Considerations on anomalous photon and Z-boson self-couplings from the Born–Infeld weak hypercharge action

Abstract

We investigate the effects of the Born–Infeld action on the Abelian sector of the electroweak model. The consequence of this approach is the emergence of anomalous couplings in the neutral sector of the Z-gauge boson and photon. These new couplings consist of quartic interactions of the photon with the Z-particle, as for example, three-photon-and-one-Z vertex. With that, we obtain the decay width of $$Z \rightarrow 3\,\gamma $$ Z → 3 γ from which we impose a bound on the Born–Infeld parameter. Other bounds are also obtained from the photon quartic couplings. Subsequently, we consider the presence of an external uniform magnetic field in connection with this Born–Infeld weak hypercharge model. The magnetic background field yields new kinematic effects, like the kinetic mixing between the photon and the Z-boson, and we obtain thereby the corresponding dispersion relations for the mixed photon-Z-particle system. Finally, we calculate the lowest-order modifications to the interaction energy for the anomalous coupling $$3\gamma -Z$$ 3 γ - Z , within the framework of the gauge-invariant but path-dependent variables formalism. Our results show that the interaction energy contains a linear term leading to the confinement of static probe charges. With the help of the potential that comes out, interparticle forces are estimated.

A Dirac-material-inspired non-linear electrodynamic model

“…Using the coefficients from (24), the refractive indices are functions of the angle θ between the magnetic background field and wave propagation direction k. In the limit β → ∞, both the refractive index go to one. Moreover, in the regime of a strong magnetic field (|B 0 | ≫ β), the first solution is n 1 ≃ 1, and the second refractive index depends only on the θ-angle…”

“…The lines intercept the horizontal axis where the birefringence is null in accord with the condition (48). Using the coefficients (24) and the physical parameters in the table I, we obtain the magnitude of the magnetic background field for the QED and the Dirac materials in which the birefringence is null : Otherwise, the condition (46) is kept for values of B 0 different from the results (50a)-(50c).…”

“…As already expressed, here we calculate the interaction energy between static point-like sources for an electrodynamics in Dirac materials under a uniform magnetic field, along the lines of refs. [20][21][22][23][24]. To do that, we compute the expectation value of the energy operator H in the physical state |Φ , which we write as H Φ .…”

The axion-photon mixing in non-linear electrodynamic scenarios

“…The measurement of the light-by-light scattering at the ATLAS Collaboration of the LHC imposes a lower bound 100 GeV on the BI parameter [34]. More stringent bounds on the BI parameter are also discussed in the electroweak model with the hypercharge sector associated with the BI model [35].…”

The axion-photon mixing in non-linear electrodynamic scenarios

“…The measurement of the light-by-light scattering at the ATLAS Collaboration of the LHC imposes a lower bound 100 GeV on the BI parameter [28]. More stringent bounds on the BI parameter also are discussed in the electroweak model with the hypercharge sector associated with the BI model [29].…”