Bounding the QCD Equation of State with the Lattice
Guy D. Moore, Tyler Gorda
Abstract
A bstract The equation of state of QCD matter at high densities is relevant for neutron star structure and for neutron star mergers and has been a focus of recent work. We show how lattice QCD simulations, free of sign problems, can provide an upper bound on the pressure as a function of quark chemical potentials. We show that at large chemical potentials this bound should become quite sharp; the difference between the upper bound on the pressure P PQ and the true pressure P is of order P PQ − P = $$ \mathcal{O} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> ( $$ {\alpha}_{\textrm{s}}^3 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>3</mml:mn> </mml:msubsup> </mml:math> P ). The corrections arise from a single Feynman diagram; its calculation would render remaining corrections $$ \mathcal{O} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> ( $$ {\alpha}_{\textrm{s}}^4 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>4</mml:mn> </mml:msubsup> </mml:math> P ).