# An application of the variational analysis to calculate the meson spectral functions - High Energy Physics - Lattice

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Abstract: We present a new method to calculate meson spectral functions SPFs on thelattice based on a variational method. Because, on a finite volume lattice, themeson SPFs have discrete spectra only, a suitable way to extract such discretesignals is needed. Using a variational method, we can calculate severaldiscrete quantities such as the position and the area of spectral peaks forlow-lying states. Moreover data accuracy can be improved by increasing thenumber of basis functions. In this report, we first confirm our method in thefree quark case and show that our method works well. Then, we apply the methodto a quenched lattice QCD simulation and calculate the charmonium SPFs for Sand P-waves at zero temperature. Our results for the ground state are wellconsistent with the position and the area of the lowest peaks of charmoniumSPFs calculated by the conventional maximum entropy method. For first excitedstates, the signals may be reliablly extracted with our method because thecharmonium mass converges to a value close to the experimental one when thenumber of basis functions is increased. We also investigate the SPFs for S-wavecharmonia at below and above $T c$. Our results suggest that $J-\psi$ and$\eta c$ may survive up to 1.4$T c$.

Author: ** H. Ohno, S. Aoki, S. Ejiri, K. Kanaya, Y. Maezawa, H. Saito, T. Umeda WHOT-QCD Collaboration**

Source: https://arxiv.org/