We review weakly-bound heavy quarkonium systems using effective field theories of QCD. We concentrate on potential Non-Relativistic QCD, which provides with a well founded connection between QCD and descriptions of the heavy quarkonium dynamics in terms of Schrödinger-like equations. This connection is obtained using standard quantum field theory techniques such as dimensional regularization, which is used throughout, and renormalization. Renormalization group equations naturally follow. Certain effort is made to illustrate how computations are performed and the necessary techniques, providing some examples. Finally, we briefly review a selected set of applications, which include spectroscopy, radiative transitions, Non-Relativistic sum rules, inclusive decays, and electromagnetic threshold production.
Recently we have proved the NRQCD factorization in heavy quarkonium production at high energy colliders at all orders in coupling constant. In this paper we extend this to non-equilibrium QCD and prove the NRQCD factorization in heavy quarkonium production at all orders in coupling constant in non-equilibrium QCD. This proof is necessary to study heavy quarkonium production from quark gluon plasma at RHIC and LHC.
Heavy quarkonium continues to play a central role in the study of nuclear matter under extremes of temperature and density in relativistic heavy-ion collisions. In this talk I report on recent developments in the theoretical description of quarkonium in-medium dynamics using the open-quantum systems approach. Not only does it provide a clear interpretation of the imaginary part of the complex heavy-quark potential but also reveals that a subtle interplay between screening and wavefunction decoherence is responsible for the melting of heavy quarkonium states.
We report the current understanding of heavy quarkonium production at high transverse momentum ($p_T$) in hadronic collisions in terms of QCD factorization. In this presentation, we highlight the role of subleading power corrections to heavy quarkonium production, which are essential to describe the $p_T$ spectrum of quarkonium at a relatively lower $p_T$. We also introduce prescription to match QCD factorization to fixed-order NRQCD factorization calculations for quarkonium production at low $p_T$.
We report a recent calculation of the heavy quarkonium energy levels and decay widths in a quark- gluon plasma whose temperature is much smaller than the inverse radius of the bound state, based on a Non-Relativistic Effective Field theory framework for heavy quarkonium at finite temperature. Relevance for the phenomenology of the Y(1S) in heavy ion collisions is also discussed.
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…
Many of the hadron-hadron cross sections required for the study of the dynamics of matter produced in relativistic heavy-ion collisions can be calculated using the quark-interchange model. Here we evaluate the low-energy dissociation cross sections of $J/ψ$, $ψ'$, $χ$, $Υ$, and $Υ'$ in collision with $π$, $ρ$, and $K$, which are important for the interpretation of heavy-quarkonium suppression as a signature for the quark gluon plasma. These comover dissociation processes also contribute to heavy-quarkonium suppression, and must be understood and incorporated in simulations of heavy-ion collisi…
By coupling the Boltzmann transport equations of both quarkonium and open heavy quarks, we investigate their dynamical evolution inside the quark-gluon plasma and study quarkonium production in heavy ion collisions. The Boltzmann transport equation of quarkonium is derived from the open quantum system formalism and effective field theory of QCD by assuming quarkonium interacts weakly with the plasma. The dissociation and recombination terms in the Boltzmann equation are calculated in potential nonrelativistic QCD. It is shown that the combination of quarkonium dissociation, recombination, open…
We explore the temperature dependence of the heavy-quarkonium interaction based on the Bhanot-Peskin leading order perturbative QCD analysis. The Wilson coefficients are computed solving the Schrodinger equation in a screened Coulomb heavy-quark potential. The inverse Mellin transform of the Wilson coefficients then allows for the computation of the 1S and 2S heavy-quarkonium gluon and pion total cross section at finite screening/temperature. As a phenomenological illustration, the temperature dependence of the 1S charmonium thermal width is determined and compared to recent lattice QCD result…
Using the variational method and supersymmetric quantum mechanic we calculate in a approximate way eigenvalues, eigenfunctions and wave functions at origin of Cornell potential. We compare results with numerical solutions for heavy quarkonia $c\bar{c}$, $b\bar{b}$ y $b\bar{c}$.
