Locating the QCD critical point through contours of constant entropy density

We propose a new method to investigate the existence and location of the conjectured high-temperature critical point of strongly interacting matter via contours of constant entropy density. By approximating these lines as a power series in the baryon chemical potential <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>μ</a:mi> <a:mi>B</a:mi> </a:msub> </a:math> , one can extrapolate them from first-principle results at zero net-baryon density, and use them to locate the quantum chromodynamics (QCD) critical point, including the associated first-order and spinodal lines. As a proof of principle, we employ currently available continuum-extrapolated lattice data from the Wuppertal-Budapest collaboration to find a critical point at a temperature and a baryon chemical potential of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:msub> <b:mi>T</b:mi> <b:mi>c</b:mi> </b:msub> <b:mo>=</b:mo> <b:mn>114.3</b:mn> <b:mo>±</b:mo> <b:mn>6.9</b:mn> </b:mrow> </b:math> MeV and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:msub> <c:mi>μ</c:mi> <c:mrow> <c:mi>B</c:mi> <c:mo>,</c:mo> <c:mi>c</c:mi> </c:mrow> </c:msub> <c:mo>=</c:mo> <c:mn>602.1</c:mn> <c:mo>±</c:mo> <c:mn>62.1</c:mn> </c:mrow> </c:math> MeV, respectively, at expansion order <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi mathvariant="script">O</d:mi> <d:mo>(</d:mo> <d:msubsup> <d:mi>μ</d:mi> <d:mi>B</d:mi> <d:mn>2</d:mn> </d:msubsup> <d:mo>)</d:mo> </d:mrow> </d:math> . We advocate for a more precise determination of the required expansion coefficients via lattice QCD simulations as a means of pinpointing the location of the critical endpoint in the phase diagram of strongly interacting matter.