Divergences in the quark number susceptibility : The origin and a cure

Abstract

Quark number susceptibility on the lattice, obtained by merely adding a $\mu N$ term with $\mu$ as the chemical potential and $N$ as the conserved quark number, has a quadratic divergence in the cut-off $a$. We show that such a divergence already exist for free fermions with a cut-off regulator. While one can eliminate it in the free lattice theory by suitably modifying the action, as is popularly done, it can simply be subtracted off as well. Computations of higher order susceptibilities, needed for estimating the location of the QCD critical point, then need a lot fewer number of quark propagators at any order. We show that this method of divergence removal works in the interacting theory.

Published version, with added discussion of the results and the appendix removed

References in corpus (5)

• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• The transition temperature in QCD
• QCD at finite chemical potential with six time slices
• Thermodynamics of the ideal overlap quarks on the lattice
• Robustness of baryon-strangeness correlation and related ratios of susceptibilities

Cited by in corpus (13)

• Chiral crossover in QCD at zero and non-zero chemical potentials
• The QCD Equation of State to $\mathcal{O}({\mu }_B^6)$ from Lattice QCD
• Higher order quark number fluctuations via imaginary chemical potentials in $N_f=2+1$ QCD
• Inhomogeneous phases in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• The phase structure of QCD
• Lattice QCD Equation of State for Nonvanishing Chemical Potential by Resumming Taylor Expansion
• Baryons in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• New Way to Resum the Lattice QCD Taylor Series Equation of State at Finite Chemical Potential
• Lattice QCD at nonzero temperature and density
• The QCD Equation of state and critical end-point estimates at $\mathcal{O}({\mu }_B^6)$
• Alternatives to the stochastic "noise vector" approach
• Taylor expansion and the Cauchy Residue Theorem for finite-density QCD
• On curing the divergences in the quark number susceptibility