Abstract
The pseudoscalar correlator is an ideal lattice probe for thermal modifications to quarkonium spectra, given that it is not compromised by a contribution from a large transport peak. We construct a perturbative spectral function incorporating resummed thermal effects around the threshold and vacuum asymptotics above the threshold, and compare the corresponding imaginary-time correlators with continuum-extrapolated lattice data for quenched SU(3) at several temperatures. Modest differences are observed, which may originate from non-perturbative mass shifts or renormalization factors, however no resonance peaks are needed for describing the quenched lattice data for charmonium at and above T ∼ 1.1Tc ∼ 350 MeV. For comparison, in the bottomonium case a good description of the lattice data is obtained with a spectral function containing a single thermally broadened resonance peak.
Highlights
In contrast to the vector channel, no transport peak is expected to be present in the pseudoscalar channel [14, 15]
The pseudoscalar correlator is an ideal lattice probe for thermal modifications to quarkonium spectra, given that it is not compromised by a contribution from a large transport peak
The inertness of the pseudoscalar correlator led ref. [16] to conclude that there is no sign of melting of the corresponding charmonium resonances
Summary
For ω ≫ 2M ≫ πT , where M denotes a pole mass, all thermal effects are small (exponentially suppressed at leading order, power-suppressed in general [22]), because thermal motion represents a minor correction to the kinematics of the decay products In this regime, the spectral function can be extracted from vacuum computations. Thermal corrections represent the dominant physics: the real-time static potential develops an imaginary part [25,26,27] which leads to the dissociation of quarkonium resonances if T ≫ αsM [28,29,30] This rich physics implies that a number of different techniques are needed for a reasonably precise estimate of the pseudoscalar spectral function.
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