Curvature of the pseudocritical line in the QCD phase diagram from mesonic lattice correlation functions

In the QCD phase diagram, the dependence of the pseudocritical temperature, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>T</a:mi> <a:mi>pc</a:mi> </a:msub> </a:math> , on the baryon chemical potential, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>μ</c:mi> <c:mi>B</c:mi> </c:msub> </c:math> , is of fundamental interest. The variation of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>T</e:mi> <e:mi>pc</e:mi> </e:msub> </e:math> with <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msub> <g:mi>μ</g:mi> <g:mi>B</g:mi> </g:msub> </g:math> is normally captured by <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>κ</i:mi> </i:math> , the coefficient of the leading (quadratic) term of the polynomial expansion of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msub> <k:mi>T</k:mi> <k:mi>pc</k:mi> </k:msub> </k:math> with <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msub> <m:mi>μ</m:mi> <m:mi>B</m:mi> </m:msub> </m:math> . In this work, we present the first calculation of <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>κ</o:mi> </o:math> using hadronic quantities. Simulating <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msub> <q:mi>N</q:mi> <q:mi>f</q:mi> </q:msub> <q:mo>=</q:mo> <q:mn>2</q:mn> <q:mo>+</q:mo> <q:mn>1</q:mn> </q:math> flavors of Wilson fermions on astsum ensembles, we calculate the <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"> <s:mi mathvariant="script">O</s:mi> <s:mo stretchy="false">(</s:mo> <s:msubsup> <s:mi>μ</s:mi> <s:mi>B</s:mi> <s:mn>2</s:mn> </s:msubsup> <s:mo stretchy="false">)</s:mo> </s:math> correction to mesonic correlation functions. By demanding degeneracy in the vector and axial-vector channels we obtain <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:msub> <x:mi>T</x:mi> <x:mi>pc</x:mi> </x:msub> <x:mo stretchy="false">(</x:mo> <x:msub> <x:mi>μ</x:mi> <x:mi>B</x:mi> </x:msub> <x:mo stretchy="false">)</x:mo> </x:math> and hence <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML" display="inline"> <bb:mi>κ</bb:mi> </bb:math> . While lacking a continuum extrapolation and being away from the physical point, our results are consistent with previous works using thermodynamic observables (renormalized chiral condensate, strange quark number susceptibility) from lattice QCD simulations with staggered fermions.