Gravitational waves (GWs) are a powerful probe of the earliest moments in the Universe, enabling us to test fundamental interactions at energy scales beyond the reach of laboratory experiments. In this work, we assess the GW capability to probe the origin of the flavour sector of the Standard Model (SM). Within the context of Froggatt-Nielsen models of fermion masses and mixing based on a gauged U(1) flavour symmetry, we investigate the formation of cosmic strings and the resulting GW background (GWB), estimating the sensitivity to the model’s parameter space of future GW experiments. Comparing these results with the bounds from low-energy flavour observables, we find that these two types of experimental probes of the model are nicely complementary. Flavour physics observables can probe low to intermediate symmetry-breaking scales $\textit{v}$ , while future GW experiments are sensitive to the opposite regime, for which the string tension is large enough to yield sizeable GW signals, and in the long run can set an upper limit on the scale as stringent as $\textit{v}$ ≲ 10 GeV. In certain scenarios, the combination of flavour constraints and future GW bounds can bring about a complete closure of the available parameter space, which illustrates how GWB searches can play an important role in testing the origin of the SM flavour sector even if that occurs at ultra-high energies.

Germany

Belgium

Simone Blasi

China

Lorenzo Calibbi

Alberto Mariotti

Kevin Turbang

Gravitational waves from cosmic strings in Froggatt-Nielsen flavour models

Preserving the unique role of the one Higgs doublet of the standard model, it is proposed that quark and lepton mass patterns, often ascribed to the Froggatt-Nielsen mechanism using nonrenormalizable higher-dimensional terms, may be enforced in a <underline>renormalizable</underline> theory of just one Higgs doublet by the scotogenic mechanism with soft symmetry breaking in the dark sector. A revised version of the original <math altimg='si1.svg'><msub><mrow><mi>A</mi></mrow><mrow><mn>4</mn></mrow></msub></math> model of charged leptons and neutrinos is discussed.

United States

Ernest Ma

Scotogenic Froggatt-Nielsen and the versatility of soft symmetry breaking

The Froggatt-Nielsen (FN) mechanism successfully explains the hierarchical structure of fermion Yukawa couplings by introducing a U(1) flavor symmetry with distinct charge assignments for different fermion generations. While some FN charge assignments have been proposed, their evaluation has largely relied on heuristic approaches. This paper systematically investigates viable FN charge assignments within the Standard Model, including both the quark and lepton sectors, using Bayesian statistical analysis. The study explores scenarios involving both the seesaw mechanism and dimension-five operators for neutrino mass generation. A comprehensive parameter scan over FN charges reveals a wide range of charge assignments consistent with observed fermion masses and mixing angles. Interestingly, negative FN charges and significant generational differences in charges are found to be viable, contrary to conventional assumptions. The analysis also compares the seesaw mechanism and dimension-five operator scenarios, finding no strong preference between them for optimal charge assignments. Furthermore, predictions for the lightest neutrino mass and effective Majorana mass relevant for neutrinoless double-beta decay are presented, highlighting regions of parameter space accessible to upcoming experiments. Finally, implications for nucleon decay are studied, demonstrating that different FN charge assignments predict significantly different nucleon decay lifetimes and branching ratios, providing a potential experimental probe for FN models.

Japan

Masahiro Ibe

Satoshi Shirai

Keiichi Watanabe

Comprehensive Bayesian exploration of Froggatt-Nielsen mechanism

<p>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 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mi>X</mi></msub></math> 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 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>X</mi><msub><mi>q</mi><mi>i</mi></msub></msub><mo stretchy="false">|</mo><mo>≤</mo><mn>4</mn></math> 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 <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">Δ</mi><mi>F</mi><mo>=</mo><mn>2</mn></math> 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.</p>

