Related papers: Zeta function regularization, anomaly and complex …
In this paper, we revisit Fujikawa's path integral formulation of the chiral anomaly and develop a generalised framework for systematically defining a regularised functional measure. This construction extends the $\eta$ regularisation…
We consider a model with arbitrary numbers of Majorana fermion fields and real scalar fields $\varphi_a$, general Yukawa couplings and a $\mathbb{Z}_4$ symmetry that forbids linear and trilinear terms in the scalar potential. Moreover,…
Glasser's Master Theorem arXiv:1308.6361v2 is essentially a restatement of Cauchy's integral Theorem reduced to a specialized form. Here we extend that theorem by introducing two new parameters, but still retain a simple form. Because of…
Apart from the qualitative features described in \cite{chm}, the renormalization group equation derived for the rotation of the fermion mass matrices are amenable to quantitative study. The equation depends on a coupling and a fudge factor…
We show that in the functional integral formalism the (finite) coefficient of the induced, Lorentz- and CPT-violating Chern-Simons term, arising from the Lorentz- and CPT-violating fermion sector, is undetermined.
Results for $\beta$-functions and anomalous dimensions in general scalar fermion theories are presented to three loops. Various constraints on the individual coefficients for each diagram following from supersymmetry are analysed. The…
One of the generalizations of multiple zeta values is the $q$-version, and in the case of finite sums, they may be expressed explicitly in polynomial form. Several results have been found when the powers of the factors in the denominator…
The Dualized Standard Model has scored a number of successes in explaining the fermion mass hierarchy and mixing pattern. This note contains updates to those results including (a) an improved treatment of neutrino oscillation free from…
Transition form factors of pi^0, eta, eta' mesons are investigated by means of the anomaly sum rule -- an exact nonperturbative relation which follows from the dispersive representation of the axial anomaly. Considering the problem of…
Understanding the structure of the fermion mixing matrices is an important question in particle physics. The quark mixing matrix is approximately diagonal while the lepton mixing matrix has large off-diagonal elements. Attempting to…
We discuss complex rephasing invariants of charged lepton and neutrino mass matrices and associated theorems which determine in general (i) the number of physically meaningful phases in these matrices and (ii) which elements of these…
$Z \to \gamma \gamma$ decay amplitude is considered and proven to be zero due to properties of polarization vectors and Bose statistics. Triangular diagrams for a pseudoscalar $\to \gamma \gamma$ and $Z \to \gamma \gamma$ processes with…
The possibility of grand unification of the standard model (SM) with fermion spectrum extended to include mirror fermions is examined. SM gauge couplings do not automatically unify. SO(10) grand unification is studied with one intermediate…
A quite fast proof of the functional equation of the Riemann zeta function. It is a modification of a proof usually overlooked in Titchmarsh's monograph.
We consider a variant expression to regularize the Euler product representation of the zeta functions, where we mainly apply to that of the Riemann zeta function in this paper. The regularization itself is identical to that of the zeta…
A brief review of problems, arising in the study of the beta-deformation, also known as "refinement", which appears as a central difficult element in a number of related modern subjects: beta \neq 1 is responsible for deviation from free…
The naive perturbation expansion for many-fermion systems is infrared divergent. One can remove these divergences by introducing counterterms. To do this without changing the model, one has to solve an inversion equation. We call this…
Equations are proposed for the description of the fermion interaction via massive and massless bosons. These equations lead to the propagators which maintain theory renormalization. These equations are also invariant with respect to the…
Using the renormalization group procedure for effective particles (RGPEP) we calculate the effective Hamiltonians in the theory of a fermion field coupled to a scalar field via the Yukawa interaction. The theory is renormalized by the…
Special functions are often defined as a Fourier or Laplace transform of a positive measure, and the positivity of the measure manifests as positive definiteness of certain matrices. The purpose of this expository note is to give a sample…