On the order of the QCD chiral phase transition for different numbers of quark flavours

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 ≲ $$ {N}_{\mathrm{f}}^{\ast } $$ N f ∗ ≲ 12. A reanalysis of already published $$ \mathcal{O} $$ 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.

The QCD chiral phase transition for different numbers of quark flavours

“…However, based on the currently available data one would have to conclude that the Columbia plot looks as in figure 8. All results reported here have been published in [21]. Finally, we note that our analysis can be applied to any discretisation with explicit first-order transitions.…”

“…In addition to those, we have implemented a new error analysis for the critical masses 𝑎𝑚 𝑐 based on bootstrap estimators, which is entirely independent of the usual 𝜒 2 -minimisation. Besides providing a crucial reliability check on the fits, this procedure typically produces slightly smaller errors [21]. Altogether, the following results are based on 120 million Monte Carlo trajectories spread over 600 different parameter combinations, obtained over a span of several years.…”

“…First, figure 4 clearly confirms the tricritical scaling behaviour, which does not get superseded by ))-plane, interpolated by next-toleading order tricritical scaling. From [21].…”

“…Since the continuum limit is represented by the origin in figure 5 (a) Fits to equation ( 6), corresponding to the first-order scenario. From [21]. 7) and ( 8), corresponding to the second-order scenario.…”

“…7) and ( 8), corresponding to the second-order scenario. From [21]. that the continuum chiral limit is inevitably approached from the crossover region, and hence can only represent a second-order transition.…”