In this paper we extend the work synthetically presented in Ref.[1] and give theoretical details and complete tables of numerical results. We exploit calculations within a Bethe-Salpeter (BS) formalism adjusted for QCD, in order to extract an ``experimental'' strong coupling α_s^{exp}(Q^2) below 1 GeV by comparison with the meson spectrum. The BS potential follows from a proper ansatz on the Wilson loop to encode confinement and is the sum of a one-gluon-exchange and a confinement terms. Besides, the common perturbative strong coupling is replaced by the ghost-free expression α_E(Q^2) according to the prescription of Analytic Perturbation Theory (APT). The agreement of α_s^{exp}(Q^2) with the APT coupling α_E(Q^2) turns out to be reasonable from 1 GeV down to the 200 MeV scale, thus confirming quantitatively the validity of the APT prescription. Below this scale, the experimental points could give a hint on the vanishing of α_s(Q^2) as Q approaches zero. This infrared behaviour would be consistent with some lattice results and a ``massive'' generalization of the APT approach. As a main result, we claim that the combined BS-APT theoretical scheme provides us with a rather satisfactory correlated understanding of very high and rather low energy phenomena from few hundreds MeV to few hundreds GeV.
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.
The 125 GeV resonance discovered at the LHC could be a heavy quarkonium pseudoscalar meson. The diagonalization of the mass matrix of the isoscalar quarkonium states $|ζ>$ and $|ζ^{0'}>$ produces the states identified with the pseudoscalar heavy quarkonium mesons $ζ^0$ and $ζ^{0'}$. For a mixing angle $ϕ\sim 36\,^{\circ}$ the mass of the bound state pseudoscalar resonance $ζ^0$ is $m_{ζ^0}\sim 125$ GeV. The decay rates of the quarkonium $ζ^0$ meson are estimated and compared to the standard model Higgs boson predictions. The importance of determining the spin-parity of the 125 GeV resonance is…
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.
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.
Non-relativistic bound state theories for QED and QCD have become fairly mature and amenable to a textbook-level understanding and computation. In this talk we give an introductory review of the following subjects related to the recent computation of the heavy quarkonium spectrum using perturbative QCD: (1) Technological developments in higher-order computation, (2) Physics predictions, (3) Challenge towards analytic evaluation of the 3-loop static QCD potential.
We review the developments of QCD multipole expansion and its applications to hadronic transitions and some radiative decays of heavy quarkonia. Theoretical predictions are compsred with updated experimental results.
We determine the hard-loop resummed propagator in an anisotropic QCD plasma in general covariant gauges and define a potential between heavy quarks from the Fourier transform of its static limit. We find that the potential exhibits angular dependence and that binding of very small quarkonium states is stronger than in an isotropic plasma.
The analytic continuation of the operator product expansion of the scattering amplitude allows to compute the heavy-quarkonium hadron total cross section. The energy dependence of the Upsilon and Upsilon' cross sections with a proton is discussed.
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.
In this talk I review the calculation of the third order corrections to the heavy quarkonium spectrum in the nonrelativistic effective theory framework and its application to the phenomenology of top quark threshold production.
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.
The hybrid quarkonium states are studied using the Born-Oppenheimer expansion. The first step in this expansion is the determination of the energy levels of the gluons in the presence of a static quark-antiquark pair as a function of the quark-antiquark separation. The spectrum of such gluonic excitations is determined from first principles using lattice QCD.
