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Register a new userCharmonia in moving frames
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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 $J^P$ in the same lattice irreducible representation. The identification of $J^P$ for these states is particularly important, since quarkonium spectra contain a number of states with different $J^P$ 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.
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We extend our study of the $Kpi$ system to moving frames and present an exploratory extraction of the masses and widths for the $K^*$ resonances by simulating $Kpi$ scattering in p-wave with $I=1/2$ on the lattice. Using $Kpi$ systems with non-vanishing total momenta allows the extraction of phase shifts at several values of $Kpi$ relative momenta. A Breit-Wigner fit of the phase renders a $K^*(892)$ resonance mass and $K^*to K pi $ coupling compatible with the experimental numbers. We also determine the $K^*(1410)$ mass assuming the experimental $K^*(1410)$ width. We contrast the resonant $I=1/2$ channel with the repulsive non-resonant $I=3/2$ channel, where the phase is found to be negative and small, in agreement with experiment.
Analyzing correlation functions of charmonia at finite temperature ($T$) on $32^3times(32-96)$ anisotropic lattices by the maximum entropy method (MEM), we find that $J/psi$ and $eta_c$ survive as distinct resonances in the plasma even up to $T simeq 1.6 T_c$ and that they eventually dissociate between $1.6 T_c$ and $1.9 T_c$ ($T_c$ is the critical temperature of deconfinement). This suggests that the deconfined plasma is non-perturbative enough to hold heavy-quark bound states. The importance of having sufficient number of temporal data points in the MEM analysis is also emphasized.
We find a strong evidence for the survival of $J/Psi$ and $eta_c$ as spatially-localized $cbar c$ (quasi-)bound states above the QCD critical temperature $T_c$, by investigating the boundary-condition dependence of their energies and spectral functions. In a finite-volume box, there arises a boundary-condition dependence for spatially spread states, while no such dependence appears for spatially compact states. In lattice QCD, we find almost {it no} spatial boundary-condition dependence for the energy of the $cbar c$ system in $J/Psi$ and $eta_c$ channels for $Tsimeq(1.11-2.07)T_c$. We also investigate the spectral function of charmonia above $T_c$ in lattice QCD using the maximum entropy method (MEM) in terms of the boundary-condition dependence. There is {it no} spatial boundary-condition dependence for the low-lying peaks corresponding to $J/Psi$ and $eta_c$ around 3GeV at $1.62T_c$. These facts indicate the survival of $J/Psi$ and $eta_c$ as compact $cbar c$ (quasi-)bound states for $T_c < T < 2T_c$.
The spectrum of charmonium resonances contains a number of unanticipated states along with several conventional quark-model excitations. The hadrons of different quantum numbers $J^P$ appear in a fairly narrow energy band, where $J^P$ refers to the spin-parity of a hadron at rest. This poses a challenge for Lattice QCD studies of (coupled-channel) meson-meson scattering aimed at the determination of scattering amplitudes and resonance pole positions. A wealth of information for this purpose can be obtained from the lattice spectra in frames with nonzero total momentum. These are particularly dense since hadrons with different $J^P$ contribute to any given lattice irreducible representation. This is because $J^P$ is not a good quantum number in flight, and also because the continuum symmetry is reduced on the lattice. In this paper we address the assignment of the underlying continuum $J^P$ quantum numbers to charmonia in flight using a $N_f = 2 + 1$ CLS ensemble. As a first step, we apply the single-hadron approach, where only interpolating fields of quark-antiquark type are used. The approach follows techniques previously applied to the light meson spectrum by the Hadron Spectrum Collaboration. The resulting spectra of charmonia with assigned $J^P$ will provide valuable information for the parameterization of (resonant) amplitudes in future determinations of resonance properties with lattice QCD.
A purely algebraic algorithm for computation of invariants (generalized Casimir operators) of Lie algebras by means of moving frames is discussed. Results on the application of the method to computation of invariants of low-dimensional Lie algebras and series of solvable Lie algebras restricted only by a required structure of the nilradical are reviewed.
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