Theories of flavor operate at various scales. Recently it has been pointed out that in the context of modular flavor symmetries certain combinations of observables are highly constrained, or even uniquely fixed, by modular invariance and holomorphicity. We find that even in the absence of supersymmetry these combinations are surprisingly immune against quantum corrections.

The A4 flavor symmetry has provided tremendous insight into the flavor structure of the lepton sector of the Standard Model, predicting a very good approximation to neutrino mixing angles, Tri-Bimaximal Mixing. A4 is spontaneously broken by a scalar called the flavon, and when this happens a number of degenerate vacua can form, resulting in so-called domain walls. These objects are not observed and hence need to be annihilated. This is usually done by explicitly breaking A4 by adding a bias term to the scalar potential. In this paper, we construct a new model invariant under A4 and Z4, which creates cosmologically viable domain walls, lifts the degeneracy of the vacuum giving a natural mechanism for domain walls to annihilate, as well as predicts realistic neutrino mixing angles; all utilizing cross couplings between flavons. The annihilation of the domain walls, with proper choice of wall tension and the consequent bias term, leads to a gravitational wave signal that is potentially detectable in near future gravitational wave experiments, and interestingly intersects with the observed Pulsar Timing Array signal.

We unify one of the most widely studied frameworks to explain the hierarchical structure of the flavor sector in the Standard Model, the Froggatt-Nielsen mechanism, with cosmic inflation. We propose that the complex scalar field, the so-called flavon, which breaks the Froggatt-Nielsen U(1) symmetry and generates the Yukawa couplings of the Standard Model, to also drive inflation, which we dub as Inflavon. After inflation ends, the decay of the inflavon reheats the Universe, establishing a novel link between early Universe cosmology and flavor physics. As concrete examples, we present realizations where the inflavon potential is described by an α-attractor potential. We then compute the resulting CMB observables, specifically the spectral index (n_s), the tensor-to-scalar ratio (r), and the amplitude of scalar perturbations (A_s) as functions of the underlying Froggatt-Nielsen model parameters. We identify the parameter space in Froggatt-Nielsen models involving the scale of Flavor symmetry breaking Λ_ FN and FN charges which is ruled out by Planck and ACT data, as well as the region that could be probed by next-generation CMB experiments like CMB-S4, SO and LiteBIRD. We also discuss inflavon as dark matter and its isocurvature constraints.

We investigate fermion mass hierarchies in models with modular flavor symmetries. Several key conclusions arise from the observation that the determinants of mass matrices transform as 1-dimensional vector-valued modular forms. We demonstrate that, under some fairly general assumptions, achieving hierarchical fermion masses requires the vacuum expectation value of the modulus τ to be located near one of the critical points, i, i∞, or ω. We also revisit the universal near-critical behavior around these points and classify the resulting mass hierarchies for the critical points i and ω. We compare the traditional Froggatt–Nielsen mechanism with its modular variant. The knowledge and boundedness of Fourier and Taylor coefficients are crucial to the predictive power of modular flavor symmetries.

We point out that specifying the finite modular group does not uniquely fix a modular flavor symmetry. We illustrate this using the finite modular group T'. Otherwise equivalent models based on different T' lead to modular forms with different properties and, hence, produce different phenomenological features. We exemplify this in various scenarios, and show that the ability of a given model to accommodate mass and other observed hierarchies depends sensitively on the way the T' is implemented.

In modular invariant models of flavor, observables must be modular invariant. The observables discussed so far in the literature are functions of the modulus τ and its conjugate, τ¯. We point out that certain combinations of observables depend only on τ, i.e. are meromorphic, and in some cases even holomorphic functions of τ. These functions, which we dub “invariants” in this Letter, are highly constrained, renormalization group invariant, and allow us to derive many of the models' features without the need for extensive parameter scans. We illustrate the robustness of these invariants in two existing models in the literature based on modular symmetries, Γ3 and Γ5. We find that, in some cases, the invariants give rise to robust relations among physical observables that are independent of τ. Furthermore, there are instances where additional symmetries exist among the invariants. These symmetries are relevant phenomenologically and may provide a dynamical way to realize symmetries of mass matrices.

