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We discuss domain walls from spontaneous breaking of Abelian discrete symmetries $Z_N$. A series of different domain wall structures are predicted, depending on the symmetry and charge assignments of scalars leading to the spontaneous symmetry breaking (SSB). A widely-existing type of domain walls are those separating degenerate vacua which are adjacent in the field space. We denote these walls as adjacency walls. In the case that $Z_N$ terms are small compared with the $U(1)$ terms, the SSB of $U(1)$ generates strings first and then adjacency walls bounded by strings are generated after the SSB of $Z_N$. For symmetries larger than $Z_3$, non-adjacent vacua exist, we regard walls separating them as non-adjacency walls. These walls are unstable if $U(1)$ is a good approximation. If the discrete symmetry is broken via multiple steps, we arrive at a complex structure that one kind of walls wrapped by another type. On the other hand, if the symmetry is broken in different directions independently, walls generated from the different breaking chains are blind to each other., 15 pages, 6 figures, 2 tables, discussions and refs added, published in PRD

Discrete symmetries are widely imposed in particle theories. It is well-known that the spontaneous breaking of discrete symmetries leads to domain walls. Current studies of domain walls have focused on those from the spontaneous breaking of a $Z_2$ symmetry. Larger discrete symmetries have multiple degenerate vacua, leading to the domain walls in principle different from the simplest $Z_2$ domain wall. We take domain walls from $Z_N$ symmetry breaking as an illustrative study, and study in detail the $Z_3$ case, in which semi-analytical results for the tension and thickness of domain walls are derived. Explicit symmetry breaking terms lead to the dynamics of domain walls collapsing more complicated than the $Z_2$ case. Gravitational wave signals deviate from those from $Z_2$ domain walls., Comment: 9 pages, 4 figures, refs and comments added, accepted for publication in PRD

The observed pattern of mixing in the neutrino sector may be explained by the presence of a non-Abelian, discrete flavour symmetry broken into residual subgroups at low energies. Many flavour models require the presence of Standard Model singlet scalars which can promptly decay to charged leptons in a flavour-violating manner. We constrain the model parameters of a generic $A_4$ leptonic flavour model using a synergy of experimental data including limits from charged lepton flavour conversion, an 8 TeV collider analysis and constraints from the anomalous magnetic moment of the muon. The most powerful constraints derive from the MEG collaborations' limit on Br$\left(\mu\to e\gamma\right)$ and the reinterpretation of an 8 TeV ATLAS search for anomalous productions of multi-leptonic final states. We quantify the exclusionary power of each of these experiments and identify regions where the constraints from collider and MEG experimental data are complementary., Comment: v1: 28 + 9 pages, 8 figures. v2: 30 + 10 pages, 10 figures. v2 consistent with JHEP accepted version where further discussion of results and several more references were added

Proton decay is a smoking gun signature of grand unified theories (GUTs). Searches by Super-Kamiokande have resulted in stringent limits on the GUT symmetry-breaking scale. The large-scale multipurpose neutrino experiments DUNE, Hyper-Kamiokande, and JUNO will either discover proton decay or further push the symmetry-breaking scale above 1016 GeV. Another possible observational consequence of GUTs is the formation of a cosmic string network produced during the breaking of the GUT to the standard model gauge group. The evolution of such a string network in the expanding Universe produces a stochastic background of gravitational waves which will be tested by a number of gravitational wave detectors over a wide frequency range. We demonstrate the nontrivial complementarity between the observation of proton decay and gravitational waves produced from cosmic strings in determining SO(10) GUT-breaking chains. We show that such observations could exclude SO(10) breaking via flipped SU(5)×U(1) or standard SU(5), while breaking via a Pati-Salam intermediate symmetry, or standard SU(5)×U(1), may be favored if a large separation of energy scales associated with proton decay and cosmic strings is indicated. We note that recent results by the NANOGrav experiment have been interpreted as evidence for cosmic strings at a scale of ∼1014 GeV. This would strongly point toward the existence of GUTs, with SO(10) being the prime candidate. We show that the combination with already available constraints from proton decay allows us to identify preferred symmetry-breaking routes to the standard model.

