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The flavour puzzle remains as one of the most intriguing enigmas of particle physics. 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 and messenger dominance, where the chiral fermions of the Standard Model are uncharged under (part of) an extended gauge symmetry, which also forbids 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. Simultaneously, this mechanism generates effective couplings of chiral fermions to the gauge bosons of the extended symmetry, leading to a predictive phenomenology connected to the origin of flavour hierarchies. We present two models of this kind, based on gauge $U(1)$ and twin Pati-Salam symmetries, that have implications for low energy flavour anomalies. Secondly, we study the framework of flavour deconstruction, where the Standard Model emerges from a non-universal gauge theory that contains a separate gauge factor for each fermion family. We argue that one of the most simple ways to achieve this is by assigning a separate gauge hypercharge to each fermion family, denoted as the "tri-hypercharge" theory. If the SM Higgs only carries third family hypercharge, then only the third family is massive at renormalisable level, and light families get their mass from higher dimensional operators. Finally, we propose a gauge unified origin for gauge non-universal frameworks such as the aforementioned tri-hypercharge theory. The model assigns a separate $SU(5)$ group to each fermion family. However, assuming that the three $SU(5)$ groups are related by a cyclic permutation symmetry $\mathbb{Z}_{3}$, then the model is described by a single gauge coupling in the ultraviolet, despite $SU(5)^{3}$ being a non-simple group., Comment: PhD thesis: https://eprints.soton.ac.uk/488650 . Comments and typos spotted are welcome

The tri-hypercharge proposal introduces a separate gauged weak hypercharge assigned to each fermion family as the origin of flavour. This is arguably one of the simplest setups for building "gauge non-universal theories of flavour" or "flavour deconstructed theories". In this paper we propose and study two minimal but ultraviolet complete and renormalisable tri-hypercharge models. We show that both models, which differ only by the heavy messengers that complete the effective theory, are able to explain the observed patterns of fermion masses and mixings (including neutrinos) with all fundamental coefficients being of $\mathcal{O}(1)$. In fact, both models translate the complicated flavour structure of the Standard Model into three simple physical scales above electroweak symmetry breaking, completely correlated with each other, that carry meaningful phenomenology. In particular, the heavy messenger sector determines the origin and size of fermion mixing, which controls the size and nature of the flavour-violating currents mediated by the two heavy $Z'$ gauge bosons of the theory. The phenomenological implications of the two minimal models are compared. In both models the lightest $Z'$ remains discoverable in dilepton searches at the LHC Run 3., Comment: 23 pages + Appendix, 2 figures. v2: Minor discussions added, conclusions unchanged. Published in JHEP

In this paper we discuss $SU(5)^{3}$ with cyclic symmetry as a possible grand unified theory (GUT). The basic idea of such a tri-unification is that there is a separate $SU(5)$ for each fermion family, with the light Higgs doublet(s) arising from the third family $SU(5)$, providing a basis for charged fermion mass hierarchies. $SU(5)^{3}$ tri-unification reconciles the idea of gauge non-universality with the idea of gauge coupling unification, opening the possibility to build consistent non-universal descriptions of Nature that are valid all the way up to the scale of grand unification. As a concrete example, we propose a grand unified embedding of the tri-hypercharge model $U(1)_Y^3$ based on an $SU(5)^{3}$ framework with cyclic symmetry. We discuss a minimal tri-hypercharge example which can account for all the quark and lepton (including neutrino) masses and mixing parameters. We show that it is possible to unify the many gauge couplings into a single gauge coupling associated with the cyclic $SU(5)^{3}$ gauge group, by assuming minimal multiplet splitting, together with a set of relatively light colour octet scalars. We also study proton decay in this example, and present the predictions for the proton lifetime in the dominant $e^+\pi^0$ channel., Comment: 19 pages + Appendix, 7 figures. v4: minor changes to scalar reps, conclusions unchanged

Several new physics scenarios that address anomalies in $B$-physics predict an enhancement of $b \rightarrow s \tau \tau$ with respect to its Standard Model prediction. Such scenarios necessarily imply modifications of the lifetime ratio $\tau_{B_{s}}/\tau_{B_{d}}$ and the lifetime difference $\Delta\Gamma_{s}$. In this work, we explore indirect bounds provided by these observables over new physics scenarios. We also estimate future projections, showing that future experimental and theoretical improvements on both $\tau_{B_{s}}/\tau_{B_{d}}$ and $\Delta\Gamma_{s}$ have the potential to provide bounds competitive with those directly extracted from $b\rightarrow s \tau \tau$ transitions. After performing a model-independent analysis, we apply our results to the particular case of leptoquark mediators proposed to address the $R_{D^{(*)}}$ anomalies., Comment: 12 pages + Appendix, 4 Figures. v2: Minor discussions added, typos corrected, conclusions unchanged. Version accepted in EPJC

We discuss a theory of flavour which can simultaneously explain and connect the origin of the Standard Model flavour hierarchies with the $U_{1}(\mathbf{3},\mathrm{\mathbf{1},2/3})$ leptoquark explanation of the $B$-decay flavour anomalies. First, we motivate the vector leptoquark $U_{1}$ as an excellent mediator to address the updated picture of $B$-anomalies. Secondly, we introduce the Twin Pati-Salam theory of flavour, which naturally provides a low scale 4321 gauge group with a TeV scale $U_{1}$. We show that both the couplings of $U_{1}$ to SM fermions and the effective SM Yukawa couplings arise from the same physics, naturally providing a pattern of dominantly left-handed $U_{1}$ couplings as most preferred by current data. Finally, we discuss the most promising signals at low energy processes that can test the model in the near future., Comment: 6 pages, 2 figures, contribution to the 2023 Electroweak session of the 57th Rencontres de Moriond