Claudia Cornella

Canada

David Curtin

Ethan T. Neil

Jedidiah O. Thompson

Mapping and probing Froggatt-Nielsen solutions to the quark flavor puzzle

We study the matching of Froggatt-Nielsen theories of flavour onto the Standard Model Effective Field Theory (SMEFT), upon integrating out a heavy Beyond-the-Standard-Model (BSM) scalar ‘flavon’ whose vacuum expectation value breaks an Abelian flavour symmetry at energies ΛFN well above the electroweak scale, ΛFN &gt; ΛSM. We include matching contributions to the infrared d SM = 6 (Warsaw basis) SMEFT sourced from ultraviolet contact terms suppressed up to order 1/   <math> <msubsup> <mi>Λ</mi> <mi>UV</mi> <mn>2</mn> </msubsup> </math>  $$ {\Lambda}_{\textrm{UV}}^2 $$  in the Froggatt-Nielsen Lagrangian, where ΛUV &gt; ΛFN is an arbitrary ultraviolet scale where further unspecified BSM particles are dynamical. This includes tree-level (one-loop) ultraviolet diagrams with d FN = 6 (5) effective vertices. We first do so with a toy model, but then generalize our findings to arbitrary Frogatt-Nielsen charges. Our results indicate a rich and non-trivial signature of Froggatt-Nielsen theories on the (otherwise) model-independent operators of the SMEFT, and we briefly speculate on extending our analysis to broader classes of BSM flavour models, e.g. non-Abelian and/or gauged theories. We thus take an important step towards determining how to use rapidly developing theoretical and experimental SMEFT technologies to gain unambiguous insight into the SM’s longstanding fermion flavour puzzle.

United Kingdom

Eetu Loisa

Jim Talbert

Froggatt-Nielsen meets the SMEFT

The Froggatt-Nielsen (FN) mechanism, a prominent framework for explaining the observed flavor hierarchies, generically predicts the existence of an axion-like particle (ALP). This work examines a class of FN models based on ℤ N  discrete symmetries. We chart the allowed parameter space from a set of theoretical considerations and construct explicit renormalizable completions with minimal field content necessary to generate consistent textures. We then conduct comprehensive phenomenological analyses of two particularly elegant ℤ4 and ℤ8 models, highlighting the interplay between the effects of the ALP and the associated UV fields. We find that the FN scale can be as low as a few TeV.

Switzerland

Admir Greljo

Aleks Smolkovič

Alessandro Valenti

Froggatt-Nielsen ALP

In this work we study the multiplicity distributions (MDs) of charged particles within jets in proton-proton collisions, which were measured by the ATLAS Collaboration in 2011, 2016 and 2019. The first dataset refers to jets with smaller transverse momenta (<math><mrow><mn>4</mn><mo>&lt;</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>&lt;</mo><mn>40</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>) whereas the other two refer to higher <math><msub><mi>p</mi><mi>T</mi></msub></math> jets (<math><mrow><mn>0.1</mn><mo>&lt;</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>&lt;</mo><mn>2.5</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></mrow></math>). We find that the lower <math><msub><mi>p</mi><mi>T</mi></msub></math> set shows no sign of KNO scaling and that the higher <math><msub><mi>p</mi><mi>T</mi></msub></math> sets gradually approach the scaling limit. For the lower <math><msub><mi>p</mi><mi>T</mi></msub></math> set the mean multiplicity as a function of <math><msub><mi>p</mi><mi>T</mi></msub></math> can be well-described by expressions derived from QCD with different approximation schemes. For higher (<math><mo>&gt;</mo><mn>500</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>) values of <math><msub><mi>p</mi><mi>T</mi></msub></math> these expressions significantly overshoot the data. We show that the behavior of the MDs can be well-represented by a sub-Poisson distribution with energy dependent parameters. In the range <math><mn>40</mn><mo>&lt;</mo><msub><mi>p</mi><mi>T</mi></msub><mo>&lt;</mo><mn>100</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> there is a transition from sub to super Poissonian behavior and the MD evolves to a geometric distribution, which shows KNO scaling. In this way we fit the MDs in all transverse momentum intervals with one single expression. We discuss the implications of this phenomenological finding.

