Abstract
As an improvement of the QCD sum rule method to study modifications of light vector mesons in nuclear matter and/or at finite temperature, we calculate the Wilson coefficients of all independent gluonic non-scalar operators up to dimension 6 in the operator product expansion (OPE) of the vector channel for light quarks. To obtain the gluon part of the light quark OPE from the heavy quark one, we also compute the heavy quark expansion of the relevant quark condensates. Together with the results for the quark operators that are already available in the literature, this completes the OPE of the vector channel in a hot or dense medium for operators up to dimension 6.
Highlights
Vector mesons in hot and/or dense matter have been in the focus of theoretical and experimental interest already for many years, primarily because some of them are expected to be indicators of the quarkgluon plasma in heavy-ion collisions [1] while others were predicted to be probes of the partial restoration of chiral symmetry in nuclear matter [2]
We have for the first time computed the Wilson coefficients, at leading order in αs, of dimension 6, spin-2 and spin-4 gluonic operators in the operator product expansion (OPE) of the vector correlator for light quarks
For self-adjoint mesons, this completes the vector channel OPE for all possible scalar and non-scalar operators up to dimension 6 that can have non-zero expectation values in a hot and/or dense medium that is invariant under parity and time reversal
Summary
Vector mesons in hot and/or dense matter have been in the focus of theoretical and experimental interest already for many years, primarily because some of them (quarkonia) are expected to be indicators of the quarkgluon plasma in heavy-ion collisions [1] while others (light vector mesons, such as ρ, ω and φ) were predicted to be probes of the partial restoration of chiral symmetry in nuclear matter [2]. The contributions of gluonic non-scalar operators to the OPE of the vector channel for light quarks up to dimension 6 have never been obtained, even though some attempts were made in Ref. We will follow the same approach and first start from the OPE of non-scalar quark operators, which can (mostly) be found in the literature [35, 42], compute the gluonic contributions of these operators via the heavy-quark expansion and subtract these from the heavy quark results of Ref. We briefly explain in Appendix A the spin decomposition of gluonic operators in D dimensions that we have used in this study
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