Discrete flavor symmetries have been an appealing approach for explaining the observed flavor structure, which is not justified in the Standard Model (SM). Typically, these models require a so-called flavon field in order to give rise to the flavor structure upon the breaking of the flavor symmetry by the vacuum expectation value (VEV) of the flavon. Generally, in order to obtain the desired vacuum alignment, a flavon potential that includes additional so-called driving fields is required. On the other hand, allowing the flavor symmetry to be modular leads to a structure where the couplings are all holomorphic functions that depend only on a complex modulus, thus greatly reducing the number of parameters in the model. We show that these elements can be combined to simultaneously explain the flavor structure and dark matter (DM) relic abundance. We present a modular model with flavon vacuum alignment that allows for realistic flavor predictions while providing a successful fermionic DM candidate.

The so-called Golden Mass Relation provides a testable correlation between charged-lepton and down-type quark masses, that arises in certain flavor models that do not rely on Grand Unification. Such models typically involve broken family symmetries. In this work, we demonstrate that realistic fermion mass relations can emerge naturally in modular invariant models, without relying on ad hoc flavon alignments. We provide a model-independent derivation of a class of mass relations that are experimentally testable. These relations are determined by both the Clebsch-Gordan coefficients of the specific finite modular group and the expansion coefficients of its modular forms, thus offering potential probes of modular invariant models. As a detailed example, we present a set of viable mass relations based on the Γ4 ≅ S4 symmetry, which have calculable deviations from the usual Golden Mass Relation.

The intersection of the cosmic and neutrino frontiers is a rich field where much discovery space still remains. Neutrinos play a pivotal role in the hot big bang cosmology, influencing the dynamics of the universe over numerous decades in cosmological history. Recent studies have made tremendous progress in understanding some properties of cosmological neutrinos, primarily their energy density. Upcoming cosmological probes will measure the energy density of relativistic particles with higher precision, but could also start probing other properties of the neutrino spectra. When convolved with results from terrestrial experiments, cosmology can become even more acute at probing new physics related to neutrinos or even Beyond the Standard Model (BSM). Any discordance between laboratory and cosmological data sets may reveal new BSM physics and/or suggest alternative models of cosmology. We give examples of the intersection between terrestrial and cosmological probes in the neutrino sector, and briefly discuss the possibilities of what different laboratory experiments may see in conjunction with cosmological observatories.

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.

Modular flavor symmetries provide us with a new, promising approach to the flavor problem. However, in their original formulation the kinetic terms of the standard model fields do not have a preferred form, thus introducing additional parameters, which limit the predictive power of this scheme. In this work, we introduce the scheme of quasi–eclectic flavor symmetries as a simple fix. These symmetries are the direct product of a modular and a traditional flavor symmetry, which are spontaneously broken to a diagonal modular flavor subgroup. This allows us to construct a version of Feruglio's model with the Kähler terms under control. At the same time, the starting point is reminiscent of what one obtains from explicit string models.

Diversity, Equity, Inclusion, and Accessibility (DEIA) are not only called for to ensure morality and justice in our society, they also support ongoing and future excellence in particle physics. Over the past decade, the particle physics community has devised programs to support DEIA along multiple axes, and the way we think about measuring and implementing these initiatives has evolved. DEIA in physics is a broad topic, so in this paper we focus on the experiences of marginalized communities and outline ways different stakeholders can build a culture of equitable access for the success of marginalized individuals. Specifically, we identify urgent needs in the following areas: (1) We need to acquire a better understanding of the status quo, both quantitatively and qualitatively, to assess the effectiveness of existing programs and to develop best practices; (2) we need to develop effective and inclusive ways to engage marginalized communities; (3) we need to create infrastructure to better support members of marginalized communities, on an academic, financial and personal level; (4) we need to create an environment conducive to equitable access and success by establishing community expectations, fostering inclusion in social interactions, and holding individuals and institutions accountable; and (5) we need to establish a mechanism to monitor progress in the area of DEIA, including the implementation of the recommendations enumerated in this paper and others during the Snowmass 2021 process.

