Dissipative effects on quarkonium spectral functions

Quarkonium at finite temperature is described as an open quantum system whose dynamics are determined by a potential $V_R\left(\mathbf{x}\right)$ and drag coefficient $\eta$, using a path integral with a nonlocal term. Path-integral Monte Carlo calculations determine the Euclidean Green function for this system to an accuracy greater than one part in a thousand and the maximum entropy method is used to determine the spectral function; challenges facing any kind of deconvolution are discussed in detail with the aim of developing intuition for when deconvolution is possible. Significant changes to the quarkonium spectral function in the $1S$ channel are found, suggesting that any description of quarkonium at finite temperature, using a potential, must also carefully consider the effect of dissipation.

Figure 1

From [4], $G\left(\tau \right)$ with and without dissipative effects.

Figure 2

The spectral functions ${\rho }_1$ (with width $\sigma =0.01\mathrm{GeV}$) and ${\rho }_2$ (with width $\sigma =0.05\mathrm{GeV}$).

Figure 3

The relative difference $\Delta G/G=(G_2(\tau ,\beta )-G_1(\tau ,\beta ))/G_2(\tau ,\beta )$ between the Green functions obtained from ${\rho }_1$ and ${\rho }_2$.

Figure 4

$G_1\left(\tau \right), G_2\left(\tau \right)$, and $\left|\Delta G\right|/G$, plotted together.

Figure 5

The spectral functions deconvolved from the test data by using different values of $\alpha$. The corresponding values of ${\chi }^2$ are shown in the legend.

Figure 6

The spectral functions deconvolved from the results in Fig. 1. The corresponding values of ${\chi }^2$ are shown in the legend.

Figure 7

The spectral functions deconvolved from the results where $\eta =0$ in Fig. 1 with different values of $\alpha$. The corresponding values of ${\chi }^2$ are shown in the legend.