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Neutrino Flavor Model Building and the Origins of Flavor and CP Violation
The neutrino sector offers one of the most sensitive probes of new physics beyond the Standard Model of Particle Physics (SM). The mechanism of neutrino mass generation is still unknown. The observed suppression of neutrino masses hints at a large scale, conceivably of the order of the scale of a rand unified theory (GUT), which is a unique feature of neutrinos that is not shared by the charged fermions. The origin of neutrino masses and mixing is part of the outstanding puzzle of fermion masses and mixings, which is not explained ab initio in the SM. Flavor model building for both quark and lepton sectors is important in order to gain a better understanding of the origin of the structure of mass hierarchy and flavor mixing, which constitute the dominant fraction of the SM parameters. Recent activities in neutrino flavor model building based on non-Abelian discrete flavor symmetries and modular flavor symmetries have been shown to be a promising direction to explore. The emerging models provide a framework that has a significantly reduced number of undetermined parameters in the flavor sector. In addition, such a framework affords a novel origin of CP violation from group theory due to the intimate connection between physical CP transformation and group theoretical properties of non-Abelian discrete groups. Model building based on non-Abelian discrete flavor symmetries and their modular variants enables the particle physics community to interpret the current and anticipated upcoming data from neutrino experiments. Non-Abelian discrete flavor symmetries and their modular variants can result from compactification of a higher-dimensional theory. Pursuit of flavor model building based on such frameworks thus also provides the connection to possible UV completions: in particular, to string theory. We emphasize the importance of constructing models in which the uncertainties of theoretical predictions are smaller than, or at most compatible with, the error bars of measurements in neutrino experiments. While there exist proof-of-principle versions of bottom-up models in which the theoretical uncertainties are under control, it is remarkable that the key ingredients of such constructions were discovered first in top-down model building. We outline how a successful unification of bottom-up and top-down ideas and techniques may guide us towards a new era of precision flavor model building in which future experimental results can give us crucial insights into the UV completion of the SM.
Constraining low-scale flavor models with ( g − 2 ) μ and lepton flavor violation
Not Available
CDRL: Certification-Driven Reinforcement Learning for Neutrino Flavor Model Discovery
Many scientific discovery problems require searching combinatorial hypothesis spaces under complex domain constraints. Reinforcement learning (RL) offers a promising approach, but existing methods rely on scalar rewards that provide limited information about why candidate solutions fail, leading agents to repeatedly explore invalid regions. We introduce Certification-Driven Reinforcement Learning (CDRL), a framework that leverages structured feedback from symbolic reasoning tools. When a candidate violates domain constraints, these tools produce certificates identifying the actions responsible for failure. CDRL converts these certificates into reusable constraints that eliminate classes of invalid solutions and guide exploration toward valid regions. We evaluate CDRL on neutrino flavor model discovery in theoretical particle physics, where the hypothesis space exceeds $10^{26}$ possible models, and compare it with the state-of-the-art RL approach previously used for this task. Across three theory spaces, CDRL achieves up to 1.95$\times$ higher valid model rates and up to 6.33$\times$ higher neutrino model rates while evaluating up to 4$\times$ fewer candidates. We further extract 40 interpretable rules from search trajectories using a post-hoc decision-tree framework and show that reusing them as soft constraints yields gains of up to 2$\times$ in valid model rates and 3$\times$ in neutrino model discovery across all three theory spaces. These results suggest that CDRL uncovers reusable structure in combinatorial search spaces and provides a general framework for scientific model discovery.
