A February 2026 proposal by Arkani-Hamed, Figueiredo, Hall, and Manzari shows that the Standard Model fermion mass hierarchy can be generated at the TeV scale by chains of vector-like quarks and leptons linked by soft flavor-symmetry-breaking mass terms, with locality along the chain suppressing flavor- and CP-violating effects. The authors explicitly defer five linked open problems: a systematic classification of viable chain geometries and flavor-symmetry choices; collider search strategies optimized for the chain signatures (single production of the largest-Yukawa vector-like states, first- and second-generation vector-like quarks, and displaced decays for chain positions p≳7p\gtrsim 7); the phenomenology of spontaneously broken flavor symmetry (flavon spectra, pseudo-Goldstone bosons, their induced flavor-changing neutral currents and rare-meson decays); the nearly degenerate vector-like-mass regime including oscillation phenomena; and an ultraviolet completion that naturally yields the required μ/M∼0.1\mu/M\sim 0.1–0.20.2 hierarchy while evading kaon and electric-dipole-moment constraints. The common scientific objective is to decide whether TeV-scale flavor deconstruction is a viable, ultraviolet-consistent, and experimentally testable origin of flavor.

Background

The origin of the observed hierarchy of Standard Model (SM) fermion masses and mixing angles — Yukawa couplings ranging from order 1 for the top quark to 10−610^{-6} for the electron — is a long-standing open problem. Generic new physics that violates flavor symmetries is so tightly constrained by flavor-changing neutral currents (FCNCs, processes where a quark or lepton changes flavor without changing electric charge) and by CP-violation and electric-dipole-moment (EDM) bounds that the dynamics responsible for flavor is commonly expected to live at scales of roughly 10210^2–10410^4 TeV, far beyond direct collider reach. Classical solutions place flavor symmetries and Froggatt–Nielsen mechanisms (where a spontaneously broken flavor symmetry suppresses Yukawa couplings by powers of a small flavon vacuum-expectation-value ratio) or extra dimensions at those high scales.

Arkani-Hamed, Figueiredo, Hall, and Manzari (arXiv:2602.17754, 2026) counter this lore with a four-dimensional class of theories at the TeV scale. The SM is augmented by vector-like quarks and leptons (heavy fermions whose left- and right-handed components transform identically under the SM gauge group, so large gauge-invariant Dirac masses MM are allowed). An Abelian flavor symmetry GFG_F forbids direct Yukawa couplings among light SM fermions; instead, soft GFG_F-breaking mass terms of order μ\mu mix heavy states with each other, and order-one Yukawa couplings connect light to heavy fields. The pattern of allowed mass terms and couplings is encoded in 'chain diagrams' reminiscent of dimensional deconstruction (the technique of Arkani-Hamed, Cohen, and Georgi, Phys. Rev. Lett. 86, 4757 (2001), in which a continuum extra dimension is mimicked by a discrete lattice of sites linked by fields). The heavy fermions 'hop' along the chain, and integrating them out yields effective SM Yukawa entries yij∼λ^ ϵnijy_{ij}\sim\hat\lambda\,\epsilon^{n_{ij}} with ϵ=μ/M∼0.1\epsilon=\mu/M\sim 0.1–0.20.2 and integer 'distances' nijn_{ij} along the chain, so the observed hierarchies follow from chain locality with only moderately small parameters. Locality also makes CP and flavor violation naturally mild: in the simplest lepton setup the open disconnected chains contain no rephasing-invariant phases, while the quark sector realizes CKM-like (Cabibbo–Kobayashi–Maskawa quark-mixing-matrix) CP violation through a controlled loop structure, and M∼M\sim TeV remains consistent with kaon, EDM, lepton-flavor-violation, and precision-electroweak constraints. A simple extension generates neutrino masses parametrically tied to the square of the electron Yukawa coupling. Related earlier 'flavor deconstruction' constructions in the gauge (non-universal-symmetry) lineage — Greljo and Isidori (Phys. Lett. B 856, 138900 (2024)) and Isidori, Paradisi, Sainaghi, and Selimovic (JHEP 02, 146 (2026)) — address the lepton/neutrino sector through deconstructed gauge symmetries rather than global flavor symmetries with vector-like chains.

