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Register a new userFrom Old Symmetries to New Symmetries: Quarks, Leptons and B-L
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Authors
Rabindra N. Mohapatra
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The Baryon-Lepton difference ($B-L$) is increasingly emerging as a possible new symmetry of the weak interactions of quarks and leptons as a way to understand the small neutrino masses. There is the possibility that current and future searches at colliders and in low energy rare processes may provide evidence for this symmetry. This paper provides a brief overview of the early developments that led to B-L as a possible symmetry beyond the standard model, and also discusses some recent developments.
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Colour $SU(3)$ group is an exact symmetry of Quantum Chromodynamics, which describes strong interactions between quarks and gluons. Supplemented by two internal symmetries, $SU(2)$ and $U(1)$, it serves as the internal symmetry of the Standard Model, describing as well the electroweak interactions of quarks and leptons. The colour$SU(3)$ symmetry is exact, while two other symmetries are broken by means of the Higgs-Kibble mechanism. The three colours and fractional quarks charges with values $1/3$ and $2/3$ suggest that the cyclic group $Z_3$ may play a crucial role in quark field dynamics. In this paper we consequently apply the $Z_3$ symmetry to field multiplets describing colour quark fields. Generalized Dirac equation for coloured $12$-component spinors is introduced and its properties are discussed. Imposing $Z_3$-graded Lorentz and Poincare covariance leads to enlargement of quark fields multiplets and incorporates additional $Z_2 times Z_3$ symmetry which leads to the appearance of three generations (families) of distinct quark doublets.
The $Kepler$ $problem$ studies the planar motion of a point mass subject to a central force whose strength varies as the inverse square of the distance to a fixed attracting center. The orbits form a 3-parameter family of unparametrized plane curves, consisting of all conics sharing a focus at the attracting center. We study the geometry and symmetry properties of this family, as well as natural 2-parameter subfamilies, such as those of fixed energy or angular momentum. Our main result is that Kepler orbits form a `flat family, that is, the local diffeomorphisms of the plane preserving this family form a 7-dimensional local group, the maximum dimension possible for the symmetry group of a 3-parameter family of plane curves (a result of S. Lie). The new symmetries are different from the well-studied `hidden symmetries of the Kepler problem, acting on energy levels in the 4-dimensional phase space of the problem. Furthermore, each 2-parameter family of Kepler orbits with fixed non-zero energy admits $mathrm{PSL}_2(mathbb{R})$ as its symmetry group and coincides with one of the items of a classification due to A. Tresse (1896) of 2nd order ODEs admitting a 3-dimensional group of point symmetries. Other items on Tresse list also appear in Keplers problem by considering repulsive instead of attractive force or motion on a surface with (non-zero) constant curvature. Underlying these newly found symmetries is a duality between Keplers plane and Minkowskis 3-space parametrizing the space of Kepler orbits.
In this talk, after a short overview of the history of the discovery of tetra-quarks and penta-quarks, we will discuss a possible interpretation of such states in the framework of a 40-years-old string junction picture that allows a unified QCD description of ordinary mesons and baryons as well as multi-quark resonances.
The soft photon theorem in U(1) gauge theories with only massless charged particles has recently been shown to be the Ward identity of an infinite-dimensional asymptotic symmetry group. This symmetry group is comprised of gauge transformations which approach angle-dependent constants at null infinity. In this paper, we extend the analysis to all U(1) theories, including those with massive charged particles such as QED.
The rare decay B to K* (to K pi) mu+ mu- is regarded as one of the crucial channels for B physics since its angular distribution gives access to many observables that offer new important tests of the Standard Model and its extensions. We point out a number of correlations among various observables which will allow a clear distinction between different New Physics (NP) scenarios. Furthermore, we discuss the decay B to K* nu anti-nu which allows for a transparent study of Z penguin effects in NP frameworks in the absence of dipole operator contributions and Higgs penguin contributions. We study all possible observables in B to K* nu anti-nu and the related b to s transitions B to K nu anti-nu and B to X_s nu anti-nu in the context of the SM and various NP models.
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