Chiral phase transition in two-flavor QCD from an imaginary chemical potential

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We investigate the order of the finite temperature chiral symmetry restoration transition for QCD with two massless fermions, by using a novel method, based on simulating imaginary values of the quark chemical potential $\mu=i\mu_i,\mu_i\in\mathbb{R}$. Our method exploits the fact that, for low enough quark mass $m$ and large enough chemical potential $\mu_i$, the chiral transition is decidedly first order, then turning into crossover at a critical mass $m_c(\mu)$. It is thus possible to determine the critical line in the $m - \mu^2$ plane, which can be safely extrapolated to the chiral limit by taking advantage of the known tricritical indices governing its shape. We test this method with standard staggered fermions and the result of our simulations is that $m_c(\mu=0)$ is positive, so that the phase transition at zero density is definitely first order in the chiral limit, on our coarse $N_t=4$ lattices with $a\simeq 0.3\,\mathrm{fm}$.