Anomaly free Froggatt-Nielsen models of flavor
We introduce two anomaly free versions of Froggatt-Nielsen (FN) models, based on either $G_{\rm FN}=U(1)^3$ or $G_{\rm FN}=U(1)$ horizontal symmetries, that generate the SM quark and lepton flavor structures. The structure of these ``inverted'' FN models is motivated by the clockwork mechanism: the chiral fields, singlets under $G_{\rm FN}$, are supplemented by chains of vector-like fermions charged under $G_{\rm FN}$. Unlike the traditional FN models the hierarchy of quark and lepton masses is obtained as an expansion in $M/\langle \phi\rangle$, where $M$ is the typical vector-like fermion mass, and $\langle \phi\rangle$ the flavon vacuum expectation value. The models can be searched for through deviations in flavor observables such as $K-\bar K$ mixing, $\mu\to e$ conversion, etc., where the present bounds restrict the masses of vector-like fermions to be above ${\mathcal O}(10^7~{\rm GeV})$. If $G_{\rm FN}$ is gauged, the models can also be probed by searching for the flavorful $Z'$ gauge bosons. In principle, the $Z'$s can be very light, and can be searched for using precision flavor, astrophysics, and beam dump experiments.
Fractional θ angle, ’t Hooft anomaly, and quantum instantons in charge-q multi-flavor Schwinger model
This work examines non-perturbative dynamics of a 2-dimensional QFT by using discrete ’t Hooft anomaly, semi-classics with circle compactification and bosonization. We focus on charge- q N -flavor Schwinger model, and also Wess-Zumino-Witten model. We first apply the recent developments of discrete ’t Hooft anomaly matching to theories on R 2 and its compactification to R× S 1 L . We then compare the ’t Hooft anomaly with dynamics of the models by explicitly constructing eigenstates and calculating physical quantities on the cylinder spacetime with periodic and flavor-twisted boundary conditions. We find different boundary conditions realize different anomalies. Especially under the twisted boundary conditions, there are Nq vacua associated with discrete chiral symmetry breaking. Chiral condensates for this case have fractional θ dependence e i θ / Nq , which provides the Nq -branch structure with soft fermion mass. We show that these behaviors at a small circumference cannot be explained by usual instantons but should be understood by “quantum” instantons, which saturate the BPS bound between classical action and quantum-induced effective potential. The effects of the quantum-instantons match the exact results obtained via bosonization within the region of applicability of semi-classics. We also argue that large- N limit of the Schwinger model with twisted boundary conditions satisfy volume independence.
Higgs-flavon mixing and LHC phenomenology in a simplified model of broken flavor symmetry
Here, the LHC phenomenology of a low-scale gauged flavor symmetry model with inverted hierarchy is studied, through introduction of a simplified model of broken flavor symmetry. A new scalar (a flavon) and a new neutral top-philic massive gauge boson emerge with mass in the TeV range, along with a new heavy fermion associated with the standard model top quark. After checking constraints from electroweak precision observables, we investigate the influence of the model on Higgs boson physics, notably on its production cross section and decay branching fractions. Limits on the flavon φ from heavy Higgs boson searches at the LHC at 7 and 8 TeV are presented. The branching fractions of the flavon are computed as a function of the flavon mass and the Higgs-flavon mixing angle. We also explore possible discovery of the flavon at 14 TeV, particularly via the φ → Z 0 Z 0 decay channel in the 2ℓ2ℓ' final state, and through standard model Higgs boson pair production φ → hh in the b¯bγγ final state. We conclude that the flavon mass range up to 500 GeV could be probed down to quite small values of the Higgs-flavon mixing angle with 100 fb –1 of integrated luminosity at 14 TeV.
Realtime dynamics of hyperon spin correlations from string fragmentation in a deformed four-flavor Schwinger model
Self-polarizing weak decays of Λ -hyperons provide unique insight into the role of entanglement in the fragmentation of QCD strings through measurements of the spin correlations of Λ Λ ¯ pairs produced in collider experiments. The simplest quantum field theory representing the underlying parton dynamics is the four-flavor massive Schwinger model plus an effective spin-flip term, where the flavors are mapped to light (up or down) and heavy (strange) quarks and their spins. This construction provides a novel way to explore hyperon spin correlations in 1 + 1 dimensions. We investigate the evolution of these correlations for different string configurations that are sensitive to the rich structure of the model Hamiltonian. Published by the American Physical Society 2024
Inference finds consistency between a neutrino flavor evolution model and Earth-based solar neutrino measurements
We continue examining statistical data assimilation (SDA), an inference methodology, to infer solutions to neutrino flavor evolution, for the first time using real - rather than simulated - data. The model represents neutrinos streaming from the Sun's center and undergoing a Mikheyev-Smirnov-Wolfenstein (MSW) resonance in flavor space, due to the radially-varying electron number density. The model neutrino energies are chosen to correspond to experimental bins in the Sudbury Neutrino Observatory (SNO) and Borexino experiments, which measure electron-flavor survival probability at Earth. In conclusion, the procedure successfully finds consistency between the observed fluxes and the model, if the MSW resonance - that is, flavor evolution due to solar electrons - is included in the dynamical equations representing the model.
