Nonperturbative renormalization of a fermion mass term in the mass-independent renormalization scheme

1999 ◽  
Vol 59 (11) ◽  
Author(s):  
Kensuke Kusaka ◽  
Hiroshi Toki ◽  
Sei Umisedo
Keyword(s):  
Mass Term ◽  
Renormalization Scheme ◽  
Fermion Mass ◽  
Nonperturbative Renormalization

scholarly journals Induced Parity Violation in Odd Dimensions

1994 ◽  
Vol 47 (4) ◽  
pp. 465 ◽  
Author(s):  
R Delbourgo ◽  
AB Waites
Keyword(s):  
Parity Violation ◽  
Mass Term ◽  
Field Theories ◽  
Fermion Mass ◽  
Odd Dimensions

One of the interesting features about field theories in odd dimensions is the induction of parity-violating terms and well-defined finite topological actions via quantum loops if a fermion mass term is originally present and conversely. Aspects of this issue are illustrated for electrodynamics in 2+ 1 and 4+ 1 dimensions.

scholarly journals THE ζ FUNCTION ANSWER TO PARITY VIOLATION IN THREE-DIMENSIONAL GAUGE THEORIES

1996 ◽  
Vol 11 (15) ◽  
pp. 2643-2660 ◽  
Author(s):  
R.E. GAMBOA SARAVÍ ◽  
G.L. ROSSINI ◽  
F.A. SCHAPOSNIK
Keyword(s):  
Gauge Field ◽  
Parity Violation ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Mass Term ◽  
Three Dimensions ◽  
Fermion Mass ◽  
Chern Simons ◽  
Fermion Current ◽  
Arbitrary Gauge

We study parity violation in (2+1)-dimensional gauge theories coupled to massive fermions. Using the ζ function regularization approach we evaluate the ground state fermion current in an arbitrary gauge field background, showing that it gets two different contributions which violate parity invariance and induce a Chern–Simons term in the gauge field effective action. One is related to the well-known classical parity breaking produced by a fermion mass term in three dimensions; the other, already present for massless fermions, is related to peculiarities of gauge-invariant regularization in odd-dimensional spaces.

scholarly journals Testing a non-perturbative mechanism for elementary fermion mass generation: lattice setup

2018 ◽  
Vol 175 ◽  
pp. 08009 ◽  
Author(s):  
Stefano Capitani ◽  
Giulia Maria de Divitiis ◽  
Petros Dimopoulos ◽  
Roberto Frezzotti ◽  
Marco Garofalo ◽  
...  
Keyword(s):  
Mass Term ◽  
Fermion Mass ◽  
Mass Generation ◽  
Complex Scalar ◽  
Abelian Gauge ◽  
Twisted Mass ◽  
Chiral Transformation ◽  
Complex Scalar Field ◽  
Stringent Test ◽  
Field Theoretical Model

In this contribution we lay down a lattice setup that allows for the nonperturbative study of a field theoretical model where a SU(2) fermion doublet, subjected to non-Abelian gauge interactions, is also coupled to a complex scalar field doublet via a Yukawa and an “irrelevant” Wilson-like term. Using naive fermions in quenched approximation and based on the renormalizedWard identities induced by purely fermionic chiral transformations, lattice observables are discussed that enable: a) in theWigner phase, the determinations of the critical Yukawa coupling value where the purely fermionic chiral transformation become a symmetry up to lattice artifacts; b) in the Nambu-Goldstone phase of the resulting critical theory, a stringent test of the actual generation of a fermion mass term of non-perturbative origin. A soft twisted fermion mass term is introduced to circumvent the problem of exceptional configurations, and observables are then calculated in the limit of vanishing twisted mass.

scholarly journals A translational flavor symmetry in the mass terms of Dirac and Majorana fermions

2021 ◽  
Author(s):  
Zhi-zhong Xing
Keyword(s):  
Mass Matrix ◽  
Mass Term ◽  
Fermion Mass ◽  
Unitary Matrix ◽  
Majorana Fermions ◽  
Flavor Symmetry ◽  
Fermion Fields ◽  
Starting Point ◽  
Current Experimental Data ◽  
Charged Leptons