This is the summary report of the Community Engagement Frontier for the Snowmass 2021 study of the future of particle physics. The report discusses a number of general issues of importance to the particle physics community, including (1) the relation of universities, national laboratories, and industry, (2) career paths for scientists engaged in particle physics, (3) diversity, equity, and inclusion, (4) physics education, (5) public education and outreach, (6) engagement with the government and public policy, and (7) the environmental and social impacts of particle physics.

This is the report for the topical group Theory of Neutrino Physics (TF11/NF08) for Snowmass 2021. This report summarizes the progress in the field of theoretical neutrino physics in the past decade, the current status of the field, and the prospects for the upcoming decade.

To achieve the highest level of intellectual excellence calls for the greatest extent of diversity. However, due to the unjust institutional and societal barriers, the field of particle physics remains as one of the least diverse fields, severely limiting the potential of our scientific achievements. In order for the US Particle Physics Community, including the accelerator science and engineering fields, to remain at the forefront of global scientific leadership, it is imperative for our community to act urgently and diligently to improve the status quo of diversity, equity, inclusion, and accessibility (DEIA). This report summarizes the community contributions and recommendations within the Diversity and Inclusion Topical Group of the Community Engagement Frontier (CEF3) at the Snowmass 2021.

Accessibility to participation in the high energy physics community can be impeded by many barriers. These barriers must be acknowledged and addressed to make access more equitable in the future. An accessibility survey, the Snowmass Summer Study attendance survey, and an improved accessibility survey were sent to the Snowmass2021 community. This paper will summarize and present the barriers that prevent people from participating in the Snowmass2021 process,recommendations for the various barriers, and discussions of resources and funding needed to enact these recommendations, based on the results of all three surveys, along with personal experiences of the community members.

We revisit the flavor symmetries arising from compactifications on tori with magnetic background fluxes. Using Euler’s Theorem, we derive closed form analytic expressions for the Yukawa couplings that are valid for arbitrary flux parameters. We discuss the modular transformations for even and odd units of magnetic flux, M, and show that they give rise to finite metaplectic groups the order of which is determined by the least common multiple of the number of zero-mode flavors involved. Unlike in models in which modular flavor symmetries are postulated, in this approach they derive from an underlying torus. This allows us to retain control over parameters, such as those governing the kinetic terms, that are free in the bottom-up approach, thus leading to an increased predictivity. In addition, the geometric picture allows us to understand the relative suppression of Yukawa couplings from their localization properties in the compact space. We also comment on the role supersymmetry plays in these constructions, and outline a path towards non-supersymmetric models with modular flavor symmetries.

In this talk, I first discuss a popular scenario of electroweak baryogenesis through varying Yukawa couplings and show that A. Braconi et al. (Phys Rev D100 (1), 015032) [1] the instability of the Higgs potential already is encountered at the TeV scale. I will next present a novel mechanism of baryogenesis through flavon decay M.-C. Chen et al. (Phys Rev D100 (1), 035011) [2]. These notes are based on an invited talk by the author at FHEP 2019 in Hyderabad, India.

Models with modular flavor symmetries have been thought to be highly predictive. We point out that these predictions are subject to corrections from non–holomorphic terms in the Lagrangean. Specifically, in the models discussed in the literature, the Kähler potential is not fixed by the symmetries, for instance. The most general Kähler potential consistent with the symmetries of the model contains additional terms with additional parameters, which reduce the predictive power of these constructions. We also comment on potential ways of how one may conceivably retain the predictivity.

The DUNE IDR describes the proposed physics program and technical designs of the DUNE Far Detector modules in preparation for the full TDR to be published in 2019. It is intended as an intermediate milestone on the path to a full TDR, justifying the technical choices that flow down from the high-level physics goals through requirements at all levels of the Project. These design choices will enable the DUNE experiment to make the ground-breaking discoveries that will help to answer fundamental physics questions. Volume 1 contains an executive summary that describes the general aims of this document. The remainder of this first volume provides a more detailed description of the DUNE physics program that drives the choice of detector technologies. It also includes concise outlines of two overarching systems that have not yet evolved to consortium structures: computing and calibration. Volumes 2 and 3 of this IDR describe, for the single-phase and dual-phase technologies, respectively, each detector module's subsystems, the technical coordination required for its design, construction, installation, and integration, and its organizational structure.