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Mapping and Probing Froggatt-Nielsen Solutions to the Quark Flavor Puzzle
High Energy Physics - Phenomenology · Submitted 13 Jun 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The resulting set of top-20 flavor charge assignments significantly enlarges the viable space of FN models but is still compact enough to enable focused phenomenological study.
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The abstract, sentence by sentence
The Froggatt-Nielsen (FN) mechanism is an elegant solution to the flavor problem. In its minimal application to the quark sector, the different quark types and generations have different charges under a $U(1)_X$ flavor symmetry. The SM Yukawa couplings are generated below the flavor breaking scale with hierarchies dictated by the quark charge assignments. Only a handful of charge assignments are generally considered in the literature. We analyze the complete space of possible charge assignments with $|X_{q_i}| \leq 4$ and perform both a set of Bayesian-inspired numerical scans and an analytical spurion analysis to identify those charge assignments that reliably generate SM-like quark mass and mixing hierarchies. The resulting set of top-20 flavor charge assignments significantly enlarges the viable space of FN models but is still compact enough to enable focused phenomenological study. We then apply our numerical methodology to demonstrate that these distinct charge assignments result in the generation of correlated flavor-violating four-quark operators characterized by significantly varied strengths, potentially differing substantially from the possibilities previously explored in the literature. Future precision measurement of $\Delta F =2 $ observables, along with increasingly accurate SM predictions, may therefore enable us to distinguish among otherwise equally plausible FN charges, thus shedding light on the UV structure of the flavor sector.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The Froggatt-Nielsen (FN) mechanism is an elegant solution to the flavor problem. | background 1.00 | 0.05 | 0.02 | asserted 1.00 |
| s1 | In its minimal application to the quark sector, the different quark types and generations have different charges under a $U(1)_X$ flavor symmetry. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s2 | The SM Yukawa couplings are generated below the flavor breaking scale with hierarchies dictated by the quark charge assignments. | background 1.00 | 0.05 | 0.02 | asserted 1.00 |
| s3 | Only a handful of charge assignments are generally considered in the literature. | gap 0.82 | 0.03 | 0.02 | asserted 0.98 |
| s4 | We analyze the complete space of possible charge assignments with $|X_{q_i}| \leq 4$ and perform both a set of Bayesian-inspired numerical scans and an analytical spurion analysis to identify those charge assignments that reliably generate SM-like quark mass and mixing hierarchies. | contribution 0.62 | 0.97 | 0.08 | asserted 0.97 |
| s5 | The resulting set of top-20 flavor charge assignments significantly enlarges the viable space of FN models but is still compact enough to enable focused phenomenological study. | result 0.76 | 0.93 | 0.29 | asserted 1.00 |
| s6 | We then apply our numerical methodology to demonstrate that these distinct charge assignments result in the generation of correlated flavor-violating four-quark operators characterized by significantly varied strengths, potentially differing substantially from the possibilities previously explored in the literature. | result 0.96 | 0.93 | 0.28 | asserted 0.96 |
| s7 | Future precision measurement of $\Delta F =2 $ observables, along with increasingly accurate SM predictions, may therefore enable us to distinguish among otherwise equally plausible FN charges, thus shedding light on the UV structure of the flavor sector. | future work 0.54 | 0.06 | 0.26 | hedged possibility 1.00 |
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The paper
Original abstract
The Froggatt-Nielsen (FN) mechanism is an elegant solution to the flavor problem. In its minimal application to the quark sector, the different quark types and generations have different charges under a $U(1)_X$ flavor symmetry. The SM Yukawa couplings are generated below the flavor breaking scale with hierarchies dictated by the quark charge assignments. Only a handful of charge assignments are generally considered in the literature. We analyze the complete space of possible charge assignments with $|X_{q_i}| \leq 4$ and perform both a set of Bayesian-inspired numerical scans and an analytical spurion analysis to identify those charge assignments that reliably generate SM-like quark mass and mixing hierarchies. The resulting set of top-20 flavor charge assignments significantly enlarges the viable space of FN models but is still compact enough to enable focused phenomenological study. We then apply our numerical methodology to demonstrate that these distinct charge assignments result in the generation of correlated flavor-violating four-quark operators characterized by significantly varied strengths, potentially differing substantially from the possibilities previously explored in the literature. Future precision measurement of $\Delta F =2 $ observables, along with increasingly accurate SM predictions, may therefore enable us to distinguish among otherwise equally plausible FN charges, thus shedding light on the UV structure of the flavor sector.
