We calculate the spectra of charmonium and bottomium in an approximation scheme which treats hard gluons perturbatively while soft gluons are expanded in a set of localized wave functions. Quark-antiquark and quark-antiquark-gluon sectors are included. Reasonable agreement with 2 parameters only is found but the spectra are too coulombic. Despite large coupling constant the admixture of the quark-antiquark-gluon sector is found to be remarkably small.
We compute the Noncommutative QCD (NCQCD) contributions to the three gluon decay modes of heavy quarkonia. For triplet quarkonia (ortho-quarkonia), the NCQCD correction to the QCD three gluon decay mode, like the standard model contribution, is infrared finite. In the case of singlet quarkonia (para-quarkonia), whose QCD three gluon decay mode has infrared singularities which are removed using one-loop corrections to the two gluon mode, we find that NCQCD contribution is also infrared finite. The calculations are performed in the weak binding limit and do not require the introduction of additi…
An effective hamiltonian for heavy quarkonia is derived from QCD by separating gluonic fields in background and quantum fields and neglecting anharmonic contributions. Mesonic states with nonperturbative gluonic components are constructed. These states are invariant under gauge changes of the background fields and form an orthogonal basis. The effective hamiltonian is diagonalized in this basis in a systematic $1/m$- and short distance expansion. For very heavy quarkonia, we obtain an effective potential similar to the phenomenological funnel potential. We compare our method to $2^{\rm nd}$ or…
QCD running coupling constant $α_s(m_c)$ and $α_s(m_b)$ are determined from heavy quarkonia $c\overline{c}$ and $b\overline{b}$ decays. The decay rates of $V\rightarrow 3g$ and $V\rightarrow e^+ e^-$ for $V=J/ψ$ and $Υ$ are estimated by taking into account both relativistic and QCD radiative corrections. The decay amplitudes are derived in the Bethe-Salpeter formalism, and the decay rates are estimated by using the meson wavefunctions which are obtained with a QCD-inspired inter-quark potential. For the $V\rightarrow 3g$ decay we find the relativistic correction to be very large and to severel…
The decay rates of $c\bar{c}$ and $b\bar{b}$ through two-photon or two-gluon annihilations are obtained by using totally relativistic decay amplitudes and a sophisticated quantum-chromodynamic potential model for heavy quarkonia. Our results for the photonic and gluonic widths of the 1S0, 3P0, and the 3P2 states are in excellent agreement with the available experimental data. The procedures and mathematical techniques used by us for the treatment of the fermion-antifermion bound states are also applicable to other decay processes.
The detailed proof of cancellation of topologically unfactorized infrared divergences in the inclusive production of lepton pair close to the threshold of heavy quarkonia is presented. To make the effects of transition between states containing heavy quark pairs, which is important in such cancellation, the final detected states are constrained to be lepton pair near the threshold of the heavy quarkonia instead of heavy quarkonia themselves. Such cancellation is crucial for the NRQCD factorization of these processes.
An effective theory approach to heavy quarkonia decays based on the $1/m_Q$ expansion is introduced. Its application to decays in which the two heavy quarks annihilate is discussed.
A scheme is presented here to cancel out the topologically unfactorized infrared divergences in the inclusive production of heavy quarkonia, which affect the NRQCD factorization of these processes. The heavy quarkonia are defined as resonance states of QCD instead of color singlet heavy quark pair. Thus the final heavy quark pair is nor necessarily to be color singlet. In addition, the heavy quarkonia are reconstructed by their decay products. As the result, transition between states containing containing heavy quarks caused by exchanges of soft gluons are also taken into account here. Such ca…
We derive a light-front Schrodinger-type equation of motion for the quark-antiquark wave function of heavy quarkonia imposing constraints from the holographic soft-wall model.
