Bottomonium Spectrum Research Articles

Bottomonium Spectrum with Screened Potential

As a sister work of [Phys. Rev. D 79 (2009) 094004], 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 χbJ (J = 0, 1, 2) states are in good agreement with experimental data, and the E1 transition rates of γ(2S) → γχbJ (1P) and γ(3S) → γχbJ (2P) (J = 0, 1, 2) all agree with data within experimental errors. In particular, the mass of γ(6S) is lowered down to match that of the γ(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.

Bottomonium spectrum from lattice QCD with2+1flavors of domain wall fermions

Recently, realistic lattice QCD calculations with 2+1 flavors of domain wall fermions and the Iwasaki gauge action have been performed by the RBC and UKQCD Collaborations. Here, results for the bottomonium spectrum computed on their gauge configurations of size 24{sup 3}x64 with a lattice spacing of approximately 0.11 fm and four different values for the light quark mass are presented. Improved lattice nonrelativistic QCD is used to treat the b quarks inside the bottomonium. The results for the radial and orbital energy splittings are found to be in good agreement with experimental measurements, indicating that systematic errors are small. The calculation of the {upsilon}(2S)-{upsilon}(1S) energy splitting provides an independent determination of the lattice spacing. For the most physical ensemble it is found to be a{sup -1}=1.740(25)(19) GeV, where the first error is statistical/fitting and the second error is an estimate of the systematic errors due to the lattice nonrelativistic QCD action.

Spectroscopy, leptonic decays and the nature of heavy quarkonia

We examine the electronic width ratios of ϒ resonances below the BB¯ threshold by means of an effective (Cornell-type) QCD potential incorporating 1/mb corrections obtained from a prior fit to the bottomonium spectrum. From our analysis we conclude that the ϒ(2S) and ϒ(3S) states should belong to the strong-coupling (nonperturbative) regime while the ϒ(1S) state should belong to the weak-coupling (perturbative) regime, in agreement with a previous study based on radiative decays.

Light [formula omitted] exotics: Molecular resonances

Highlights in the search for nonconventional (non- q q ¯ ) meson states are the π 1 ( 1400 ) and π 1 ( 1600 ) exotic candidates. Should they exist, mounting theoretical arguments suggest that they are tetraquark molecular resonances excitable by meson rescattering. We report a new tetraquark calculation within a model field theory approximation to Quantum Chromodynamics in the Coulomb gauge supporting this conjecture. We also strengthen this claim by consistently contrasting results with exotic state predictions for hybrid ( q q ¯ g ) mesons within the same theoretical framework. Our findings confirm that molecular-like configurations involving two color singlets (a resonance, not a bound state) are clearly favored over hybrid or color-exotic tetraquark meson ( q q ¯ q q ¯ atoms) formation. Finally, to assist needed further experimental searches we document a useful off-plane correlator for establishing the structure of these exotic systems along with similar, but anticipated much narrower, states that should exist in the charmonium and bottomonium spectra.

A SYSTEMATIC STUDY ON NONRELATIVISTIC QUARKONIUM INTERACTION

A recently proposed strictly phenomenological static quark–antiquark potential belonging to the generality V(r) = -Ar-α + κrβ + V0 is tested with heavy quarkonia in the context of the shifted large N-expansion method. This nonrelativistic potential model fits the spin-averaged mass spectra of the [Formula: see text], [Formula: see text] and [Formula: see text] quarkonia within a few MeV and also the five experimentally known leptonic decay widths of the [Formula: see text] and [Formula: see text] vector states. Further, we compute the hyperfine splittings of the bottomonium spectrum as well as the fine and hyperfine splittings of the charmonium spectrum. We give predictions for not yet observed Bc splittings. The model is then used to predict the masses of the remaining quarkonia and the leptonic decay widths of the two pseudoscalar [Formula: see text] states. Our results are compared with other models to gauge the reliability of the predictions and point out differences.

