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

Understand

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.