A quarkonium model of the recently discovered X boson at 125 GeV is investigated. Two isosinglet $J^{PC}=0^{-+}$ resonances $ζ$ and $ζ'$ mix and their masses are determined by the masses of the bottomonium and toponium eigenstates. This mixing is enhanced by the non-perturbative gluon interaction produced by an axial $U_A(1)$ anomaly. The resonance $ζ$ is identified with the 125 GeV boson X, while the heavier $ζ'$ resonance has a mass 230 GeV. We assess the most recent data for the decay mode $X\rightarrow ZZ^*\rightarrow$ 4 leptons with a critical discussion of the determination of the parity…
By using conformable fractional of the Nikiforov-Uvarov (CF-NU) method, the radial Schrodinger equation is analytically solved. The energy eigenvalues and corresponding functions are obtained, in which the dependent temperature potential is employed. The effect of fraction-order parameter is studied on heavy-quarkonium masses such as charmonium and bottomonium in a hot QCD medium in the 3D and the higher dimensional space. A comparison is studied with recent works. We conclude that the fractional-order plays an important role in a hot QCD medium in the 3D and higher-dimensional space.
Using the non-relativisitc reduction of Coulomb gauge QCD we compute spectrum of the low mass hybrid mesons containing a heavy quark-antiquark pair. The gluon degrees of freedom are treated in the mean field approximation calibrated to the gluelump spectrum. We discuss the role of the non-abelian nature of the QCD Coulomb interaction in the ordering of the spin-parity levels.
We compute the total cross section of a heavy quarkonium on a hadron target in leading twist QCD, including target mass corrections. Our method relies on the analytical continuation of the operator product expansion of the scattering amplitude, obtained long ago by Bhanot and Peskin. The cross section has a simple partonic form, which allows us to investigate the phenomenology of J/psi and Upsilon dissociation by both pions and protons.
The process of exclusive electroproduction of vector quarkonium (EEQ), $e p\to epV$, is per se an interesting topic in studies of quarkonium production mechanism, QCD description of diffractive interaction and nucleon structure. We investigate this process in the framework of nonrelativistic QCD and QCD collinear factorization at the next-to-leading order QCD accuracy. The perturbative convergence behavior is discussed in a large range of photon virtuality $Q^2$. The $J/ψ$ large-$Q^2$ electroproduction data at HERA can be well explained, and the $Υ$ differential production rate is predicted. T…
In this talk, we present the QCD factorization formula for heavy quarkonium production at large $p_T$ with factorized leading-power and next-to-leading power contributions in the $1/p_T$ expansion. We show that the leading order analytical calculations in this QCD factorization approach can reproduce effectively the full next-to-leading order numerical results derived using non-relativistic QCD (NRQCD) factorization formalism. We demonstrate that the next-to-leading power contributions are crucial to the description of the channels that are the most relevant for the rate as well as polarizatio…
We use Ward identities of broken scale invariance to infer the amount of scalar glueball--$\bar{q}q$ meson mixing from the ratio of quark and gluon condensates in the QCD vacuum. Assuming dominance by a single scalar state, as suggested by a phase-shift analysis, we find a mixing angle $γ\sim 36^{\circ}$, corresponding to near-maximal mixing of the glueball and $\bar{s}s$ components.
There are many outstanding discrepancies comparing the predictions of perturbative QCD and measurements of the rate of production and decay of heavy quark systems. The problems include the $J/ψ\to ρπ$ puzzle, leading charmed particle effects, the anomalous behavior of the heavy quark sea components of structure functions, anomalous nuclear target effects, and the large rates observed for single and double quarkonium production at large $x_F$ and large $p_T$. I argue that these anomalies may be associated with nonperturbative effects in the higher Fock structure of hadron wavefunctions.
