Minimal complete tri-hypercharge theories of flavour

Abstract

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.

Figures (7)

• Figure 1: Diagrams at the origin of light down-quark masses and mixing in Model 1. Similar diagrams are obtained in the up-sector by replacing $d_{i}^{c}\rightarrow u_{i}^{c}$, $D_{12,13,23}\rightarrow U_{12,13,23}$, $\tilde{\phi}_{\ell12,23}\rightarrow\phi_{\ell12,23}$ and $H_{3}^{d}\rightarrow H_{3}^{u}$, and also for the charged lepton sector by replacing $q_{i}\rightarrow\ell_{i}$, $d_{i}^{c}\rightarrow e_{i}^{c}$, $D_{12,13,23}\rightarrow E_{12,13,23}$ and $\phi_{q12,23}\rightarrow\phi_{\ell12,23}$.
• Figure 2: Illustrative spectrum of NP scales in Models 1 and 2. Notice that the hyperons $\phi$, third family Higgs doublets $H^{u,d}_{3}$, messenger neutrinos $N$ and messenger up-type quarks $U$ are common to both models.
• Figure 3: Diagrams at the origin of light down-quarks and charged lepton masses in Model 2. The up-sector is described by diagrams such as those of Fig. \ref{['fig:DiagramsModel1']}.
• Figure 4: Illustrative diagrams for the generation of effective Majorana masses for active neutrinos, where $i=1,2$.
• Figure 5: Leading contributions to $\mu\rightarrow e\gamma$ mediated by $Z'_{12}$ (left) and by $Z'_{23}$ (right). The crosses denote mass insertions, with the photon lines not shown.