The typical velocity of a heavy quark in a quarkonium is a widely used quantity, in this paper, based on the relativistic Bethe-Salpeter equation method, we calculate the average values ${\overline{|\boldsymbol{q}|^n}}$ and $ \overline{|\boldsymbol{v}|^n}\equiv v^n$ of a heavy quark in a $S$ wave or $P$ wave quarkonium rest frame, where $\boldsymbol{q}$ and $\boldsymbol{v}$ are the three dimensional momentum and velocity, $n=1,2,3,4$. For a charm quark in $J/ψ$, we obtained $v_{J/ψ}=0.46$, $v^2_{J/ψ}=0.26$, $v^3_{J/ψ}=0.18$, and $v^4_{J/ψ}=0.14$, for a bottom quark in $Υ(1S)$, $v_{Υ(1S)}=0.24$, $v^2_{Υ(1S)}=0.072$, $v^3_{Υ(1S)}=0.025$, and $v^4_{Υ(1S)}=0.010$. The values indicate that ${v^n} >{v^{n_1}}\cdot{v^{n_2}}$, where $n_1+n_2=n$, which is correct for all the charmonia and bottomonia. Our results also show the poor convergence if we make the {speed} expansion in charmonium system, but good for bottomonium. Based on the $v^n$ values and the following obtained relations $v^n_{4S} > v^n_{3S}> v^n_{2S}>v^n_{1S}$, $v^n_{4P} > v^n_{3P}> v^n_{2P}>v^n_{1P}$ and $v^n_{mP}>v^n_{mS}$ ($n,m=1,2,3,4$), we conclude that highly excited quarkonia have larger relativistic corrections than those of the corresponding low excited and ground states, and there are large relativistic corrections in charmonium system.
The $η$ production in the $(n,n')$ bottomonium transitions $Υ(n) \to Υ(n') η, $ is studied in the method used before for dipion heavy quarkonia transitions. The widths $Γ_η(n,n')$ are calculated without fitting parameters for $n=2,3,4,5, n'=1$.Resulting $Γ_η(4,1)$ is found to be large in agreement with recent data.
In this paper we study the high energy exclusive photoproduction of heavy quarkonia pairs in the leading order of the strong coupling constant $α_{s}$. In the suggested mechanism the quarkonia pairs are produced with opposite charge parities, and have predominantly oppositely directed transverse momenta. Using the Color Glass Condensate approach, we estimated numerically the production cross-sections in the kinematics of the forthcoming electron-proton colliders, as well as proton-ion colliders in ultraperipheral collisions. We found that the cross-sections are within the reach of planned expe…
Proton-proton collisions at the LHC provide the ground for tests of the strong interactions through the study of the production mechanisms for quarkonia and hadrons containing charm or beauty flavours. This review addresses recent results and includes studies of kinematical correlations, polarisation and associated production. QCD-based models are briefly discussed and compared to measurements.
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.
Rare Higgs decays into a pair of heavy vector quarkonia, $h\to VV$ ($V=J/Ψ$, $Υ$ etc.), have been investigated in the standard model. Different from the past literature in which these decays are thought to be only dominated by the longitudinally polarized final states, we also include the transitions, which proceed through $h\to γ^*γ^*$/$h\to Vγ^*$, followed by $γ^*\to V$. The final vector quarkonia via these ways are dominantly transversely polarized. Our calculation however shows that these transitions could lead to significant contributions to the decay rate, especially for the charmonium f…
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…
Agreement with the measured electronic widths of the $ψ(4040)$, $ψ(4415)$, and $Υ(11019)$ resonances is shown to be reached if two effects are taken into account: a flattening of the confining potential at large distances and a total screening of the gluon-exchange interaction at $r\ga 1.2$ fm. The leptonic widths of the unobserved $Υ(7S)$ and $ψ(5S)$ resonances: $Γ_{e^+e^-}(Υ(7S))=0.11$ keV and $Γ(ψ(5S))\approx 0.54$ keV are predicted.
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.
In a covariant Bethe-Salpeter-equation approach and with a rainbow-ladder truncated model of QCD, we investigate the use of an effective interaction with the goal of reproducing QCD phenomenology. We extend previous studies and present results for ground and excited meson states in the bottomonium and charmonium systems, where the results are surprisingly good for most states. In addition, we formulate a critical outlook on states with exotic quantum numbers as well as the light-quark domain.
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.
