Abstract
The nature of the QCD chiral phase transition in the limit of vanishing quark masses has remained elusive for a long time, since it cannot be simulated directly on the lattice and is strongly cutoff-dependent. We report on a comprehensive ongoing study using unimproved staggered fermions with Nf ∈ [2, 8] mass-degenerate flavours on Nτ ∈ {4, 6, 8} lattices, in which we locate the chiral critical surface separating regions with first-order transitions from crossover regions in the bare parameter space of the lattice theory. Employing the fact that it terminates in a tricritical line, this surface can be extrapolated to the chiral limit using tricritical scaling with known exponents. Knowing the order of the transitions in the lattice parameter space, conclusions for approaching the continuum chiral limit in the proper order can be drawn. While a narrow first-order region cannot be ruled out, we find initial evidence consistent with a second-order chiral transition in all massless theories with Nf ≤ 6, and possibly up to the onset of the conformal window at 9 ≲ {N}_{mathrm{f}}^{ast } ≲ 12. A reanalysis of already published mathcal{O} (a)-improved Nf = 3 Wilson data on Nτ ∈ [4, 12] is also consistent with tricritical scaling, and the associated change from first to second-order on the way to the continuum chiral limit. We discuss a modified Columbia plot and a phase diagram for many-flavour QCD that reflect these possible features.
Highlights
Wilson discretisations break chiral symmetry partially or entirely, so that the continuum limit has to be taken before the chiral limit can be approached
We report on a comprehensive ongoing study using unimproved staggered fermions with Nf ∈ [2, 8] mass-degenerate flavours on Nτ ∈ {4, 6, 8} lattices, in which we locate the chiral critical surface separating regions with first-order transitions from crossover regions in the bare parameter space of the lattice theory
We have conducted a comprehensive analysis of the finite temperature chiral transitions observed in the bare parameter space {β, am, Nf, Nτ } of lattice QCD with unimproved staggered fermions
Summary
To motivate our analysis by the general picture, we briefly summarise current knowledge about the chiral phase transition. The critical temperature of the chiral phase transition was determined using HISQ fermions tuned to the physical strange quark mass, simulating a sequence of decreasing light quark masses down to ∼ 58 MeV in the crossover region [25]. These were extrapolated to the chiral limit employing the well-known scaling relation. A similar investigation with twisted mass Wilson fermions based on slightly larger pion masses confirms this behaviour [26]
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