Fernandez Navarro, Mario
(2024)
Theories of flavour from the Planck scale to the electroweak scale.
*University of Southampton, Doctoral Thesis*, 308pp.

## Abstract

The flavour puzzle remains as one of the most intriguing enigmas of particle physics. *A priori*, there is no apparent reason for the existence of three identical families of fundamental fermions in Nature. Moreover, the high number of free parameters in the flavour sector, along with their particular hierarchical patterns, suggest the existence of new physics that provide a dynamical explanation for the flavour structure of the Standard Model: such a theory describing the complicated flavour sector in terms of simple and natural principles is called a *theory of flavour*.

In this thesis, we propose and study theories of flavour which generically hint to a multi-scale origin of flavour. First we explore the idea of fermiophobic models, where the fermion mass hierarchies and the smallness of quark mixing are explained via the mechanism of messenger dominance. The general idea is that the chiral fermions of the Standard Model are uncharged under (part of) an extended gauge symmetry, which also forbids the presence of Yukawa couplings for chiral fermions. These are generated effectively due to the presence of hierarchically heavy messengers, including vector-like fermions and/or heavy Higgs doublets. The heavy messengers may also induce effective couplings for the chiral fermions to TeV-scale gauge bosons associated to the spontaneous breaking of the extended symmetry, leading to a predictive phenomenology connected to the origin of flavour hierarchies.

First we apply this idea to an extension ofthe Standard Model by a *U(1)'* local abelian factor, where we seek to provide a significant contribution to the anomalous magnetic moment of the muon via exchange of a heavy *Z'∼*(**1**,**1**,0) boson, and we find an interesting correlation with a suppression of the Higgs decay to two photons. Then we apply the same idea to a twin Pati-Salam symmetry which provides a TeV-scale vector leptoquark *U _{1}∼*(

**3**,

**1**,2/3) that can explain the so-called

*B*-physics anomalies. We find that this model can be tested due to the correlated enhancement of key low-energy observables, and also via direct production of the new heavy degrees of freedom at the LHC.

Secondly, we leave behind the ideas of messenger dominance and fermiophobic models to study the possibility that the Standard Model originates from a non-universal gauge theory in the ultraviolet. We argue that one of the most simple ways to achieve this is by assigning a separate gauge hypercharge to each fermion family at high energies, spontaneously broken down to the usual weak hypercharge which is the diagonal subgroup. This simple framework denoted as *tri-hypercharge *avoids the family replication of the Standard Model, and could be the first step towards a deep non-universal gauge structure in the ultraviolet. If the Higgs doublet(s) only carries third family hypercharge, then only third family renormalisable Yukawa couplings are allowed by the gauge symmetry. However, non-renormalisable Yukawa couplings for the light families may be induced by the high scale scalar fields which break the three hypercharges down to the usual weak hypercharge, providing an explanation for fermion mass hierarchies and the smallness of quark mixing. Interestingly, in order to explain neutrino mixing, it is useful to introduce right-handed neutrinos which carry non-zero hypercharges (although their sum must vanish), which then turn out to get Majorana masses at the lowest scale of symmetry breaking, that could be as low as a few TeV. In fact, we find that the model has a rich phenomenology via *Z'* bosons if the new physics scales are relatively low: from flavour-violating observables to LHC physics and electroweak precision observables.

Finally, we propose a gauge unified origin for gauge non-universal frameworks such as the aforementioned tri-hypercharge theory. The model consists on assigning a separate *SU(5)* group to each fermion family. However, assuming that the three *SU(5)* groups are related by a cyclic permutation symmetry Z_{3}, then the model is described by a single gauge coupling in the ultraviolet, despite *SU(5) ^{3}* being a non-simple group. First, we show a general

*SU(5)*

^{3}*tri-unification*framework where gauge non-universal theories of flavour may be embedded, and secondly we construct a minimal tri-hypercharge example which can account for all the quark and lepton (including neutrino) masses and mixing parameters, with the five gauge couplings of the tri-hypercharge group unifying at the GUT scale into a single gauge coupling associated to the cyclic

*SU(5)*group, and we study the implications for the stability of the proton in such a setup.

^{3}**PhD_Thesis_MarioFernandezNavarro_PDFA - Version of Record**

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