Search results for "abelian"
showing 10 items of 208 documents
Bilarge neutrino mixing and Abelian flavor symmetry
2012
We explore two bilarge neutrino mixing Anzatze within the context of Abelian flavor symmetry theories: (BL1) sin theta(12) similar to lambda, sin theta(13) similar to lambda, sin theta(23) similar to lambda, and (BL2) sin theta(12) similar to lambda, sin theta(13) similar to lambda, sin theta(23) similar to 1 - lambda. The first pattern is proposed by two of us and is favored if the atmospheric mixing angle theta(23) lies in the first octant, while the second one is preferred for the second octant of theta(23). In order to reproduce the second texture, we find that the flavor symmetry should be U(1) x Z(m), while for the first pattern the flavor symmetry should be extended to U(1) x Z(m) x …
New Schwinger-Dyson equations for non-Abelian gauge theories
2008
We show that the application of the pinch technique to the conventional Schwinger-Dyson equations for the gluon propagator, gluon-quark vertex, and three-gluon vertex, gives rise to new equations endowed with special properties. The new series coincides with the one obtained in the Feynman gauge of the background field method, thus capturing the extensive gauge cancellations implemented by the pinch technique at the level of individual Green's functions. Its building blocks are the fully dressed pinch technique Green's functions obeying Abelian all-order Ward identities instead of the Slavnov-Taylor identites satisfied by their conventional counterparts. As a result, and contrary to the sta…
Yukawa sector of multi-Higgs-doublet models in the presence of Abelian symmetries
2013
A general method for classifying the possible quark models of a multi-Higgs-doublet model, in the presence of Abelian symmetries, is presented. All the possible sets of textures that can be present in a given sector are shown, thus turning the determination of the flavor models into a combinatorial problem. Several symmetry implementations are studied for two and three Higgs doublet models. Some models' implementations are explored in great detail, with a particular emphasis on models known as Branco-Grimus-Lavoura and nearest-neighbor-interaction. Several considerations on the flavor changing neutral currents of multi-Higgs models are also given.
Breit-Wigner formalism for non-Abelian theories
2003
The consistent description of resonant transition amplitudes within the framework of perturbative field theories necessitates the definition and resummation of off-shell Green's functions, which must respect several crucial physical requirements. In particular, the generalization of the usual Breit-Wigner formalism in a non-Abelian context constitutes a highly non-trivial problem, related to the fact that the conventionally defined Green's functions are unphysical. We briefly review the main field-theoretical difficulties arising when attempting to use such Green's functions outside the confines of a fixed order perturbative calculation, and explain how this task has been successfully accom…
Fun with the Abelian Higgs model
2013
In calculations of the elementary scalar spectra of spontaneously broken gauge theories there are a number of subtleties which, though it is often unnecessary to deal with them in the order-of-magnitude type of calculations, have to be taken into account if fully consistent results are sought for. Within the "canonical" effective-potential approach these are, for instance: the need to handle infinite series of nested commutators of derivatives of field-dependent mass matrices, the need to cope with spurious IR divergences emerging in the consistent leading-order approximation and, in particular, the need to account for the fine interplay between the renormalization effects in the one-and tw…
The Non-Abelian Vector Gauge Particle ρ
2020
So far we have shown how pion self-interaction and pion-mass generation are tied together. This phenomenon, a result of the three-dimensional non-linear realization of the triplet isotopic pion field, is a consequence of a dimensional reduction from four-dimensional Euclidean space to a three-dimensional curved isotopic space with positive curvature, i.e., by way of chiral-symmetry breaking and subsequent pionic mass generation in a curved isotopic spin background with K = λ2, λ = 2f0∕mπ, which is taken from low-energy π − N interaction.
Nilpotence of orbits under monodromy and the length of Melnikov functions
2021
Abstract Let F ∈ ℂ [ x , y ] be a polynomial, γ ( z ) ∈ π 1 ( F − 1 ( z ) ) a non-trivial cycle in a generic fiber of F and let ω be a polynomial 1-form, thus defining a polynomial deformation d F + e ω = 0 of the integrable foliation given by F . We study different invariants: the orbit depth k , the nilpotence class n , the derivative length d associated with the couple ( F , γ ) . These invariants bind the length l of the first nonzero Melnikov function of the deformation d F + e ω along γ . We analyze the variation of the aforementioned invariants in a simple but informative example, in which the polynomial F is defined by a product of four lines. We study as well the relation of this b…
Spectrum of the non-abelian phase in Kitaev's honeycomb lattice model
2008
The spectral properties of Kitaev's honeycomb lattice model are investigated both analytically and numerically with the focus on the non-abelian phase of the model. After summarizing the fermionization technique which maps spins into free Majorana fermions, we evaluate the spectrum of sparse vortex configurations and derive the interaction between two vortices as a function of their separation. We consider the effect vortices can have on the fermionic spectrum as well as on the phase transition between the abelian and non-abelian phases. We explicitly demonstrate the $2^n$-fold ground state degeneracy in the presence of $2n$ well separated vortices and the lifting of the degeneracy due to t…
Quantum walks and non-Abelian discrete gauge theory
2016
A new family of discrete-time quantum walks (DTQWs) on the line with an exact discrete $U(N)$ gauge invariance is introduced. It is shown that the continuous limit of these DTQWs, when it exists, coincides with the dynamics of a Dirac fermion coupled to usual $U(N)$ gauge fields in $2D$ spacetime. A discrete generalization of the usual $U(N)$ curvature is also constructed. An alternate interpretation of these results in terms of superimposed $U(1)$ Maxwell fields and $SU(N)$ gauge fields is discussed in the Appendix. Numerical simulations are also presented, which explore the convergence of the DTQWs towards their continuous limit and which also compare the DTQWs with classical (i.e. non-qu…
Breaking Symmetry Effects on Heavy Tetraquarks
2017
In this contribution we present symmetry arguments that can be applied to study the stability of four-quark systems with two different masses. The role played by different symmetry breaking effects and the non-Abelian algebra of color forces is discussed in detail. In the particular case of hidden-flavor all-heavy four-quark states, QQ (Q) over bar(Q) over bar, the system becomes unstable for standard color-additive models. Differences and similarities between Qq (Q) over bar(q) over bar and QQ (q) over bar(q) over bar configurations are presented. In the latter case, its stability when the mass ratio M/m increases was established almost forty years ago. In the former case, we find a kind o…