Equation of State of Cold Quark Matter to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msubsup><mml:mi>ln</mml:mi><mml:msub><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>
Tyler Gorda, Risto Paatelainen, Saga Säppi, Kaapo Seppänen
Abstract
Accurately understanding the equation of state (EOS) of high-density, zero-temperature quark matter plays an essential role in constraining the behavior of dense strongly interacting matter inside the cores of neutron stars. In this Letter, we study the weak-coupling expansion of the EOS of cold quark matter and derive the complete, gauge-invariant contributions from the long-wavelength, dynamically screened gluonic sector at next-to-next-to-next-to-leading order (N3LO) in the strong coupling constant ${\ensuremath{\alpha}}_{s}$. This elevates the EOS result to the $O({\ensuremath{\alpha}}_{s}^{3}\mathrm{ln}{\ensuremath{\alpha}}_{s})$ level, leaving only one unknown constant from the unscreened sector at N3LO, and places it on par with its high-temperature counterpart from 2003.