The chirality-flow formalism for the standard model

In a recent paper we introduced the chirality-flow formalism, a method for simple and transparent calculations of Feynman diagrams based on the left- and right-chiral $$\mathfrak {sl}(2,\mathbb {C})$$ sl ( 2 , C ) nature of spacetime. While our previous work focused on massless QED and QCD at tree-level, we here extend the chirality-flow formalism to the full (tree-level) Standard Model, including massive particles and electroweak interactions – for which the W-interaction simplifies elegantly due to its chiral nature. We illustrate how values of Feynman diagrams can be immediately written down with some representative examples.

The Standard Model of Electroweak Interactions

In this chapter, we summarize the structure of the standard EW theory and specify the couplings of the intermediate vector bosons W±, Z and of the Higgs particle with the fermions and among themselves, as dictated by the gauge symmetry plus the observed matter content and the requirement of renormalizability

Gauge covariant approach to the electroweak interactions of mesons in the Nambu–Jona-Lasinio model with spin-1 states

An extended Nambu–Jona-Lasinio (NJL) model with chiral group [Formula: see text] and spin-0 and spin-1 four quark interactions is used to develop the gauge covariant approach to the diagonalization of the [Formula: see text] mixing in the presence of electroweak forces. This allows for manifestly gauge covariant description of both the non-anomalous and anomalous parts of the effective Lagrangian. It is shown that in the non-anomalous sector the theory is equivalent to the standard non-covariant approach.

Production of the triply charged leptons at the LHC

The neutrino masses can be ascribed to some operators of higher dimension than the Weinberg operator, so that the energy scale of underlying theory can be lowered to an accessible level for the ongoing or upcoming colliders. We hereby consider an interesting model in this connection where quintuplet fermions with hypercharge [Formula: see text]2 are introduced and therefore the neutrino masses are produced by dimension-11 operators. These exotic fermions can be pairly produced at the LHC via electroweak interactions and subsequently decay to multiple leptons. We simulate the relevant signal and backgrounds of the triply charged fermion in this model, and give the needed integrated luminosity to observe such a particle at the 13 TeV LHC.