We discuss the $SU(5)$ grand unified extension of flavour models with multiple modular symmetries. The proposed model involves two modular $S_4$ groups, one acting in the charged fermion sector, associated with a modulus field value $\tau_T$ with residual $Z_3^T$ symmetry, and one acting in the right-handed neutrino sector, associated with another modulus field value $\tau_{SU}$ with residual $Z_2^{SU}$ symmetry. Quark and lepton mass hierarchies are naturally generated with the help of weightons, which are SM singlet fields, where their non-zero modular weights play the role of Froggatt-Nielsen charges. The model predicts TM$_1$ lepton mixing, and neutrinoless double beta decay at rates close to the sensitivity of current and future experiments, for both normal and inverted orderings, with suppressed corrections from charged lepton mixing due to the triangular form of its Yukawa matrix., Comment: 24 pages, 4 figures, 3 tables, refs and comments added, published in JHEP

Non-Abelian discrete symmetries have been widely used to explain the patterns of lepton masses and flavor mixing. In these models, a given symmetry is assumed at a high scale and then is spontaneously broken by scalars (the flavons), which acquire vacuum expectation values. Typically, the resulting leading order predictions for the oscillation parameters require corrections in order to comply with neutrino oscillation data. We introduce such corrections through an explicit small breaking of the symmetry. This has the advantage of solving the cosmological problems of these models without resorting to inflation. The explicit breaking induces an energy difference or "bias" between different vacua and drives the evolution of the domain walls, unavoidably produced after the symmetry breaking, towards their annihilation. Importantly, the wall annihilation leads to gravitational waves which may be observed in current and/or future experiments. We show that a distinctive pattern of gravitational waves with multiple overlapped peaks is generated when walls annihilate, which is within the reach of future detectors. We also show that cosmic walls from discrete flavor symmetries can be cosmologically safe for any spontaneous breaking scale between 1 and $10^{18}$ GeV, if the bias is chosen adequately, without the need to inflate the walls away. We use as an example a particular $A_4$ model in which an explicit breaking is included in right-handed neutrino mass terms., 33 pages, 4 figures. Matches published version. Missing reference added

The $CP$ violation in the neutrino transition electromagnetic dipole moment is discussed in the context of the Standard Model with an arbitrary number of right-handed singlet neutrinos. A full one-loop calculation of the neutrino electromagnetic form factors is performed in the Feynman gauge. A non-zero $CP$ asymmetry is generated by a required threshold condition for the neutrino masses along with non-vanishing $CP$ violating phases in the lepton flavour mixing matrix. We follow the paradiagm of $CP$ violation in neutrino oscillations to parametrise the flavour mixing contribution into a series of Jarlskog-like parameters. This formalism is then applied to a minimal seesaw model with two heavy right-handed neutrinos denoted $N_1$ and $N_2$. We observe that the $CP$ asymmetries for decays into light neutrinos $N\to \nu\gamma$ are extremely suppressed, maximally around $10^{-17}$. However the $CP$ asymmetry for $N_2 \to N_1 \gamma$ can reach of order unity. Even if the Dirac $CP$ phase $\delta$ is the only source of $CP$ violation, a large $CP$ asymmetry around $10^{-5}$-$10^{-3}$ is comfortably achieved., Comment: 15 pages, 3 figures, title updated and refs added, published in JHEP

The idea of modular invariance provides a novel explanation of flavour mixing. Within the context of finite modular symmetries $\Gamma_N$ and for a given element $\gamma \in \Gamma_N$, we present an algorithm for finding stabilisers (specific values for moduli fields $\tau_\gamma$ which remain unchanged under the action associated to $\gamma$). We then employ this algorithm to find all stabilisers for each element of finite modular groups for $N=2$ to $5$, namely, $\Gamma_2\simeq S_3$, $\Gamma_3\simeq A_4$, $\Gamma_4\simeq S_4$ and $\Gamma_5\simeq A_5$. These stabilisers then leave preserved a specific cyclic subgroup of $\Gamma_N$. This is of interest to build models of fermionic mixing where each fermionic sector preserves a separate residual symmetry., Comment: 18 pages, 5 figures, 4 tables, accepted for publication in JHEP

