The chiral quark condensate and pion decay constant in nuclear matter at next-to-leading order

TL;DR

This paper evaluates the in-medium chiral quark condensate and pion decay constant at next-to-leading order in nuclear matter, revealing the dominance of long-range pion effects and confirming the Gell-Mann-Oakes-Renner relation.

Contribution

It provides a detailed next-to-leading order calculation of the in-medium chiral condensate and pion decay constant, including full iteration of nucleon-nucleon interactions, highlighting the role of pion contributions.

Findings

Long-range pion contributions dominate the in-medium quark condensate.

Nucleon-nucleon interactions have a minor effect on the condensate in neutron matter.

The Gell-Mann-Oakes-Renner relation holds up to next-to-leading order in nuclear matter.

Abstract

Making use of the recently developed chiral power counting for the physics of nuclear matter [1,2], we evaluate the in-medium chiral quark condensate up to next-to-leading order for both symmetric nuclear matter and neutron matter. Our calculation includes the full in-medium iteration of the leading order local and one-pion exchange nucleon-nucleon interactions. Interestingly, we find a cancellation between the contributions stemming from the quark mass dependence of the nucleon mass appearing in the in-medium nucleon-nucleon interactions. Only the contributions originating from the explicit quark mass dependence of the pion mass survive. This cancellation is the reason of previous observations concerning the dominant role of the long-range pion contributions and the suppression of short-range nucleon-nucleon interactions. We find that the linear density contribution to the in-medium chiral quark condensate is only slightly modified for pure neutron matter by the nucleon-nucleon interactions. For symmetric nuclear matter the in-medium corrections are larger, although smaller compared to other approaches due to the full iteration of the lowest order nucleon-nucleon tree-level amplitudes. Our calculation satisfies the Hellmann-Feynman theorem to the order worked out. Also we address the problem of calculating the leading in-medium corrections to the pion decay constant. We find that there are no extra in-medium corrections that violate the Gell-Mann-Oakes-Renner relation up to next-to-leading order.