Encouraged by recent developments in AdS/QCD models for light quark system, we study heavy quarkonium in the framework of the AdS/QCD models. We calculate the masses of $c\bar c$ vector meson states using the AdS/QCD models at zero and at finite temperature. Among the models adopted in this work, we find that the soft wall model describes the low-lying heavy quark meson states at zero temperature relatively well. At finite temperature, we observe that once the bound state is above $T_c$, its mass will increase with temperature until it dissociates at a temperature of around $494 {\rm MeV}$. It…
The Abelian decomposition of QCD which decomposes the gluons to the color neutral binding gluons (the neurons) and the colored valence gluons (the chromons) gauge independently naturally generalizes the quark model to the quark and chromon model which could play the central role in hadron spectroscopy. We discuss the color reflection symmetry, the fundamental symmetry of the quark and chromon model, and explain how it describes the glueballs and the glueball-quarkonium mixing in QCD. We present the numerical analysis of glueball-quarkonium mixing in $0^{++}$, $2^{++}$, and $0^{-+}$ sectors bel…
We use QCD Laplace sum-rules to explore mixing between conventional mesons and hybrids in the heavy quarkonium vector $J^{PC}\!=\!1^{--}$ channel. Our cross-correlator includes perturbation theory and contributions proportional to the four-dimensional and six-dimensional gluon condensates. We input experimentally determined charmonium and bottomonium hadron masses into both single and multi-resonance models in order to test them for conventional meson and hybrid components. In the charmonium sector we find evidence for meson-hybrid mixing in the $J/ψ$ and a $\approx4.3$ GeV resonance. In the b…
Applying asymptotic expansions at threshold, we compute the two-loop QCD correction to the short-distance coefficient that governs the leptonic decay $ψ\to l^+ l^-$ of a S-wave quarkonium state and discuss its impact on the relation between the quarkonium non-relativistic wave function at the origin and the quarkonium decay constant in full QCD.
The next to leading order (NLO) quarkonium-hadron cross section is calculated in perturbative QCD. The corresponding leading order (LO) result was performed by Peskin more than 20 years ago using the operator product expansion (OPE). In this work, the calculation is performed using the Bethe-Salpeter amplitude and the factorization formula. The soft divergence appearing in the intermediate stages of the calculations are shown to vanish after adding all possible crossed terms, while the collinear divergences are eliminated by mass factorization. Applying the result to the Upsilon system, one fi…
Hadronic annihilation rate of $1^{+-}$ heavy quarkonium is given to next-to-leading order in $α_s$ and leading order in $v^2$ using a recently developed factorization formalism which is based on NRQCD. The result includes both the annihilation of P-wave color-singlet $Q\bar{Q}$ component, and the annihilation of S-wave color-octet $Q\bar{Q}$ component of the quarkonium. The notorious infrared divergences due to soft gluons, i.e., the Logarithms associated with the binding energy, encountered in previous perturbative calculations of $1^{+-}$ quarkonium decays are found to be explicitly cancelle…
We complete the leading-log renormalization group scaling of the NRQCD Lagrangian at $O(1/m^2)$. The next-to-next-to-leading-log renormalization group scaling of the potential NRQCD Lagrangian (as far as the singlet is concerned) is also obtained in the situation $mα_s \gg Λ_{QCD}$. As a by-product, we obtain the heavy quarkonium spectrum with the same accuracy in the situation $mα_s^2 \simg Λ_{QCD}$. When $Λ_{QCD} \ll mα_s^2$, this is equivalent to obtain the whole set of $O(mα_s^{(n+4)} \ln^n α_s)$ terms in the heavy quarkonium spectrum. The implications of our results in the non-perturbativ…
Recent advances in lattice and continuum QCD have given us new insights into quarkonium physics. These set of lectures are intend for the uninitiated. We first give a physical picture of quarkonium and describe the hybrids states established in lattice QCD. Then we give an unorthodox presentation of Non-Relativistic QCD (NRQCD) including a novel method for the application of spin-symmetries. Finally we describe the prototypical application of NRQCD: cancellation of infrared divergences in decays of P-wave quarkonia.
