As a sister work of Ref.[1], we incorporate the color-screening effect due to light quark pair creation into the heavy quark-antiquark potential, and investigate the effects of screened potential on the spectrum of bottomonium. We calculate the masses, electromagnetic decays, and E1 transitions of bottomonium states. We find that the fine splittings between $χ_{bJ}$ (J=0,1,2) states are in good agreement with experimental data, and the E1 transition rates of $Υ(2S)\toγχ_{bJ}(1P)$ and $Υ(3S)\toγχ_{bJ}(2P)$ (J=0,1,2) all agree with data within experimental errors. In particular, the mass of $Υ(6S)$ is lowered down to match that of the $Υ(11020)$, which is smaller than the predictions of the linear potential models by more than 100 MeV. Comparison between charmonium and bottomonium in some related problems is also discussed.
Recent lattice QCD calculations suggest a rather abrupt transition in the confinig potential from a linear to a constant behavior. We analyze the effects of such a fast deconfinement in the simplest non-relativistic system, bottomonium.
A new non relativistic quark model to calculate the spectrum of heavy quark mesons is developed. The model is based on an interquark potential interaction that implicitly incorporates screening effects from meson-meson configurations. An analysis of the bottomonium spectrum shows the appearance of extra states as compared to conventional non screened potential models.
A generalized screened potential model (GSPM), recently developed to study the bottomonium spectrum, is applied to the calculation of charmonium masses and electromagnetic widths. The presence in the GSPM of more quark-antiquark bound states than in conventional non screened potential models, allows for the assignment of GSPM states to cataloged non conventional $J^{++}$ charmonium resonances as well as for the prediction of new (non cataloged) $J^{++}$ states. The results obtained seem to indicate that a reasonable overall description of $J^{++}$ charmonium resonances is feasible.
We fit the lattice QCD data of Kaczmarek et al for the free energy F1 and internal energy U1 with a class of Coulomb, constant and linear potentials, both pure and screened, matching the large distance to the short distance parts of the lattice QCD finite temperature energies. We also include the hyperfine potential in F1 and U1. We detail the bottomonium (and charmonium) binding and the melting temperatures, both for the groundstate and for the excited states, relevant for Hard Probes in Heavy Ion Collisions at LHC, where temperatures well above Tc will be reached, much higher than the temper…
The one-loop corrections to the bottomonium mass spectrum due to the finite charm mass are evaluated in the framework of the relativistic quark model. The obtained corrections are compared with the results of perturbative QCD.
We study the bottomonium spectrum in the nonrelativistic quark model with the coupled-channel effects. The mass shifts and valence $b\bar{b}$ component are evaluated to be rather large. We find that the hadronic loop effects can be partially absorbed into a reselection of the model parameters. No bottomonium state except $Υ(5\,^1S_0)$ and $Υ(5\,^3S_1)$ with mass around 10890 MeV is found in the quark models both with and without coupled-channel effects, so we suggest that $Y_{b}(10890)$ is an exotic state beyond the quark model, if it is confirmed to be a new resonance. The predictions for the…
We study the bottomonium spectrum using a relativistic potential model in the momentum space. This model is based on a complete one gluon exchange interaction with a momentum dependent screening factor to account for the effects due to virtual pair creation that appear close to the decay thresholds. The overall model does not make use of nonrelativistic approximations. We fit well established bottomonium states below the open charm threshold and predict the rest of the spectrum up to $\approx 11200$ MeV and $J^{PC}=3^{--}$. Uncertainties are treated rigorously and propagated in full to the par…
The charmonium (bottomonim) binding at finite temperature is studied with static potentials extracted from the lattice QCD data of Kaczmarek et al. The bottomonium spectrum is also studied. This is relevant for Hard Probes in Heavy Ion Collisions.
Recently it has been shown that the gross structure of the bottomonium spectrum is reproduced reasonably well within the non-relativistic boundstate theory based on perturbative QCD. In that calculation, however, the fine splittings and the S-P level splittings are predicted to be considerably narrower than the corresponding experimental values. We investigate the bottomonium spectrum within a specific framework based on perturbative QCD, which incorporates all the corrections up to O(alpha_S^5 m_b) and O(alpha_S^4 m_b), respectively, in the computations of the fine splittings and the S-P spli…
In this work, we obtain the Schrödinger equation solutions for the Kratzer potential plus screened Coulomb potential model using the series expansion method. The energy eigenvalues is obtained in non-relativistic regime and the corresponding unnormalized eigenfunction. Three special cases were obtained. We applied the present results to calculate heavy-meson masses of charmonium and bottomonium , and we got the numerical values for 1S, 2S, 1P,2P, 3S, 4S ,1D,2D and 1F states. The results are in good agreement with experimental data and the work of other researchers.
