Finite-energy sum rules at finite chemical potential and zero temperature

Abstract In this article we explore the effect of chemical potential at zero temperature in the implementation of in-medium effects in the perturbative sector in finite energy sum rules. For this purpose, we explore the axial, axial-pseudoscalar and pseudoscalar current correlators involving charged pions. The inclusion of non-normal ordered condensates with chemical potential effects in the operator mixing is considered. As a result, the contribution of the operator mixing with chemical potential dependence cancels all the explicit chemical potential contribution of the perturbative sector, aligned with the so-called “silver blaze problem”. We find an abrupt transition when $$\mu =\sqrt{s_0}/2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mo>=</mml:mo> <mml:msqrt> <mml:msub> <mml:mi>s</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:msqrt> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> , with $$s_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>s</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> representing the hadronic continuum threshold. Exploring beyond this critical chemical potential we found similarities with low-energy effective meson models at high chemical potential.