Sound velocity peak and conformality in isospin QCD

Abstract

We study zero temperature equations of state (EOS) in isospin QCD within a quark-meson model which is renormalizable and hence eliminates high density artifacts in models with the ultraviolet cutoff (e.g., Nambu-Jona-Lasinio type models models). The model exhibits a crossover transition of pion condensations from the Bose-Einstein-Condensation regime at low density to the Bardeen-Cooper-Schrieffer regime at high density. The EOS stiffens quickly and approaches the quark matter regime at density significantly less than the density for pions to spatially overlap. The squared sound velocity <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msubsup><a:mi>c</a:mi><a:mi>s</a:mi><a:mn>2</a:mn></a:msubsup></a:math> develops a peak in the crossover region, and then gradually relaxes to the conformal value <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mn>1</c:mn><c:mo>/</c:mo><c:mn>3</c:mn></c:math> from above, in contrast to the perturbative QCD results which predicts the approach from below. In the context of QCD computations, this opposite trend is in part due to the lack of gluon exchanges in our model, and also due to the nonperturbative power corrections arising from the condensates. We argue that with large power corrections the trace anomaly can be negative. Our EOS reproduces the qualitative trend of the lattice results from the BEC to the BCS regime, implying that the quark-meson model captures relevant effective degrees of freedom. The BCS gap in our model is <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi mathvariant="normal">Δ</e:mi><e:mo>≃</e:mo><e:mn>300</e:mn><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mi>MeV</e:mi></e:math> in the quark matter domain, and naive application of the BCS relation for the critical temperature <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msub><h:mi>T</h:mi><h:mi>c</h:mi></h:msub><h:mo>≃</h:mo><h:mn>0.57</h:mn><h:mi mathvariant="normal">Δ</h:mi></h:math> yields the estimate <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>T</k:mi><k:mi>c</k:mi></k:msub><k:mo>≃</k:mo><k:mn>170</k:mn><k:mtext> </k:mtext><k:mtext> </k:mtext><k:mi>MeV</k:mi></k:math>, in good agreement with the lattice data. Published by the American Physical Society 2024

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