scholarly journals Lorentz invariant CPT breaking in the Dirac equation

2017 ◽  
Vol 32 (09) ◽  
pp. 1741014 ◽  
Author(s):  
Kazuo Fujikawa ◽  
Anca Tureanu
Keyword(s):  
Dirac Equation ◽  
Explicit Construction ◽  
Mass Splitting ◽  
Negative Energy ◽  
Coordinate Space ◽  
Step Functions ◽  
The Standard Model ◽  
Breaking Mechanism ◽  
Mass Degeneracy ◽  
Breaking Term

If one modifies the Dirac equation in momentum space to [Formula: see text], the symmetry of positive and negative energy eigenvalues is lifted by [Formula: see text] for a small [Formula: see text]. The mass degeneracy of the particle and antiparticle is thus lifted in a Lorentz invariant manner since the combinations [Formula: see text] with step functions are manifestly Lorentz invariant. We explain an explicit construction of this CPT breaking term in coordinate space, which is Lorentz invariant but nonlocal at the distance scale of the Planck length. The application of this Lorentz invariant CPT breaking mechanism to the possible mass splitting of the neutrino and antineutrino in the Standard Model is briefly discussed.

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.

scholarly journals An explicit construction of the dimension-9 operator basis in the standard model effective field theory

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Yi Liao ◽  
Xiao-Dong Ma
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Effective Field Theory ◽  
Equations Of Motion ◽  
Baryon Number ◽  
Explicit Construction ◽  
Effective Field ◽  
Starting Point ◽  
The Standard Model ◽  
Symmetry Relations

Abstract We investigate systematically dimension-9 operators in the standard model effective field theory which contains only standard model fields and respects its gauge symmetry. With the help of the Hilbert series approach to classifying operators according to their lepton and baryon numbers and their field contents, we construct the basis of operators explicitly. We remove redundant operators by employing various kinematic and algebraic relations including integration by parts, equations of motion, Schouten identities, Dirac matrix and Fierz identities, and Bianchi identities. We confirm counting of independent operators by analyzing their flavor symmetry relations. All operators violate lepton or baryon number or both, and are thus non-Hermitian. Including Hermitian conjugated operators there are $$ {\left.384\right|}_{\Delta B=0}^{\Delta L=\pm 2}+{\left.10\right|}_{\Delta B=\pm 2}^{\Delta L=0}+{\left.4\right|}_{\Delta B=\pm 1}^{\Delta L=\pm 3}+{\left.236\right|}_{\Delta B=\pm 1}^{\Delta L=\mp 1} $$ 384 Δ B = 0 Δ L = ± 2 + 10 Δ B = ± 2 Δ L = 0 + 4 Δ B = ± 1 Δ L = ± 3 + 236 Δ B = ± 1 Δ L = ∓ 1 operators without referring to fermion generations, and $$ {\left.44874\right|}_{\Delta B=0}^{\Delta L=\pm 2}+{\left.2862\right|}_{\Delta B=\pm 2}^{\Delta L=0}+{\left.486\right|}_{\Delta B=\pm 1}^{\Delta L=\pm 3}+{\left.42234\right|}_{\Delta B=\mp 1}^{\Delta L=\pm 1} $$ 44874 Δ B = 0 Δ L = ± 2 + 2862 Δ B = ± 2 Δ L = 0 + 486 Δ B = ± 1 Δ L = ± 3 + 42234 Δ B = ∓ 1 Δ L = ± 1 operators when three generations of fermions are referred to, where ∆L, ∆B denote the net lepton and baryon numbers of the operators. Our result provides a starting point for consistent phenomenological studies associated with dimension-9 operators.

scholarly journals Characters and group invariant polynomials of (super)fields: road to “Lagrangian”

2020 ◽  
Vol 80 (10) ◽  
Author(s):  
Upalaparna Banerjee ◽  
Joydeep Chakrabortty ◽  
Suraj Prakash ◽  
Shakeel Ur Rahaman
Keyword(s):  
Standard Model ◽  
Explicit Construction ◽  
Effective Field ◽  
Compact Groups ◽  
Group Invariant ◽  
Fundamental Particles ◽  
Quantum Numbers ◽  
The Standard Model ◽  
Mass Dimension ◽  
Complete Set