We calculate the heavy quarkonium energy levels and decay widths in a quark-gluon plasma, whose temperature T and screening mass m_D satisfy the hierarchy m alpha_s >> T >> m alpha_s^2 >> m_D (m being the heavy-quark mass), at order m alpha_s^5. We first sequentially integrate out the scales m, m alpha_s and T, and, next, we carry out the calculations in the resulting effective theory using techniques of integration by regions. A collinear region is identified, which contributes at this order. We also discuss the implications of our results concerning heavy quarkonium suppression in heavy ion …
Using the open quantum system formalism and effective field theory of QCD, we derive the Boltzmann transport equation of quarkonium inside the quark-gluon plasma. Our derivation illuminates that the success of transport equations in quarkonium phenomenology is closely related to the separation of scales in the problem.
Recently we have proved color octet NRQCD factorization of S-wave heavy quarkonium production at all orders in coupling constant at high energy colliders in Eur. Phys. J. C76 (2016) 448. In this paper we extend this to prove color octet NRQCD factorization of P-wave heavy quarkonium production at all orders in coupling constant at high energy colliders. We find that while the color octet NRQCD S-wave non-perturbative matrix element contains two gauge-links in the adjoint representation of SU(3), the color octet NRQCD P-wave non-perturbative matrix element contains four gauge-links in the funda…
The strong interaction between heavy quarks and the quark gluon plasma makes the open and hidden charm hadrons be sensitive probes of the deconfinement phase transition in high energy nuclear collisions. Both the cold and hot nuclear matter effects change with the colliding energy and significantly influence the heavy quark and charmonium yield and their transverse momentum distributions. The ratio of averaged quarkonium transverse momentum square and the elliptic flow reveal the nature of the QCD medium created in heavy ion collisions at SPS, RHIC and LHC energies.
We examine three different ways a heavy quarkonium can dissociate at high temperatures. The heavy quarkonium can dissociate spontaneously when it becomes unbound at a temperature above its dissociation temperature. Following the recent work of Digal, Petreczky, and Satz, we calculate the dissociation temperatures of heavy quarkonia taking into account the angular momentum selection rules and using a temperature-dependent potential inferred from lattice gauge calculations. We find that the selection rules change the dissociation temperatures substantially for charmonia but only slightly for bot…
Recently we have proved NRQCD color octet factorization of S-wave and P-wave heavy quarkonia production at all orders in coupling constant in QCD in vacuum at high energy colliders in Eur. Phys. J. C76 (2016) 448 and in arXiv:1807.04722 [hep-ph] respectively. In this paper we extend this to prove NRQCD color octet factorization of P-wave heavy quarkonium production in non-equilibrium QCD at RHIC and LHC at all orders in coupling constant. This proof is necessary to study the quark-gluon plasma at RHIC and LHC.
We investigate the low transverse momentum heavy quarkonium ($J/ψ$, $Υ$) productions in the forward rapidity region of $pp$ and $pA$ collisions at the LHC as an important probe to the transverse momentum tomography of the gluons in hadrons in the Color Glass Condensate (CGC) framework. By implementing the Sudakov resummation consistently in the CGC formalism, we achieve an excellent agreement between the improved CGC calculations and the LHC data. We show that both the small-$x$ and the Sudakov effects are essential for a complete description of heavy quarkonium productions in the low transver…
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…
We review the recent theoretical progress in heavy quarkonium spectroscopy within the boundstate theory based on perturbative QCD. New microscopic pictures of the heavy quarkonium systems are obtained.
