Abstract
On extending the Standard Model (SM) Lagrangian, through a non-linear Born–Infeld (BI) hypercharge term with a parameter β (of dimensions of [mass] 2 ), a finite energy monopole solution was claimed by Arunasalam and Kobakhidze. We report on a new class of solutions within this framework that was missed in the earlier analysis. This new class was discovered on performing consistent analytic asymptotic analyses of the nonlinear differential equations describing the model; the shooting method used in numerical solutions to boundary value problems for ordinary differential equations is replaced in our approach by a method that uses diagonal Padé approximants. Our work uses the ansatz proposed by Cho and Maison to generate a static and spherically-symmetric monopole with finite energy and differs from that used in the solution of Arunasalam and Kobakhidze. Estimates of the total energy of the monopole are given, and detection prospects at colliders are briefly discussed.
Highlights
It is a curious fact that Maxwell initially wrote as one of his eponymous equations: ~ = μ H. ~ curl A (1)~ is the electromagnetic vector potential; and μ is the ~ AThe magnetic field is denoted by H;~ is a non-singular vector, : magnetic permeability
The work of ‘t Hooft and Polyakov [2,3] provides a detailed paradigm on magnetic monopole soliton solutions, which arise in quantum field theories with simple gauge groups (such as SU (3) and grand unified groups SU (5)), under spontaneous symmetry breaking
We have discussed some novel semi-analytic monopole solutions in the framework of the phenomenological Lagrangian (10), which constitutes an extension of the Standard Model (SM) by a non-linear Born–Infeld Lagrangian for the hypercharge sector only
Summary
It is a curious fact that Maxwell initially wrote as one of his eponymous equations:. The work of ‘t Hooft and Polyakov [2,3] provides a detailed paradigm on magnetic monopole soliton solutions, which arise in quantum field theories with simple gauge groups (such as SU (3) and grand unified groups SU (5)), under spontaneous symmetry breaking In such solutions, Dirac’s quantisation arises as a topological property of mappings associated with the solution and not because of a Dirac string. The full standard model gauge group admits such non-linear extensions, it suffices for our phenomenological purposes to restrict our attention only to the Born–Infeld extension of the hypercharge sector and seek monopole solutions of the CM type, following Arunasalam and Kobakhidze in Ref.
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