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 ${N}_{\mathrm{f}}$ of degenerate quarks. If the transition in the chiral limit is first order for ${N}_{\mathrm{f}}\ensuremath{\ge}3$, a second-order transition for ${N}_{\mathrm{f}}=2$ 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. Noninteger numbers of fermion flavors are easily implemented within the staggered fermion discretization. Exploratory simulations at $\ensuremath{\mu}=0$ and ${N}_{\mathrm{f}}=2.8$, 2.6, 2.4, 2.2, 2.1, on coarse ${N}_{\ensuremath{\tau}}=4$ lattices, indeed show a smooth variation of the critical mass mapping out a critical line in the ($m$, ${N}_{\mathrm{f}}$) plane. For the smallest masses, the line appears consistent with tricritical scaling, allowing for an extrapolation to the chiral limit.
Highlights
Knowledge of the nature of the chiral phase transition of QCD with two flavors of massless quarks is of great importance for further progress in various directions of particle and heavy ion physics
The ordering of kurtosis values for a fixed mass m as function of the volume depends, as expected, on whether m lies in the crossover region (B4 increases with Nσ) or in the firstorder region (B4 decreases with Nσ), mZ2 being the mass at
We investigated the nature of the chiral phase transition in the (m, Nf) plane with Nf interpreted as a continuous parameter in the path integral formulation of the theory
Summary
Knowledge of the nature of the chiral phase transition of QCD with two flavors of massless quarks is of great importance for further progress in various directions of particle and heavy ion physics. For all Nτ’s investigated so far, the first-order region is vastly smaller for staggered discretizations, suggesting that the latter have the smaller cut-off effects in the critical quark mass configuration It remains a formidably difficult task to determine whether or not a finite first-order region survives in the continuum limit. If a continuous parameter is varied such as to weaken the transition, like increasing the strange quark mass ms, the 3-state coexistence may terminate in a tricritical point, which governs the functional behavior of the second-order boundary lines emanating from it by known critical exponents If such a boundary line can be followed into the tricritical scaling regime, an extrapolation becomes possible.
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