We consider for the first time level 7 modular invariant flavour models where the lepton mixing originates from the breaking of modular symmetry and couplings responsible for lepton masses are modular forms. The latter are decomposed into irreducible multiplets of the finite modular group $\Gamma_7$, which is isomorphic to $PSL(2,Z_{7})$, the projective special linear group of two dimensional matrices over the finite Galois field of seven elements, containing 168 elements, sometimes written as $PSL_2(7)$ or $\Sigma(168)$. At weight 2, there are 26 linearly independent modular forms, organised into a triplet, a septet and two octets of $\Gamma_7$. A full list of modular forms up to weight 8 are provided. Assuming the absence of flavons, the simplest modular-invariant models based on $\Gamma_7$ are constructed, in which neutrinos gain masses via either the Weinberg operator or the type-I seesaw mechanism, and their predictions compared to experiment., Comment: 45 pages, 3 figures

Nonstandard interactions (NSIs), possible subleading effects originating from new physics beyond the Standard Model, may affect the propagation of neutrinos and eventually contribute to measurements of neutrino oscillations. Besides this, $ \mu-\tau $ reflection symmetry, naturally predicted by non-Abelian discrete flavor symmetries, has been very successful in explaining the observed leptonic mixing patterns. In this work, we study the combined effect of both. We present an $S_4$ flavor model with $\mu-\tau$ reflection symmetry realized in both neutrino masses and NSIs. Under this formalism, we perform a detailed study for the upcoming neutrino experiments DUNE and T2HK. Our simulation results show that under the $\mu-\tau $ reflection symmetry, NSI parameters are further constrained and the mass ordering sensitivity is less affected by the presence of NSIs., Comment: 24 pages, 6 figures. Version to appear in PRD

We discuss a minimal flavor model with twin modular symmetries, leading to trimaximal ${\mathrm{TM}}_{1}$ lepton mixing in which the first column of the tri-bimaximal lepton mixing matrix is preserved. The model involves two modular ${S}_{4}$ groups, one acting in the neutrino sector, associated with a modulus field value ${\ensuremath{\tau}}_{SU}$ with residual ${Z}_{2}^{SU}$ symmetry, and one acting in the charged lepton sector, associated with a modulus field value ${\ensuremath{\tau}}_{T}$ with residual ${Z}_{3}^{T}$ symmetry. Apart from the predictions of ${\mathrm{TM}}_{1}$ mixing, the model leads to a new neutrino mass sum rule which implies lower bounds on neutrino masses close to current limits from neutrinoless double beta decay experiments and cosmology.

We explore the concept of effective alignments: contractions of multiple flavour symmetry breaking flavon fields. These contractions give rise to directions that are hard or impossible to obtain directly by breaking the flavour symmetry. Within this context, and using $S_4$ as the flavour symmetry to exemplify, we perform a phenomenological check of lepton flavour models built from pairing any two effective alignments up to order 2 (in flavon contractions). The check is performed for each pair of effective alignments in a framework with models of constrained sequential dominance type, in a basis where the charged leptons are diagonal. We thus obtain an indication of which effective alignments are interesting for model building, within this so-called $S_4$ landscape. We find three types of viable topologies and provide examples of models realizing this strategy for each topology., Comment: 18 pages, 5 figures, 6 tables

We develop a general formalism for multiple moduli and their associated modular symmetries. We apply this formalism to an example based on three moduli with finite modular symmetries $S_4^A$, $S_4^B$ and $S_4^C$, associated with two right-handed neutrinos and the charged lepton sector, respectively. The symmetry is broken by two bi-triplet scalars to the diagonal $S_4$ subgroup. The low energy effective theory involves the three independent moduli fields $\tau_A$, $\tau_B$ and $\tau_C$, which preserve the residual modular subgroups $Z_3^A$, $Z_2^B$ and $Z_3^C$, in their respective sectors, leading to trimaximal TM$_1$ lepton mixing, consistent with current data, without flavons., Comment: 31 pages, 1 figure, 6 tables, refs and comments added

