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FLASY 2018 is the 7th FLASY workshop on flavour symmetries. The workshop brings together researchers in the fields of flavour symmetries, neutrino physics, accelerator physics and cosmology to present new results, stimulate discussion and new collaborations.
This year's FLASY conference will be held at the Physics Department of the University of Basel in the city of Basel, Switzerland. The University of Basel is the oldest university in Switzerland.
Interested parties are invited to register for the conference and submit their abstract for the talk they would like to present. Plenary talks will be selected from the submitted abstracts; in the case of a large number of participants/abstracts, a parallel session may also be organized.
G. Bhattacharyya (Saha Institute Kolkata)
A. Buras (T. U. Munich)
G. Burdman (U. Sao Paulo)
G. Hiller (U. Dortmund)
T. Kephart (U. Vanderbilt)
S. King (U. Southampton)
M. Lindner (Max Planck Inst. Heidelberg)
E. Ma (University of California Riverside)
M. Mondragon (UNAM, Mexico)
S. Morisi (Naples U.)
Y. Nir (Weizmann Institute)
H. Päs (T. U. Dortmund)
M. Tanimoto (Niigata U.)
J. W. F. Valle (IFIC/CSIC-Universidad de Valencia)
Stefan Antusch
Christian Hohl
Aisha Lang (secretary)
Vasja Susič
We perform a scan of non-Abelian discrete symmetries capable of quantizing Yukawa-type couplings appearing in leptoquark extensions of the Standard Model (SM). Leptoquark models with particular flavour structures, i.e. Yukawa textures, yield lepton non-universal signatures in B hadron decay observables, in particular the ratios R_{D^(\star),K^(star)} currently deviating from SM predictions. We assume that residual flavour symmetries control SM and leptoquark couplings and subsequently derive explicit representations of their generators, which by construction depend on free parameters from the respective Yukawa sectors. By scanning over quantizations of these parameters and closing the groups generated by the associated representations, we explore this model space in a bottom-up and model independent way, ultimately finding multiple finite groups capable of explaining observations.
Time dependent CP-violation phenomena are a powerful tool to precisely measure fundamental parameters of the Standard Model and search for New Physics. The Belle II experiment is a substantial upgrade of the Belle detector and will operate at the SuperKEKB energy-asymmetric $e^+ e^-$ collider. The accelerator has already successfully completed the first phase of commissioning and first electron positron collisions in Belle II have just been recorded. The design luminosity of SuperKEKB is $8 \times 10^{35}$ cm$^{-2}$s$^{-1}$ and the Belle II experiment aims to record 50 ab$^{-1}$ of data, a factor of 50 more than the Belle experiment. This dataset will greatly improve the present knowledge, particularly on the CKM angles $\beta$ and $\alpha$ by measuring a wide spectrum of B-meson decays, including many with neutral particles in the final state. In this talk we will present estimates of the sensitivity to $\beta$ in the golden channels $B\to c\bar cs$ and in the penguin-dominated modes $B^0\to\eta’ K^0$, $\phi K^0$, $K_S\pi^0(\gamma)$. A study for the time-dependent analysis of $B^0\to\pi^0\pi^0$, relevant for the measurement of $\alpha$, and feasible only in the clean environment of an $e^+ e^-$ collider, will also be given.
We analyze the factorization to subleading power in the flavor changing neutral current processes $\bar B\rightarrow X_{s} \ell^+ \ell^-$ and $\bar B\rightarrow X_{d} \ell^+ \ell^-$. In particular, we compute the so-called resolved contributions and explore the numerical impact on observables. In these contributions the virtual photon couples to light partons instead of connecting directly to the effective weak-interaction vertex.
As distinctive feature, the resolved contributions remain nonlocal when the hadronic mass cut is released. Therefore, they reflect an irreducible uncertainty not dependent on the hadronic mass cut. They factorize in hard functions describing physics at the high scale $m_b$, in so-called jet functions characterizing the physics at the hadronic final state $X_s$ which corresponds to an invariant mass of order $\sqrt{m_b \Lambda_{\rm QCD}}$, and in soft functions, so-called shape functions, parametrizing the hadronic physics at the scale $\Lambda_{\rm QCD}$. Knowing the explicit form of the latter, one can derive general properties of such shape functions which allow for precise estimates of the corresponding uncertainties.