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References
How the literature uses it
18 arXiv papers cite this in 29 sentences
Papers citing it · 12 sentences without a confident label
Uses its method or tool 1 paper
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Finally, following [ref] , we can calculate the ALP production in $K→πa$ processes using the Lagrangian for weak interactions in the chiral perturbation theory.
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We also show bounds from $K$-$K̅$ mixing in the heavy-$Z'$ regime ($v_F < 1.2×10^7$ GeV) from Smolkovi'c et al. [ref] , and from flavor-changing neutral currents ($v_F < 1.0×10^6$ GeV) from Cornella et al. [ref] .
Gravitational Waves from hybrid defects as probe of Flavor symmetry breaking: Machine-Learning Approach · SNR and GW Analysis Strategy · 0.94
Compares with it 3 papers
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I of Ref. [ref] , we find that our model has smaller $χ^2$.
Predictions of $m_{ee}$ and neutrino mass from a consistent Froggatt-Nielsen model · The consistent Forggatt-Nielsen model · 0.96
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Note also that some of our favorable FN charges overlap with the FN charges discussed in Refs. [ref] up to redundancy of FN charge assignments.
Comprehensive Bayesian Exploration of Froggatt-Nielsen Mechanism · Quark sector · 0.99
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It is instructive to compare the ninths framework with the systematic integer-charge FN analyses of Cornella, Curtin, Neil, and Thompson [ref] .
Flavor in Ninths and a Discrete Gauge Origin of the QCD Axion · Comparison with Integer-Charge FN Models · 1.00
Cites it as background 10 papers
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Recently, there are some works that did a blanket search to find optimal FN charge assignment [ref] .
Predictions of $m_{ee}$ and neutrino mass from a consistent Froggatt-Nielsen model · Introduction · 0.81
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Despite being extensively studied in the literature [ref] , systematically exploring the model space of FN theories is a challenging task.
Two Flavon Froggatt-Nielsen Models with Genetic Algorithms · Introduction · 0.86
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The choice of $U(1)$ charges is highly non-unique and involves a trade-off [ref] .
Hierarchies from Higher Flavor Spin · Introduction · 0.84
What it cites · 35 sentences without a confident label
Uses the method or tool of 1 paper
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(Similarly for $X_u$, or $X_d$.) In addition, following [ref] we remove “mirror” charges which are related by multiplying all of the charges $X$ by $-1$ (and then enforcing the above ordering convention).
Minimal Froggatt-Nielsen Textures · Systematic exploration of Froggatt-Nielsen Models · 0.89
Compares with 4 papers
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Some of these good textures correspond to those identified already in the literature, but, to the best of our knowledge, most of them have not been considered before.[Texture 3 first appeared in the seminal papers [ref] .]
Mass Matrix Models · Systematic exploration of Froggatt-Nielsen Models · 0.95
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Some of these good textures correspond to those identified already in the literature, but, to the best of our knowledge, most of them have not been considered before.[Texture 3 first appeared in the seminal papers [ref] .]
Mass Matrix Models: The Sequel · Systematic exploration of Froggatt-Nielsen Models · 0.95
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We believe this more accurately reflects the intended spirit of the FN solution, that the SM hierarchies should emerge “naturally.”[Our approach to quantifying flavour naturalness is very similar to [ref] , though that study focused on lepton CP violation in the MSSM for a handful of natural charge assignments.
Spontaneous CP Violation and Horizontal Symmetry in the MSSM: Toward Lepton Flavor Naturalness · Introduction · 0.83
Cites as support 1 paper
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As pointed out in Ref. [ref] , flavor charge assignments beyond the few canonical choices can generate close matches to the SM, seemingly with natural $𝒪(1)$ choices for the various coefficients.
Minimal Froggatt-Nielsen Textures · Introduction · 0.98
Cites as background 19 papers
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This strategy, expanded in [ref] , became known as the Froggatt-Nielsen (FN) mechanism (see e.g. Ref. [ref] for a modern review).
Mass Matrix Models: The Sequel · Introduction · 0.93
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This strategy, expanded in [ref] , became known as the Froggatt-Nielsen (FN) mechanism (see e.g. Ref. [ref] for a modern review).
Snowmass White Paper: Flavor Model Building · Introduction · 0.93
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This strategy, expanded in [ref] , became known as the Froggatt-Nielsen (FN) mechanism (see e.g. Ref. [ref] for a modern review).
Mass Matrix Models · Introduction · 0.93
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