Abstract
The thermal restoration of chiral symmetry in QCD is known to proceed by an analytic crossover, which is widely expected to turn into a phase transition with a critical endpoint as the baryon density is increased. In the absence of a genuine solution to the sign problem of lattice QCD, simulations at zero and imaginary baryon chemical potential in a parameter space enlarged by a variable number of quark flavours and quark masses constitute a viable way to constrain the location of a possible non-analytic phase transition and its critical endpoint. In this article I review recent progress towards an understanding of the nature of the transition in the massless limit, and its critical temperature at zero density. Combined with increasingly detailed studies of the physical crossover region, current data bound a possible critical point to μB ≳ 3T.
Highlights
Many salient features of the spectrum of hadrons and their interactions observed in nature are determined by the near-chiral symmetry of the QCD Lagrangian and its spontaneous breaking by the QCD vacuum
The thermal restoration of chiral symmetry in QCD is known to proceed by an analytic crossover, which is widely expected to turn into a phase transition with a critical endpoint as the baryon density is increased
In the absence of a genuine solution to the sign problem of lattice QCD, simulations at zero and imaginary baryon chemical potential in a parameter space enlarged by a variable number of quark flavours and quark masses constitute a viable way to constrain the location of a possible non-analytic phase transition and its critical endpoint
Summary
Many salient features of the spectrum of hadrons and their interactions observed in nature are determined by the near-chiral symmetry of the QCD Lagrangian and its spontaneous breaking by the QCD vacuum. In a hot and/or dense medium, chiral symmetry is expected to be gradually restored once the temperature exceeds T ą„ 160 MeV or the baryon chemical potential μB ą„ 1 GeV. Associated with this change of the realised symmetry, one expects a change of dynamics and its underlying degrees of freedom which, asymptotically, should become quarks and gluons. The low energy scales of the transition region demand a non-perturbative first principles approach like lattice QCD. Besides giving theoretical insight into the interplay of symmetries and dynamics in controlled situations, such studies provide constraints on the physical phase diagram, which are beginning to become phenomenologically relevant. I will focus on developments suggesting a modified version of the Columbia plot and constraints on the location of a possible critical point
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