We examined the effects of the weak magnetic field on the dissociation of heavy quarkonia immersed in a thermal medium of quarks and gluons. For that purpose, we have revisited the general structure of gluon self-energy tensor in the presence of a weak magnetic field in thermal medium and obtained the relevant structure functions. The structure functions give the real and imaginary parts of the resummed gluon propagator, which further give the respective dielectric permittivities. The real and imaginary parts of the dielectric permittivity will be used to evaluate the real and imaginary parts of the complex heavy quark potential. The real-part of the potential is found to be more screened, whereas the magnitude of the imaginary-part of the potential gets increased on increasing the value of both temperature and magnetic field. In addition to this, we have observed that the real-part gets slightly more screened while the imaginary part gets increased in the presence of a weak magnetic field as compared to their counterparts in the absence of a magnetic field. The increase in the screening of the real-part of the potential leads to the decrease of binding energies of $J/Ψ$ and $Υ$, whereas the increase in the magnitude of the imaginary part leads to the increase of thermal width with the temperature and magnetic field both. Also the binding energy and thermal width in the presence of weak magnetic field become smaller and larger, respectively, as compared to that in the pure thermal case. We have finally obtained the dissociation temperatures for $J/Ψ$ and $Υ$, which become slightly lower in the presence of weak magnetic field. This observation leads to the slightly early dissociation of quarkonia because of the presence of a weak magnetic field.
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…
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…
Complex-energy spectrum and dissociation of heavy quarkonia in an anisotropic collisional quark-gluon plasma
School of Physical Sciences, National Institute of Science Education and Research, An OCC of Homi Bhabha National Institute（物理科学学院，国家科学教育与研究中心，霍米·巴巴国立学院）
n this paper I discuss what we can learn about quarkonium dissociation from lattice-potential based models. Special emphasis is given to results obtained in agreement by different models, and to the relevance of lattice QCD for potential models. Future directions are also discussed.
Using a temperature-dependent potential obtained from lattice gauge calculations, we study the stability of heavy quarkonia in the quark-gluon plasma. We find that only the Upsilon(1S) and the eta_b(1S) are bound in the quark-gluon plasma, and have a small binding energy. The quark-gluon plasma may be revealed by an Upsilon(1S) dilepton peak with an invariant mass close to twice the current b quark mass, which is lower than the Upsilon(1S) mass in free space. The quarkonia Upsilon(1S) and eta_b(1S) can dissociate by collision with quarks and gluons in the quark-gluon plasma. We evaluate the di…
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…
At the chiral restoration/deconfinement transition, most hadrons undergo a Mott transition from being bound states in the confined phase to resonances in the deconfined phase. We investigate the consequences of this qualitative change in the hadron spectrum on final state interactions of charmonium in hot and dense matter, and show that the Mott effect for D-mesons leads to a critical enhancement of the J/$ψ$ dissociation rate. Anomalous J/psi suppression in the NA50 experiment is discussed as well as the role of the Mott effect for the heavy flavor kinetics in future experiments at the LHC. T…
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.
To study the stability of heavy quarkonia in quark-gluon plasma, we use a color-singlet Q-Qbar potential determined previously to be a well-defined linear combination of the free energy F_1 and the internal energy U_1. Using the lattice gauge results of Kaczmarek et al., the dissociation temperatures of J/psi and chi_b in quenched QCD are found to be 1.62Tc and 1.18Tc respectively, in good agreement with spectral function analyses. The dissociation temperature of J/psi in full QCD with 2 flavors is 1.42Tc. Thus, the presence of dynamical quarks in full QCD lowers the dissociation temperature o…
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 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.
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.
Using the potential model and thermodynamical quantities obtained in lattice gauge calculations, we determine the spontaneous dissociation temperatures of color-singlet quarkonia and the `quark drip lines' which separate the region of bound $Q\bar Q$ states from the unbound region. The dissociation temperatures of $J/ψ$ and $χ_b$ in quenched QCD are found to be 1.62$T_c$ and $1.18T_c$ respectively, in good agreement with spectral function analyses. The dissociation temperature of $J/ψ$ in full QCD with 2 flavors is found to be 1.42$T_c$. For possible bound quarkonium states with light quarks, …
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.
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…
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.
Recent lattice calculations showed that the quarkonia will survive beyond the phase transition temperature, and will dissolve at different temperatures depending on the type of the quarkonium. In this work, we calculate the thermal width of the quarkonium at finite temperature before it dissolves into open heavy quarks. The input of the calculation are the parton quarkonium dissociation cross section to NLO in QCD, the quarkonium wave function in a temperature-dependent potential from lattice QCD, and a thermal distribution of partons with thermal masses. We find that for the J/psi, the total …
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 $S$-…
We investigate the Mott effect for heavy quarkonia due to Debye screening of the heavy quark potential in a plasma of massless quarks and antiquarks. The influence of residual color correlation is investigated by coupling the light quark sector to a temporal gauge field driven by the Polyakov loop potential. This leads to an increase of the Mott dissociation temperatures for quarkonia states which stabilizes in particular the excited states, but has marginal effect on the ground states.
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.
Emphasizing the possibility of moderate suppression of heavy quarkonium states, we invite some attention towards the issue of real time evolution of quarkonia during the cooling phase of quark gluon plasma(QGP). In this context, we have used time dependent perturbation theory to show that $Υ(1S)$, $Υ(2S)$, $J/Ψ$ can further be dissociated in the medium at a temperature below their dissociation thresholds even though they survive the Debye screening. We have presented and compared the dissociation probabilities and dissociation rates of these states in real and complex valued potential in this …
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.
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.
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 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.
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…
