Next-to-leading order perturbative QCD corrections to baryon correlators in matter

We compute the next-to-leading order (NLO) perturbative QCD corrections to the correlators of nucleon interpolating currents in relativistic nuclear matter. The main new result is the calculation of the $\mathcal{O}({\alpha }_s)$ perturbative corrections to the coefficient functions of the vector quark condensate in matter. This condensate appears in matter due to the violation of Lorentz invariance. The NLO perturbative QCD corrections turn out to be large which implies that the NLO corrections must be included in a sum rule analysis of the properties of both bound nucleons and relativistic nuclear matter.

Figure 1

LO (a) and NLO propagator-type (b) as well as fish-type (c) corrections of the baryonic two-point correlator.

Figure 2

Propagator (a) and dipropagator (b) correction with open Dirac indices.

Figure 3

Ordinary (a) and crossover part (b) of the Wick contraction for the operators $O_{1,2}$ in a symbolic representation. The arrows indicate the direction for the quark current within the correlator, the dashed lines are inverted by using transposition and charge conjugation.

Figure 4

New modules for the correlator corrections including condensates: condensate correction (a) and condensate-propagator correction consisting of two diagrams (b).

Figure 5

LO contribution (a) and NLO contributions (b–e) to the correlation function including a (scalar or vector) condensate.