The long standing deviation of the measured value of $\epsilon'/\epsilon$ from the Standard Model prediction calls for a rigorous analysis of effects beyond the Standard Model (BSM) to $K\rightarrow \pi \pi$ decays. In this talk I will present results of scalar-scalar and tensor-tensor matrix elements relevant for $\epsilon'/\epsilon$, which have been obtained for the first time recently, using the Dual QCD approach. Furthermore I will present a master formula which allows to compute the value of $\epsilon'/\epsilon$ in any given BSM scenario.
The 760 ton ICARUS T600 detector performed a successful three-year physics run at the underground LNGS laboratories studying neutrino oscillations with the CNGS neutrino beam from CERN, and searching for atmospheric neutrino interactions. ICARUS performed a sensitive search for LSND like anomalous nu_e appearance in the CNGS beam, which contributed to constrain the allowed parameters to a narrow region around Δm2~eV2, where all the experimental results can be coherently accommodated at 90% C.L. The T600 detector underwent a significant overhauling at CERN and has now been moved to Fermilab, to be soon exposed to the Booster Neutrino Beam to search for sterile neutrino within the SBN program, devoted to definitively clarify the open questions of the presently observed neutrino anomalies.
The proposed contribution will address ICARUS achievements, its status and plans for the new run and the ongoing analyses also finalized to the next physics run at Fermilab.
Sterile neutrinos are among the most attractive extensions of the SM to generate the light neutrino masses observed in neutrino oscillation experiments.
When the sterile neutrinos are subject to a protective symmetry, they can have masses around the electroweak scale and potentially large neutrino Yukawa couplings, which makes them testable at planned future particle colliders.
In this talk I discuss the production and decay channels at electron-positron, proton-proton and electron-proton colliders and provide a complete list of the leading order signatures for sterile neutrino searches.
Among other things, I also discuss several novel and exotic search channels, such as displaced vertex searches and heavy neutrino-antineutrino oscillation.
The possible sensitivities for the active-sterile mixings and the heavy neutrino masses at the future circular colliders, as studied at CERN within the FCC study, will be presented.
The existence of non-baryonic Dark Matter (DM) is well established by cosmological and astrophysical probes, however its detailed nature still remains elusive. Among the extensions of the Standard Model explaining the DM relic aboundance, the simplest one is the addition of an inert scalar to the theory. In this talk I intend to give a brief review of this scenario and its possible connection with neutrino physics. I will in particular outline the discrete dark matter mechanism, which consist in extending the SM with a non-Abelian flavor symmetry. In this scenario, when the flavor symmetry is spontaneously broken by means of a flavon field at the see-saw scale, it will explain the neutrino mixing patterns and at the same time will render the dark matter stable.
A new data analysis was performed, based on looser selection criteria and multivariate approach. Oscillation parameters and nu_tau cross-section have been determined with a reduced statistical uncertainty, and the discovery of tau neutrino appearance is confirmed with an improved significance level. Moreover, the search for electron neutrino events has been extended to the full dataset, exploiting an improved method for the electron neutrino energy estimation. New limits have been set in the 3+1 neutrino model.
The $\mu\tau$-reflection symmetry is a simple symmetry capable of predicting all the unknown CP phases of the lepton sector and the atmospheric angle but too simple to predict the absolute neutrino mass scale or the mass ordering.
By combining this symmetry with a discrete abelian symmetry in a nontrivial way
we can additionally enforce a texture-zero for the heavy neutrino mass matrix which is transmitted to the inverse of the light neutrino mass matrix.
A highly predictive scenario emerges where the lightest neutrino mass is fixed to be in the few meV range for one solution with normal ordering (NO) and two
solutions with inverted ordering (IO). Another NO solution allows the lightest
mass to be in the region from few meV to tens of meV.
Moreover, the heavy neutrino sector is controlled solely by two free parameters.