We present new results on the calculation of the dark matter relic abundance within the Higgs induced right-handed (RH) neutrino mixing model, solving the associated density matrix equation. For a benchmark value of the dark matter mass $M_{\rm DM} = 220\,{\rm TeV}$, we show the evolution of the abundance and how this depends on reheat temperature, dark matter lifetime and source RH neutrino mass $M_{\rm S}$, with the assumption $M_{\rm S} < M_{\rm DM}$. We compare the results with those obtained within the Landau-Zener approximation, showing that the latter largely overestimates the final abundance giving some analytical insight. However, we also notice that since in the density matrix formalism the production is non-resonant, this allows source RH neutrino masses below the W boson mass, making dark matter more stable at large mass values. This opens an allowed region for initial vanishing source RH neutrino abundance. For example, for $M_{\rm S} \gtrsim 1\,{\rm GeV}$, we find $M_{\rm DM}\gtrsim 20\,{\rm PeV}$. Otherwise, for $M_{\rm S} > M_W\sim 100\,{\rm GeV}$, one has to assume a thermalisation of the source RH neutrinos prior to the freeze-in of the dark matter abundance. This results into a large allowed range for $M_{\rm DM}$, depending on $M_{\rm S}$. For example, imposing $M_{\rm S} \gtrsim 300\,{\rm GeV}$, allowing also successful leptogenesis, we find $0.5 \lesssim M_{\rm DM}/{\rm TeV} \lesssim 500$. We also discuss in detail leptogenesis with two quasi-degenerate RH neutrinos, showing a case when observed dark matter abundance and matter-antimatter asymmetry are simultaneously reproduced. Finally, we comment on how an initial thermal source RH neutrino abundance can be justified and on how our results suggest that also the interesting case where $M_{\rm DM} < M_{\rm S}$, embeddable in usual high scale two RH neutrino seesaw models, might be viable., 46 pages, 7 figures; v2: appendices B and C added, it matches version to be published in JCAP

The radiative decay of neutral fermions has been studied for decades but $CP$ violation induced within such a paradigm has evaded attention. $CP$ violation in these processes can produce an asymmetry between circularly polarised directions of the radiated photons and produces an important source of net circular polarisation in particle and astroparticle physics observables. The results presented in this work outlines the general connection between $CP$ violation and circular polarisation for both Dirac and Majorana fermions and can be used for any class of models that produce such radiative decays. The total $CP$ violation is calculated based on a widely studied Yukawa interaction considered in both active and sterile neutrino radiative decay scenarios as well as searches for dark matter via direct detection and collider signatures. Finally, the phenomenological implications of the formalism on keV sterile neutrino decay, leptogenesis-induced right-handed neutrino radiative decay and IceCube-driven heavy dark matter decay are discussed., Comment: 25 pages, 3 figures, discussions added, published in JHEP

We discuss the breaking of $SO(3)$ down to finite family symmetries such as $A_4$, $S_4$ and $A_5$ using supersymmetric potentials for the first time. We analyse in detail the case of supersymmetric $A_4$ and its finite subgroups $Z_3$ and $Z_2$. We then propose a supersymmetric $A_4$ model of leptons along these lines, originating from $SO(3)\times U(1)$, which leads to a phenomenologically acceptable pattern of lepton mixing and masses once subleading corrections are taken into account. We also discuss the phenomenological consequences of having a gauged $SO(3)$, leading to massive gauge bosons, and show that all domain wall problems are resolved in this model., 39 pages, 2 figures, refs added, published version

The polarisation of sunlight after scattering off the atmosphere was first described by Chandrasekhar using a geometrical description of Rayleigh interactions. Kosowsky later extended Chandrasekhar's formalism by using Quantum Field Theory (QFT) to describe the polarisation of the Cosmological Microwave Background radiation. Here we focus on a case that is rarely discussed in the literature, namely the polarisation of high energy radiation after scattering off particles. After demonstrating why the geometrical and low energy QFT approaches fail in this case, we establish the transport formalism that allows to describe the change of polarisation of high energy photons when they propagate through space or the atmosphere. We primarily focus on Compton interactions but our approach is general enough to describe e.g. the scattering of high energy photons off new particles or through new interactions. Finally we determine the conditions for a circularly polarised $\gamma$--ray signal to keep the same level of circular polarisation as it propagates through its environment., Comment: 34 pages, 8 figures, 6 appendices, typos corrected, explanations and references added, matches JCAP published version

