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Anomaly-free model building with algebraic geometry

Rathsman, Johan LU and Tellander, Felix (2019) In Physical Review D 100(5).
Abstract

We present a method to find anomaly-free gauged Froggatt-Nielsen type models using results from algebraic geometry. These methods should be of general interest for model building beyond the Standard Model (SM) when rational charges are required. We consider models with a gauged U(1) flavor symmetry with one flavon and two Higgs doublets and three right-handed SM singlets to provide three model examples based on different physical assumptions. The models we study are anomaly-free with no SM neutral heavy chiral fermions, anomaly-free with SM neutral heavy chiral fermions, and supersymmetric with SM neutral heavy chiral fermions where the anomalies cancel via the Green-Schwarz mechanism. With these different models we show how algebraic... (More)

We present a method to find anomaly-free gauged Froggatt-Nielsen type models using results from algebraic geometry. These methods should be of general interest for model building beyond the Standard Model (SM) when rational charges are required. We consider models with a gauged U(1) flavor symmetry with one flavon and two Higgs doublets and three right-handed SM singlets to provide three model examples based on different physical assumptions. The models we study are anomaly-free with no SM neutral heavy chiral fermions, anomaly-free with SM neutral heavy chiral fermions, and supersymmetric with SM neutral heavy chiral fermions where the anomalies cancel via the Green-Schwarz mechanism. With these different models we show how algebraic methods may be used in model building, both to reduce the charge constraints by calculation of Gröbner bases and to find rational solutions to cubic equations using Mordell-Weil generators. Using these tools we find three phenomenologically viable models explaining the observed flavor structure.

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type
Contribution to journal
publication status
published
subject
in
Physical Review D
volume
100
issue
5
article number
055032
publisher
American Physical Society
external identifiers
  • scopus:85073022474
ISSN
2470-0010
DOI
10.1103/PhysRevD.100.055032
language
English
LU publication?
yes
id
f883b73a-5ee7-459d-ad12-7fda5a2ac046
date added to LUP
2022-04-04 09:10:07
date last changed
2023-01-01 21:16:00
@article{f883b73a-5ee7-459d-ad12-7fda5a2ac046,
  abstract     = {{<p>We present a method to find anomaly-free gauged Froggatt-Nielsen type models using results from algebraic geometry. These methods should be of general interest for model building beyond the Standard Model (SM) when rational charges are required. We consider models with a gauged U(1) flavor symmetry with one flavon and two Higgs doublets and three right-handed SM singlets to provide three model examples based on different physical assumptions. The models we study are anomaly-free with no SM neutral heavy chiral fermions, anomaly-free with SM neutral heavy chiral fermions, and supersymmetric with SM neutral heavy chiral fermions where the anomalies cancel via the Green-Schwarz mechanism. With these different models we show how algebraic methods may be used in model building, both to reduce the charge constraints by calculation of Gröbner bases and to find rational solutions to cubic equations using Mordell-Weil generators. Using these tools we find three phenomenologically viable models explaining the observed flavor structure.</p>}},
  author       = {{Rathsman, Johan and Tellander, Felix}},
  issn         = {{2470-0010}},
  language     = {{eng}},
  month        = {{09}},
  number       = {{5}},
  publisher    = {{American Physical Society}},
  series       = {{Physical Review D}},
  title        = {{Anomaly-free model building with algebraic geometry}},
  url          = {{http://dx.doi.org/10.1103/PhysRevD.100.055032}},
  doi          = {{10.1103/PhysRevD.100.055032}},
  volume       = {{100}},
  year         = {{2019}},
}