Testing the mechanism of lepton compositeness

Abstract

Strict gauge invariance requires that physical left-handed leptons are actually bound states of the elementary left-handed lepton doublet and the Higgs field within the standard model. That they nonetheless behave almost like pure elementary particles is explained by the Fr"ohlich-Morchio-Strocchi mechanism. Using lattice gauge theory, we test and confirm this mechanism for fermions. Though, due to the current inaccessibility of non-Abelian gauged Weyl fermions on the lattice, a model which contains vectorial leptons but which obeys all other relevant symmetries has been simulated.

The Bloch Nordsieck (BN) restoration for ll ̅ → qq ̅

“…Assuming a fully exclusive measurement, however, it is safe to assume that the Higgs fields in (5) act primarily as spectators. This is also supported by investigations of the substructure of the bound state (2) [6,9]. This is akin to the situation in hadron scattering where the other partons are also spectators.…”

“…Bloch-Nordsieck restoration in ¯ → ¯ Franziska Reiner Thus, to this order the masses of both doublet members are the ones of the elementary electron and neutrino. This mechanism is general, and has been extensively tested on the lattice [5], especially also for fermions [6], and is supported non-perturbatively. Furthermore, this expansion can be systematically put into a perturbative framework [7].…”

Gauge Symmetries, Symmetry Breaking, and Gauge-Invariant Approaches

“…The above mentioned problem in the 𝜇 2 > 0 phase is avoided in the alternative invariant FMS approach to the model, which is also the one for which serious perturbative and lattice calculations have been done [e. g. Afferrante, Maas, Sondenheimer, and Törek (2021); Dudal et al (2020);Dudal, van Egmond, et al (2021); Maas (2019); Maas and Sondenheimer (2020); Maas and Törek (2018); Sondenheimer (2020)], so is most easily weighted against the standard literature. It has also the advantage of being easily generalisable to SU (𝑛) gauge theories.…”

Bloch-Nordsieck restoration in llbar -> qqbar

“…Thus, to this order the masses of both doublet members are the ones of the elementary electron and neutrino. This mechanism is general, and has been extensively tested on the lattice [5], especially also for fermions [6], and is supported non-perturbatively. Furthermore, this expansion can be systematically put into a perturbative framework [7].…”