WARD–TAKAHASHI IDENTITIES AND THE SPIN-0 COMPONENTS OF W AND Z FIELDS

2004 ◽  
Vol 19 (28) ◽  
pp. 4813-4823
Author(s):  
BING AN LI
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Axial Vector ◽  
The Masses

The Ward–Takahashi (WT) identities of the axial-vector currents and the charged vector currents of fermions are changed after spontaneous symmetry breaking. The spin-0 components of Z and W fields are revealed from the changed WT identities. The masses of these spin-0 components are at 1014 GeV. They are ghosts.

Masses of W and Z bosons without spontaneous symmetry breaking

2001 ◽  
Vol 16 (supp01a) ◽  
pp. 351-353
Author(s):  
Bing An Li
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Axial Vector ◽  
Z Bosons ◽  
Dynamical Symmetry ◽  
Fermion Mass ◽  
Electroweak Theory ◽  
Dynamical Symmetry Breaking ◽  
Vector Component ◽  
The Masses

A new dynamical symmetry breaking of SU(2)L × U(1) caused by the combination of the axial-vector component and the fermion mass is found in electroweak theory. The masses of the W and the Z bosons are obtained to be [Formula: see text] and [Formula: see text]. The Fermi constant is determined to be [Formula: see text].

scholarly journals THEORY OF ELECTROWEAK INTERACTIONS WITHOUT SPONTANEOUS SYMMETRY BREAKING

2001 ◽  
Vol 16 (25) ◽  
pp. 4171-4188 ◽  
Author(s):  
BING AN LI
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Z Boson ◽  
W Boson ◽  
Axial Vector ◽  
Fermion Mass ◽  
Electroweak Theory ◽  
Intermediate Boson ◽  
Generating Functional ◽  
Fermion Masses

An electroweak theory without spontaneous symmetry breaking is studied in this paper. A new symmetry breaking of SU (2)L × U (1), axial-vector symmetry breaking, caused by the combination of the axial-vector component of the intermediate boson and the fermion mass is found in electroweak theory. The mass of the W boson is resulted in the combination of the axial-vector symmetry breaking and the explicit symmetry breaking by the fermion masses. The Z boson gains mass from the axial-vector symmetry breaking only. [Formula: see text], [Formula: see text], and [Formula: see text] are obtained. They are in excellent agreement with data. The SU (2)L × U (1) invariant generating functional of the Green functions is constructed and the theory is proved to be renormalizable.

Chiral Symmetry

2019 ◽  
pp. 217-230
Author(s):  
Michael E. Peskin
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Chiral Symmetry ◽  
Goldstone Boson ◽  
Spontaneous Breaking ◽  
Quark Masses ◽  
Zero Mass ◽  
K Mesons ◽  
The Masses

This chapter introduces chiral symmetry, the extra symmetry that QCD acquires when the masses of quarks are set to zero. It introduces the concept of spontaneous symmetry breaking and explains the spontaneous breaking of chiral symmetry in QCD. It introduces the concept of a Goldstone boson, a particle that has zero mass as the result of spontaneous symmetry breaking, and explains how this concept explains properties of the pi and K mesons and allows us to determine the underlying values of the quark masses.

scholarly journals A semiclassical approach for the Higgs boson

2014 ◽  
Vol 29 (32) ◽  
pp. 1450196
Author(s):  
Amir H. Fariborz ◽  
Renata Jora ◽  
Joseph Schechter
Keyword(s):  
Higgs Boson ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Equations Of Motion ◽  
Tree Level ◽  
Semiclassical Approach ◽  
Gauge Bosons ◽  
The Masses ◽  
Simple Tree

Starting from the equations of motion of the fields in a theory with spontaneous symmetry breaking and by making some simple assumptions regarding their behavior we derive simple tree level relations between the mass of the Higgs boson in the theory and the masses of the gauge bosons corresponding to the broken generators. We show that these mass relations have a clear meaning if both the scalars and the gauge bosons in the theory are composite states made of two fermions.

scholarly journals EXPLICIT BREAKING OF SO(3) WITH HIGGS FIELDS IN THE REPRESENTATIONS ℓ = 2 AND ℓ = 3

2003 ◽  
Vol 18 (26) ◽  
pp. 4817-4827 ◽  
Author(s):  
MEHMET KOCA ◽  
RAMAZAN KOÇ ◽  
HAYRIYE TÜTÜNCÜLER
Keyword(s):  
Liquid Crystals ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Cosmic Strings ◽  
Gauge Bosons ◽  
Goldstone Bosons ◽  
The Masses ◽  
Higgs Fields

A gauged SO(3) symmetry is broken into its little groups of the representations ℓ = 2 and ℓ = 3. Explicit Higgs potentials leading to the spontaneous symmetry breaking are constructed. The masses of the gauge bosons and Higgs particles are calculated in terms of the renormalizable potentials. Emergence of Goldstone bosons arising from the absence of certain potential terms is also discussed. Analogous structures between the cosmic strings and disclinations of liquid crystals are noted.

The “Higgs” Boson, and its Field in the “Vacuum”

2018 ◽  
pp. 122-128
Author(s):  
Alvaro De Rújula
Keyword(s):  
Higgs Boson ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Experimental Test ◽  
Higgs Field ◽  
Expectation Value ◽  
The Masses

Spontaneous symmetry breaking. The symmetric Higgs bottle and its asymmetric state of lowest energy. The “expectation value” of the Higgs field in the vacuum. Why and how the vacuum is not void, it is a substance, the mother of them all. Understanding the generation of the masses of particles (other than the Higgs boson and the massless photon and gluons). The experimental test of this mass-generating mechanism. The Higgs-boson discovery fest. The “discovery channels” and the experimentalists’ insufficient acknowledgments.

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.

Spontaneous symmetry breaking of dislocation core in SrTiO3

2021 ◽  
pp. 100453
Author(s):  
Hetian Chen ◽  
Di Yi ◽  
Ben Xu ◽  
Jing Ma ◽  
Cewen Nan
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Dislocation Core

scholarly journals Tachyons and Solitons in Spontaneous Symmetry Breaking in the Frame of Field Theory

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1358
Author(s):  
Yiannis Contoyiannis ◽  
Michael P. Hanias ◽  
Pericles Papadopoulos ◽  
Stavros G. Stavrinides ◽  
Myron Kampitakis ◽  
...  
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Critical Point ◽  
Universality Class ◽  
Lattice Simulation ◽  
Ginzburg Landau ◽  
Spin Lattice ◽  
Nuclear Collisions ◽  
Ising Spin ◽  
Relativistic Nuclear Collisions

This paper presents our study of the presence of the unstable critical point in spontaneous symmetry breaking (SSB) in the framework of Ginzburg–Landau (G-L) free energy. Through a 3D Ising spin lattice simulation, we found a zone of hysteresis where the unstable critical point continued to exist, despite the system having entered the broken symmetry phase. Within the hysteresis zone, the presence of the kink–antikink SSB solitons expands and, therefore, these can be observed. In scalar field theories, such as Higgs fields, the mass of this soliton inside the hysteresis zone could behave as a tachyon mass, namely as an imaginary quantity. Due to the fact that groups Ζ(2) and SU(2) belong to the same universality class, one expects that, in future experiments of ultra-relativistic nuclear collisions, in addition to the expected bosons condensations, structures of tachyon fields could appear.

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