Recently, a new perturbative QCD factorization formalism for heavy quarkonium production at a large transverse momentum was proposed. Phenomenological application of this new approach relies on our knowledge of a large number of universal fragmentation functions (FFs) at an input factorization scale $μ_0\gtrsim 2m_Q$ with heavy quark mass $m_Q$, which are nonperturbative, and in principle, should be extracted from data. With heavy quark mass $m_Q\gg Λ_{\rm QCD}$, we calculate these input FFs in terms of non-relativistic QCD (NRQCD) factorization. In a companion paper, we calculated these input…
We calculate the ${\cal O}(α_s^3)$ short-distance, QCD collinear-factorized coefficient functions for all partonic channels that include the production of a heavy quark pair at short distances. This provides the first power correction to the collinear-factorized inclusive hadronic production of heavy quarkonia at large transverse momentum, $p_T$, including the full leading-order perturbative contributions to the production of heavy quark pairs in all color and spin states employed in NRQCD treatments of this process. We discuss the role of the first power correction in the production rates and…
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 othe…
I review recent progress in heavy quarkonium physics from an effective field theory perspective. In this unifying framework, I discuss advances in perturbative calculations for low-lying quarkonium observables and in lattice calculations for high-lying ones, and progress and lasting puzzles in quarkonium production.
Motivated by recent applications of the open quantum system formalism to understand quarkonium transport in the quark-gluon plasma, we develop a set of coupled Boltzmann equations for open heavy quark-antiquark pairs and quarkonia. Our approach keeps track of the correlation between the heavy quark-antiquark pair from quarkonium dissociation and thus is able to account for both uncorrelated and correlated recombination. By solving the coupled Boltzmann equations for current heavy ion collision experiments, we find correlated recombination is crucial to describe the data of bottomonia nuclear m…
We present a perturbative QCD factorization formalism for the production of heavy quarkonia of large transverse momentum $p_T$ at collider energies, which includes both the leading power (LP) and next-to-leading power (NLP) contributions to the cross section in the $m_Q^2/p_T^2$ expansion for heavy quark mass $m_Q$. We estimate fragmentation functions in the non-relativistic QCD formalism, and reproduce the bulk of the large enhancement found in explicit NLO calculations in the color singlet model. Heavy quarkonia produced from NLP channels prefer longitudinal polarization.
We examine three different ways a heavy quarkonium can dissociate at temperatures below the quark-gluon plasma phase transition temperature T_c: spontaneous dissociation, dissociation by thermalization, and dissociation by collision with hadrons. We evaluate the cross sections for the dissociation of J/psi and Upsilon in collision with pion as a function of temperature, using the quark-interchange model of Barnes and Swanson. We also evaluate the dissociation temperatures for various quarkonia, and the fraction of quarkonium lying above the dissociation threshold as a function of temperature, …
In the framework of a specific scheme of the QCD sum rules for $S$-wave levels of the heavy quarkonium, one derives an expression, relating the energetic density of quarkonium states and universal characteristics in the heavy quarkonium physics, such as the difference between the masses of a heavy quark $Q$ and meson $(Q\bar q)$ and the number of heavy quarkonium levels below the threshold of $(Q\bar Q) \to (Q\bar q) + (\bar Q q)$ decay.
In the framework of a specific scheme of the QCD sum rules for $S$-wave levels of the heavy quarkonium, one derives expressions, relating the leptonic constants, the energetic density of quarkonium states and universal characteristics in the heavy quarkonium physics, such as the difference between the masses of heavy quark $Q$ and meson $(Q\bar q)$ and the number of heavy quarkonium levels below the threshold of $(Q\bar Q) \to (Q\bar q) + (\bar Q q)$ decay.
