A framework for dynamical generation of flavor mixing

Abstract

We present a dynamical mechanismà la Nambu-Jona-Lasinio [1] for the generation of masses and mixing for two interacting fermion fields. The analysis is carried out in the framework introduced long ago by Umezawa et al. [2], in which mass generation is achieved via inequivalent representations, and that we generalize to the case of two generations. The method allows a clear identification of the vacuum structure for each physical phase, confirming previous results [3] about the distinct physical nature of the vacuum for fields with definite mass and fields with definite flavor. Implications for the leptonic sector of the Standard Model are briefly discussed.

On the rôle of rotations and Bogoliubov transformations in neutrino mixing

“…It is interesting to observe that the Bogoliubov transformations are indeed responsible for the mass shift and thus the results of this paper can lead to further insight in the interplay between mixing phenomenon and mass generation in a dynamical perspective as recently discussed in Refs. [31].…”

“…We can now consider the ratio ∆S f k,i /∆E k,i , where the latter is the gap energy defined in the previous Section Eq. (31) for the field i, obtaining β k,i = ∆S f k,i /∆E k,i = − ln tan 2 Γ k /ω k,i , which, however, depends on the momentum. In fact, unlike the standard TFD case, in which the parameter γ k is determined only by the relation in Eq.…”

Some nontrivial aspects of Poincaré and CPT invariance of flavor vacuum

“…Here we do not specify the origin of this condensate, which can be motivated by physics beyond SM as is done, e.g., in Refs. [24][25][26]. This would, in turn, indicate the necessity for a dynamical origin of mixing.…”

“…Such a modification of the dispersion relations for the flavor states can be understood as an "environmental" effect of quantumgravitational degrees of freedom in a concrete model of quantum gravity within the framework of string/brane theory, the so-called D-foam model [23]. In this context, the scattering between open strings, representing flavored matter, and D0-branes, which are viewed as Poincarésymmetry-breaking point-like space-time defects, of quantum-gravitational stringy nature, is modeled by an effective theory, which entails the dynamical generation of mixing via flavor vacuum condensates [24,25], in agreement with the generic feature of the flavor vacuum [7], mentioned previously. Such a vacuum structure can also be obtained via algebraic, i.e., nonperturbative methods, in the case of two [26] and three flavor [27] models with SUðnÞ L × SUðnÞ R × Uð1Þ V chiral flavor symmetry.…”

Functional integrals and inequivalent representations in Quantum Field Theory

“…(19) represents the dynamical map of the system: hereα † k and α k are the creation and annihilation operator, respectively, for the physical excitations (quasi-particles) of the system. Their energetic spectrum is given by Eq.…”