The bottomonium spectrum is far from being established. The structures of higher vector states, including the $Υ(10580)$, $Υ(10860)$, and $Υ(11020)$ states, are still in dispute. In addition, whether the $Υ(10750)$ signal which was recently observed by the Belle Collaboration is a normal $b\bar{b}$ state or not should be examined. Faced with such a situation, we carried out a systematic investigation of the bottomonium spectrum in the scheme of the relativistic flux tube (RFT) model. A Chew-Frautschi like formula was derived analytically for the spin average mass of bottomonium states. We furt…
Stimulated by the exciting progress in the observation of new bottomonium states, we study the bottomonium spectrum. To calculate the mass spectrum, we adopt a nonrelativistic screened potential model. The radial Schrödinger equation is solved with the three-point difference central method, where the spin-dependent potentials are dealt with non-perturbatively. With this treatment, the corrections of the spin-dependent potentials to the wave functions can be included successfully. Furthermore, we calculate the electromagnetic transitions of the $nS$ ($n\leq 4$), $nP$ ($n\leq 3$), and $nD$ ($n\l…
The coulomb plus linear (Cornell) potential is used to investigate the mass spectrum of bottomonium. Gaussian wave function is used in position and momentum space to estimate values of potential and kinetic energies, respectively. Based on our calculations, we study newly observed ${{\mathit Υ}{(10860)}}$ as an admixture of $4^{3}S_{1}$ with $4^{3}D_{1}$, and ${{\mathit Υ}{(10753)}}$ as an admixture of $6^{3}S_{1}$ with $4^{3}D_{1}$ also, we try to assign ${{\boldsymbol Υ}{(11020)}}$ as a pure $4^{3}D_{1}$ bottomonium state. We also study the Regge trajectories in the $(J,M^{2})$ and $(n_r,M^{…
We revisit the bottomonium spectrum motivated by the recently exciting experimental progress in the observation of new bottomonium states, both conventional and unconventional. Our framework is a nonrelativistic constituent quark model which has been applied to a wide range of hadronic observables from the light to the heavy quark sector and thus the model parameters are completely constrained. Beyond the spectrum, we provide a large number of electromagnetic, strong and hadronic decays in order to discuss the quark content of the bottomonium states and give more insights about the better way …
The mass spectrum of $b\bar{b}$ states has been obtained using the phenomenological relativistic quark model (RQM). The Hamiltonian used in the investigation has confinement potential and confined one gluon exchange potential (COGEP). In the frame work of RQM a study of M1 and E1 radiative decays of $b\bar{b}$ states have been made. The weak decay widths in the spectator quark approximation have been estimated. An overall agreement is obtained with the experimental masses and decay widths.
We present results on the bottomonium spectrum at temperatures above and below the deconfinement crossover temperature, $T_c$, from dynamical lattice QCD simulations. The heavy quark is treated with a non-relativistic effective field theory on the lattice and serves as a probe of the hot medium. Ensembles with a finer spatial lattice spacing and a greater range of temperatures below $T_c$ than those previously employed by this collaboration are used. In addition, there are $N_f=2+1$ flavours of Wilson clover quark in the sea with $M_π\approx400$ MeV and we perform a more careful tuning of the …
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.
We extend the formalism based on perturbative QCD that was developed in our previous work, and compute the hyperfine splittings of the bottomonium spectrum as well as the fine and hyperfine splittings of the charmonium spectrum. All the corrections up to O(alpha_s^5 m) are included in the computations. We find agreement (with respect to theoretical uncertainties) with the experimental values whenever available and give predictions for not yet observed splittings.
