Abstract:We study the 2HDM contribution to the muon anomalous magnetic moment a µ and present the complete two-loop result, particularly for the bosonic contribution. We focus on the Aligned 2HDM, which has general Yukawa couplings and contains the type I, II, X, Y models as special cases. The result is expressed with physical parameters: three Higgs boson masses, Yukawa couplings, two mixing angles, and one quartic potential parameter. We show that the result can be split into several parts, each of which has a simple parameter dependence, and we document their general behavior. Taking into account constraints on parameters, we find that the full 2HDM contribution to a µ can accommodate the current experimental value, and the complete two-loop bosonic contribution can amount to (2 · · · 4) × 10 −10 , more than the future experimental uncertainty.

The quark-meson model is often used as a low-energy effective model for QCD to study the chiral transition at finite temperature T, baryon chemical potential μ B , and isospin chemical potential μ I . We determine the parameters of the model by matching the meson and quark masses, as well as the pion decay constant to their physical values using the on shell (OS) and modified minimal subtraction (MS) schemes. In this paper, the existence of different phases at zero temperature is studied. In particular, we investigate the competition between an inhomogeneous chiral condensate and a homogeneous pion condensate. For the inhomogeneity, we use a chiral-density wave ansatz. For a sigma mass of 600 MeV, we find that an inhomogeneous chiral condensate exists only for pion masses below approximately 37 MeV. We also show that due to our parameter fixing, the onset of pion condensation takes place exactly at μ

In this paper, we calculate the equation of state of two-flavor finite isospin chiral perturbation theory at nextto-leading order in the pion-condensed phase at zero temperature. We show that the transition from the vacuum phase to a Bose-condensed phase is of second order. While the tree-level result has been known for some time, surprisingly quantum effects have not yet been incorporated into the equation of state. We find that the corrections to the quantities we compute, namely the isospin density, pressure, and equation of state, increase with increasing isospin chemical potential. We compare our results to recent lattice simulations of 2+1 flavor QCD with physical quark masses. The agreement with the lattice results is generally good and improves somewhat as we go from leading order to next-to-leading order in χPT.

We use the Polyakov-loop extended two-flavor quark-meson model as a low-energy effective model for QCD to study the phase diagram in the µI -T plane where µI is the isospin chemical potential. In particular, we focus on the Bose condensation of charged pions. At T = 0, the onset of pion condensation is at µI = 1 2 mπ in accordance with exact results. The phase transition to a Bosecondensed phase is of second order for all values of µI and in the O(2) universality class. The chiral critical line joins the critical line for pion condensation at a point whose position depends on the Polyakov-loop potential and the sigma mass. For larger values of µI these curves are on top of each other. The deconfinement line enters smoothly the phase with the broken O(2) symmetry. We compare our results with recent lattice simulations and find overall good agreement.1 Or their Polyakov-loop extended versions (PNJL and PQM).

Pion stars consisting of Bose-Einstein condensed charged pions have recently been proposed as a new class of compact stars. We use the two-particle irreducible effective action to leading order in the 1/N -expansion to describe charged and neutrals pions as well as the sigma particle. Tuning the parameters in the Lagrangian correctly, the onset of Bose-Einstein condesation of charged pions is exactly at µI = mπ, where µI is the isospin chemical potential. We calculate the pressure, energy density, and equation of state, which are used as input to the Tolman-Oppenheimer-Volkoff equations. Solving these equations, we obtain the mass-radius relation for pion stars. Global electric charge neutrality is ensured by adding the contribution to the pressure and energy density from a gas of free relativistic leptons. We compare our results with those of recent lattice simulations and find good agreement. The masses of the pion stars are up to approximately 200 solar masses while the corresponding radii are of the order of 10 5 km.