A Low Scale for Quark-Lepton Unification
Abstract
The measured fermion masses may be pointing to the scale of quark-lepton unification. Studying the renormalization-group evolution of the Standard Model Yukawa couplings, we find that yτ=yb and yμ=3ys occur at nearly the same scale, around 106 GeV, while the first generation reaches the Georgi-Jarlskog relation ye≃ yd/3 at order 108 GeV and can arise from the same Clebsch structure through a simple hierarchical flavor texture. This pattern naturally suggests low-scale Pati-Salam symmetry. We show that flavor mixing and finite threshold corrections preserve this picture. If the electron mass has an independent origin, the two heavier-generation relations can be realized in theories with a unification scale as low as (5-7)×105 GeV. We identify two simple theories that accommodate all three relations and in which the measured masses fix the flavor structure. The first unifies all three generations at 4.6+1.2−0.9×106 GeV; the second, with symmetric Yukawa matrices, at 1.5+0.7−0.5×107 GeV, and predicts |Vcb|=0.042±0.002. Their shared light-family texture fixes the relevant vector-leptoquark couplings, making μ→ e conversion in nuclei a direct test of unification: upcoming searches will probe part of the region selected by the two theories, and proposed facilities could cover it completely.
Related
- QCD and electroweak phase transitions with hidden scale invariance: implications for primordial black holes, quark-lepton nuggets and gravitational waves
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- Precision-Era Reassessment of Modified Quark--Lepton Complementarity: NuFIT 6.1, Phase-Convention Covariance and Lepton-Number Violation
- Search for single production of a vector-like B' quark decaying to a top quark and a W boson in the single-lepton final state in proton-proton collisions at √s = 13 TeV
- Cosmological constraints on extra radiation and early dark energy with lepton asymmetry and varying quark masses
BibTeX
@misc{hall2026scale,
title = {{A Low Scale for Quark-Lepton Unification}},
author = {Lawrence J. Hall and Claudio Andrea Manzari and Clara Murgui},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33152},
eprint = {2610.33152},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33152},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Low Scale for Quark-Lepton Unification
AU - Lawrence J. Hall
AU - Claudio Andrea Manzari
AU - Clara Murgui
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.33152
UR - https://arxiv.org/abs/2610.33152
AB - The measured fermion masses may be pointing to the scale of quark-lepton unification. Studying the renormalization-group evolution of the Standard Model Yukawa couplings, we find that y_τ=y_b and y_μ=3y_s occur at nearly the same scale, around 10^6 GeV, while the first generation reaches the Georgi-Jarlskog relation y_e≃ y_d/3 at order 10^8 GeV and can arise from the same Clebsch structure through a simple hierarchical flavor texture. This pattern naturally suggests low-scale Pati-Salam symmetry. We show that flavor mixing and finite threshold corrections preserve this picture. If the electron mass has an independent origin, the two heavier-generation relations can be realized in theories with a unification scale as low as (5-7)×10^5 GeV. We identify two simple theories that accommodate all three relations and in which the measured masses fix the flavor structure. The first unifies all three generations at 4.6^+1.2_−0.9×10^6 GeV; the second, with symmetric Yukawa matrices, at 1.5^+0.7_−0.5×10^7 GeV, and predicts |V_cb|=0.042±0.002. Their shared light-family texture fixes the relevant vector-leptoquark couplings, making μ→ e conversion in nuclei a direct test of unification: upcoming searches will probe part of the region selected by the two theories, and proposed facilities could cover it completely.
ER -