In this work we calculate the mass spectrum, weak decay constants, two photon decay widths, and two gluon decay widths of ground (1S), and radially excited (2S,3S,...) states of pseudoscalar charmoniuum and bottomonium such as $η_{c}$ and $η_{b}$, as well as the mass spectrum and leptonic decay constants of ground state (1S), excited (2S,1D,3S,2D,4S,and 3D) states of vector charmonium and bottomonium such as $J/ψ$, and $Υ$, using the formulation of Bethe-Salpeter equation under covariant Instantaneous Ansatz (CIA). Our results are in good agreement with data (where ever available) and other mo…
We calculate the full spectrum of D-wave states in the Upsilon system in lattice QCD for the first time, using an improved version of NonRelativistic QCD on coarse and fine "second generation" gluon field configurations from the MILC collaboration that include the effect of up, down, strange and charm quarks in the sea. Taking the 2S-1S splitting to set the lattice spacing, we determine the ^3D_2 - 1S splitting to 2.3%, and find agreement with experiment. Our prediction of the fine structure relative to the ^3D_2 gives the ^3D_3 at 10.181(5) GeV and the ^3D_1 at 10.147(6) GeV. We also discuss …
The low-lying spectrum of the quark model is shown to be robust under the effects of `unquenching'. In contrast, the use of screened potentials is shown to be of limited use in models of hadrons. Applications to unquenching the lattice Wilson loop potential and to glueball mixing in the adiabatic hybrid spectrum are also presented.
We investigate the quarkonia correlators in QCD with no light quarks within a potential model with different screened potentials. Our results for the temperature dependence of the charmonium and bottomonium correlators are qualitatively consistent with existing and preliminary lattice results. We identify however, a much reacher structure in the correlators than the one seen on the lattice.
We investigate the modification of S and P wave states in the bottomonium spectrum above and below the deconfinement crossover temperature through their spectral functions obtained from the maximum entropy method. Anisotropic ensembles with $N_f=2+1$ Wilson clover fermions with tadpole-improvement are used while the bottom quark is treated with an improved non-relativistic action. We observe significant modifications of the P wave $χ_{b1}$ ground state directly above the crossover temperature, $T_c$, while the S wave $Υ$ ground state remains relatively unchanged up to temperatures of almost $2…
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.
The work is devoted to the description of baryon mass spectrum in the quasy-relativistic quark potential model. For cosidering 3 - quark system advantageous is the use of hyperspherical functions. For obtaining the mass - seguence of $Δ_{33}-$isobar the numerical computations were carryed out with the use of screened QCD - motivated potential, the use of which gives quite acceptable results even in the nonrelativistic approximation.
We present multiple results on the production of loosely-bound molecules in bottomonium annihilations and $e^+e^-$ collisions at $\sqrt{s} = 10.58$ GeV. We perform the first comprehensive test of several models for deuteron production against all the existing data in this energy region. We fit the free parameters of the models to reproduce the observed cross sections, and we predict the deuteron spectrum and production and the cross section for the $e^+e^- \to d\bar{d} + X$ process both at the $Υ(1,2,3S)$ resonances and at $\sqrt{s}=10.58$ GeV. The predicted spectra show differences but are al…
We study the universal static potential $V_{\rm st}(r)$ and the force, which are fully determined by two fundamental parameters: the string tension $σ=0.18\pm 0.02$ GeV$^2$ and the QCD constants $Λ_{\bar{\rm MS}}(n_f)$, taken from pQCD, while the infrared (IR) regulator $M_{\rm B}$ is taken from the background perturbation theory and expressed via the string tension. The vector couplings $α_{\rm V}(r)$ in the static potential and $α_{\rm F}(r)$ in the static force, as well as the characteristic scales, $r_1(n_f=3)$ and $r_0(n_f=3)$, are calculated and compared to lattice data. The result $r_0Λ…
We compute the electric dipole moment (EDM) of the bottom quark in minimal supersymmetric model (SUSY) with explicit CP violation. We estimate its upper bound to be 10^(-20) e-cm where the dominant contribution comes from the charginos for most of the SUSY parameter space. We also find that chargino contribution is directly correlated with the branching fraction of the B\to X_s γdecay. Furthermore, we analyze the formation of 1 P_1 resonance of the (\bar{b}b) system in e^+ e^- annihilation, and show that the CP-violating transition amplitude, induced solely by the b-quark EDM, is significantly…
The bottomonium spectrum is the perfect testing ground for the confining potential and unitarisation effects. The bottom quark is about three times heavier than the charm quark, so that $b\bar{b}$ systems probe primarily the short-range part of that potential. Also, the much smaller colour-hyperfine interaction in the $B$ mesons make the $B\bar{B}$ threshold lie significantly higher than the $D\bar{D}$ threshold in charmonium, on a relative scale of course. A further complicating circumstance is that none of the experimentally observed vector $b\bar{b}$ mesons has been positively identified as…
We generalize a forward light-by-light scattering sum rule to the case of heavy quarkonium radiative transitions. We apply such sum rule to the bottomonium states, and use available data on radiative transitions in its evaluation. For the transitions that are not known experimentally, we provide theoretical estimates within a potential model, and consider the spread between similar approaches in the literature as an estimate for the model error. For the $Υ(1S)$, $Υ(2S)$, and $Υ(3S)$ states we observe that, due to a cancellation between transitions involving $χ_{b0}, χ_{b1}$, and $χ_{b2}$ state…
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 "naive" 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 …
We show that in a quark model scheme the use of a screened potential, suggested by lattice QCD, instead of an infinitely rising one with the interquark distance, provides a more adequate description of the high-energy baryon spectrum. In particular an almost perfect parallelism between the predicted and observed number of states comes out throwing new light about the so-called missing resonance problem.