Within the framework of nonrelativistic quark-antiquark Cornell potential model formalism, we study the annihilation of heavy quarkonia. We determine their annihilation widths resulting into digluon, dilepton, $3γ$, $3g$ and $γgg$ and compare our findings with the available theoretical results and experimental data. We also provide the charge radii and absolute square of radial Schrödinger wave function at zero quark-antiquark separation for heavy quarkonia and $B_c$ mesons.
The binding energy spectra of the heavy quarkonia are calculated by solving the Schrödinger equations with Coulomb plus confining potentials. Statistical properties of the obtained spectra are studied by plotting nearest level spacing distribution histograms.
In the framework of QCD sum rules one uses a scheme, allowing one to apply the conditions of both nonrelativistic heavy quark motion inside mesons and independence of nonsplitting nS-state density on the heavy quark flavours. In the leading order an analitic expression is derived for leptonic constants of both heavy quarkonia and heavy mesons with a single heavy quark. The expression allows one explicitly to determine scaling properties of the constants.
The new approach to decays of heavy quarkonia, based on factorization and expansions in powers of the relative velocity of the valence quarks is reviewed.
We investigate some consequences of the possibility that heavy quarkonia in a quark-gluon plasma possess different (quasi-) bound states, between which transitions are possible. In particular, we show that the time-evolution eigenstates in the medium are mixtures of the vacuum eigenstates. This leads to abundance ratios of quarkonia that differ from those predicted in statistical models or in the sequential-melting picture.
We discuss systems containing a heavy quark and a heavy antiquark in the infinite mass limit of QCD. Studying the limit of equal velocities for both heavy particles, we formulate an effective theory approach to heavy quarkonia-like systems. The method is well suited to processes in which the two heavy quarks annihilate, such as electromagnetic and strong decays of charmonium and bottomonium and weak decays of $B_c$.
We discriminate gluonic hadrons from conventional $q\bar q$ states by surveying radial and orbital excitations of all I=0 and I=1 $n\bar n$ systems anticipated up to 2.1 GeV. We give detailed predictions of their quasi-two-body branching fractions and identify characteristic decay modes that can isolate quarkonia. Several of the ``missing mesons'' with L$_{q\bar q}=2$ and L$_{q\bar q}=3$ are predicted to decay dominantly into certain S+P and S+D modes, and should appear in experimental searches for hybrids in the same mass region. We also consider the topical issues of whether some of the rece…
Muon pair production in exclusive radiative decays $χ_{cJ}\to J/ψμμ$, $χ_{bJ}\toΥμμ$ are considered. We present numerical values of the branching fractions and distributions over various kinematical variables.
Two complementary approaches to the theory of heavy quarkonia are discussed. The nonrelativistic potential models give amazingly accurate predictions, but lack a theoretical justification. The expansion in powers of $v/c$ is theoretically very acceptable, but is not as good in giving numerical predictions. The importance of combining these two approaches is stressed.
A new version for the relativistic generalization of the wide class of static quark--antiquark confining potentials is suggested. The comparison of this approach with other ones, known in literature, is considered. With the use of Logunov--Tavkhelidze quasipotential approach the first--order retardation corrections to the heavy quarkonia mass spectrum are calculated. As expected, these corrections turn out to be small for all low--lying heavy meson states.
This talk is based on results obtained for masses and wave functions of heavy quarkonia in a light-front Hamiltonian formulation of QCD with just one flavor of quarks using an ansatz for the mass-gap for gluons. Since the calculated spectra compare reasonably well with data, some further steps one can make are discussed.
A model based on a nonrelativistic potential supplemented by spin dependent terms of the Breit-Fermi type is described. This model reproduces the known masses of the $\bar{b}b$ quarkonia within 1MeV and the known masses of the $\bar{c}c$ quarkonia within 5MeV. Many predictions are made, some of them, e.g. for the fine splittings of the high $L$ states of the $\bar{b}b$ quarkonia and of the mass spectrum of the $\bar{b}c$ quarkonia, significantly different from previous predictions made by other authors.
