Quarkonium Spectrum Research Articles

Spectroscopy and annihilation decay widths of charmonium and bottomonium excitations

We study the charmonium ( cc¯ ) and bottomonium ( bb¯ ) spectra, using Cornell potential with additional constant potential term in a non-relativistic framework, with spin-dependent corrections corresponding to the spin–spin, spin–orbit, and tensor interactions added perturbatively. We predict the masses of low-lying and excited states of charmonium and bottomonium up to n = 6 and L = 2. We analyze the radial and orbital Regge trajectories of both the systems and investigate their departure from linearity. Further, we estimate the wave function at the origin and, consequently, predict the decay widths of charmonium and bottomonium states annihilating to leptons and photons. Also, we investigate the effect of scale dependence of the wave function at the origin and the strong coupling constant on the predictions of annihilation decay widths. We compare our predictions of heavy quarkonium spectra and decay widths with experimental results and other theoretical models.

Effect of continuum states on the double-heavy hadron spectra

We present the leading order coupling of double-heavy hadrons to heavy hadron pairs in Born-Oppenheimer effective field theory. We obtain the expressions for the contribution of heavy hadron pairs to the masses and widths of double-heavy hadrons. We apply our result for the specific case of the coupling of the lowest lying heavy hybrids and Ds∗D¯s∗Bs∗B¯s∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {D}_{(s)}^{\\left(\\ast \\right)}{\\overline{D}}_{(s)}^{\\left(\\ast \\right)}\\left({B}_{(s)}^{\\left(\\ast \\right)}{\\overline{B}}_{(s)}^{\\left(\\ast \\right)}\\right) $$\\end{document} obtaining a set of selection rules for the decays. We build a model for the coupling potential and compute the corresponding decay widths and the contributions to the mass of the heavy hybrids. We compare our results with the experimental exotic quarkonium spectrum and discuss the most likely experimental candidates for quarkonium hybrids.

XYZ states: An experimental point-of-view

Since 2003, a new family of states without a clear theoretical interpretation has been measured in the heavy quarkonium spectrum, the so-called X Y Z states. While the nature of these states is so far unclear, the experimental search is one of the most active fields in the intensity frontier. In this review, the most important and representative results obtained in this field in recent years are going to be illustrated, providing insights into the nature of these exotic states. The focus will be on the experimental side, describing how it is possible to investigate their exotic nature with respect to the conventional quarkonium states.

Quarkonium production in p+p collisions at RHIC and LHC

Quarkonium production mechanism is still an unresolved question. This paper provides an overview of recent quarkonium production studies performed at RHIC and LHC in p + p collisions at a wide range of collision energies. After a brief explanation of representative theoretical models, experimental results of the quarkonium spectra and polarizations are presented with comparison to the model calculations. The spectra are overall rather well described by production model calculations, with a few exceptions, while no significant polarization is observed beyond large uncertainties for J/ψ and ϒ, and thus no constraint on the models is obtained at present. Recently, new observables have been measured such as charged particle multiplicity dependence of quarkonium production, which provides a way to understand the interplay between hard and soft processes, and associated production of quarkonium (J/ψ in jets and double production), which provides more information about production mechanism. A trend of non-linear increase of quarkonium production with increasing the particle multiplicity is observed both at RHIC and LHC, but it is reproduced by most models and further studies and more data are needed in order to differentiate them. Meanwhile, the first measurements of J/ψ in jets show that it is produced with larger activity within a jet than simulated by PYTHIA. A comment on the study of J/ψ-hadron femtoscopic correlations to measure their mutual interaction is also given. In summary, the production mechanism remains a puzzle, but more precise studies will be possible with upcoming RHIC and LHC runs.

Unquenching the Quark Model in a Nonperturbative Scheme

In recent years, the discovery in quarkonium spectrum of several states not predicted by the naive quark model has awakened a lot of interest. A possible description of such states requires the enlargement of the quark model by introducing quark-antiquark pair creation or continuum coupling effects. The unquenching of the quark models is a way to take these new components into account. In the spirit of the Cornell Model, this is usually done by coupling perturbatively a quark-antiquark state with definite quantum numbers to the meson-meson channel with the closest threshold. In this work we present a method to coupled quark-antiquark states with meson-meson channels, taking into account effectively the nonperturbative coupling to all quark-antiquark states with the same quantum numbers. The method will be applied to the study of the X(3872) resonance and a comparison with the perturbative calculation will be performed.