We propose a tri-hypercharge (TH) embedding of the Standard Model (SM) in which a separate gauged weak hypercharge is associated with each fermion family. In this way, every quark and lepton multiplet carries unique gauge quantum numbers under the extended gauge group, providing the starting point for a theory of flavour. If the Higgs doublets only carry third family hypercharge, then only third family renormalisable Yukawa couplings are allowed. However, non-renormalisable Yukawa couplings may be induced by the high scale Higgs fields (hyperons) which break the three hypercharges down to the SM hypercharge, providing an explanation for fermion mass hierarchies and the smallness of CKM quark mixing. Following a similar methodology, we study the origin of neutrino masses and mixing in this model. Due to the TH gauge symmetry, the implementation of a seesaw mechanism naturally leads to a low scale seesaw, where the right-handed neutrinos in the model may be as light as the TeV scale. We present simple examples of hyperon fields which can reproduce all quark and lepton (including neutrino) masses and mixing. After a preliminary phenomenological study, we conclude that one of the massive $Z'$ bosons can be as light as a few TeV, with implications for flavour-violating observables, LHC physics and electroweak precision observables., Comment: 22 pages + Appendix, 2 figures. v2: Minor discussions added, conclusions unchanged. Published in JHEP

In this manuscript, based on arXiv:2209.00276, I present a model which can simultaneously explain and connect the flavour hierarchies of the Standard Model with flavour anomalies in $B$-physics. I will briefly introduce the model and highlight the main features, including a common origin of Yukawa couplings and vector leptoquark $U_{1}$ couplings to Standard Model fermions. A GIM-like mechanism allows for large leptoquark couplings which can explain the $B$-anomalies, while protecting from the most dangerous FCNCs that could be mediated by a heavy coloron and $Z'$. Finally, I will highlight some of the most promising signals at low energy processes which can test the model in the upcoming future. The analysis has been updated with the late 2022 measurements of $R_{K^{(*)}}$ by LHCb., Comment: 8 pages + references, 4 figures, Contribution to the Proceedings of the 8th Symposium on Prospects in the Physics of Discrete Symmetries (DISCRETE 2022), 7-11 November 2022, Baden-Baden, Germany, v2: A few references added

We perform a comprehensive phenomenological analysis of the twin Pati-Salam theory of flavour, focussing on the parameter space relevant for interpreting the $B$-anomalies via vector leptoquark $U_1$ exchange. This model provides a very predictive framework in which the $U_1$ couplings and the Yukawa couplings find a common origin via mixing of chiral quarks and leptons with vector-like fermions, providing a direct link between the $B$-anomalies and the fermion masses and mixing. We propose and study a simplified model with three vector-like fermion families, in the massless first family approximation, and show that the second and third family charged fermion masses and mixings and the $B$-anomalies can be simultaneously explained and related. The model has the proper flavour structure to be compatible with all low-energy observables, and leads to predictions in promising observables such as $\tau\rightarrow3\mu$, $\tau\rightarrow\mu\gamma$ and $B\rightarrow K^{(*)}\nu\bar{\nu}$ at Belle II and LHCb. The model also predicts a rich spectrum of TeV scale gauge bosons and vector-like fermions, all accessible to the LHC. In this updated version we have included an extended analysis considering the new 2022 LHCb data on $R_{K^{(*)}}$, which has slightly shifted the preferred parameter space with respect to the 2021 case. The model can still explain the $R_{D^{(*)}}$ anomalies at 1$\sigma$ in a narrow window, however we expect small deviations from the SM on the $R_{K^{(*)}}$ ratios, to be tested in the future via more precise measurements by the LHCb collaboration. We also predict $\Delta R_{D}= \Delta R_{D^{*}}$, with future measurements shifting the world averages to slightly smaller central values., Comment: 44 pages + appendices and references, 14 figures. v5: Typos corrected

We discuss a simple renormalisable, gauge invariant model with a fermiophobic $Z'$ boson: it has no couplings to the three Standard Model (SM) chiral families, but does couple to a fourth vector-like (VL) family. The SM Higgs couples to the fourth VL lepton, leading to an enhanced contribution to the muon anomalous magnetic moment $\left(g-2\right)_{\mu}$. The latter contribution requires a non-vanishing coupling of $Z'$ to right-handed muons, which arises within this model due to mixing effects between the SM and VL fermions, along with $Z'$ couplings to the second generation SM lepton doublet and third generation SM quark doublet. This model can simultaneously account for the measured $B$-decay ratios $R_{K^{(*)}}$ and $\left(g-2\right)_{\mu}$. We identify the parameter space where this explanation is consistent with existing experimental constraints coming from $B_{s}-\bar{B}_{s}$ mixing, neutrino trident production and collider searches. We also check that the SM Higgs coupling to the fourth VL lepton does not produce a dangerous contribution to the Higgs diphoton decay., Comment: 26 pages, 12 Figures, 3 Tables