Searching for the QCD critical end point using multipoint Padé approximations

Using the multipoint Padé approach, we locate Lee-Yang edge singularities of the quantum chromodynamics (QCD) pressure in the complex baryon chemical potential plane. These singularities are extracted from singularities in the net baryon-number density calculated in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>N</a:mi> <a:mi>f</a:mi> </a:msub> <a:mo>=</a:mo> <a:mn>2</a:mn> <a:mo>+</a:mo> <a:mn>1</a:mn> </a:math> lattice QCD at physical quark mass and purely imaginary chemical potential. Taking an appropriate scaling ansatz in the vicinity of the conjectured QCD critical end point, we extrapolate the singularities on <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>N</c:mi> <c:mi>τ</c:mi> </c:msub> <c:mo>=</c:mo> <c:mn>6</c:mn> </c:math> lattices to pure real baryon chemical potential to estimate the position of the critical end point (CEP). We find <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msup> <e:mi>T</e:mi> <e:mi>CEP</e:mi> </e:msup> <e:mo>=</e:mo> <e:mn>10</e:mn> <e:msubsup> <e:mn>2</e:mn> <e:mrow> <e:mo>−</e:mo> <e:mn>23</e:mn> </e:mrow> <e:mrow> <e:mo>+</e:mo> <e:mn>11</e:mn> </e:mrow> </e:msubsup> <e:mtext> </e:mtext> <e:mtext> </e:mtext> <e:mi>MeV</e:mi> </e:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:msubsup> <g:mi>μ</g:mi> <g:mi>B</g:mi> <g:mi>CEP</g:mi> </g:msubsup> <g:mo>=</g:mo> <g:mn>42</g:mn> <g:msubsup> <g:mn>8</g:mn> <g:mrow> <g:mo>−</g:mo> <g:mn>74</g:mn> </g:mrow> <g:mrow> <g:mo>+</g:mo> <g:mn>162</g:mn> </g:mrow> </g:msubsup> <g:mtext> </g:mtext> <g:mtext> </g:mtext> <g:mi>MeV</g:mi> </g:math> , which compares well with recent estimates in the literature. For the slope of the transition line at the critical point we find <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mo>−</i:mo> <i:mn>0.16</i:mn> <i:mo stretchy="false">(</i:mo> <i:mn>20</i:mn> <i:mo stretchy="false">)</i:mo> </i:math> .