S-Wave Heavy Quarkonium Spectra: Mass, Decays, and Transitions

In this paper we revisited phenomenological potentials. We studied S-wave heavy quarkonium spectra by two potential models. The first one is power potential and the second one is logarithmic potential. We calculated spin averaged masses, hyperfine splittings, Regge trajectories of pseudoscalar and vector mesons, decay constants, leptonic decay widths, two-photon and two-gluon decay widths, and some allowed M1 transitions. We studied ground and 4 radially excited S-wave charmonium and bottomonium states via solving nonrelativistic Schrödinger equation. Although the potentials which were studied in this paper are not directly QCD motivated potential, obtained results agree well with experimental data and other theoretical studies.

Charmonia in moving frames

Lattice simulation of charmonium resonances with non-zero momentum provides additional information on the two-meson scattering matrices. However, the reduced rotational symmetry in a moving frame renders a number of states with different JP in the same lattice irreducible representation. The identification of JP for these states is particularly important, since quarkonium spectra contain a number of states with different JP in a relatively narrow energy region. Preliminary results concerning spin-identification are presented in relation to our study of charmonium resonances in flight on the Nf = 2 + 1 CLS ensembles.

Theory Concepts for Heavy Exotic Mesons

Some of the currently most popular conjectures for the structure of the recently discovered heavy mesons that do not find a place in the quark model quarkonium spectrum are sketched. Furthermore, some observables are identified that should allow one to identify the most prominent components of individual states.

Coulomb artifacts and breakdown of perturbative matching in lattice NRQCD

By studying an explicit analytical solution of the Schrödinger equation with the Coulomb potential on the lattice we demonstrate a breakdown of perturbative matching for the description of the Coulomb artifacts in lattice NRQCD, which leads to a large systematic error in the predictions for the heavy quarkonium spectrum. The breakdown is a result of a fine interplay between the short and long distance effects specific to the lattice regularization of NRQCD. We show how the problem can be solved by matching the lattice and continuum results for the solution of the full Schrödinger equation without the expansion in the Coulomb interaction.

Thermal quarkonium physics in the pseudoscalar channel

The pseudoscalar correlator is an ideal lattice probe for thermal modifications to quarkonium spectra, given that it is not compromised by a contribution from a large transport peak. We construct a perturbative spectral function incorporating resummed thermal effects around the threshold and vacuum asymptotics above the threshold, and compare the corresponding imaginary-time correlators with continuum-extrapolated lattice data for quenched SU(3) at several temperatures. Modest differences are observed, which may originate from non-perturbative mass shifts or renormalization factors, however no resonance peaks are needed for describing the quenched lattice data for charmonium at and above T ∼ 1.1Tc ∼ 350 MeV. For comparison, in the bottomonium case a good description of the lattice data is obtained with a spectral function containing a single thermally broadened resonance peak.

Coulomb artifacts and bottomonium hyperfine splitting in lattice NRQCD

We study the role of the lattice artifacts associated with the Coulomb binding effects in the analysis of the heavy quarkonium within lattice NRQCD. We find that a “na¨ıve” perturbative matching generates spurious linear Coulomb artifacts, which result in a large systematic error in the lattice predictions for the heavy quarkonium spectrum. This effect is responsible, in particular, for the discrepancy between the recent determinations of the bottomonium hyperfine splitting in the radiatively improved lattice NRQCD [1, 2]. We show that the correct matching procedure which provides full control over discretization errors is based on the asymptotic expansion of the lattice theory about the continuum limit, which gives MY(1S) − Mηb(1S) = 52.9 ± 5.5 MeV [1].

The non-perturbative unquenched quark model

In recent years states in the quarkonium spectrum not expected in the naive quark model have appeared and created a lot of interest. In the theoretical side the study of the effect of meson-meson thresholds in the spectrum have been performed in different approximations. In a quark model framework, and in the spirit of the Cornell model, when a meson-meson threshold is included, the coupling to all the quark-antiquark states have to be considered. In practice only the closest states are included perturbatively. In this contribution we will present a framework in which we couple quark-antiquark states with meson-meson states non-perturbatively, taking into account effectively the coupling to all quark-antiquark states. The method will be applied to the study of the X (3872) and a comparison with the perturbative calculation will be performed.

Quark confinement potential examined by excitation energy of the Λcand Λbbaryons in a quark–diquark model

The possibility to have diquark configuration in heavy baryons, such as Lambda_c and Lambda_b, is examined by a nonrelativistic potential model with a heavy quark and a light scalar diquark. Assuming that the Lambda_c and Lambda_b baryons are composed of the heavy quark and the point-like scalar-isoscalar ud diquark, we solve the two-body Schrodinger equation with the Coulomb plus linear potential and obtain the energy spectra for the heavy baryons. Contrary to our expectation, it is found that the potential determined by the quarkonium spectra fails to reproduce the excitation spectra of the Lambda_c and Lambda_b in the quark-diquark picture, while the Lambda_c and Lambda_b spectra is reproduced with a half strength of the confinement string tension than for the quarkonium. The finite size effect of the diquark is also examined and it is found that introduction of a finite size diquark would resolve the failure of the spectrum reproduction. The Xi_c excitation energy is also calculated and is found to be smaller than Lambda_c in the quark-diquark model. This is not consistent with the experimental observation.