The hyperfine splitting in heavy quarkonia is considered in its relation to the leptonic decay rates with the account of relativistic and radiative corrections. The calculated decay rates agree well with the available experimental data, while the predicted η_c(2S) mass is significantly smaller than the value measured recently by the Belle Collaboration.
In the quark-gluon plasma (QGP), it is well known that the evolution of quarkonia is affected by the screening of the interaction between the quark and the anti-quark. In addition, exchange of energy and color with the surrounding medium can be included via the incorporation of noise terms in the evolution Hamiltonian. For noise correlated locally in time, these dynamics have been studied in a simple setting by Kajimoto et al.[PHYS. REV. D 97, 014003(2018)]. We extend this calculation by considering non-Abelian dynamics for a three-dimensional wavefunction. We also propose a modification of th…
We model the spectral effect of open flavor meson-meson thresholds in heavy quarkonia. The proposed energy dependent quark-antiquark static potential tries to incorporate in a quark model scheme the results from unquenched lattice calculations. A good qualitative and a reasonable quantitative description of charmonium and bottomonium, including the "new charmonium-like" states, is obtained.
This report is devoted to the analytical calculation of heavy quarkonia production processes in modern experiments such as LHC, B-factories and superB-factories in computer. Theoretical description of heavy quarkonia is based on the factorization theorem. This theorem leads to special structure of the production amplitudes which can be used to develop computer algorithm which calculates these amplitudes automatically. This report is devoted to the description of this algorithm. As an example of its application we present the results of the calculation of double charmonia production in bottomon…
Based on the two Higgs doublet model, we study the effect of Higgs-boson exchange on the (super)heavy quarkonium \bar QQ, which induces a strong attractive force between a (super)heavy quark Q and an antiquark \bar Q. An interesting application is the decay of (super)heavy quarkonia \bar QQ into a Higgs boson associated with gauge bosons. The criterion for making the \bar QQ bound state is studied. We also show that non-perturbative effects due to gluonic field fluctuations are rather small in such a heavy quark sector. Possible enhancement for productions and decays of \bar QQ bound states ma…
Screening effects from sea pairs on the quark-antiquark static potential are analyzed phenomenologically from the light-quark to the heavy-quark meson spectra. From the high excited light-quark meson spectrum a universal form for the screened static potential is proposed. This potential is then succesfully applied to heavy quarkonia. Our results suggest the assignment of X(4260) to the 4s state of charmonium and the possible existence of a 5s bottomonium resonance around 10748 MeV.
Exclusive photoproduction of heavy quarkonia at HERA is analyzed in the framework of the Regge-eikonal approach together with the nonrelativistic bound state formalism. Total and differential cross-sections for the process $γ+p\to (Q\bar{Q})_{1S}+p$ are calculated. The model predicts cross-sections of Exclusive Double Diffractive Events (EDDE) at TeVatron and LHC.
Heavy quarkonium production is a powerful implement to study the strong interaction dynamics and QCD theory. Fragmentation is the dominant production mechanism for heavy quarkonia with large transverse momentum. With the large heavy quark mass, the relative motion of the heavy quark pair inside a heavy quarkonium is effectively nonrelativistic and it is also well-known that their fragmentation functions can be calculated in the perturbative QCD framework. Here, we analytically calculate the process-independent fragmentation functions for a gluon to split into the spin-singlet and -triplet $S$-…
Leading twist light cone distribution amplitudes (LCDAs) are key ingredients in calculating various hadronic amplitudes using light cone QCD sum rules. This work concentrates on calculating the leading twist LCDAs of P-wave heavy quarkonia. Quark model wavefunctions for the ground, first and second excited states of P-wave charmonia and bottomonia have been calculated, and are used for calculating the relevant LCDAs and leptonic decay constants.