Considering the fact that some excited states of the heavy quarkonia (charmonium and bottomonium) still missing in experimental observations and potential applications of the relevant wave functions of the bound states, we re-analyze the spectrum and the relevant wave functions of the heavy quarkonia within the framework of Bethe-Salpeter (B.S.) equation with a proper QCD-inspired kernel. Such a kernel for the heavy quarkonia, relating to potential of non-relativistic quark model, is instantaneous, so we call the corresponding B.S. equation as BS-In equation throughout the paper. Particularly,…
The bottomonium spectrum is computed in dynamical 2+1 flavor lattice QCD, using NRQCD for the b quarks. The main calculations in this work are based on gauge field ensembles generated by the RBC and UKQCD collaborations with the Iwasaki action for the gluons and a domain-wall action for the sea quarks. Lattice spacing values of approximately 0.08 fm and 0.11 fm are used, and simultaneous chiral extrapolations to the physical pion mass are performed. As a test for gluon discretization errors, the calculations are repeated on two ensembles generated by the MILC collaboration with the Luscher-Wei…
Possible effects of the color screened confinement potential are investigated. Color screened linear potential with a large string tension $T=(0.26-0.32)GeV^2$ is suggested by a study of the $c\bar c$ and $b\bar b$ spectra. The $ψ(4160)$ and $ψ(4415)$ are respectively assigned as the $ψ(4S)$-dominated and the $ψ(5S)$ $c\bar c$ states. Satisfactory results for the masses and leptonic widths (with QCD radiative corrections) of $c\bar c$ and $b\bar b$ states are obtained.
In this work, we calculate the mass spectrum of the bottom mesons with a modified nonrelativistic quark model by involving the screening effect, and explore their strong decay properties within the $^3P_0$ model. Our results suggest that the $B_1(5721)$, $B^*_2(5747)$, $B_J(5840)$, and $B_J(5970)$ could be reasonably assigned as the $B_1^\prime(1P)$, $B(1^3P_2)$, $B(2^1S_0)$, and $B(1^3D_3)$ respectively. The more precise measurements of the excited bottom mesons are crucial to confirm these assignments.
Using the quark-antiquark interactions obtained in the framework of the bootstrap method we construct a potential model, investigate the possibility of describing of heavy quarkonia and calculate the bottomonium spectrum. The potential of the interaction was obtained as a nonrelativistic limit of the relativistic quark-antiquark amplitudes Q{\bar Q} -> Q\bar Q.