Neutrinos and flavor symmetries
We discuss the recent progress of flavor models with the non-Abelian discrete symmetry in the lepton sector focusing on the θ{sub 13} and CP violating phase. In both direct approach and indirect approach of the flavor symmetry, the non-vanishing θ{sub 13} is predictable. The flavor symmetry with the generalised CP symmetry can also predicts the CP violating phase. We show the phenomenological analyses of neutrino mixing for the typical flavor models.
Flavor gauge models below the Fermi scale
The mass and weak interaction eigenstates for the quarks of the third generation are very well aligned, an empirical fact for which the Standard Model offers no explanation. We explore the possibility that this alignment is due to an additional gauge symmetry in the third generation. Specifically, we construct and analyze an explicit, renormalizable model with a gauge boson, $X$, corresponding to the $B-L$ symmetry of the third family. Having a relatively light (in the MeV to multi-GeV range), flavor-nonuniversal gauge boson results in a variety of constraints from different sources. By systematically analyzing 20 different constraints, we identify the most sensitive probes: kaon, $B^+$, $D^+$ and Upsilon decays, $D-\bar{D}^0$ mixing, atomic parity violation, and neutrino scattering and oscillations. For the new gauge coupling $g_X$ in the range $(10^{-2} - 10^{-4})$ the model is shown to be consistent with the data. Possible ways of testing the model in $b$ physics, top and $Z$ decays, direct collider production and neutrino oscillation experiments, where one can observe nonstandard matter effects, are outlined. The choice of leptons to carry the new force is ambiguous, resulting in additional phenomenological implications, such as non-universality in semileptonic bottom decays. In conclusion, the proposed framework provides interesting connections between neutrino oscillations, flavor and collider physics.
Latest Results from MINOS and MINOS+
The MINOS and MINOS+ experiments collected accelerator beam neutrino and antineutrino data for 11 years corresponding to peak energies of 3 GeV and 6 GeV, respectively, over a baseline of 735 km. These proceedings report on new limits and constraints set by MINOS and MINOS+ in and beyond the standard three-flavor paradigm. The atmospheric neutrino mass splitting in the three-flavor model is measured to be (2.42 ± 0.09) × 10 -3 eV 2 for normal mass ordering and $-({2.48}_{-0.11}^{+0.09})\times {10}^{-3}{\ {\rm{eV}}}^{2}$ for inverted mass ordering. Constraints are set on sterile neutrinos and antineutrinos in the four-flavor model by looking for sterile-driven ν μ and ${\bar{\nu }}_{{\rm{\mu }}}$ disappearance and sterile-driven ν e and ${\bar{\nu }}_{{\rm{e}}}$ appearance. A combination of the MINOS four-flavor ν μ disappearance search and the Daya Bay and Bugey-3 four-flavor ${\bar{\nu }}_{{\rm{e}}}$ disappearance searches excludes the parameter space allowed by LSND and MiniBooNE for ${\rm{\Delta }}{m}_{41}^{2}\lt 0.8{\ {\rm{eV}}}^{2}$ at 90% C.L. The size of large extra dimensions is constrained to be smaller than 0.17 μm at 90% C.L. in the limit of a vanishing lightest active neutrino mass. In conclusion, a search for non-standard ν e and ${\bar{\nu }}_{{\rm{e}}}$ appearance in MINOS is presented.
Left-right SU(4) vector leptoquark model for flavor anomalies
Not Available
Interplay between resonant leptogenesis, neutrinoless double beta decay and collider signals in a model with flavor and CP symmetries
Not Available