Gauge and Higgs boson masses revisited
Paulo Roberto Silva
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Abstract
In this work, the mass of the Higgs boson is calculated, its comparison with the W and Z boson masses established, and the μ 2 and λ parameters of the Higgs potential are fixed. This is done by looking at the ground states of three and four dimensional harmonic oscillators, and getting inferences from the strong black hole as well the MIT bag model formalisms. An "exact" relationship linking the masses of these bosons, advanced by DNA Forrester, is also taken in account. The Standard Model (SM) of Particle Physics is a theory describing the visible part of the stuff of the universe [1]. The SM Lagrangian contains fermionic fields, which excitations are quarks and leptons, and bosonic fields the mediators of the interactions and having as excitations the photon, W and Z bosons, and gluons. However, in order to give leptons and quarks (current) masses, and also to give masses to the W and Z bosons of the weak interactions, these fermionic and bosonic fields must interact (couple) with another spin-zero field:-the Higgs field. The quantum excitation of the Higgs field produces a Higgs boson (please see: "Higgs boson" in Wikipedia [2], and references cited therein). The Higgs mechanism, indeed also proposed by Robert Brout and François Englert; Gerald Guralnik, C. Richard Hagen, and Tom Kibble; besides Peter Higgs himself, gives particles their masses (current masses in the quark case).[3,4,5].The Higgs mechanism works through the process called spontaneous symmetry breaking [6]. As was pointed out by Wilczek [7], the mass of the Higgs particle itself is not explained in the theory, but appears as a free parameter. Here we are going to focus on the Higgs and Electroweak sectors of the SM.
Key takeaways
- In this work dealing with the estimate of the Higgs mass and its relationship with the masses of W and Z bosons, we take in account the ground states of harmonic oscillators considered in both three (3-d)and four (4-d) dimensions.
- We start with a Higgs potential as a function of a scalar field ϕ, and write
- Making the requirement that the vacuum of this (4-d) HO coincides with the value of ϕ 0 = v, where the Higgs potential acquires its minimum, we can write
- We propose that the mass term squared (appearing in the coefficient of the ϕ 2 -term in the Higgs potential) is provided by the square of the ground state energy of this 3-d HO.
- The insertion of μ, given by (12) into the vacuum expectation value (VEV) of the Higgs field, yields v = 2√2 μ = (6√2 ∕ π) M Z .
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