Flavour hierarchies from radiative corrections in latticed theory space

TL;DR

The paper presents a concrete SM embedding of a latticed theory-space mechanism that generates charged-fermion mass hierarchies: only one generation acquires mass at tree level, while the lighter generations gain masses radiatively through controlled non-locality induced by a minimal $U(1)_X$-extended sector with five vectorlike fermion pairs per SM type. It shows that with $N_f=3$ and $N=5$, the observed fermion masses and CKM pattern can be reproduced, and considers a rich set of BSM effects, including FCNCs mediated by the new gauge boson and by the $Z$ and Higgs bosons, with phenomenology that can be tested at current and near-future experiments. Three benchmark solutions with $M_X=1,5,10$ TeV illustrate viable regions, with S1 largely excluded by direct searches and precision/FCNC bounds, while S2 and S3 remain compatible, predicting top-partner states near the TeV scale and distinctive flavor signals. The work also discusses neutrino masses within the same framework and emphasizes the novelty of achieving flavour hierarchies from radiative non-locality in latticed theory space, achieving a significantly lower new-physics scale than traditional radiative scenarios.

Abstract

It has recently been shown that when $N_f$ generations of chiral fermions are coupled in a specific manner to $N$ (with $N \geq 2N_f-1$) pairs of vectorlike fermions whose mass terms form a one-dimensional lattice-like structure in theory space, locality along the lattice ensures that only a single fermion generation acquires a mass at tree level. Radiative corrections can induce controlled departures from locality in the latticed space, thereby generating suppressed but non-vanishing masses for the remaining $N_f-1$ generations. In this work, we present an explicit implementation of this mechanism to address the flavour hierarchies of the Standard Model. After delineating the minimal extensions of the gauge, scalar, and Yukawa sectors required for feasible implementation of the mechanism, we demonstrate that the framework successfully reproduces the observed charged-fermion mass spectrum and quark mixing pattern. We analyse the new-physics effects arising from the extended sectors and confront them with existing constraints from direct, indirect searches and precision measurements. It is shown that a viable realisation of the mechanism allows the spectrum of vectorlike fermions and additional gauge boson to lie at scales as low as $\mathcal{O}(5)\,\mathrm{TeV}$ with the lightest states typically corresponding to top partners. This stands in sharp contrast to conventional radiative mass-generation scenarios, in which phenomenological constraints typically impose a lower bound on the new-physics scale of order a few hundred to several thousand TeV.

Figures (5)

• Figure 1: Diagrammatic representation of the next-to-leading-order origin of fermion masses in two approaches; see the text for details. On the left, the second-generation SM fermions ($f_{L2}$, $f_{R2}$) couple directly to the loop mediator(s). On the right, $f_{L2}$ and $f_{R2}$ couple indirectly through vectorlike fermions, with the relevant couplings between the latter arising only radiatively. The simple crosses denote a tree-level mass insertion, while the encircled represents the one induced radiatively.
• Figure 2: Topology of mass terms between the chiral and chain fermions as given by Eqs. (\ref{['Lm']},\ref{['MFC']}) for $N_f=3$ and $N=5$.
• Figure 3: The mass ratios computed from Eqs. (\ref{['m1_eff']},\ref{['m1eff_diag']}) as a function of $t$ for $M_X = 10^4$ GeV, $\mu_\alpha = 174$ GeV, $\mu_\alpha = M_X/\sqrt{2}$ and $W = 2 M_X$.
• Figure 4: Mass spectra of the vector-like fermions $U_i$, $D_i$, and $E_i$ for the benchmark solutions. The red dashed lines indicate the current most stringent direct-search exclusion limits for each type of vectorlike fermion.
• Figure 5: Interaction topology implementing the latticed version of "inverse-seesaw mechanism". $\nu_{R \alpha}$ acquire Majorana masses while the mass terms involving $N_{R \alpha}$ and $\nu_{R \alpha}$ arise through $U(1)_X$ breaking.