We make comments on ref.[Z.Phys. C73, 541 (1997)], and provide partial wave analysis to the decays of excited heavy S-wave $1^-$ quarkonia into the basic $1^-$ quarkonia state plus $ππ$. It is revealed that there exist contributions of D-wave transition in $ψ'\longrightarrow J/ψππ$, $Υ(2S)\longrightarrow Υ(1S) ππ$ and $Υ(3S)\longrightarrow Υ(1S) ππ$ by using the data-fitting results in ref.[Z.Phys C73, 541 (1997)]. A possible experimental method to measure the D-wave directly is discussed.
It is shown that $BR(χ_{b1}(1P)\rightarrow Z\rightarrow e^+e^-)\simeq 3.3\cdot 10^{-7}$, $BR(χ_{b1}(2P)\rightarrow Z\rightarrow e^+e^-)\simeq 4.1\cdot 10^{-7}$ and $BR(χ_{c1}(1P)\rightarrow Z\rightarrow e^+e^-)\simeq 10^{-8}$ that give a good chance to search for the direct production of pseudovector $^3P_1$ heavy quarkonia in $e^+e^-$ collisions ($e^+e^-\rightarrow Z\rightarrow ^3P_1$) even at current facilities not to mention $b$ and $c-τ$ factories. Leading radiative corrections to annihilation of quarkonia in QCD are discussed.
In this paper we show that heavy quarckonium states, similar to light mesons, form Regge trajectories in $(n,M^2)$ and $(M^2,J)$ planes and the slope of these trajectories is independent on the quantum numbers of the mesons. This fact can be useful for the prediction of the masses of heavy quarkonia and the determination of the quantum numbers of the newly discovered states.
This is an elementary introduction to the recent significant theoretical progress in the field of heavy quarkonium physics. We show how renormalon cancellation takes place in the heavy quarkonium system, such as bottomonium and (remnant of) toponium resonance, and how this notion is useful in extracting the MSbar masses of the bottom and top quarks.
To include the explicit valence gluon degrees of freedom into spectroscopy of the lowest states of heavy quarkonia, we consider, within an adiabatic model, the properties of the lowest hybrid $\bar{Q}Qg$-mesons and estimate the effects of their mixing with low-lying vector $\bar{c}c$-charmonia. The perspectives of compatibility of the resulting picture with data are discussed.
In present work we discuss the production of heavy quarkonia and diquarks in $pp$-interactions. The aim is to take into account the production of bound states of quarks originating from independent parton scatterings. This production is regulated by constraints on the invariant mass of constituents. Such an approach leads to larger value of the diquark production cross section than traditional consideration in single parton scattering. This production mechanism of doubly heavy baryons can sooner be verified by modern experiments (e.g. LHCb). We also discuss related contributions to double and …
The perturbative renormalization group for light-front QCD Hamiltonian produces a logarithmically rising interquark potential already in second order, when all gluons are neglected. There is a question if this approach produces also color van der Waals forces between heavy quarkonia and of what kind. This article shows that such forces do exist and estimates their strength, with the result that they are on the border of exclusion in naive approach, while more advanced calculation is possible in QCD.
It is shown that $BR(χ_{b1}(1P)\rightarrow Z\rightarrow e^+e^-)\simeq 3.3\cdot 10^{-7}$, $BR(χ_{b1}(2P)\rightarrow Z\rightarrow e^+e^-)\simeq 4.1\cdot 10^{-7}$ and $BR(χ_{c1}(1P)\rightarrow Z\rightarrow e^+e^-)\simeq 10^{-8}$ that give a good chance to search for the direct production of pseudovector $^3P_1$ heavy quarkonia in $e^+e^-$ collisions ($e^+e^-\rightarrow Z\rightarrow ^3P_1$) even at current facilities not to mention $b$ and $c-τ$ factories.
