The QCD chiral phase transition from non-integer numbers of flavors

Abstract

Attempts to extract the order of the chiral transition of QCD at zero chemical potential, with two dynamical flavors of massless quarks, from simulations with progressively decreasing pion mass have remained inconclusive because of their increasing numerical cost. In an alternative approach to this problem, we consider the path integral as a function of continuous number $N_{\text{f}}$ of degenerate quarks. If the transition in the chiral limit is first-order for $N_{\text{f}}\ge 3$, a second-order transition for $N_{\text{f}}=2$ then requires a tricritical point in between. This in turn implies tricritical scaling of the critical boundary line between the first-order and crossover regions as the chiral limit is approached. Non-integer numbers of fermion flavors are easily implemented within the staggered fermion discretization. Exploratory simulations at $\mu =0$ and $N_{\text{f}}=2.8,2.6,2.4,2.2,2.1$, on coarse $N_{\tau }=4$ lattices, indeed show a smooth variation of the critical mass mapping out a critical line in the $(m,N_{\text{f}})$-plane. For the smallest masses the line appears consistent with tricritical scaling, allowing for an extrapolation to the chiral limit.

10 pages, 8 figures, 2 tables, minor changes to match the version published in PRD

References in corpus (8)

• The chiral phase transition in two-flavor QCD from imaginary chemical potential
• The Roberge-Weiss endpoint in N_f = 2 QCD
• On the strength of the $U_A(1)$ anomaly at the chiral phase transition in $N_f=2$ QCD
• The $N_f=2$ QCD chiral phase transition with Wilson fermions at zero and imaginary chemical potential
• Critical point phase transition for finite temperature 3-flavor QCD with non-perturbatively O($a$) improved Wilson fermions at $N_{\mathrm{t}}=10$
• Roberge-Weiss transition in $N_{\text{f}}=2$ QCD with Wilson fermions and $N_{\tau }=6$
• Exploring the nature of chiral phase transition in two-flavor QCD using extra heavy quarks
• Curvature of the critical line on the plane of quark chemical potential and pseudo scalar meson mass for three-flavor QCD

Cited by in corpus (11)

• QCD at finite temperature and chemical potential from Dyson-Schwinger equations
• On the order of the QCD chiral phase transition for different numbers of quark flavours
• Chiral Susceptibility in (2+1)-flavour QCD
• Deconfinement critical point of lattice QCD with $N_{\mathrm{f}}=2$ Wilson fermions
• QCD phase transitions in the light quark chiral limit
• Lattice Constraints on the QCD Chiral Phase Transition at Finite Temperature and Baryon Density
• Constraining the QCD phase diagram at finite temperature and density
• Finite size and cut-off effects on the Roberge-Weiss transition in $N_{\text{f}}=2$ QCD with Staggered fermions
• Overview of the QCD phase diagram -- Recent progress from the lattice
• Gliding down the QCD transition line, from $N_f=2$ till the onset of conformality
• On the nature of the QCD chiral phase transition with imaginary chemical potential