27pTA-5 格子QCDで決定したクォーク間ポテンシャルによるクォーコニウムスペクトル(27pTA 格子QCD・ハドロン構造・相互作用,理論核物理領域)

27pTA-5 格子QCDで決定したクォーク間ポテンシャルによるクォーコニウムスペクトル(27pTA 格子QCD・ハドロン構造・相互作用,理論核物理領域)

Perturbative heavy quarkonium spectrum at next-to-next-to-next-to-leading order

We compute the energy levels of some of the lower-lying heavy quarkonium states perturbatively up to O(αs5m) and O(αs5mlogαs). Stability of the predictions depends crucially on the unknown 4-loop pole-MS¯ mass relation. We discuss the current status of the predictions with respect to the observed bottomonium spectrum.

Bottomonium in the plasma: Lattice results

We present results on the heavy quarkonium spectrum and spectral functions obtained by performing large-scale simulations of QCD for temperatures ranging from about 100 to 500 MeV, in the same range as those explored by LHC experiments. We discuss our method and perspectives for further improvements towards the goal of full control over the many systematic uncertainties of these studies.

Making confining strings out of mesons

The light mesons such as $\ensuremath{\pi}$, $\ensuremath{\rho}$, $\ensuremath{\omega}$, ${f}_{0}$, and ${a}_{0}$ are possible candidates of magnetic degrees of freedom, if a magnetic dual picture of QCD exists. We construct a linear sigma model to describe spontaneous breaking of the magnetic gauge group, in which there is a stable vortex configuration of vector and scalar mesons. We numerically examine whether such a string can be interpreted as the confining string. By using meson masses and couplings as inputs, we calculate the tension of the string as well as the strength of the Coulomb force between static quarks. They are found to be consistent with those inferred from the quarkonium spectrum and the Regge trajectories of hadrons. By using the same Lagrangian, the critical temperature of the QCD phase transition is estimated, and a nontrivial flavor dependence is predicted. We also discuss a possible connection between the Seiberg duality and the magnetic model we studied.

Non-relativistic spectrum of two-color QCD at non-zero baryon density

The heavy quarkonium spectrum of Two Color QCD (QC2D) at non-zero quark chemical potential μ and temperature T with μ/T≫1 has been calculated in both S- and P-wave channels using a lattice non-relativistic formulation of QC2D. As μ is varied, the quarkonium spectra reveal three separate regions, corroborating previous findings that there are three distinct physical regimes of QC2D at low temperature and high baryon density: hadronic matter, quark/quarkyonic matter, and deconfined matter. The results are interpreted in terms of the formation of heavy-light Qq states in the two-color baryonic medium.

Next-to-leading ultrasoft running of the heavy quarkonium potentials and spectrum: Spin-independent case

We compute the next-to-leading logarithmic (NLL) ultrasoft running of the spin-independent singlet potentials up to ${\cal O}(1/m^2)$, and the corresponding contribution to the spectrum. This includes the static energy at next-to-next-to-next-to-leading logarithmic (NNNLL) order. As a byproduct of these results one could obtain the heavy quarkonium spectrum with N$^3$LL accuracy for $l\not=0$ (angular momentum) and $s=0$ (spin) states, setting the stage for the full analytic and numerical N$^3$LL analysis of such quantity. We also compute the next-to-next-to-next-to-next-to-leading order (N$^4$LO) ultrasoft spin-independent contribution to the heavy quarkonium mass and static energy.

Heavy quarkonium spectra and its decays in a nonrelativistic model with Hulthen potential

In this paper, we have made a comprehensive study of S wave quarkonium spectra in the general framework of a nonrelativistic potential model. The full potential used in our model consists of a Hulthen potential and a confining linear potential. The spin hyperfine interaction is introduced to obtain the masses of the pseudoscalar and vector mesons. The three-dimensional harmonic oscillator wavefunction is used as a trial wavefunction to obtain the mass spectra. The model parameters and the wavefunction that reproduce the mass spectra of and mesons are used to investigate the decay constants, leptonic decay widths, two-photon and two-gluon decay widths, and radiative decay widths of the S wave and mesons. The obtained values are compared with the experimental results and with the values obtained from other theoretical models. The predictions from our model are found to be in good agreement with the experimental results.