Abstract
We investigate the chiral phase structure of three flavor QCD in a background $U(1)$ magnetic field using the standard staggered action and the Wilson plaquette gauge action. We perform simulations on lattices with a temporal extent of $N_\tau=4$ and four spatial extents of $N_\sigma = 8,16, 20$ and 24. We choose a smaller-than-physical quark mass in lattice spacing as $am = 0.030$ such that there exists a crossover transition at vanishing magnetic fields, and adopt two values of magnetic field strength in lattice spacing $a \sqrt{ e{B}}\simeq 1.5$ and 2. We find that the transition becomes stronger in the presence of a background magnetic field, and turns into a first order as seen from the volume scaling of the order parameter susceptibility as well as the metastable states in the time history of the chiral condensate. On the other hand, the chiral condensate and transition temperature always increase with $B$ even within the regime of a first order phase transition. This suggests that the discrepancy in the behavior of chiral condensates and transition temperature as a function of $B$ between earlier lattice studies using larger-than-physical pion masses with standard staggered fermions and those using physical pions with improved staggered fermions is mainly due to lattice cutoff effects.
Highlights
Strong magnetic fields have been shown to have many significant impacts on the properties of systems governed by strong interaction, and they may have observable consequences in heavy-ion collision experiments as well as magnetized neutron stars [1,2]
Lattice studies of Nf 1⁄4 2 QCD with standard staggered fermions and largerthan-physical pions on Nτ 1⁄4 4 lattices found the so-called magnetic catalyses, which means that the chiral condensate increases monotonically with increasing B [3]
In this paper we investigate the transition of Nf 1⁄4 3 QCD in background magnetic fields with a quark mass corresponding to pion mass estimated as ∼280 MeV at vanishing magnetic field
Summary
Strong magnetic fields have been shown to have many significant impacts on the properties of systems governed by strong interaction, and they may have observable consequences in heavy-ion collision experiments as well as magnetized neutron stars [1,2]. At the vanishing magnetic field the true first order phase transition is not yet observed, and state-of-the-art estimates on the critical pion mass mcπ based on lattice QCD simulations are mcπ ≲ 50 MeV using improved staggered fermions [13,14] and mcπ ≲ 110 MeV using clover-improved Wilson fermions [15,16]. Since the background magnetic field always enhances the strength of the transition one may wonder whether it could enlarge the first order chiral phase transition region in Nf 1⁄4 3 QCD, i.e., having a larger value of the critical pion mass. The usage of standard staggered fermions with a small quark mass renders us to understand whether the discrepancy in the behavior of chiral condensate and transition temperature as a function of the magnetic field strength in [3,11] is ascribed to the lattice cutoff effects. The preliminary results have been reported in [18]
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