We develop a formalism for computing inclusive production cross sections of heavy quarkonia based on the nonrelativistic QCD and the potential nonrelativistic QCD effective field theories. Our formalism applies to strongly coupled quarkonia, which include excited charmonium and bottomonium states. Analogously to heavy quarkonium decay processes, we express nonrelativistic QCD long-distance matrix elements in terms of quarkonium wavefunctions at the origin and universal gluonic correlators. Our expressions for the long-distance matrix elements are valid up to corrections of order $1/N_c^2$. The…
We present non-perturbative results for the spectrum of heavy quarkonia. Using an anisotropic formulation of Lattice QCD we achieved an unprecedented control over statistical and systematic errors. We also study relativistic corrections to the leading order predictions for heavy hybrids and conventional bound states.
Two-photon decay rates of pseudoscalar, scalar and tensor states of charmonium and bottomonium are calculated in the framework of the relativistic quark model. Both relativistic effects and one-loop radiative corrections are taken into account. The obtained results are compared with other theoretical predictions and available experimental data.
We compute derived quantities for various values of the model parameter of the Cornell potential model for the S-wave heavy quarkonia with radial quantum numbers n=1, 2, and 3. Our results can be used to determine leading and relative-order-v^2 nonrelativistic quantum chromodynamics matrix elements for S-wave charmonia and bottomonia such as psi(2S), eta_c(2S), and Upsilon(nS) for n=1, 2, and 3. These matrix elements will be essential ingredients for resumming relativistic corrections to processes involving those S-wave heavy quarkonium states.
Quenched lattice data for the quark-antiquark interaction (in terms of heavy quark free energies) in the color singlet channel at finite temperatures are fitted and used within the nonrelativistic Schroedinger equation formalism to obtain binding energies and scattering phase shifts for the lowest eigenstates in the charmonium and bottomonium systems in a hot gluon plasma. The partial dissociation rate due to the Bhanot-Peskin process is calculated using different assumptions for the gluon distribution function, including free massless gluons, massive gluons, and massive damped gluons. It is d…
Hadroproductions of charmonium and bottomonium $χ_J$ in polarized $pp$ collisions at RHIC energies are studied. Two--spin asymmetries $A_{LL}^{χ_J}(pp)$ for these reactions are very good parameters for examining the polarized gluon distributions in a proton.
By assuming the existence of (quasi)-linear Regge trajectories for heavy quarkonia in the low energy region, we derive a new, sixth power, meson mass relation which shows good agreement with experiment for both charmed and beauty mesons. This relation may be reduced to a quadratic Gell-Mann-Okubo type formula by fitting the values of the Regge slopes of these (quasi)-linear trajectories. For charmed mesons, such a formula holds with an accuracy of $\sim 1$%, and is in qualitative agreement with the relation obtained previously by the application of the linear spectrum to a meson hexadecuplet.
Quarkonia -- mesons made of a heavy quark and anti-quark -- have been extensively studied experimentally. Theoretical calculations of quarkonia based on lattice QCD are possible with control over the systematic errors. The comparison with experimental measurements of the quarkonia spectra leads to determinations of Standard Model parameters: the strong coupling, $α_s$, and the heavy quark masses.
Finite-temperature spectra of heavy quarkonia are calculated by combining potential model and thermofield dynamics formalisms. The mass spectra of the heavy quarkonia with various quark contents are calculated. It is found that binding mass of the quarkonium decreases as temperature increases.
We compute NRQCD long-distance matrix elements that appear in the inclusive production cross sections of $P$-wave heavy quarkonia in the framework of potential NRQCD. The formalism developed in this work applies to strongly coupled charmonia and bottomonia. This makes possible the determination of color-octet NRQCD long-distance matrix elements without relying on measured cross section data, which has not been possible so far. We obtain results for inclusive production cross sections of $χ_{cJ}$ and $χ_{bJ}$ at the LHC, which are in good agreement with measurements.
