In this paper, we study two-color, two-flavor QCD using chiral perturbation theory at next-to-leading order when the diquark chemical potential (\(\mu _{\mathrm{B}}\)) is equal to the isospin chemical potential (\(\mu _{\mathrm{I}}\)). For chemical potentials larger than the physical pion mass, the system is in a multicomponent superfluid phase with both pions and diquarks. We construct the one-loop effective potential using \(\chi \)PT in the presence of an external multicomponent superfluid source and use the effective potential to calculate the chiral condensate, the multicomponent superfluid condensate and the (multicomponent) superfluid density. We also find the critical chemical potential and the order of the phase transition from the normal phase to the multicomponent condensed phase at next-to-leading order. The phase transition remains second order (as at tree level), and the critical chemical potential is equal to the one-loop renormalized diquark (or pion) mass.

在本文中，当二夸克化学势（\（\ mu _ {\ mathrm {B}} \））等于n时，我们使用手性扰动理论以次先顺序研究了两种颜色，两种风味的QCD。同位旋化学势（\（\亩_ {\ mathrm {I}} \） ）。对于大于物理离子质量的化学势，该系统处于由双离子和双夸克组成的多组分超流体相。我们使用\（\ chi \）构造一环有效电位PT在存在外部多组分超流体源的情况下，并使用有效电势来计算手性冷凝物，多组分超流体冷凝物和（多组分）超流体密度。我们还发现了临界化学势，以及从正相到多组分缩合相的相变顺序接近于领先的顺序。相变保持二阶（在树级），并且临界化学势等于单环重归一化的夸克（或介子）质量。