Recently we have proved factorization of infrared divergences in NRQCD S-wave heavy quarkonium production at high energy colliders at all orders in coupling constant. One of the problem which still exists in the higher order pQCD calculation of color singlet P-wave heavy quarkonium production/anihillation is the appearance of non-canceling infrared divergences due to real soft gluons exchange, although no such infrared divergences are present in the color singlet S-wave heavy quarkonium. In this paper we find that since the non-perturbative matrix element of the color singlet P-wave heavy quar…
Recently it has been shown that the peak of the quarkonium entropy at the deconfinement transition is related to the emergent entropic force which destructs the quarkonium. Using the AdS/CFT correspondence, we consider dissociation of a moving heavy quarkonium by entropic force. We find that the entropic force destructs the moving quarkonium easier than the static case which is expected from perturbative weakly coupled plasma. By considering the Maxwell charge, we study the effect of medium on the destruction of heavy quarkonium. It is shown that the quarkonium dissociates easier in the medium…
We discuss factorization in heavy quarkonium production in high energy collisions using NRQCD. Infrared divergences at NNLO are not matched by conventional NRQCD matrix elements. However, we show that gauge invariance and factorization require that conventional NRQCD production matrix elements be modified to include Wilson lines or non-abelian gauge links. With this modification NRQCD factorization for heavy quarkonium production is restored at NNLO.
Some recent progress and a personal selection of open problems in heavy quarkonium physics (spectroscopy, decay and production) inspired by the activity of the Quarkonium Working Group are reviewed.
We review recent theoretical developments in heavy quarkonium physics from the point of view of Effective Field Theories of QCD. We discuss Non-Relativistic QCD and concentrate on potential Non-Relativistic QCD. Our main goal will be to derive QCD Schrödinger-like equations that govern the heavy quarkonium physics in the weak and strong coupling regime. We also discuss a selected set of applications, which include spectroscopy, inclusive decays and electromagnetic threshold production.
In this report we review recent progress achieved in the understanding of heavy quarkonium under extreme conditions from a theory perspective. Its focus lies both on quarkonium properties in thermal equilibrium, as well as recent developments towards a genuine real-time description, valid also out-of-equilibrium. We will give an overview of the theory tools developed and deployed over the last decade, including effective field theories, lattice field theory simulations, modern methods for spectral reconstructions and the the open-quantum systems paradigm. The report will discuss in detail the …
We study the transition of a heavy quark pair from octet to singlet color configurations at next-to-next-to-leading order (NNLO) in heavy quarkonium production. We show that the infrared singularities in this process are consistent with NRQCD factorization to all orders in the heavy quark relative velocity v. This factorization requires the gauge-completed matrix elements that we introduced previously to prove NNLO factorization to order v ^2.
We report on a recent QCD based research on hybrid mesons containing $c\bar c$ or $b\bar b$ quarks. We present results for the spectrum, the decay widths to heavy quarkonium, and the role of mixing with the latter. We point out that mixing with heavy quarkonium provides a potentially large source of spin symmetry breaking. We identify candidates to hybrid mesons among the so called XYZ states in the charmonium and bottomonium spectrum.
The value of quarkonium wave function at the origin is an important quantity while studying many physical problems concerning a heavy quarkonium. This is because that it is widely used to evaluate the production and decay amplitudes of the heavy quarkonium within the effective filed theory framework, e.g., the non-relativistic QCD (NRQCD). In this paper, the value of the Schr${\rm \ddot{o}}$dinger radial wave function or its first nonvanishing derivative at zero quark-antiquark separation, i.e., $|(|c\bar{c})[n]\rangle$-, $|(|b\bar{c})[n]\rangle$-, and $|(b\bar{b})[n]\rangle$-quarkonium, have …
Using a specific scheme of the QCD sum rules for heavy quarkonium in the leading approximation over the inverse heavy quark mass, one gets the estimate of the difference between the masses of the heavy meson and heavy quark $\bar Λ= 0.59\pm 0.02$ GeV.
A calculation of the melting temperatures of heavy quarkonium states with the holographic potential was introduced in a previous work. In this paper, we consider the holographic potential at sub-leading order, which permits finite coupling corrections to be taken into account. It is found that this correction lowers the dissociation temperatures of heavy quarkonium.
