Algebraic vacuum limits of QCD condensates from in-medium projections of Lorentz tensors

TL;DR

This paper develops a method to relate QCD condensates in medium and vacuum by using Lorentz tensor decompositions, providing new constraints and consistency checks for theoretical models involving in-medium QCD effects.

Contribution

It introduces a general framework for in-medium Lorentz decomposition of QCD operators, linking vacuum and in-medium condensates and enabling analysis of higher-rank operators.

Findings

Derived constraints among QCD condensates in medium and vacuum.

Provided consistency checks for vacuum saturation hypothesis.

Illustrated the method with four-quark condensates of mass dimension six.

Abstract

Utilizing the in-medium Lorentz decomposition of operators generating QCD condensates we derive general constraints among the latter ones by the requirement of a smooth transition from medium to vacuum. In this way we relate the vacuum limits of heretofore unrelated condensates and provide consistency checks for the vacuum saturation hypothesis and the heavy quark mass expansion. The results are general and depend only on the rank and symmetry of the Lorentz tensors to be decomposed. The derived prescription enables to uniquely and directly identify operator product expansion contributions which are algebraically specific for in-medium situations and in particular useful for operators with a higher rank, i.e. larger than three. Four-quark condensates in mass dimension six are exemplified.