Abstract Requiring the effective mass term for a category of fundamental Dirac or Majorana fermions of the same electric charge to be invariant under the translational transformations $\psi^{}_{\alpha \rm L (R)} \to \psi^{}_{\alpha \rm L (R)} + n^{}_{\alpha} z^{}_{\psi \rm L(R)}$ in the flavor space, where $n^{}_\alpha$ and $z^{}_{\psi \rm L(R)}$ stand respectively for the flavor-dependent complex numbers and a constant spinor field anticommuting with the fermion fields, we show that $n^{}_\alpha$ can be identified as the elements $U^{}_{\alpha i}$ in the $i$-th column of the unitary matrix $U$ used to diagonalize the corresponding Hermitian or symmetric fermion mass matrix $M^{}_\psi$, and $m^{}_i = 0$ holds accordingly. We find that the reverse is also true. Now that the mass spectra of charged leptons, up- and down-type quarks are all strongly hierarchical and current experimental data allow the lightest neutrino to be massless, we argue that the zero mass limit for the first-family fermions and the translational flavor symmetry behind it should be a natural starting point for building viable fermion mass models.

scholarly journals An improved holographic nodal line semimetal

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Yan Liu ◽  
Xin-Meng Wu
Keyword(s):  
Mass Term ◽  
Nodal Line ◽  
Duality Relation ◽  
Strongly Coupled ◽  
Nodal Lines ◽  
Form Field ◽  
Improved Model ◽  
Fermionic Spectrum ◽  
Chern Simons ◽  
Tensor Operators

Abstract We study an improved holographic model for the strongly coupled nodal line semimetal which satisfies the duality relation between the rank two tensor operators $$ \overline{\psi}{\gamma}^{\mu v}\psi $$ ψ ¯ γ μv ψ and $$ \overline{\psi}{\gamma}^{\mu v}{\gamma}^5\psi $$ ψ ¯ γ μv γ 5 ψ . We introduce a Chern-Simons term and a mass term in the bulk for a complex two form field which is dual to the above tensor operators and the duality relation is automatically satisfied from holography. We find that there exists a quantum phase transition from a topological nodal line semimetal phase to a trivial phase. In the topological phase, there exist multiple nodal lines in the fermionic spectrum which are topologically nontrivial. The bulk geometries are different from the previous model without the duality constraint, while the resulting properties are qualitatively similar to those in that model. This improved model provides a more natural ground to analyze transports or other properties of strongly coupled nodal line semimetals.

scholarly journals Electroweak SU(2)L × U(1)Y model with strong spontaneously fermion-mass-generating gauge dynamics

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Petr Beneš ◽  
Jiří Hošek ◽  
Adam Smetana
Keyword(s):  
Chiral Symmetry Breaking ◽  
Axial Vector ◽  
Higgs Sector ◽  
Dyson Equation ◽  
Mass Splitting ◽  
Fermion Mass ◽  
Goldstone Bosons ◽  
The Standard Model ◽  
Exploratory Stage ◽  
The Masses

Abstract Higgs sector of the Standard model (SM) is replaced by quantum flavor dynamics (QFD), the gauged flavor SU(3)f symmetry with scale Λ. Anomaly freedom requires addition of three νR. The approximate QFD Schwinger-Dyson equation for the Euclidean infrared fermion self-energies Σf(p2) has the spontaneous-chiral-symmetry-breaking solutions ideal for seesaw: (1) Σf(p2) = $$ {M}_{fR}^2/p $$ M fR 2 / p where three Majorana masses MfR of νfR are of order Λ. (2) Σf(p2) = $$ {m}_f^2/p $$ m f 2 / p where three Dirac masses mf = m(0)1 + m(3)λ3 + m(8)λ8 of SM fermions are exponentially suppressed w.r.t. Λ, and degenerate for all SM fermions in f. (1) MfR break SU(3)f symmetry completely; m(3), m(8) superimpose the tiny breaking to U(1) × U(1). All flavor gluons thus acquire self-consistently the masses ∼ Λ. (2) All mf break the electroweak SU(2)L × U(1)Y to U(1)em. Symmetry partners of the composite Nambu-Goldstone bosons are the genuine Higgs particles: (1) three νR-composed Higgses χi with masses ∼ Λ. (2) Two new SM-fermion-composed Higgses h3, h8 with masses ∼ m(3), m(8), respectively. (3) The SM-like SM-fermion-composed Higgs h with mass ∼ m(0), the effective Fermi scale. Σf(p2)-dependent vertices in the electroweak Ward-Takahashi identities imply: the axial-vector ones give rise to the W and Z masses at Fermi scale. The polar-vector ones give rise to the fermion mass splitting in f. At the present exploratory stage the splitting comes out unrealistic.

Quantum-mechanical treatment of the Skyrme Lagrangean, and a new mass term

1987 ◽  
Vol 58 (7) ◽  
pp. 651-653 ◽  
Author(s):  
K. Fujii ◽  
K-I. Sato ◽  
N. Toyota ◽  
A. P. Kobushkin
Keyword(s):  
Mechanical Treatment ◽  
Mass Term ◽  
Quantum Mechanical ◽  
Quantum Mechanical Treatment
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