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/…
Recently the proof of factorization in heavy quarkonium production in NRQCD color octet mechanism is given at next-to-next-to-leading order (NNLO) in coupling constant by using diagrammatic method of QCD. In this paper we prove factorization in heavy quarkonium production in NRQCD color octet mechanism at all order in coupling constant by using path integral method of QCD. Our proof is valid to all powers in the heavy quark relative velocity. We find that the gauge invariance and the factorization at all order in coupling constant require gauge-completed non-perturbative NRQCD matrix elements …
The issue of chiral extrapolations in heavy quarkonium systems is discussed. We show that the light quark mass dependence of the properties of heavy quarkonia is not always suppressed. For quarkonia close to an open flavor threshold, even a nonanalytic chiral extrapolation is needed. Both these nontrivial facts are demonstrated to appear in the decay widths of the hindered M1 transitions between the first radially excited and ground state P-wave charmonia. The results at a pion mass of about 500 MeV could deviate from the value at the physical pion mass by a factor of two. Our findings show th…
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.
QCD nonrelativistic effective field theories (NREFT) are the modern and most suitable frame to describe heavy quarkonium properties. Here I summarize few relevant concepts and some of the interesting physical applications (spectrum, decays, production) of NREFT.
Using a specific scheme of the QCD sum rules, one derives an universal formula for the mass differences for the $nS$-levels of heavy qiarkonium. This relation does not depend on the flavours of the heavy quarks, composing the quarkonium, and it is in a good agreement with the experimental mass values for the $ψ$- and $Υ$-families.
I review some recent progress and open problems in the calculation of heavy-quarkonium inclusive decay widths into light particles in the framework of QCD non-relativistic effective field theories.
QCD nonrelativistic effective field theories (NREFT) are the modern and most suitable frame to describe heavy quarkonium properties. In this talk I summarize few relevant concepts and some interesting physical applications of NREFT.
FDCHQHP is a Fortran package to calculate the transverse momentum (p_t) distribution of yield and polarization for heavy quarkonium hadroproduction at next-to-leading-order (NLO) based on non-relativistic QCD(NRQCD) framework. It contains the complete color-singlet and color-octet intermediate states in present theoretical level, and is available to calculate different polarization parameters in different frames. As the LHC running now and in the future, it supplies a very useful tool to obtain theoretical prediction on the heavy quarkonium hadroproduction.
Recent developments in heavy quarknoium physics are reviewed in brief, including (i) nonrelativistic QCD(NRQCD), (ii) the importance of color-octet $(Q\bar{Q})$ components in the decay and the production of a physical heavy quarkonium state, (iii) limitation of the NRQCD factorization and (iv) the double humps in the $ππ$ spectrum in the decay $Υ(3S) \to Υ(1S) ππ$.
We compute the complete leading-log terms of the next-to-next-to-next-to-leading-order corrections to potential NRQCD. As a by-product we obtain the leading logs at $O(mα_s^5)$ in the heavy quarkonium spectrum. These leading logs, when $Λ_{QCD} \ll mα_s^2$, give the complete $O(mα_s^5 \ln α_s)$ corrections to the heavy quarkonium spectrum.
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.
The bound states of a heavy quark and antiquark ($c\bar{c}, b\bar{b}$) are ideal probes to explore the quark-gluon plasma created in relativistic heavy-ion collisions at the RHIC and LHC. Not only have they become experimentally accessible with high precision but also efficient tools, so called effective field theories (EFT) have been developed to treat them theoretically. Here we present recent progress in understanding the in-medium behavior of heavy-quarkonium with the help of EFT's combined with non-perturbative and first principles simulations in lattice QCD. In particular we discuss comp…
An introduction to the recent developments in perturbative heavy quarkonium physics is given. Covered are the effective theories NRQCD, pNRQCD and vNRQCD, the threshold expansion, the role of renormalons, and applications to bottom and top quark physics.
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.