Imposing non-Abelian discrete flavour symmetries to neutrino non-standard interactions (NSIs) is discussed for the first time. For definiteness, we choose $A_4$ as the flavour symmetry, which is subsequently broken to the residual symmetry $Z_2$ in the neutrino sector. We provide a general discussion on flavour structures of NSIs from higher-dimensional operators ($d\leqslant8$) without inducing unnecessary tree-level 4-charged-fermion interactions. Both $A_4$- and $Z_2$-motivated NSI textures are obtained. UV completions of higher-dimensional operators lead to extra experimental constraints on NSI textures. We study the implementation of matter-effect NSIs in DUNE from phenomenological point of view, and discover that DUNE can test $A_4$ with a high level of statistics. We also present exclusion limits of sum rules suggested by UV-complete models. Our result shows that the NSI effects, though predicted to be small for DUNE, could provide useful information that might extend our understanding of the flavour symmetry., 41 pages, 6 figures, 13 tables, discussions and references added, published in PRD

In this Letter, we introduce leptogenesis via a varying Weinberg operator from a semi-classical perspective. This mechanism is motivated by the breaking of an underlying symmetry which triggers a phase transition that causes the coupling of the Weinberg operator to become dynamical. Consequently, a lepton anti-lepton asymmetry arises from the interference of the Weinberg operator at two different spacetime points. Using this semi-classical approach, we treat the Higgs as a background field and show a reflection asymmetry between the leptons and anti-leptons is generated in the vicinity of the bubble wall. We solve the equations of motion of the lepton and anti-lepton quasiparticles to obtain the final lepton asymmetry., Comment: 7 pages, 1 figure, comments and refs added, published version

Aspects of 3-neutrino mixing and oscillations in vacuum and in matter with constant density are investigated working with a real form of the neutrino Hamiltonian. We find the (approximate) equalities $\theta^m_{23} = \theta_{23}$ and $\delta^m = \delta$, $\theta_{23}$ ($\theta^m_{23}$) and $\delta$ ($\delta^m$) being respectively the atmospheric neutrino mixing angle and the Dirac CP violation phase in vacuum (in matter) of the neutrino mixing matrix, which are shown to represent excellent approximations for the conditions of the T2K (T2HK), T2HKK, NO$\nu$A and DUNE neutrino oscillation experiments. A new derivation of the known relation $\sin2\theta^m_{23} \sin\delta^m = \sin2\theta_{23} \sin\delta$ is presented and it is used to obtain a correlation between the shifts of $\theta_{23}$ and $\delta$ due to the matter effect. A derivation of the relation between the rephasing invariants which determine the magnitude of CP and T violating effects in 3-flavour neutrino oscillations in vacuum, $J_{\rm CP}$, and of the T violating effects in matter with constant density, $J^{m}_{\rm T} \equiv J^{m}$, reported in \cite{Krastev:1988yu} without a proof, is presented. It is shown that the function $F$ which appears in this relation, $J^{m} = J_{\rm CP}\,F$, and whose explicit form was given in \cite{Krastev:1988yu}, coincides with the function $\tilde{F}$ in the similar relation $J^{m} = J_{\rm CP}\tilde{F}$ derived in \cite{Naumov:1991ju}, although $F$ and $\tilde{F}$ are expressed in terms of different sets of neutrino mass and mixing parameters and have completely different forms., Comment: 17 pages, 6 figures, refs added, published in PLB

The Weinberg operator is a well-known solution to explain light neutrino masses. This operator violates lepton number and can provide non-equilibrium dynamics in the early Universe due to the suppression of tiny neutrino masses. A lot of underlying symmetries proposed in the lepton sector strongly motivate the existence of phase transitions at high scale. During the phase transition, the coupling of the Weinberg operator may be time-dependent, and the lepton asymmetry is generated by the interference of Weinberg operators at different times. This mechanism does not require any explicit new particles beyond the standard model or seesaw models.

