arXiv subjects

Tsou Sheung Tsun

Publications and source records attributed to Tsou Sheung Tsun.

14 recordsLinked to original sources

arXiv2023

Search for new physics in semileptonic decays of K and B as implied by the g-2 anomaly in FSM

The framed standard model (FSM), constructed to explain, with some success, why there should be 3 and apparently only 3 generations of quarks and leptons in nature falling into a hierarchical mass and mixing pattern, suggests also, among other things, a scalar boson U, with mass around 17 MeV and small couplings to quarks and leptons, which might explain the g-2 anomaly reported in experiment. The U arises in FSM initially as a state in the predicted `hidden sector' with mass around 17 MeV, which mixes with the standard model (SM) Higgs $h_W$, acquiring thereby a coupling to quarks and leptons and a mass just below 17 MeV. The initial purpose of the present paper is to check whether this proposal is compatible with experiment on semileptonic decays of Ks and Bs where the U can also appear. The answer to this we find is affirmative, in that the contribution of U to new physics as calculated in the FSM remains within the experimental bounds, but only if $m_U$ lies within a narrow range just below the unmixed mass. As a result from this, one has an estimate $m_U \sim 15 - 17$ MeV for the mass of $U$, and from some further considerations the estimate $Γ_U \sim 0.02$ eV for its width, both of which may be useful for an eventual search for it in experiment. And, if found, it will be, for the FSM, not just the discovery of a predicted new particle, but the opening of a window into a whole ``hidden sector" containing at least some, perhaps ven the bulk, of the dark matter in the universe.

hep-ph↗

arXiv2021

Dualized Gravity beyond Linear Approximation

We will construct a loop space formalism for general relativity, and construct the Polyakov variables as connections for such a loop space. We will use these Polyakov variables to construct a dual theory of gravity beyond linear approximation. It will be demonstrated that this loop space duality reduces to the Hodge duality for linearized gravity. Furthermore, a loop space curvature will be constructed from this Polyakov variable. It will be shown that this loop space curvature vanishes in the absence of topological defects, and so it can be used to investigate gravitational monopoles. We will also construct the suitable monopole charge for such gravitational monopoles.

gr-qc↗

arXiv2017

Topological Defects in a Deformed Gauge Theory

In this paper, we will analyse the topological defects in a deformation of a non-abelian gauge theory using the Polyakov variables. The gauge theory will be deformed by the existence of a minimum measurable length scale in the background spacetime. We will construct the Polyakov loops for this deformed non-abelian gauge theory, and use these deformed loop space variables for obtaining a deformed loop space curvature. It will be demonstrated that this curvature will vanish if the deformed Bianchi identities are satisfied. However, it is possible that the original Bianchi identities are satisfied, but the deformed Bianchi identities are violated at the leading order in the deformation parameter, due to some topological defects. Thus, topological defects could be produced purely from a deformation of the background geometry.

hep-th↗

arXiv2015

Supersymmetric Duality in Deformed Superloop Space

In this paper, we will analyse the superloop space formalism for a four dimensional supersymmetric Yang-Mills theory in deformed superspace. We will deform the $\mathcal{N} =1$ superspace by imposing non-anticommutativity. This non-anticommutative deformation of the superspace will break half the supersymmetry of the original theory. So, this theory will have $\mathcal{N} =1/2$ supersymmetry. We will analyse the superloop space duality for this deformed supersymmetric Yang-Mills theory using the $\mathcal{N} =1/2$ superspace formalism. We will demonstrate that the sources in the original theory will become monopoles in the dual theory, and the monopoles in the original theory will become sources in the dual theory.

hep-th↗

arXiv2015

Supersymmetric Duality in Superloop Space

In this paper we constructed superloop space duality for a four dimensional supersymmetric Yang-Mills theory with $\mathcal{N} =1$ supersymmetry. This duality reduces to the ordinary loop space duality for the ordinary Yang-Mills theory. It also reduces to the Hodge duality for an abelian gauge theory. Furthermore, the electric charges, which are the sources in the original theory, appear as monopoles in the dual theory. Whereas, the magnetic charges, which appear as monopoles in the original theory, become sources in the dual theory.

hep-th↗

arXiv2014

Monopoles in Superloop Space

In this paper, we will analyse a four dimensional gauge theory with $\mathcal{N} =1$ supersymmetry in superloop space formalism. We will thus obtain an expression for the connection in the infinite-dimensional superloop space. We will then use this connection to obtain an expression for the curvature of the infinite-dimensional superloop space. We will also show that this curvature is proportional to the Bianchi identity in spacetime. Thus, in absence of a monopole this curvature will vanish. However, it will not vanish if the superloop intersects the world-line of a monopole because the Bianchi will not hold at that point.

hep-th↗

arXiv2014

Polyakov Loops for the ABJ Theory

In this paper we will first construct Polyakov loops for the ABJ theory. Then we will construct the connection and curvature in this loop space. We will also analyse certain generalization of Polyakov loops and apply them to the ABJ theory. Finally, we will use this formalism for analysing topological defects like monopoles in the ABJ theory.

hep-th↗

arXiv2001

Neutrinoless Double Beta Decay in the Dualized Standard Model

The Dualized Standard Model offers a {\it raison d'être} for 3 fermion generations and an explanation for their distinctive mass and mixing patterns, reproducing to a reasonable accuracy the empirical mixing matrix and mass spectrum for both quarks and leptons in terms of just a few parameters. With its parameters thus fixed, the result is a highly predictive framework. In particular, it is shown that it gives explicit parameter-free predictions for neutrinoless double beta decays. For $^{76}Ge$, it predicts a half-life of $10^{28}-10^{30}$ years, which satisfies the present experimental lower bound of $1.8 \times 10^{25}$ years.

