Next-to-Next-to-Next-to-Leading Order Pressure of Cold Quark Matter: Leading Logarithm
Tyler Gorda (Department of Physics, University of Virginia, Charlottesville, Virginia 22904, USA, Helsinki Institute of Physics and Department of Physics, FI-00014 University of Helsinki, Finland); Aleksi Kurkela (Faculty of Science and Technology, University of Stavanger, 4036 Stavanger, Norway, Theoretical Physics Department, CERN, 1211 Geneva, Switzerland); Paul Romatschke (Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA, Department of Physics, University of Colorado Boulder, Boulder, Colorado 80302, USA); Saga Säppi (Helsinki Institute of Physics and Department of Physics, FI-00014 University of Helsinki, Finland); Aleksi Vuorinen (Helsinki Institute of Physics and Department of Physics, FI-00014 University of Helsinki, Finland)
At high baryon chemical potential , the equation of state of QCD allows a weak-coupling expansion in the QCD coupling . The result is currently known up to and including the full next-to-next-to-leading order . Starting at this order, the computations are complicated by the modification of particle propagation in a dense medium, which necessitates nonperturbative treatment of the scale . We apply a hard-thermal-loop scheme for capturing the contributions of this scale to the weak-coupling expansion, and we use it to determine the leading-logarithm contribution to next-to-next-to-next-to-leading order: . This result is the first improvement to the equation of state of massless cold quark matter in 40 years. The new term is negligibly small and thus significantly increases our confidence in the applicability of the weak-coupling expansion.