Speed of sound peak in isospin QCD: A natural prediction of the medium separation scheme

We present predictions for the zero-temperature equation of state at finite isospin density using the Nambu-Jona-Lasinio (NJL) model within the medium separation scheme (MSS)—a scheme that explicitly disentangles medium effects from the ultraviolet divergent vacuum terms. Recent lattice QCD results reveal a nonmonotonic speed of sound ( <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> ) as a function of isospin chemical potential ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>μ</c:mi> <c:mi>I</c:mi> </c:msub> </c:math> ), exhibiting explicit violation of the conformal bound <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msubsup> <e:mi>c</e:mi> <e:mi>s</e:mi> <e:mn>2</e:mn> </e:msubsup> <e:mo>=</e:mo> <e:mn>1</e:mn> <e:mo>/</e:mo> <e:mn>3</e:mn> </e:math> . These findings have attracted significant theoretical interest, as established models—including the NJL model—failed to anticipate this behavior prior to lattice simulations. Conventional NJL implementations yield unphysical artifacts, often attributed to regularization scale sensitivity stemming from nonrenormalizability. However, in this work, we demonstrate that the standard NJL framework combined with MSS quantitatively reproduces state-of-the-art lattice data for isospin QCD.