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.

Gauge hierarchies for chiral SU(N) × SU(N) groups

1976 ◽  
Vol 54 (16) ◽  
pp. 1660-1663 ◽  
Author(s):  
Shalom Eliezer
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Gauge Theories ◽  
Vacuum Expectation ◽  
Coupling Constants ◽  
Spontaneous Breaking ◽  
Text Representation ◽  
Algebraic Equations ◽  
Expectation Values ◽  
Special Case

We have presented a special case where a hierarchy of spontaneous breaking of the symmetries can be achieved in conventional gauge theories (i.e. the Higgs scalars are elementary bosons and the coupling constants of the quartic interactions are small). We break spontaneously the chiral group SU(N) × SU(N) with Higgs scalars transforming like the (N, [Formula: see text]) representation of SU(N) × SU(N). By minimizing the potential we obtain a set of algebraic equations of the type[Formula: see text]where ηj are the vacuum expectation values of the Higgs scalars and μi2 and Aij are parameters. In order to get a hierarchy of spontaneous symmetry breaking we obtain the condition det Aij = 0.

scholarly journals Spontaneous Symmetry Breaking in 5D Conformally Invariant Gravity

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Taeyoon Moon ◽  
Phillial Oh
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Conformal Symmetry ◽  
Brane World ◽  
Spontaneous Breaking ◽  
Warp Factor ◽  
Translational Symmetry ◽  
Tensor Perturbation ◽  
Conformally Invariant ◽  
Conformal Quantum Mechanics

We explore the possibility of the spontaneous symmetry breaking in 5D conformally invariant gravity, whose action consists of a scalar field nonminimally coupled to the curvature with its potential. Performing dimensional reduction via ADM decomposition, we find that the model allows an exact solution giving rise to the 4D Minkowski vacuum. Exploiting the conformal invariance with Gaussian warp factor, we show that it also admits a solution which implements the spontaneous breaking of conformal symmetry. We investigate its stability by performing the tensor perturbation and find the resulting system is described by the conformal quantum mechanics. Possible applications to the spontaneous symmetry breaking of time-translational symmetry along the dynamical fifth direction and the brane-world scenario are discussed.

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.

NEUTRAL PION PHOTOPRODUCTION ON THE PROTON AND THE CLOUDY-BAG MODEL

1992 ◽  
Vol 07 (21) ◽  
pp. 5231-5244
Author(s):  
A.N. TABACHENKO
Keyword(s):  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Electric Dipole ◽  
Neutral Pion ◽  
Chiral Symmetry Breaking ◽  
Pion Photoproduction ◽  
Additional Contribution ◽  
Bag Model ◽  
Neutral Pions ◽  
Quark Masses

In the cloudy-bag model, the value of the electric dipole amplitude of the photoproduction of neutral pions off protons at threshold connected with the additional contribution from the chiral symmetry breaking interaction is evaluated. If this additional contribution is included in the amplitude of the photoproduction of neutral pions off protons at threshold, the discrepancy between the LET predictions and the measured value of the electric dipole amplitude [Formula: see text] can be resolved for the values of quark masses and bag radii which are close to the generally used values.

scholarly journals NEW ANGLE ON THE STRONG CP AND CHIRAL SYMMETRY PROBLEMS FROM A ROTATING MASS MATRIX

2009 ◽  
Vol 24 (01) ◽  
pp. 101-112 ◽  
Author(s):  
JOSÉ BORDES ◽  
HONG-MO CHAN ◽  
TSOU SHEUNG TSUN
Keyword(s):  
Chiral Symmetry ◽  
Chiral Symmetry Breaking ◽  
Mass Matrix ◽  
Energy Scale ◽  
Fermion Mass ◽  
Mass Hierarchy ◽  
Quark Masses ◽  
Chiral Transformation ◽  
The Masses ◽  
Fermion Mass Matrix

It is shown that when the mass matrix changes in orientation (i.e. rotates) in generation space for a changing energy scale, the masses of the lower generations are not given just by its eigenvalues. In particular, these masses need not be zero even when the eigenvalues are zero. In that case, the strong CP problem can be avoided by removing the unwanted θ term by a chiral transformation not in contradiction with the nonvanishing quark masses experimentally observed. Similarly, a rotating mass matrix may shed new light on the problem of chiral symmetry breaking. That the fermion mass matrix may so rotate with the scale has been suggested before as a possible explanation for up–down fermion mixing and fermion mass hierarchy, giving results in good agreement with experiment.

Calculation of chiral-symmetry breaking and pion properties as a Goldstone boson

1991 ◽  
Vol 43 (5) ◽  
pp. 1717-1725 ◽  
Author(s):  
Yuan-ben Dai ◽  
Chao-shang Huang ◽  
Dong-sheng Liu
Keyword(s):  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Chiral Symmetry Breaking ◽  
Goldstone Boson

Dynamical chiral-symmetry breaking and determination of the quark masses

1988 ◽  
Vol 38 (1) ◽  
pp. 238-278 ◽  
Author(s):  
A. Barducci ◽  
R. Casalbuoni ◽  
S. De Curtis ◽  
D. Dominici ◽  
R. Gatto
Keyword(s):  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Chiral Symmetry Breaking ◽  
Dynamical Chiral Symmetry Breaking ◽  
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.

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