The Static Force in Background Perturbation Theory

The static force $F_B(r)$ and the strong coupling $\alpha_F(r)$, which defines the gluon-exchange part of $F_B(r)$, are studied in QCD background perturbation theory (BPT). In the region $r\la 0.6 $ fm $\alpha_F(r)$ turns out to be essentially smaller than the coupling $\alpha_B(r)$ in the static potential. For the dimensionless function $\Phi_B(r) = r^2 F_B(r)$ the characteristic values $\Phi_B(r_1) =1.0$ and $\Phi_B(r_0)=1.65$ are shown to be reached at the following $Q\bar Q$ separations: $r_1\sqrt{\sigma} =0.77, r_0\sqrt{\sigma} =1.09$ in quenched approximation and $r_1\sqrt{\sigma}=0.72, r_0\sqrt{\sigma}=1.04$ for $n_f =3$. The numbers obtained appear to be by only 8% smaller than those calculated in lattice QCD while the values of the couplings $\alpha_F(r_1)$ and $\alpha_F(r_0)$ in BPT are by $\sim 30% (n_f =3)$ and $50% (n_f=0)$ larger than corresponding lattice couplings. With the use of the BPT potential good description of the bottomonium spectrum is obtained.

Fine and hyperfine splittings of charmonium and bottomonium: an improved perturbative QCD approach

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(αS5m) 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.

Geometrization of vacuum condensate effects in quarkonium potential model

A potential model is suggested in which the dependences of reduced quark mass and interquark potential on coordinates are considered within the framework of the hypothesis of the geometric description of nonperturbative vacuum effects. The existence of the vacuum condensate is modelled by geometric properties of inside-hadron space which is identified with an effective Riemann space with closed topology. For the Schrödinger equation the exact analytical solutions are obtained and the spin-dependent relativistic corrections are calculated. The model gives a good fit to charmonium and bottomonium spectra. The phenomenological conclusions concerning nonperturbative effects are given. The model also suggests a testable prediction for the dependence of reduced mass on coordinates.

The Ψ spectrum from lattice QCD with 2 + 1 flavors of dynamical quarks

We describe the bottomonium spectrum obtained on the MILL configurations which incorporate 2+1 flavors of dynamical quarks. We compare to quenched and 2 flavor results also on MILL configurations. We show that the lattice spacing determination using different quantities shows clear signs of convergence with 2+1 flavors and give results for the leptonic width and hyperfine splitting, in the form of the ratio of the 1st excited state of the Ψ to that of the ground state.

Improved perturbative QCD approach to the bottomonium spectrum

Recently it has been shown that the gross structure of the bottomonium spectrum is reproduced reasonably well within the nonrelativistic bound state 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 $\mathcal{O}({\ensuremath{\alpha}}_{S}^{5}{m}_{b})$ and $\mathcal{O}({\ensuremath{\alpha}}_{S}^{4}{m}_{b}),$ respectively, in the computations of the fine splittings and the $S--P$ splittings. We find that the agreement with the experimental data for the fine splittings improves drastically due to an enhancement of the wave functions close to the origin as compared to the Coulomb wave functions. The agreement of the $S--P$ splittings with the experimental data also becomes better. We find that natural scales of the fine splittings and the $S--P$ splittings are larger than those of the bound states themselves. On the other hand, the predictions of the level spacings between consecutive principal quantum numbers depend rather strongly on the scale $\ensuremath{\mu}$ of the operator $\ensuremath{\propto}{C}_{A}{/(m}_{b}{r}^{2}).$ The agreement of the whole spectrum with the experimental data is much better than the previous predictions when $\ensuremath{\mu}\ensuremath{\simeq}3--4\mathrm{GeV}$ for ${\ensuremath{\alpha}}_{S}{(M}_{Z})=0.1181.$ There seems to be a phenomenological preference for some suppression mechanism for the above operator.

Relativistic bottomonium spectrum from anisotropic lattices

We report on a first relativistic calculation of the quenched bottomonium spectrum from anisotropic lattices. Using a very fine discretisation in the temporal direction we were able to go beyond the non-relativistic approximation and perform a continuum extrapolation of our results from five different lattice spacings (0.04-0.17 fm) and two anisotropies (4 and 5). We investigate several systematic errors within the quenched approximation and compare our results with those from non-relativistic simulations.

