New approach to lattice QCD at finite density: reweighting without an overlap problem

Approaches to finite baryon density lattice QCD usually suffer from uncontrolled systematic uncertainties in addition to the well-known sign problem. We test a method - sign reweighting - that works directly at finite chemical potential and is yet free from any such uncontrolled systematics: with this approach the only problem is the sign problem itself. In practice the approach involves the generation of configurations with the positive fermionic weights given by the absolute value of the real part of the quark determinant, and a reweighting by a sign. There are only two sectors, +1 and -1 and as long as the average $\left\langle \pm \right\rangle \neq 0$ (with respect to the positive weight) this discrete reweighting has no overlap problem - unlike reweighting from $\mu=0$ - and the results are reliable. We also present results based on this algorithm on the phase diagram of lattice QCD with two different actions: as a first test, we apply the method to calculate the position of the critical endpoint with unimproved staggered fermions at $N_\tau=4$; as a second application, we study the phase diagram with 2stout improved staggered fermions at $N_\tau=6$. This second one is already a reasonably fine lattice - relevant for phenomenology. We demonstrate that the method penetrates the region of the phase diagram where the Taylor and imaginary chemical potential methods lose predictive power.