Abstract
Finite temperature charmonium spectral functions in the pseudoscalar and vector channels are studied in lattice QCD with 2+1 flavours of dynamical Wilson quarks, on fine isotropic lattices (with a lattice spacing of 0.057 fm), with a non-physical pion mass of $m_{\pi} \approx$ 545 MeV. The highest temperature studied is approximately $1.4 T_c$. Up to this temperature no significant variation of the spectral function is seen in the pseudoscalar channel. The vector channel shows some temperature dependence, which seems to be consistent with a temperature dependent low frequency peak related to heavy quark transport, plus a temperature independent term at \omega>0. These results are in accord with previous calculations using the quenched approximation.
Highlights
Finite temperature charmonium spectral functions in the pseudoscalar and vector channels are studied in lattice QCD with 2+1 flavours of dynamical Wilson quarks, on fine isotropic lattices, with a non-physical pion mass of mπ ≈ 545 MeV
The vector channel shows some temperature dependence, which seems to be consistent with a temperature dependent low frequency peak related to heavy quark transport, plus a temperature independent term at ω > 0
The Maximum Entropy Method (MEM) reconstruction of the spectral functions is hampered by the limited number of data points at higher temperatures, so the highest temperature we used for MEM reconstruction was approximately 1.3Tc
Summary
The spectral function (SF) of a correlator of self-adjoint operators is the imaginary part of the Fourier-transform of the real time retarded correlator [19]. Where q is the quark field and ΓH = γ5, γi for the pseudoscalar and vector channels respectively It can be shown, that the SF is related to the Euclidean correlator — calculable on the lattice — by an integral transform. Is the integral kernel, and the Euclidean correlator (at zero chemical potential) is: G(τ, p) = DH> (−iτ, p) = d3xeipx Tτ JH (−iτ, x)JH (0, 0). Knowledge of these SFs is of great importance. If the transport coefficient is non vanishing, we expect some finite value of ρ/ω for small ω This implies the presence of a transport peak.
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