The 125 GeV resonance discovered at the LHC could be a heavy quarkonium, spin 0 pseudoscalar meson $ζ^0$. The decay rates of the $ζ^0$ meson resonance are calculated and compared to the standard model Higgs boson decay rates. The branching ratios and signal strengths for $ζ\rightarrowγγ$, $ζ\rightarrow Zγ$, $ζ\rightarrow ZZ^*$ and $ζ\rightarrow WW^*$ are approximately the same as the Higgs boson branching ratios and signal strengths. The decay rates for $ζ\rightarrowτ^+τ^-$, $ζ\rightarrow b\bar b$ and $ζ\rightarrow c\bar c$ are suppressed compared to the Higgs boson decay rates. Accurate branc…
Hard diffractive photo- and electroproduction of heavy vector mesons ($J/ψ$ and $Υ$) is evaluated within the leading $α_s\ln{Q^2 \overΛ_{QCD}^2}$ approximation of QCD. In difference from our earlier work on that subject, also the production of transversely polarized vector mesons is calculated. Special emphasis is placed on the role of the vector meson's $q\bar q$ light-cone wave function. In that context, conventional non-relativistic quarkonium models and a light-front QCD bound state calculation are critically examined and confronted with QCD expectations. Our numerical analysis finds a sig…
Supersymmetric standard model has a parity violation in QCD through chiral quark-squark-gluino interactions with non-degenerate masses between left-handed and right-handed squarks. Since experiments have not show any parity violations in QCD yet, a bound for the mass degeneracy between left-handed and right-handed squarks should exist. In this paper we try to obtain this bound for each squark. At first, we investigate a non-degeneracy bound between $m_{\tilde{c}_L}$ and $m_{\tilde{c}_R}$ from experimental data of charmonium decay. Next, we estimate the non-degeneracy bounds for $\tilde{u}$ and…
We consider a different power counting in potential NRQCD by incorporating the static potential exactly in the leading order Hamiltonian. We compute the leading relativistic corrections to the inclusive electromagnetic decay ratios in this new scheme. The effect of this new power counting is found to be large (even for top). We produce an updated value for the $η_b$ decay to two photons. This scheme also brings consistency between the weak coupling computation and the experimental value of the charmonium decay ratio.
We examine angular distributions of leptons arising from the decay of J/psi in inclusive hadroproduction. Taking into account feed-down contributions from chi_{1,2}, a flat distribution emerges without fine tuning parameters. Changes in the ratio of direct to total J/psi cross sections would change this distribution significantly. Such angular distributions are, therefore, confirmatory tests of the J/psi suppression signal for the production of a quark-gluon plasma. Related effects are predicted for the Upsilon.
We calculate the fragmentation function for charm quark into J/psi at the QCD next-to-leading-order (NLO) and find that the produced J/psi is of larger momentum fraction than it is at the leading-order. Based on the fragmentation function and partonic processes calculated at the NLO, the transverse momentum distribution on J/psi hadroproduction associated with a charm c (or \bar{c}) jet are predicted. We find that the distribution is enhanced by a factor of 2.0--3.3 at the NLO as p_t increased from 10 GeV to 100 GeV and it is measurable at the LHC with charm tagger. The measurement at the LHC …
QCD Laplace sum rules are used to calculate heavy quarkonium (charmonium and bottomonium) hybrid masses in several distinct $J^{PC}$ channels. Previous studies of heavy quarkonium hybrids did not include the effects of dimension-six condensates, leading to unstable sum rules and unreliable mass predictions in some channels. We have updated these sum rules to include dimension-six condensates, providing new mass predictions for the spectra of heavy quarkonium hybrids. We confirm the finding of other approaches that the negative-parity $J^{PC}=(0,1,2)^{-+},\,1^{--}$ states form the lightest hybr…
We study the energy spectrum of bottomonium in perturbative QCD, taking alpha_s(Mz)=0.1181 +/- 0.0020 as input and fixing m_b^{MSbar}(m_b^{MSbar}) on the Upsilon(1S) mass. Contrary to wide beliefs, perturbative QCD reproduces reasonably well the gross structure of the spectrum as long as the coupling constant remains smaller than one. We perform a detailed analysis and discuss the size of non-perturbative effects. A new qualitative picture on the structure of the bottomonium spectrum is provided. The lowest-lying (c,cbar) and (b,cbar) states are also examined.