hep-ph↗

arXiv1999

Coherent Muon-Electron conversion in the Dualized Standard Model

Muon-electron conversion in nuclei is considered in the framework of the Dualized Standard Model. The ratio $B_{μ-e}$ of the conversion rate to the total muon capture rate is derived, and computed for several nuclei in a parameter-free calculation using parameters previously determined in different physical contexts. The values obtained all lie within the present experimental bounds, but some are so close as to seem readily accessible to experiments already being planned. Similar considerations are applied also to muon-electron conversion in muonium but give rates many orders of magnitude below the present experiment limit.

hep-ph↗

arXiv1996

Rudiments of Dual Feynman Rules for Yang-Mills Monopoles in Loop Space

Dual Feynman rules for Dirac monopoles in Yang-Mills fields are obtained by the Wu-Yang (1976) criterion in which dynamics result as a consequence of the constraint defining the monopole as a topological obstruction in the field. The usual path-integral approach is adopted, but using loop space variables of the type introduced by Polyakov (1980). An anti-symmetric tensor potential $L_{μν}[ξ|s]$ appears as the Lagrange multiplier for the Wu-Yang constraint which has to be gauge-fixed because of the ``magnetic'' $\widetilde{U}$-symmetry of the theory. Two sets of ghosts are thus introduced, which subsequently integrate out and decouple. The generating functional is then calculated to order $g^0$ and expanded in a series in $\widetilde{g}$. It is shown to be expressible in terms of a local ``dual potential'' $\widetilde{A}_μ(x)$ found earlier, which has the same progagator and the same interaction vertex with the monopole field as those of the ordinary Yang-Mills potential $A_μ$ with a colour charge, indicating thus a certain degree of dual symmetry in the theory. For the abelian case the Feynman rules obtained here are the same as in QED to all orders in $g$, as expected by dual symmetry.

hep-th↗

arXiv1995

A Generalized Duality Symmetry for Nonabelian Yang-Mills Fields

It is shown that classical nonsupersymmetric Yang-Mills theory in 4 dimensions is symmetric under a generalized dual transform which reduces to the usual dual *-operation for electromagnetism. The parallel phase transport $\tilde{A}_μ(x)$ constructed earlier for monopoles is seen to function also as a potential in giving full description of the gauge field, playing thus an entirely dual symmetric role to the usual potential $A_μ(x)$. Sources of $A$ are monopoles of $\tilde{A}$ and vice versa, and the Wu-Yang criterion for monopoles is found to yield as equations of motion the standard Wong and Yang-Mills equations for respectively the classical and Dirac point charge; this applies whether the charge is electric or magnetic, the two cases being related just by a dual transform. The dual transformation itself is explicit, though somewhat complicated, being given in terms of loop space variables of the Polyakov type.

hep-th↗

arXiv1995

A Nonabelian Yang-Mills Analogue of Classical Electromagnetic Duality

The classic question of a nonabelian Yang-Mills analogue to electromagnetic duality is here examined in a minimalist fashion at the strictly 4-dimensional, classical field and point charge level. A generalisation of the abelian Hodge star duality is found which, though not yet known to give dual symmetry, reproduces analogues to many dual properties of the abelian theory. For example, there is a dual potential, but it is a 2-indexed tensor $T_{μν}$ of the Freedman-Townsend type. Though not itself functioning as such, $T_{μν}$ gives rise to a dual parallel transport, $\tilde{A}_μ$, for the phase of the wave function of the colour magnetic charge, this last being a monopole of the Yang-Mills field but a source of the dual field. The standard colour (electric) charge itself is found to be a monopole of $\tilde{A}_μ$. At the same time, the gauge symmetry is found doubled from say $SU(N)$ to $SU(N) \times SU(N)$. A novel feature is that all equations of motion, including the standard Yang-Mills and Wong equations, are here derived from a `universal' principle, namely the Wu-Yang (1976) criterion for monopoles, where interactions arise purely as a consequence of the topological definition of the monopole charge. The technique used is the loop space formulation of Polyakov (1980).

hep-th↗

arXiv1993

Classical and Quantum Mechanics of Dirac-like Topological Charges in Yang-Mills Fields

Most nonabelian gauge theories admit the existence of conserved and quantized topological charges as generalizations of the Dirac monopole. Their interactions are dictated by topology. In this paper, previous work in deriving classical equations of motion for these charges is extended to quantized particles described by Dirac wave functions. The resulting equations show intriguing similarities to the Yang-Mills theory. Further, although the system is not dual symmetric, its gauge symmetry is nevertheless doubled as in the abelian case from $G$ to $G \times G$, where the second $G$ has opposite parity to the first but is mediated instead by an antisymmetric second-rank tensor potential. (hep-th/yymmnnn)

hep-th↗

arXiv1993

Tensor Gauge Potentials in Loop Space Formulation of Yang-Mills Fields

Abstrac: It is shown that an antisymmetric rank-two tensor gauge potential of the type first found in string and supersymmetry theories occurs also in ordinary Yang-Mills theory when formulated in loop space, where it appears as a Lagrange multiplier for a zero curvature constraint necessary and sufficient for removing the inherent redundancy of loop variables. It is then further shown that the tensor potential acts there as the parallel `phase' transport for monopoles. (hep-th/yymmnnn)

hep-th↗