Pseudo-Goldstone excitations in chiral Yukawa-theories with quadratic explicit symmetry breaking

摘要

The symmetry breakdown pattern is studied in models containing one fermion flavor multiplet and a multicomponent scalar field, supplemented with a chiral Yukawa-interaction, and in presence of an explicit symmetry breaking source quadratic in the scalar field. In a detailed investigation of the model with U_L(1) × U_R(1) chiral symmetry, it is shown that by diminishing the strength of quadratic explicit symmetry breaking, one can still keep stable the mass ratio of the fermionic and the pseudo-Goldstone excitation. At the same time, the mass ratio of the two bosonic excitations appears to approach a unique limiting value depending only on the infrared value of the first ratio but not on the microscopic (ultraviolet) coupling values. These observations receive a general interpretation by the existence of a slowly drifting partial fixed line located in the symmetric phase. Understanding the general conditions for its existence allows the construction of a similar theory with U_L (2) × U_R (2) chiral symmetry. All results of the present investigation were obtained with a nonperturbative functional renormalization group technique making use of the first two approximations to the gradient expansion of the effective action.