Flavour models typically rely on flavons - scalars that break the family symmetry by acquiring vacuum expectation values in specific directions. We develop the idea of effective alignments, i.e.\ cases where the contractions of multiple flavons give rise to directions that are hard or impossible to obtain directly by breaking the family symmetry. Focusing on the example where the symmetry is $S_4$, we list the effective alignments that can be obtained from flavons vacuum expectation values that arise naturally from $S_4$. Using those effective alignments as building blocks, it is possible to construct flavour models, for example by using the effective alignments in constrained sequential dominance models. We illustrate how to obtain several of the mixing schemes in the literature, and explicitly construct renormalizable models for three viable cases, two of which lead to trimaximal mixing scenarios., 32 pages, 16 figures, discussions on cross couplings added, published version

We develop an economical approach to connect flavon cross couplings with flavour mixing. A non-zero reactor mixing angle and almost maximal CP violation arise from cross couplings between flavons in the charged lepton and neutrino sectors. Within this approach, we analyze how cross couplings contribute to charged lepton-flavour-violating decays. We find branching ratio sum rules of these processes and observe that the electroweak-scale flavour symmetry is consistent with current experimental data.

We discuss two theoretical motivations of precision measurements of oscillation parameters. One is the guidance for flavour model building with flavour symmetries, and the other is the connection with the origin of matter-antimatter asymmetry. We also present our recent progress in these aspects, a new approach of flavour model building based on cross coupling in the flavon potential and a novel mechanism of leptogenesis via phase transition.

International audience; The decay of the lightest nucleus with Tz=−3 , 22 Si, was studied by a silicon array. A charged-particle group at 5600 (70) keV in the decay-energy spectrum was identified experimentally as β -delayed two-proton emission from the isobaric analog state (IAS) of 22 Al. Experimental results of the IAS fed by a superallowed Fermi transition were compared with our large-scale shell-model calculations. The ground-state mass of 22 Si was obtained indirectly in the experiment for the first time. Two-proton separation energy for 22 Si is deduced to be −108 (125) keV, which indicates that it is a very marginal candidate for two-proton ground-state emission.

We discuss reactor antineutrino oscillations with non-standard interactions (NSIs) at the neutrino production and detection processes. The neutrino oscillation probability is calculated with a parametrization of the NSI parameters by splitting them into the averages and differences of the production and detection processes respectively. The average parts induce constant shifts of the neutrino mixing angles from their true values, and the difference parts can generate the energy (and baseline) dependent corrections to the initial mass-squared differences. We stress that only the shifts of mass-squared differences are measurable in reactor antineutrino experiments. Taking Jiangmen Underground Neutrino Observatory (JUNO) as an example, we analyze how NSIs influence the standard neutrino measurements and to what extent we can constrain the NSI parameters., Comment: a typo in Eq.(25) fixed after published version, discussion and conclusion unchanged

We present a warped extra dimension model with the custodial symmetry SU(2)(L) x SU(2)(R) x U(1)(X) x P-LR based on the flavor symmetry S-4 X Z(2) x Z(2)', and the neutrinos are taken to be Dirac particles. At leading order, the democratic lepton mixing is derived exactly, and the high-dimensional operators introduce corrections of order lambda(c) to all the three lepton mixing angles such that agreement with the experimental data can be achieved. The neutrino mass spectrum is predicted to be of the inverted hierarchy and the second octant of theta(23) is preferred. We suggest the modified democratic mixing, which is obtained by permuting the second and the third rows of the democratic mixing matrix, should be a good first order approximation to understanding sizable theta(13) and the first octant of theta(23). The constraints on the model from the electroweak precision measurements are discussed. Furthermore, we investigate the lepton mixing patterns for all the possible residual symmetries G(nu) and G(l) in the neutrino and charged lepton sectors, respectively. (C) 2013 Elsevier B.V. All rights reserved.