Theories of flavour from the Planck scale to the electroweak scale

Abstract

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.

Figures (56)

• Figure 1: Higgs scalar potential for the case $m_{H}^{2}<0$ in terms of the neutral component of the Higgs doublet, $\phi$. Figure taken from Ellis:2015tba.
• Figure 2: Fermion mass hierarchies between the different families and charge sectors.
• Figure 4: Two-loop RGE of the inverse gauge couplings $\alpha_{a}^{-1}=4\pi/g_{a}^{2}$ in the SM (dashed lines) and the MSSM (solid lines). In the MSSM case, the sparticle masses are treated as a common threshold varied between 750 GeV and 2.5 TeV, and $\alpha_{3}(M_{Z})$ is varied between 0.117 and 0.120. Figure taken from Martin:1997ns.
• Figure 5: Reach in new physics scale of present and future facilities, from generic dimension-six operators. The colour coding of observables is: green for mesons, blue for leptons, yellow for EDMs, red for Higgs flavoured couplings and purple for the top quark. The grey columns illustrate the reach of direct flavour-blind searches and EW precision measurements. The operator coefficients are taken to be either $\sim$ 1 (plain coloured columns) or suppressed by MFV factors (hatch filled surfaces). Light (dark) colours correspond to present data (mid-term prospects, including HL-LHC, Belle II, MEG II, Mu3e, Mu2e, COMET, ACME, PIK and SNS). Figure taken from EuropeanStrategyforParticlePhysicsPreparatoryGroup:2019qin.
• Figure 6: Multi-scale picture for a theory of flavour: $v_{23}$ denotes the low scale where $U(2)^{5}$ is approximately preserved, and the hierarchy $m_{2}/m_{3}$ is explained. $v_{12}$ denotes the higher scale where $U(2)^{5}$ is explicitly broken and the hierarchy $m_{1}/m_{2}$ is explained.