Anomaly cancellation with an extra gauge boson

Abstract

Many extensions of the Standard Model include an extra gauge boson, whose couplings to fermions are constrained by the requirement that anomalies cancel. We find a general solution to the resulting diophantine equations in the plausible case where the chiral fermion content is that of the Standard Model plus 3 right-handed neutrinos.

A $ν$ Supersymmetric Anomaly-free Atlas

“…The first mirrors the method of Ref. [18] which exploits a special point of PQ 19 that is a 'double point' of both the cubic and quadratic. A second new method is presented here.…”

“…Similar geometric methods were employed to find an analytic solution to the more difficult problem of sm ⊕ u(1) anomaly-free charge assignments in the specific case of SM fermion content, plus three righthanded (RH) neutrinos (i.e. SM-singlet chiral fermion fields which may carry X charge) [18]. The number of solutions is formally infinite, 3 unlike the case of semi-simple SM extensions with identical fermionic field content, where there is a list of 340 [20].…”

“…In case a height larger than 10 is required, we will also provide a general analytic solution to the anomaly cancellation conditions. This relies on using the same geometric framing in which the SM-plus-3 RH neutrino case was solved [18]; we take the opportunity to demonstrate a new technique to solve such problems, although the technique used in Ref. [18] would also have worked.…”

“…This relies on using the same geometric framing in which the SM-plus-3 RH neutrino case was solved [18]; we take the opportunity to demonstrate a new technique to solve such problems, although the technique used in Ref. [18] would also have worked.…”

Anomaly-free $U(1)^m$ extensions of the Standard Model

“…Then a general solution was found for the first two equations [20], and for this solution, it was given a geometric interpretation [25]. While the present work was being written, the full system of equations was solved using this geometric method [26]. Other aspects of this system of equations including (3) where also explored [21,27,28].…”