Tri-hypercharge: a separate gauged weak hypercharge for each fermion family as the origin of flavour

TL;DR

The paper introduces a tri-hypercharge ($U(1)_{Y_1}\times U(1)_{Y_2}\times U(1)_{Y_3}$) extension of the SM, assigning a separate weak hypercharge to each fermion family to seed flavour structure. Yukawa hierarchies arise from non-renormalisable operators mediated by hyperons that break the TH group to the SM in a cascade, naturally yielding a hierarchical pattern with an accidental $U(2)^5$ symmetry for the light families. The authors develop two concrete models with different hyperon content to describe charged-fermion masses, CKM mixing, and neutrino masses via a low-scale seesaw, and they study the resulting phenomenology of two $Z'$ bosons: a heavy $Z'_{12}$ and a potentially TeV-scale $Z'_{23}$. They find that $Z'_{23}$ could be accessible at the LHC and future colliders while $Z'_{12}$ is more constrained by flavour-changing processes, with a rich set of implications for flavour observables and electroweak precision measurements. Overall, the TH framework offers a bottom-up route to explain fermion mass hierarchies and mixings while predicting testable TeV-scale gauge phenomena and light vector-like neutrinos.

Abstract

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.

Figures (3)

• Figure 1: Diagram showing the different energy scales in tri-hypercharge, along with the approximate flavour symmetries that apply at each scale: $v_{23}$ 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.
• Figure 2: Parameter space of the high scale breaking, where $M_{Z'_{12}}$ is the mass of the heavy $Z'_{12}$ gauge boson and $g_{1}$, $g_{2}$ are the gauge couplings of the $U(1)_{Y_{1}}$ and $U(1)_{Y_{2}}$ groups, respectively. For simplicity, we assume $g_{1}$ and $g_{2}$ to be similar, and the non-generic fermion mixing predicted by Model 2 in Section \ref{['subsec:Model-2:-Five']}. Shaded regions in the plot depict 95% CL exclusions over the parameter space. The dashed line represents the natural benchmark $g_{1}\simeq g_{2}\simeq g_{3}\simeq\sqrt{3}g_{Y}$ motivated in the main text.
• Figure 3: Parameter space of the low scale breaking, where $M_{Z'_{23}}$ is the mass of the heavy $Z'_{23}$ gauge boson and $g_{3}$ is the gauge coupling of the $U(1)_{Y_{3}}$ group. The gauge coupling $g_{12}$ is fixed in terms of $g_{3}$ and $g_{Y}$ via Eq. \ref{['eq:gauge_couplings']}, and we consider the non-generic fermion mixing predicted by Model 2 in Section \ref{['subsec:Model-2:-Five']}. Shaded regions in the plot depict 95% CL exclusions over the parameter space, with the exception of the green (light green) region which is preferred by a global fit to $b\rightarrow s\mu\mu$ data at 2$\sigma$ (3$\sigma$) Alguero:2023jeh. The dashed line represents the natural benchmark $g_{1}\simeq g_{2}\simeq g_{3}\simeq\sqrt{3}g_{Y}$ motivated in the main text. The dashed-dotted line represents the contour where $\mathcal{B}(\tau\rightarrow3\mu)=10^{-12}$.