The $η$ production in the $(n,n')$ bottomonium transitions $Υ(n) \to Υ(n') η, $ is studied in the method used before for dipion heavy quarkonia transitions. The widths $Γ_η(n,n')$ are calculated without fitting parameters for $n=2,3,4,5, n'=1$. Resulting $Γ_η(4,1)$ is found to be large in agreement with recent data. Multipole expansion method is shown to be inadequate for large size systems considered.
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 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…
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 $B_c$.
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.
Quarkonia are some of the most important probes of the medium created in relativistic heavy ion collision experiments, but it is still difficult to get quantitative results for its behavior in the plasma. Here I discuss the decay width of a heavy quarkonium system, and calculate the gluodissociation width of bottomonia. In the end I comment on study of quarkonia as open quantum systems.
Within the standard model, we have investigated rare $Z$-boson decays into double heavy quarkonia, $Z\to VV$ and $Z\to VP$ with $V$ denoting vector and $P$ denoting pseudoscalar quarkonia, respectively. It is assumed that the leading-order QCD diagrams would give the dominant contributions to these processes, and the corresponding branching fractions, for instance, ${\cal B}(Z\to J/ΨJ/Ψ)$ has been estimated to be around $10^{-13}$ in the literature. However, these decays could also happen through the electromagnetic transition $Z\to Vγ^*$ and $Z\to Pγ^*$, with the virtual photon transforming i…
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.
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.
We revisit the transport coefficients of heavy quarkonia moving in high-temperature QCD plasmas. The thermal width and mass shift for heavy quarkonia are closely related to the momentum diffusion coefficient and its dispersive counterpart for heavy quarks, respectively. For quarkonium at rest in plasmas the longitudinal gluon part of the color-singlet self-energy diagram is sufficient to determine the leading-order thermal width, whereas the momentum dependence is obtained from the transverse gluon channel. Using the quarkonium-gluon effective vertex based on the dipole interaction of color ch…
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…
We summarize and discuss some of the experimental and theoretical results on heavy flavor, quarkonia, and electro-weak probes presented at Quark Matter 2012.
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 $S$-…
It is shown that the molecular model for the X{3872) state contradicts the new experimental data as well as the old ones. It is suggested to study the χ_{c1} and χ_{b1} states in the e+e-\toχ_{c1}/χ_{b1} reactions.
This writeup summarizes recent CMS results on quarkonia measurements in pp, pPb and PbPb collisions at LHC. The excellent muon detection capability of CMS allows measurement of charmonia states at high transverse momentum ($p_T$) while the $Υ$ states can be reconstructed starting at zero $p_T$. The absolute and relative yields of different charmonia and bottomonia states modified in PbPb collisions (over pp collisions) are described. The vertexing capability of CMS enables measurement of B meson energy loss via its decay to J/$ψ$. An overview of these measurements is given. How these measureme…
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 …
We compute the color-singlet and color-octet nonrelativistic QCD (NRQCD) long-distance matrix elements for inclusive production of $P$-wave quarkonia in the framework of potential NRQCD. In this way, the color-octet NRQCD long-distance matrix element can be determined without relying on measured cross section data, which has not been possible so far. We obtain inclusive cross sections of $χ_{cJ}$ and $χ_{bJ}$ at the LHC, which are in good agreement with data. In principle, the formalism developed in this Letter can be applied to all inclusive production processes of heavy quarkonia.
We study the properties of quarkonia inside a bulk-viscous quark gluon plasma. The non-equilibrium nature of the medium is encoded in the deformed distribution functions of thermal quarks and gluons, with which we compute the dielectric permittivity within the hard thermal loop approximation at one-loop. The modified dielectric permittivity is used to calculate the in-medium heavy quark potential, and using the potential we compute spectral functions, which reflect the physical properties of heavy quarkonia. We discuss how the bulk viscous effect influences quantities such as binding energies …
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 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.
In our quest to win a deeper understanding of how QCD actually works, the study of the binding of heavy quarkonia and heavy-flavor hadrons to atomic nuclei offers enormous promise. Modern experimental facilities such as FAIR, Jefferson Lab at 12 GeV and J-PARC offer exciting new experimental opportunities to study such systems. These experimental advances are complemented by new theoretical approaches and predictions, which will both guide these experimental efforts and be informed and improved by them. This review will outline the main theoretical approaches, beginning with QCD itself, summar…
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.