The letter's collider phenomenology is only exploratory: vector-like states decay only through their Yukawa couplings (E→νW,eZ,ehE\to\nu W, eZ, eh and U,D→qW,qZ,qhU,D\to qW, qZ, qh with 2:1:1 branching ratios); the states with the largest Yukawa couplings can be singly produced; states pp steps down the chain have Yukawas of order ϵp\epsilon^p, so for p≳7p\gtrsim 7 the decay length becomes macroscopic, cτ∼102p−15 c\tau\sim 10^{2p-15}\,cm; and if the vector-like masses are nearly degenerate within O(ϵ)O(\epsilon), the physics changes qualitatively to degenerate perturbation theory with oscillations between nearly degenerate species. The authors state that a detailed investigation of all these signals, and a systematic exploration of the model space, are left to future work, as is the question of what ultraviolet dynamics generates the required ϵ=μ/M∼0.1\epsilon=\mu/M\sim 0.1–0.20.2 hierarchy — in particular whether it can arise from spontaneously broken flavor symmetry with light flavons and pseudo-Goldstone bosons (light scalars left over when an approximate continuous symmetry breaks) without inducing excessive FCNCs, rare-meson decays, kaon CP violation, or EDMs.

Problem Statement

Determine whether TeV-scale flavor deconstruction — the Arkani-Hamed–Figueiredo–Hall–Manzari framework in which Standard-Model Yukawa entries arise as yij∼λ^ (μ/M)nijy_{ij}\sim\hat\lambda\,(\mu/M)^{n_{ij}} from chains of vector-like quarks and leptons with soft flavor-symmetry-breaking hopping terms μ\mu and vector-like masses M∼M\sim TeV — is a viable, ultraviolet-consistent, and experimentally testable origin of the fermion mass hierarchy. This single objective is discharged through five jointly linked questions the source explicitly defers: (1) classify the space of chain geometries and flavor-symmetry choices beyond the illustrative models, and determine which TeV-scale vector-like spectra are consistent with all flavor and CP constraints; (2) develop collider search strategies optimized for the chain signatures — single production of the largest-Yukawa vector-like states, discovery prospects for first- and second-generation-coupled vector-like quarks, and displaced-decay searches for chain positions p≳7p\gtrsim 7; (3) analyze the parameter space and phenomenology of spontaneously broken flavor symmetry in this framework, including flavon spectra, pseudo-Goldstone bosons, light pseudoscalars, and their induced flavor-changing neutral currents and rare-meson decays; (4) characterize the nearly degenerate vector-like-mass regime — oscillation phenomena between nearly degenerate species, the transition between degenerate perturbation theory and hierarchical-site behavior, and the observables that discriminate these regimes; and (5) construct ultraviolet dynamics that generates the required μ/M∼0.1\mu/M\sim 0.1–0.20.2 hierarchy naturally while keeping scalar-sector masses and CP phases consistent with kaon and electric-dipole-moment bounds. Each of the five questions is an independently assessable deliverable, and a substantive answer to any one is a partial contribution to the objective, which is addressed in full only when all five are treated. Answers to the different components must be mutually consistent, since all five constrain the same underlying chain framework, but this consistency is a quality requirement on the answers rather than a precondition for addressing any single component.

References

  1. Nima Arkani-Hamed, Carolina Figueiredo, Lawrence J. Hall, Claudio Andrea Manzari, "Generating the fermion mass hierarchy at the TeV scale", arXiv:2602.17754 (2026), DOI 10.48550/arxiv.2602.17754, https://arxiv.org/abs/2602.17754 (primary source)
  2. Nima Arkani-Hamed, Andrew G. Cohen, Howard Georgi, "(De)constructing dimensions", Phys. Rev. Lett. 86, 4757 (2001), DOI 10.1103/PhysRevLett.86.4757, arXiv:hep-th/0104005, https://arxiv.org/abs/hep-th/0104005
  3. Admir Greljo, Gino Isidori, "Neutrino anarchy from flavor deconstruction", Phys. Lett. B 856, 138900 (2024), DOI 10.1016/j.physletb.2024.138900, arXiv:2406.01696, https://arxiv.org/abs/2406.01696
  4. Gino Isidori, Paride Paradisi, Andrea Sainaghi, Nudzeim Selimovic, "Anarchic neutrinos from flavor deconstruction: phenomenology of the lepton sector", JHEP 02, 146 (2026), DOI 10.1007/JHEP02(2026)146, arXiv:2510.23703, https://arxiv.org/abs/2510.23703
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