Study of the polarized heavy quarkonium production in recently proposed QCD factorization formalism requires knowledge of a large number of input fragmentation functions (FFs) from a single parton or a heavy quark-antiquark pair to a polarized heavy quarkonium. In this paper, we calculate these FFs at the input scale in terms of nonrelativistic QCD (NRQCD) factorization. We derive all relevant polarized NRQCD long-distance matrix elements based symmetries and propose a self-consistent scheme to define them in arbitrary $d$ dimensions. We then calculate polarized input FFs contributed from all …
We calculate the next-to-leading order (NLO) quantum chromodynamics (QCD) corrections to $γ+γ\to η_c+c+\bar{c}$, $γ+γ\to η_b+b+\bar{b}$ and $γ+γ\to B_c+b+\bar{c}$ processes in the framework of non-relativistic QCD (NRQCD) factorization formalism. The cross sections at the SuperKEKB electron-positron collider, as well as the future collider like the Circular Electron Positron Collider (CEPC), are evaluated. Numerical results indicate that the NLO corrections are significant, and the uncertainties in theoretical predictions with NLO corrections are reduced as expected. Due to the high luminosity…
We review a number of results for the spectrum and inclusive decays of heavy quarkonium systems which can be derived from QCD under well controlled approximations. They essentially follow from the hierarchy of scales in these systems, which can be efficiently exploited using non-relativistic effective field theories. In particular, we discuss under which conditions non-relativistic potential models emerge as effective theories of QCD.
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.
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 $p_T$.
Heavy quarkonium production in the framework of the non-relativistic quantum chromodynamics and leading order of the parton Reggeization approach at the Tevatron and LHC is discussed. In this note, we compare our predictions for the bottomonium production at the LHC due to the color-singlet approximation of the non-relativistic quantum chromodynamics with CMS and LHCb data. It is found, that in the production of Upsilon(1S) states, the color-singlet mechanism is dominating, whereas to describe the data for the inclusive Upsilon(2S) and Upsilon(3S) production, the color- octet contributions sho…
Substantial anisotropies should occur in the hot expanding QCD plasma produced in relativistic heavy-ion collisions due to non-vanishing shear viscosity. We discuss the form of the real-time, hard thermal loop resummed propagator for static gluons in the presence of such anisotropies and the consequences for quarkonium binding. It has been predicted that the propagator develops an imaginary part due to Landau damping at high temperature. This generates a much larger width of quarkonium states than the Appelquist-Politzer vacuum estimate corresponding to decay into three gluons. We argue that t…
We use QCD Laplace sum-rules to study meson-hybrid mixing in vector ($1^{--}$) heavy quarkonium. We compute the QCD cross-correlator between a heavy meson current and a heavy hybrid current within the operator product expansion. In addition to leading-order perturbation theory, we include four- and six-dimensional gluon condensate contributions as well as a six-dimensional quark condensate contribution. We construct several single and multi-resonance models that take known hadron masses as inputs. We investigate which resonances couple to both currents and so exhibit meson-hybrid mixing. Compa…
We review recent developments in heavy-quarkonium phenomenology within the nonrelativistic QCD factorization approach. Main issues we consider in this work include the polarization of prompt J/psi at the Fermilab Tevatron and the large relativistic and QCD corrections to double-charmonium production at the B factories. We also consider inclusive charm production in bottomonia decays.
The research presented here uses QCD sum rules (QSR) to study exotic hadrons. There are several themes in this work. First is the use of QSR to predict the masses of exotic hadrons that may exist among the heavy quarkonium-like states. The second theme is the application of sophisticated loop integration methods in order to obtain more complete theoretical results. These in turn can be extended to higher orders in the perturbative expansion in order to predict the properties of exotic hadrons more accurately. The third theme involves developing a renormalization methodology for these higher or…
The heavy quark-antiquark potential is accessible in perturbative QCD and in lattice simulations. The perturbative short-distance part of the potential is contructed via a restricted Fourier transform, covering the momentum region where perturbative QCD is applicable. We show that for the leading order static term as well as for the mass dependent corrections, the perturbative part can be matched at intermediate distances with results from lattice QCD. From these matched potentials, quarkonium spectra with a single free parameter (the heavy quark mass) are derived and compared with empirical s…
