Abstract
We investigate the fate of the Roberge-Weiss endpoint transition and its connection with the restoration of chiral symmetry as the chiral limit of $N_f = 2+1$ QCD is approached. We adopt a stout staggered discretization on lattices with $N_t = 4$ sites in the temporal direction; the chiral limit is approached maintaining a constant physical value of the strange-to-light mass ratio and exploring three different light quark masses, corresponding to pseudo-Goldstone pion masses $m_\pi \simeq 100, 70$ and 50 MeV around the transition. A finite size scaling analysis provides evidence that the transition remains second order, in the 3D Ising universality class, in all the explored mass range. The residual chiral symmetry of the staggered action also allows us to investigate the relation between the Roberge-Weiss endpoint transition and the chiral restoration transition as the chiral limit is approached: our results, including the critical scaling of the chiral condensate, are consistent with a coincidence of the two transitions in the chiral limit; however we are not able to discern the symmetry controlling the critical behavior, because the critical indexes relevant to the scaling of the chiral condensate are very close to each other for the two possible universality classes (3D Ising or O(2)).
Highlights
In order to better visualize the quality of our approach to the chiral limit, in Fig. 2 we show, for a fixed value of the bare gauge coupling β 1⁄4 3.39, the values obtained for the pseudo-Goldstone pion and for mðπ1Þ as a function of the square root of the light bare quark mass; values have been obtained by interpolation of those given in pcloffiffiffisffiffiely the prediction of chiral ml, the first excited pion is instead much less affected by the change of aml
We have investigated the fate of the Roberge-Weiss endpoint transition and its relation with the restoration of chiral symmetry as the chiral limit of Nf 1⁄4 2 þ 1 QCD is approached
We have worked at fixed values of the bare quark masses around the transition points, in order to exploit multihistogram methods, maintaining a physical strange-to-light mass ratio and exploring three different light quark masses, aml 1⁄4 0.003, 0.0015 and 0.00075, corresponding respectively to pseudo-Goldstone pion masses mπ ≃ 100, 70 and 50 MeV around the transition
Summary
Numerical investigation of QCD or QCD-like theories in the presence of imaginary chemical potentials coupled to quark number operators has been the subject of various lattice studies [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]. QCD with fermions in the adjoint representation [66] In this case, results obtained at finite quark mass show that the two transitions are generically close to each other; what happens in the chiral limit, where both symmetries are exact, is unknown. Even at finite lattice spacing, the staggered discretization provides a remnant of the chiral symmetry which becomes exact as the bare quark mass is extrapolated to zero: it corresponds to a single generator of the original chiral group, it breaks spontaneously at low temperature, leading to a single massless pion, and it gets restored at the chiral transition temperature Tχ.
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