Phase diagram of twisted mass lattice QCD
Abstract
We use the effective chiral Lagrangian to analyze the phase diagram of two-flavor twisted mass lattice QCD as a function of the normal and twisted masses, generalizing previous work for the untwisted theory. We first determine the chiral Lagrangian including discretization effects up to next-to-leading order (NLO) in a combined expansion in which m2π/(4πfπ)2∼aΛ (a being the lattice spacing, and Λ=ΛQCD). We then focus on the region where m2π/(4πfπ)2∼(aΛ)2, in which case competition between leading and NLO terms can lead to phase transitions. As for untwisted Wilson fermions, we find two possible phase diagrams, depending on the sign of a coefficient in the chiral Lagrangian. For one sign, there is an Aoki phase for pure Wilson fermions, with flavor and parity broken, but this is washed out into a crossover if the twisted mass is nonvanishing. For the other sign, there is a first order transition for pure Wilson fermions, and we find that this transition extends into the twisted mass plane, ending with two symmetrical second order points at which the mass of the neutral pion vanishes. We provide graphs of the condensate and pion masses for both scenarios, and note a simple mathematical relation between them. These results may be of importance to numerical simulations.
- Publication:
-
Physical Review D
- Pub Date:
- November 2004
- DOI:
- 10.1103/PhysRevD.70.094029
- arXiv:
- arXiv:hep-lat/0407025
- Bibcode:
- 2004PhRvD..70i4029S
- Keywords:
-
- 12.39.Fe;
- 11.30.Hv;
- 11.30.Rd;
- 12.38.Gc;
- Chiral Lagrangians;
- Flavor symmetries;
- Chiral symmetries;
- Lattice QCD calculations;
- High Energy Physics - Lattice
- E-Print:
- 13 pages, 5 figures, small clarifying comments added in introduction, minor typos fixed. Version to be published in Phys. Rev. D