Journal of High Energy Physics

, 2019:82 | Cite as

An anomaly-free atlas: charting the space of flavour-dependent gauged U(1) extensions of the Standard Model

  • B. C. Allanach
  • Joe DavighiEmail author
  • Scott Melville
Open Access
Regular Article - Theoretical Physics


Spontaneously broken, flavour-dependent, gauged U(1) extensions of the Standard Model (SM) have many phenomenological uses. We chart the space of solutions to the gauge anomaly cancellation equations in such extensions, for both the SM chiral fermion content and the SM plus (up to) three right-handed neutrinos (SMνR). Methods from Diophantine analysis allow us to efficiently index the solutions arithmetically, and produce the complete solution space in particular cases. In order to solve the general case, we build a computer program which cycles through possible U(1) charge assignments, providing all solutions for charges up to some pre-defined maximum absolute charge. Lists of anomaly-free U(1) charge assignments result, which corroborate the results of our Diophantine analysis. We make these lists, which may be queried for further desirable properties, publicly available. This previously uncharted space of anomaly-free charge assignments has been little explored until now, paving the way for future model building and phenomenological studies.


Beyond Standard Model Effective Field Theories Quark Masses and SM Parameters 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.DAMTPUniversity of CambridgeCambridgeU.K.
  2. 2.Emmanuel CollegeUniversity of CambridgeCambridgeU.K.

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