Relativistic bottomonium spectrum from anisotropic lattices

We report on our results from a fully relativistic simulation of the quenched bottomonium spectrum. Using an anisotropic formulation of Lattice QCD, we were able to retain a very fine resolution into the temporal direction for a range of different lattice spacings. At fixed renormalized anisotropy we study the scaling properties of the spectrum and compare our results with non-relativistic calculations.

Determining hybrid content of heavy quarkonia using lattice nonrelativistic QCD

Using lowest-order lattice NRQCD to create heavy meson propagators and applying the spin-dependent interaction, c B (−g/2m q σ · B , at varying intermediate time slices, we compute the off-diagonal matrix element of the Hamiltonian for the quarkonium-hybrid two-state system. Diagonalizing this two-state Hamiltonian, the admixture of hybrid (| QQ̄g〉) in the ground state is found. We present results from a set of quenched lattices with an interpolation in quark mass to match the bottomonium spectrum.

Measurement of the hybrid content of heavy quarkonia using lattice nonrelativistic QCD

Using lowest-order lattice nonrelativistic QCD to create heavy meson propagators and applying the spin-dependent interaction, ${c}_{B}(\ensuremath{-}{g/2m}_{q})\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}\ensuremath{\cdot}\stackrel{\ensuremath{\rightarrow}}{B},$ at varying intermediate time slices, we compute the off-diagonal matrix element of the Hamiltonian for the quarkonium-hybrid two-state system. Thus far, we have results for one set of quenched lattices with an interpolation in quark mass to match the bottomonium spectrum. After diagonalization of the two-state Hamiltonian, we find the ground state of the $\ensuremath{\Upsilon}$ to show a ${0.0035(1)c}_{B}^{2}$ (with ${c}_{B}^{2}\ensuremath{\sim}1.5--3.1)$ probability admixture of hybrid, $|b\overline{b}g〉.$

Quarkonium spectroscopy and perturbative QCD: a new perspective

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 unquenched ϒ spectrum

We describe the bottomonium spectrum obtained on the UKQCD dynamical ensembles and its comparison to quenched results. We include a determination of α s and m b from the dynamical results.

αSfromΥspectroscopy with dynamical Wilson fermions

We estimate the QCD coupling constant from a lattice calculation of the bottomonium spectrum. The second order perturbative expansion of the plaquette expectation value is employed to determine ${\ensuremath{\alpha}}_{S}$ at a scale set by the $2S\ensuremath{-}1S$ and $1P\ensuremath{-}1S$ level splittings. The latter are computed in NRQCD in a dynamical gauge field background with two degenerate flavors of Wilson quarks at intermediate masses and extrapolated to the chiral limit. Combining the ${N}_{f}=2$ result with the quenched result at equal lattice spacing we extrapolate to the physical number of light flavors to find a value of ${\ensuremath{\alpha}}_{\overline{\mathrm{MS}}}^{(5)}{(m}_{Z})=0.1118(17).$ The error quoted covers both statistical and systematic uncertainties in the scale determination. An additional $5%$ uncertainty comes from the choice of the underlying sea quark formulation and from truncation errors in perturbative expansions.

Properties of heavy quarkonia and related states

Mass levels and widths of very heavy quarkonia and similar onium resonances of squarks, color octet and sextet constituents are studied in the mass range of 50 to 1000 GeV. The heavy quark potential with QCD two-loop improved short-distance behavior that gives a good description of the charmonium and bottomonium spectra is used, and the results are given for several values of the QCD scale parameter Λ MS (4) in the range between 0.1 and 0.4 GeV. We present parametrizations for the first ten S-wave quarkonium resonances, which are relevant if the top quark is relatively light ( m t≲125 GeV) or if a heavy fourth-generation quark with suppressed weak decay rates exists. We also discuss the onset of coulombic behavior and the possible effects of Higgs boson exchange on superheavy quarkonia.

Predicting charmonium and bottomonium spectra with a quark harmonic oscillator.

We present a simple application of the three-dimensional harmonic oscillator which should provide a very nice particle physics example to be presented in introductory undergraduate quantum mechanics course. The idea is to use the nonrelativistic quark model to calculate the spin-averaged mass levels of the charmonium and bottomonium spectra.