generation quarks, is the best candidate among the fourth generation quarkonia to be produced at the LHC and VLHC. The production of this J^{PC} = 0^{-+} resonance is discussed and the background processes are studied to obtain the integrated luminosity limits for the discovery, depending on its mass.
Quarkonium production in proton-nucleus collisions is a powerful tool to disentangle cold nuclear matter effects. A model based on coherent energy loss is able to explain the available quarkonium suppression data in a broad range of rapidities, from fixed-target to collider energies, suggesting cold energy loss to be the dominant effect in quarkonium suppression in p-A collisions. This could be further tested in a high-energy fixed-target experiment using a proton or nucleus beam. The nuclear modification factors of J/$ψ$ and $Υ$ as a function of rapidity are computed in p-A collisions at $\sq…
Heavy quarkonium ($Υ$) production at low transverse momentum ($P_\perp$) in high-energy hadronic collisions is revisited from the point of view of transverse momentum dependent (TMD) framework. We perform resummation of double logarithmic correction associated with initial-state soft gluon shower for $b\bar b$ production by employing Collins-Soper-Sterman (CSS) formalism. We show that the CSS formalism provides a nice description of $Υ$ production data in p+$\rm\bar{p}$ collisions at Tevatron and p+p collisions at the LHC.
We discuss the theory of inclusive production of heavy quarkonium, the comparison between theory and experiment, and the expected nuclear effects in cold nuclear targets. We also present predictions, based on Nonrelativistic QCD (NRQCD), for quarkonium production cross sections in the LHC energy range. We find that nuclear effects in the production cross sections are largely independent of the sizes of the NRQCD matrix elements, the charmonium state that is produced and, in the color-octet case, largely independent of the partonic subprocess that produces the heavy quark-antiquark pair.
The quarkonium plus photon production in coherent hadron-hadron interactions at the LHC is studied using the non-relativistic QCD factorization formalism. We investigate a set of kinematic distributions and compute the total cross sections for $J/Ψ+ γ$ production. Our results demonstrate the feasibility of such process in the LHC kinematic regime and explore the possibilities for the Future Circular Collider, where higher event yields can be achieved.
In this paper we study the inclusive and diffractive double quarkonium production. Based on the nonrelativistic QCD (NRQCD) factorization formalism for the quarkonium production mechanism we estimate the rapidity and transverse momentum dependence of the cross section for the $J/ΨJ/Ψ$ and $ΥΥ$ production in diffractive processes at LHC energies. The contributions of the color-singlet and color-octet channels are estimated and predictions for the total cross sections in the kinematical regions of the LHC experiments are also presented. Our results demonstrate that the contribution of diffractiv…
We review heavy quark and quarkonium production in high energy hadronic collisions. We discuss the status of the theoretical calculations and their uncertainties. We then compare the current theoretical results with the most recent measurements from the tevatron collider experiments.
The decay $Z^{0}\rightarrow Q+ \ell^{+}\ell^{-}$, where $Q$ is a $J^{PC}=1^{--}$ quarkonium state, has a very clean final state, which should make it easy to detect. The branching ratio of this mode is greater than $10^{-6}$ for $ρ$, $ϕ$, and $ψ$, indicating that these processes may be detectable at LEP.
Heavy quarkonium suppression was proposed long ago as a signal of the formation of a deconfined phase in heavy ion collisions. Originally the mechanism responsible for this suppression was thought to be color screening. However perturbative computations and recent lattice studies suggest the existence of an imaginary part of the potential which could have a more important role for suppression than screening. In this work we review some general aspects of effective field theories for heavy quarkonium in the medium and discuss the physical phenomena behind the imaginary part of the potential and…
In this contribution we briefly discuss an ongoing phenomenological programme on quarkonium production in unpolarized and polarized proton-proton collisions in a fixed target setup at LHCb, the LHCSpin project. Within a TMD approach, we aim at considering in particular: the relative role of the NRQCD color-singlet and color-octet production mechanisms, both for unpolarized and polarized quarkonium production; the study of azimuthal and transverse single-spin asymmetries as a phenomenological tool for learning about the almost unknown gluon Sivers function; the role of initial- and final-state …
We describe a precursor in heavy quarkonium production in terms of a coherent admixture of states of different color, spin, and angular momentum quantum numbers, and obtain the production amplitudes for different quarkonium bound states by projecting out this precursor state onto these bound states. The precursor is absorbed in its passage through a nucleus in a pA reaction, and the total cross section between this precursor with a nucleon can be calculated with the two-gluon model of the Pomeron. Such a description of coherent precursors and their subsequent interactions with nucleons can exp…