AbstractThe dynamics of the subatomic fundamental particles, represented by quantum fields, and their interactions are determined uniquely by the assigned transformation properties, i.e., the quantum numbers associated with the underlying symmetry of the model under consideration. These fields constitute a finite number of group invariant operators which are assembled to build a polynomial, known as the Lagrangian of that particular model. The order of the polynomial is determined by the mass dimension. In this paper, we have introduced an automated $${\texttt {Mathematica}}^{\tiny \textregistered }$$ Mathematica ® package, GrIP, that computes the complete set of operators that form a basis at each such order for a model containing any number of fields transforming under connected compact groups. The spacetime symmetry is restricted to the Lorentz group. The first part of the paper is dedicated to formulating the algorithm of GrIP. In this context, the detailed and explicit construction of the characters of different representations corresponding to connected compact groups and respective Haar measures have been discussed in terms of the coordinates of their respective maximal torus. In the second part, we have documented the user manual of GrIP that captures the generic features of the main program and guides to prepare the input file. We have attached a sub-program CHaar to compute characters and Haar measures for $$SU(N), SO(2N), SO(2N+1), Sp(2N)$$ S U ( N ) , S O ( 2 N ) , S O ( 2 N + 1 ) , S p ( 2 N ) . This program works very efficiently to find out the higher mass (non-supersymmetric) and canonical (supersymmetric) dimensional operators relevant to the effective field theory (EFT). We have demonstrated the working principles with two examples: the standard model (SM) and the minimal supersymmetric standard model (MSSM). We have further highlighted important features of GrIP, e.g., identification of effective operators leading to specific rare processes linked with the violation of baryon and lepton numbers, using several beyond standard model (BSM) scenarios. We have also tabulated a complete set of dimension-6 operators for each such model. Some of the operators possess rich flavour structures which are discussed in detail. This work paves the way towards BSM-EFT.

scholarly journals THE MASS OF THE NEUTRINOS

2010 ◽  
Vol 19 (11) ◽  
pp. 2285-2292
Author(s):  
B. G. SIDHARTH
Keyword(s):  
Dirac Equation ◽  
Standard Model ◽  
Special Relativity ◽  
Lorentz Invariance ◽  
The Standard Model

In the theory of the Dirac equation and in the standard model, the neutrino is massless. Both these theories use Lorentz invariance. In modern approaches however, spacetime is no longer smooth, and this modifies special relativity. We show how such a modification throws up the mass of the neutrino.

scholarly journals Quantum backflow in solutions to the Dirac equation of the spin-1 2 free particle

2018 ◽  
Vol 33 (32) ◽  
pp. 1850186 ◽  
Author(s):  
Hong-Yi Su ◽  
Jing-Ling Chen
Keyword(s):  
Quantum Mechanics ◽  
Dirac Equation ◽  
Relativistic Particle ◽  
Relativistic Quantum ◽  
Free Particle ◽  
Negative Energy ◽  
Dirac Particle ◽  
Relativistic Quantum Mechanics ◽  
Probability Current ◽  
Negative Probability

It was known that a free, non-relativistic particle in a superposition of positive momenta can, in certain cases, bear a negative probability current — hence termed quantum backflow. Here, it is shown that more variations can be brought about for a free Dirac particle, particularly when negative-energy solutions are taken into account. Since any Dirac particle can be understood as an antiparticle that acts oppositely (and vice versa), quantum backflow is found to arise in the superposition (i) of a well-defined momentum but different signs of energies, or more remarkably (ii) of different signs of both momenta and energies. Neither of these cases has a counterpart in non-relativistic quantum mechanics. A generalization by using the field-theoretic formalism is also presented and discussed.

scholarly journals Neutrino mass generation from the perspective of presymmetry

2019 ◽  
Vol 34 (34) ◽  
pp. 1950284
Author(s):  
Ernesto A. Matute
Keyword(s):  
Topological Charge ◽  
Mass Splitting ◽  
High Scale ◽  
Sterile Neutrinos ◽  
Mass Generation ◽  
The Standard Model ◽  
Induced Charge ◽  
Neutrino Mass Generation ◽  
Gauge Anomalies ◽  
Topological Charges

The Standard Model (SM) with one right-handed neutrino per generation is revisited with presymmetry being the global [Formula: see text] symmetry of an electroweak theory of leptons and quarks with initially postulated symmetric fractional charges. The cancellation of gauge anomalies and the non-perturbative normalization of lepton charges proceed through the mixing of local and topological charges, the global [Formula: see text] measuring the induced charge associated with a unit of topological charge, and the mathematical replacement of the original fractional charges with the experimentally observed ones. The [Formula: see text] symmetry of the SM with Dirac neutrinos is seen as a residual presymmetry. High-scale and low-scale seesaw mechanisms proposed to explain the mass of neutrinos are examined from the perspective of presymmetry, be they of Majorana or pseudo-Dirac type. We find that the tiny mass splitting in pseudo-Dirac neutrinos and the mass of heavy neutrinos ride on the opposite ends of the seesaw. We show that pseudo-Dirac neutrinos contain extra sterile neutrinos with imprints of presymmetry and for heavy ones we get constraints favoring the low-scale linear seesaw over the inverse variant.

