Finite density QCD phase structure from strangeness fluctuations

Charting the phase diagram of quantum chromodynamics (QCD) at large density is a challenging task due to the complex action problem in lattice simulations. Through simulations at imaginary baryon chemical potential <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msub> <a:mi>μ</a:mi> <a:mi>B</a:mi> </a:msub> </a:math> we observe that, if the strangeness neutrality condition is imposed, both the strangeness chemical potential <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>μ</c:mi> <c:mi>S</c:mi> </c:msub> <c:mo>/</c:mo> <c:msub> <c:mi>μ</c:mi> <c:mi>B</c:mi> </c:msub> </c:math> and the strangeness susceptibility <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msubsup> <e:mi>χ</e:mi> <e:mn>2</e:mn> <e:mi>S</e:mi> </e:msubsup> </e:math> take on constant values at the chiral transition for varying <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> . We present new lattice data to extrapolate contours of constant <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msub> <i:mi>μ</i:mi> <i:mi>S</i:mi> </i:msub> <i:mo>/</i:mo> <i:msub> <i:mi>μ</i:mi> <i:mi>B</i:mi> </i:msub> </i:math> or <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:msubsup> <k:mi>χ</k:mi> <k:mn>2</k:mn> <k:mi>S</k:mi> </k:msubsup> </k:math> to finite baryon chemical potential. We argue that they are good proxies for the QCD crossover because, as we show, they are only mildly influenced by criticality and by finite volume effects. We obtain continuum limits for these proxies up to <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:mo>=</m:mo> <m:mn>400</m:mn> <m:mtext> </m:mtext> <m:mtext> </m:mtext> <m:mi>MeV</m:mi> </m:math> , through a next-to-next-to-leading order ( <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msup> <o:mi mathvariant="normal">N</o:mi> <o:mn>2</o:mn> </o:msup> <o:mi>LO</o:mi> </o:math> ) Taylor expansion based on large-statistics data on <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:msup> <r:mn>16</r:mn> <r:mn>3</r:mn> </r:msup> <r:mo>×</r:mo> <r:mn>8</r:mn> </r:math> , <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:msup> <t:mn>20</t:mn> <t:mn>3</t:mn> </t:msup> <t:mo>×</t:mo> <t:mn>10</t:mn> </t:math> and <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"> <v:msup> <v:mn>24</v:mn> <v:mn>3</v:mn> </v:msup> <v:mo>×</v:mo> <v:mn>12</v:mn> </v:math> lattices with our 4HEX improved staggered action. We show that these are in excellent agreement with existing results for the chiral transition and, strikingly, also with analogous contours obtained with the hadron resonance gas (HRG) model. On the <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:msup> <x:mn>16</x:mn> <x:mn>3</x:mn> </x:msup> <x:mo>×</x:mo> <x:mn>8</x:mn> </x:math> lattice, we carry out the expansion up to next-to-next-to-next-to-next-to-leading order ( <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"> <z:msup> <z:mi mathvariant="normal">N</z:mi> <z:mn>4</z:mn> </z:msup> <z:mi>LO</z:mi> </z:math> ), and extend the extrapolation beyond <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:msub> <cb:mi>μ</cb:mi> <cb:mi>B</cb:mi> </cb:msub> <cb:mo>=</cb:mo> <cb:mn>500</cb:mn> <cb:mtext> </cb:mtext> <cb:mtext> </cb:mtext> <cb:mi>MeV</cb:mi> </cb:math> , again finding perfect agreement with the HRG model. This suggests that the crossover line constructed from this proxy starts deviating from the chemical freeze-out line near <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"> <eb:msub> <eb:mi>μ</eb:mi> <eb:mi>B</eb:mi> </eb:msub> <eb:mo>≈</eb:mo> <eb:mn>500</eb:mn> <eb:mtext> </eb:mtext> <eb:mtext> </eb:mtext> <eb:mi>MeV</eb:mi> </eb:math> , as expected but not yet observed.