Brazil

G. R. Germano

F. S. Navarra

Poland

G. Wilk

Z. Wlodarczyk

Emergence of Koba-Nielsen-Olsen scaling in multiplicity distributions in jets produced at the LHC

We study the large mass hierarchy and <math><mi>C</mi><mi>P</mi></math> violation in the modular symmetric quark flavor models without fine-tuning. Mass matrices are written in terms of modular forms. Modular forms near the modular fixed points are approximately given by <math><msup><mi>ϵ</mi><mi>p</mi></msup></math>, where <math><mi>ϵ</mi></math> and <math><mi>p</mi></math> denote the small deviation from the fixed points and their residual charges. Thus, mass matrices have the hierarchical structures depending on the residual charges and have a possibility describing the large mass hierarchy without fine-tuning. Similar structures of mass matrices are also obtained in Froggatt-Nielsen models. Nevertheless, it seems to be difficult to induce a sufficient amount of <math><mi>C</mi><mi>P</mi></math> violation by a single small complex parameter <math><mi>ϵ</mi></math>. To realize the large mass hierarchy as well as sizable <math><mi>C</mi><mi>P</mi></math> violation, multimoduli are required. We show the mass matrix structures with multimoduli that are consistent with quark flavor observables including the <math><mi>C</mi><mi>P</mi></math> phase. We also discuss the origins of the large mass hierarchy and <math><mi>C</mi><mi>P</mi></math> violation in such mass matrix structures.

Shota Kikuchi

Tatsuo Kobayashi

Kaito Nasu

<math><mi>C</mi><mi>P</mi></math> phase in modular flavor models and discrete Froggatt-Nielsen models

In this paper, the Nielsen geometric method is used to study the position dependence of the Nielsen complexity for the thermofield double state of a harmonic oscillator. We present the state shift under the influence of an external electric field and demonstrate its importance for the construction of the corresponding circuit. By numerical analysis, we investigate the effect of the frequency and the external field on the dynamics of complexity. Our observation reveals that the system's complexity diminishes considerably with the rise of the frequency. Furthermore, our findings indicate that the complexity exhibits a distinct behavior under a feeble external electric field, as it grows more intricate with the escalation of the frequency. However, with higher magnitudes of the electric field, the system reverts to its prior behavior. We also remark on the influence of the reference state's frequency on the complexity.

Iran

F. Khorasani

Reza Pirmoradian

M. Reza Tanhayi

Position dependence of Nielsen complexity for the thermofield double state

The seesaw mechanism is the most attractive mechanism to explain the small neutrino masses, which predicts the neutrinoless double beta decay (<math><mn>0</mn><mi>ν</mi><mi>β</mi><mi>β</mi></math>) of the nucleus. Thus the discovery of <math><mn>0</mn><mi>ν</mi><mi>β</mi><mi>β</mi></math> is extremely important for future particle physics. However, the present data on the neutrino oscillation is not sufficient to predict the value of <math><msub><mi>m</mi><mrow><mi>e</mi><mi>e</mi></mrow></msub></math> as well as the neutrino mass <math><msubsup><mi>m</mi><mi>ν</mi><mi>i</mi></msubsup></math>. In this short article, by adopting a simple and consistent Froggatt-Nielsen model, which can well explain the observed masses and mixing angles of quark and lepton sectors, we calculate the distribution of <math><msub><mi>m</mi><mrow><mi>e</mi><mi>e</mi></mrow></msub></math> and <math><msubsup><mi>m</mi><mi>ν</mi><mi>i</mi></msubsup></math>. Interestingly, a relatively large part of the preferred parameter space can be detected in the near future.

Yu-Cheng Qiu

Jin-Wei Wang

Tsutomu T. Yanagida

Predictions of <math><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>e</mi><mi>e</mi></mrow></msub></mrow></math> and neutrino mass from a consistent Froggatt-Nielsen model