scholarly journals Neutrino–antineutrino mass splitting in the Standard Model and baryogenesis

2015 ◽  
Vol 743 ◽  
pp. 39-45 ◽  
Author(s):  
Kazuo Fujikawa ◽  
Anca Tureanu
Keyword(s):  
Standard Model ◽  
Mass Splitting ◽  
The Standard Model

scholarly journals ENHANCED GLUINO BOX CONTRIBUTION TO ∊′/∊ IN SUSY

2001 ◽  
Vol 16 (supp01b) ◽  
pp. 675-679 ◽  
Author(s):  
MATTHIAS NEUBERT
Keyword(s):  
Standard Model ◽  
Neutral Current ◽  
Mass Splitting ◽  
The Standard Model ◽  
Order Of Magnitude ◽  
The Right ◽  
Moderate Mass

We show that in supersymmetric extensions of the Standard Model gluino box diagrams can yield a large CP-violating [Formula: see text] contribution to [Formula: see text] flavor-chaging neutral current processes, which feeds into the I=2 isospin amplitude in K→ππ decays. This contribution only requires moderate mass splitting between the right-handed squarks ũR and [Formula: see text], and persists for squark masses of order 1 TeV. Taking into account current bounds on Im [Formula: see text] from [Formula: see text] mixing, the resulting contribution to ∊′/∊ could naturally be an order of magnitude larger than the measured value.

scholarly journals DSMesons in Asymmetric Hot and Dense Hadronic Matter

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Divakar Pathak ◽  
Amruta Mishra
Keyword(s):  
Heavy Ion ◽  
Mass Splitting ◽  
Hadronic Matter ◽  
Isospin Asymmetry ◽  
Baryonic Density ◽  
Significant Difference ◽  
Strangeness Content ◽  
Mass Degeneracy ◽  
The Masses ◽  
Ion Collision

The in-medium properties ofDSmesons are investigated within the framework of an effective hadronic model, which is a generalization of a chiralSU(3)model, toSU(4), in order to study the interactions of the charmed hadrons. In the present work, theDSmesons are observed to experience net attractive interactions in a dense hadronic medium, hence reducing the masses of theDS+andDS-mesons from the vacuum values. While this conclusion holds in both nuclear and hyperonic media, the magnitude of the mass drop is observed to intensify with the inclusion of strangeness in the medium. Additionally, in hyperonic medium, the mass degeneracy of theDSmesons is observed to be broken, due to opposite signs of the Weinberg-Tomozawa interaction term in the Lagrangian density. Along with the magnitude of the mass drops, the mass splitting betweenDS+andDS-mesons is also observed to grow with an increase in baryonic density and strangeness content of the medium. However, all medium effects analyzed are found to be weakly dependent on isospin asymmetry and temperature. We discuss the possible implications emanating from this analysis, which are all expected to make a significant difference to observables in heavy ion collision experiments, especially the upcoming Compressed Baryonic Matter (CBM) experiment at the future Facility for Antiproton and Ion Research (FAIR), GSI, where matter at high baryonic densities is planned to be produced.

Explanation of the Quantum-Mechanical Particle-Wave Duality through the Emission of Watt-Less Gravitational Waves by the Dirac Equation

2016 ◽  
Vol 71 (1) ◽  
pp. 53-57 ◽  
Author(s):  
Friedwardt Winterberg
Keyword(s):  
Gravitational Field ◽  
Dirac Equation ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Negative Energy ◽  
Quantum Mechanical ◽  
Field Equations ◽  
Negative Mass ◽  
Pilot Wave ◽  
Extended Theories Of Gravity

AbstractAn explanation of the quantum-mechanical particle-wave duality is given by the watt-less emission of gravitational waves from a particle described by the Dirac equation. This explanation is possible through the existence of negative energy, and hence negative mass solutions of Einstein’s gravitational field equations. They permit to understand the Dirac equation as the equation for a gravitationally bound positive–negative mass (pole–dipole particle) two-body configuration, with the mass of the Dirac particle equal to the positive mass of the gravitational field binding the positive with the negative mass particle, and with the mass particles making a luminal “Zitterbewegung” (quivering motion), emitting a watt-less oscillating positive–negative space curvature wave. It is shown that this thusly produced “Zitterbewegung” reproduces the quantum potential of the Madelung-transformed Schrödinger equation. The watt-less gravitational wave emitted by the quivering particles is conjectured to be de Broglie’s pilot wave. The hypothesised connection of the Dirac equation to gravitational wave physics could, with the failure to detect gravitational waves by the LIGO antennas and pulsar timing arrays, give a clue to extended theories of gravity, or a correction of astrophysical models for the generation of such waves.

Sign in / Sign up

Export Citation Format

Share Document