The velocity dependence of the thermal width of heavy quarkonia traveling with respect to the quark gluon plasma is calculated up to the NLO in perturbative QCD. At the LO, the width decreases with increasing speed, whereas at the NLO it increases with a magnitude approximately proportional to the expectation value of the relative velocity between the quarkonium and a parton in thermal equilibrium. Such an asymptotic behavior is due to the NLO dissociation cross section converging to a nonvanishing value in the high energy limit.
Within NRQCD factorization framework, in this work we compute, at the lowest order in velocity expansion, the next-to-leading-order (NLO) perturbative corrections to the short-distance coefficients associated with heavy quark fragmentation into the ${}^1S_0^{(1,8)}$ components of a heavy quarkonium. Starting from the Collins and Soper's operator definition of the quark fragmentation function, we apply the sector decomposition method to facilitate the numerical manipulation. It is found that the NLO QCD corrections have a significant impact.
Although individual levels of toponium will be unobservable, the top--anti--top system near threshold fulfills all requirements of a rigorous perturbation theory in QCD for weakly bound systems. Corresponding techniques from positronium may thus be transferred successfully to this case. After clarifying the effect of a non-zero width we calculate the $t\bar{t}$ potential to be used for the calculation of e.g. the cross-sections near threshold.
A nonrelativistic Hamiltonian with plausible spin dependent corrections is proposed for the quarkonia below their respective strong decay thresholds. With only six free parameters this model reproduces the nine known masses of the bottomonia within about 1 MeV, the six known masses of the charmonia within a few MeV and the five known leptonic decay widths of the ${}^3S_1$ states within about {20 %}. The model is then used to predict the masses of the remaining 43 quarkonia (some of them for the first time) and of the leptonic decay widths of the two ${}^1S_0(\bar{b}c)$ states. Comparison with …
The N-dimensional radial Schrödinger equation has been solved using the analytical exact iteration method (AEIM), in which the Cornell potential is generalized to finite temperature and chemical potential. The energy eigenvalues have been calculated in the N-dimensional space for any state (n, l). The present results have been applied for studying quarkonium properties such as charmonium and bottomonium masses. The binding energies and the mass spectra of heavy quarkonia are studied in the N-dimensional space. The dissociation temperatures for different states of heavy quarkonia are calculated…
A thermal potential can be defined to facilitate understanding the behavior of quarkonia in quark-gluon plasma. A nonperturbative evaluation of this potential from lattice QCD is difficult, as it involves real-time corelation function, and has often involved the use of Bayesian analysis, with its associated systematics. In this work we show that using the properties of the static quarkonia thermal correlation functions, one can directly extract a thermal potential for quarkonia from Euclidean Wilson loop data. This leads to a controlled extraction, and allows us to judge the suitability of var…
Heavy $c\bar c$ and $b\bar b $ quarkonia are considered as systems confined within a hard-wall potential shaped after a linear combination of a cotangent-- with a square co-secant function. Wave functions and energy spectra are then obtained in closed forms in solving by the Nikiforov-Uvarov method the associated radial Schrödinger equation in the presence of a centrifugal term. The interest in this potential is that in one parametrization it can account for a conformal symmetry of the strong interaction, and in another for its perturbation, a reason for which we here employ it to study status…
In this brief review, we examine carefully and critically the status of search for the $h_c$ [$ψ(1^1P_1)$] charmonium state and the $h_b$ [$Υ(1^1P_1)$] bottonium state, initiated by the E760 experiment. Recent experimental studies at CLEO/BABAR/BELLE are examined in the light of new theoretical and phenomenological understanding.
Using the expression of the dynamical gluon mass obtained through the operator product expansion we discuss the relevance of gluon mass effects in the decays V -> hadrons (V = J/Psi, Upsilon). Relativistic and radiative corrections are also introduced to calculate alpha_s(m_c) and alpha_s(m_b) comparing them with other values available in the literature. The effects of dynamical gluon masses are negligible for Upsilon decay but important for J/Psi decay.
