Abstract
Chiral electroweak anomalies predict baryon (B) and lepton (L) violating fermion interactions, which can be dressed with large numbers of Higgs and gauge bosons. The estimation of the total B + L-violating rate from an initial two-particle state — potentially observable at colliders — has been the subject of an intense discussion, mainly centered on the resummation of boson emission, which is believed to contribute to the cross-section with an exponential function of the energy, yet with an exponent (the “holy-grail” function) which is not fully known in the energy range of interest. In this article we focus instead on the effect of fermions beyond the Standard-Model (SM) in the polynomial contributions to the rate. It is shown that B + L processes involving the new fermions have a polynomial contribution that can be several orders of magnitude greater than in the SM, for high centre-of-mass energies and light enough masses. We also present calculations that hint at a simple dependence of the holy grail function on the heavy fermion masses. Thus, if anomalous B + L violating interactions are ever detected at high-energy colliders, they could be associated with new physics.
Highlights
If anomalous B + L violating interactions are ever detected at high-energy colliders, they could be associated with new physics
From these cosmological effects, the B + L violating interactions could be potentially observable at colliders, which would involve striking signatures arising from hard processes with at least twelve SM fermions
The first quantitative estimates in ref. [23] and [24] offered striking results: the rate involving the minimum of 12 SM fermions remains exponentially small, amplitudes involving the emission of gauge bosons raise with powers of the centre-of-mass energy, and the incl√usive rate involves an exponential function of the energy, which becomes unsuppressed for s ∼ Esph
Summary
Instanton calculations rely on semiclassical (saddle-point) approximations to the path integral [19] (see e.g. [58] for a pedagogical introduction). Ψkl sector — the inverse factors of Mk∗l in (3.22) cancel the factors of Mk∗l in the instanton density CM (ρ)CI (ρ), giving no net power dependence on the mass Mkl. for a Majorana spinor Ψmm, Green functions with Nm0 m/2 fermion pairs — half the number of zero modes — have no dependence on Mm∗ m. By amputating these Green functions with ordinary propagators, one can identify the corresponding interactions in the effective Lagrangian which involve ordinary scalars and gauge bosons, aside from fermions This can be done with the aid of the following identities, valid once one includes corrections in the constrained instanton formalism [23]: Aaμ(p). With g(ρ) the running coupling as in equation (3.20)
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