QCD phase diagram in a magnetic background for different values of the pion mass

Abstract

We investigate the behavior of the pseudo-critical temperature of N f = 2+1 QCD as a function of a static magnetic background field for different values of the pion mass, going up to mπ ≃ 660 MeV. The study is performed by lattice QCD simulations, adopting a stout staggered discretization of the theory on lattices with Nt = 6 slices in the Euclidean temporal direction; for each value of the pion mass the temperature is changed moving along a line of constant physics. We find that the decrease of Tc as a function of B, which is observed for physical quark masses, persists in the whole explored mass range, even if the relative variation of Tc appears to be a decreasing function of mπ, approaching zero in the quenched limit. The location of Tc is based on the renormalized quark condensate and its susceptibility; determinations based on the Polyakov loop lead to compatible results. On the contrary, inverse magnetic catalysis, i.e. the decrease of the quark condensate as a function of B in some temperature range around Tc, is not observed when the pion mass is high enough. That supports the idea that inverse magnetic catalysis might be a secondary phenomenon, while the modifications induced by the magnetic background on the gauge field distribution and on the confining properties of the medium could play a primary role in the whole range of pion masses.

Magnetic catalysis and inverse catalysis for heavy pions

“…Results supporting IMC were also obtained by further lattice simulations [10][11][12]. It was then believed that MC and IMC corresponded to T c being respectively an increasing or decreasing function of B, but a recent study has shown that as the pion mass is increased, the behavior near T c crosses over from IMC to MC, while T c remains a decreasing function of B all along [13].…”

“…6 of Ref. [13]) for comparison. While the different scale-setting procedure obviously leads to quantitatively different results from ours, the qualitative behaviors match nicely.…”

“…We remark furthermore that the lattice scale could also be set in a mass-dependent manner -this approach was followed in Ref. [13], which employs w 0 at the physical point and assumes that it is independent of m. Since there is no preferred choice when dealing with physics off the real world, a comparison between different scale-setting procedures does not assess a systematic error, but rather the robustness of the resulting qualitative pictures. A comparison to the results of Ref.…”

“…The dependence on the pion mass was also the subject of Ref. [13]. Here we employ a larger set of pion masses to follow more closely the transition from IMC to MC.…”

“…Moreover, we employ a different, mass-independent scale-setting procedure to assess the robustness of the qualitative picture obtained in Ref. [13] against different ways to build QCD for unphysical pion masses.…”