We explore the spectrum of excited and exotic bottomonia using lattice QCD. Highly excited states are identified with masses up to 11,000 MeV, many of which can be grouped into supermultiplets matching those of the quark model while exotic spin--parity--charge-conjugation quantum numbers $J^{PC}=0^{+-},\,1^{-+},\,2^{+-}$ that cannot be formed from $\bar{q}q$ alone are also identified. Single-meson operator constructions are used that have good $J^{PC}$ in the continuum, these are found to overlap well onto heavy quark states with $J\le4$. A continuum $J^{PC}$ is assigned to each level, based o…
It is suggested the modification of traditional potential model, in which nontrivial structure of inside-hadron vacuum condensate is simulated by geometric properties of inside-hadron space. Confinement of quarks is ensured by closed effective (Riemannian) space. Interquark potential represents itself Coulomb's low in the effective space (Poisson equation). In the framework of such approach the quarks dynamics completely is defined only by metric of the effective space, which in turn in conformally-Euclidean case (we consider) is defined by sole phenomenological function. Also it is supposed, …
Heavy Quarkonium Spectrum and Decay Constants from a Neural-Network-Based Holographic Model
University of South China（南华大学）；Key Laboratory of Advanced Nuclear Energy Design and Safety, Ministry of Education（教育部先进核能安全与设计重点实验室）；INFN — Istituto Nazionale di Fisica Nucleare — Sezione di Bari（意大利国家核物理研究所巴里分部）
This work is devoted to the discussion and characterization of the tensor $2^{-(-)}$ meson spectrum, by making use of the Coulomb gauge Hamiltonian approach to QCD, with the interactions being given by an improved confining potential and a transverse hyperfine interaction, whose kernel is a Yukawa-type potential. Our aim is to study the basic features of $2^{-(-)}$ mesons within an unified framework through the whole range of quark masses. We concentrate our investigation on predictions of expected but yet-unobserved ground states of unflavored light mesons and on charmonium and bottomonium st…
Using the same quenched limit as input, we compare the charmonium spectra predicted by the coupled-channel model and the screened potential model in the mass region below 4 GeV, in which the contributions from decay channels involving P-wave (as well as even higher excited) D mesons can be neglected. We find that the two models have similar global features in describing charmonium spectrum since they embody the same effect of the vacuum polarization of dynamical light quark pairs. This agreement is encouraging for using the screened potential to further describe the mass spectrum of higher cha…
The non-perturbative nature of QCD at hadronic scales implied the development of phenomenological approaches such as quark models or, more recently, computer-based calculations using Lattice QCD. However, the unique properties of heavy quarkonium systems allow an entire calculation in terms of non-relativistic perturbative QCD. In this work, the bottomonium spectrum, up to $n = 3$, and the ground state charmonium states, are analyzed in the framework of Non-Relativistic Quantum Chromodynamics at N$^3$LO. For bottomonium, finite charm quark mass effects in the QCD potential and the $\overline{M…
We study some possible experimental consequences of new physics on the spectrum and decays of bottomonium states below $B\bar{B}$ threshold. In addition to lepton universality breaking in Upsilon decays, large widths of pseudoscalar $η_b$ resonances and mixing with a non-standard CP-odd light Higgs boson might smooth and shift the signal peak from hindered radiative M1 transitions between $Υ$ and $η_b$ states in the photon energy spectrum, as searched by CLEO. We also stress the relevance of forthcoming results from CLEO on leptonic branching fractions of $Υ$ resonances to definitely check our…
We show the results of a quark model calculation of the bottomonium spectrum with self energy corrections due to the coupling to the meson-meson continuum. The bare masses used in the calculation are computed within the relativized quark model by Godfrey and Isgur. We also give results for the open-bottom strong decay amplitudes of higher bottomonia in a 3P0 model.
The $q\bar q$ spectrum is studied in a generalized constituent quark model constrained in the study of the $NN$ phenomenology and the baryon spectrum. An overall good fit to the available experimental data is obtained. A detailed analysis of all sectors from the light-pseudoscalar and vector mesons to bottomonium is performed paying special attention to the existence and nature of some non well-established states. These results should serve as a complementary tool in distinguishing conventional quark model mesons from glueballs, hybrids or multiquark states.
In this contribution, we briefly discuss the results for charmonium and bottomonium spectra with self-energy corrections in the unquenched quark model, due to the coupling to the meson-meson continuum. The UQM formalism can be extended to include also the effects of hybrid mesons, i.e. hybrid loops. Finally, we discuss the results of a calculation of hybrid mesons spectrum in Coulomb Gauge QCD.
The QCD string model is employed to evaluate the masses of orbitally and radially excited heavy-light mesons and lightest hybrids in the spectrum of charmonium and bottomonium. The number of parameters of the model is reduced to only seven which are the string tension, the two values of the strong coupling constant (one for heavy-light and $\bar{c}c$ mesons and one for $\bar{b}b$ mesons), and the four overall spectrum shift constants which depend on the quark contents of the particular meson or hybrid family. A few well-established states in the spectrum of heavy-light and heavy-heavy mesons a…
The $B$-factories and Large Hadron Collider experiments have demonstrated the ability to observe and measure the properties of bottomonium mesons. In order to discover missing states it is useful to know their properties to develop a successful search strategy. To this end we calculate the masses and decay properties of excited bottomonium states. We use the relativized quark model to calculate the masses and wavefunctions and the $^3P_0$ quark-pair creation model to calculate decay widths to open bottom. We also summarize results for radiative transitions, annihilation decays, hadronic transi…