The effective mass for neutrinoless double beta decay can be predicted and
leptogenesis is successful for some solutions and some parameter regions.
Neutrino is recognized to have a tiny but non-zero mass by some physical phenomena, such as the neutrino oscillation. However, the Standard Model cannot fully describe how the neutrinos get their masses. The beyond Standard Model which adds the necessary modification for this problem has been required. As a possibility to solve the neutrino mass problem, the seesaw mechanism has been suggested. We studied the tiny masses of neutrinos by using the type-I seesaw mechanism. This mechanism extends the Standard Model by introducing heavy right-handed neutrinos. As for this attractive mechanism, we discussed the CP violation in neutrino oscillation with the three generations model. We also referred to the relationship between this model and those symmetries breaking. We calculated the general form of Jarlskog invariant, which is a characteristic invariant of CP violation, in terms of three generation Dirac mass matrices and three right-handed neutrino masses. The model with three generations completely includes the minimal-seesaw model with only two right-handed neutrinos and could produces more visions.
We consider the four zero texture model, which include minimum necessary parameters and classify them according to their configuration of zero or non-zero elements. By means of this classification, we can distinguish the types which deduce automatically CP violation and three massless neutrinos. We performed numerical analysis for some models, by allocating parameters on the Dirac mass matrix and the lightest neutrino mass, and accept the data within the range of values of flavor mixing angles obtained by experiments, then refer to the correlations among parameters and physical quantities. These results can be prediction for physics related to , for example, neutrinoless double beta decay and leptogenesis.
Welcome reception with grill
In this talk we discuss various Theories of Flavour from the Planck scale to the Electroweak Scale, ranging from SUSY GUTs with Flavour Symmetry (with or without extra dimensions) to Flavourful Z' Models at the Electroweak scale capable of accounting for R_K(*).
I will discuss an extension of the Standard Model (SM) by a full new generation of quarks and leptons which are vector-like (VL) under the SM gauge group but chiral with respect to a new flavor dependent U(1) gauge symmetry. The model can simultaneously explain the deviations of the muon g-2 and lepton flavor universality in B-meson decays without conflicting with the data on Higgs decays, lepton flavor violation, or B-Bbar mixing. Fitting the anomalies, the model predicts VL quarks, leptons and a massive Z', all at the TeV scale. Furthermore, Lepton-flavor violating tau decays to three muons or mu+gamma are predicted to be within reach of Belle II. For model building, an interesting feature of the model is the automatic suppression of flavor changing Higgs, Z, and Z' couplings to SM generations which we have understood analytically.
We will consider solving the neutral current B anomalies called the R_K and R_K^* puzzles with light mediators. We will lay out the conditions required to solve the anomalies and be consistent will all constraints. We will then consider a scenario where the required interaction can arise and consider the implications in other sectors like coherent neutrino scattering.
Lepton flavor violation (LVF) is a striking signature of potential beyond the Standard Model physics. The search for LFV with the ATLAS detector is reported in searches focusing on the decay of the Higgs boson, the Z boson and of a heavy neutral gauge boson, Z', using pp collisions data with a center of mass energy of 8 TeV and 13 TeV.
We develop a 3-3-1 model with new charged leptons where the cancellation
of gauge anomalies fixes the number of fermion generations. Symmetry
breaking is achieved effectively with two scalar triplets so that the
scalar spectrum at the TeV scale contains just a charged and two CP even
scalars. Such a scalar sector is simpler than the one in the Two Higgs
Doublet Model, hence more attractive for phenomenological studies, and
has no flavor changing neutral currents (FCNC) mediated by scalars
except for the ones due to the mixing of Standard Model (SM) fermions
with heavy fermions. We identify a global residual symmetry of the model
which is later broken explicitly, with the introduction of effective
operators, in such a way that all fermions become massive. The masses so
generated require less fine-tuning for most of the SM fermions, and FCNC
are naturally suppressed by the small mixing between the third family of
quarks and the rest. The effective setting is justified by an
ultraviolet completion of the model from which the effective operators
emerge naturally. A detailed particle mass spectrum is presented, and an
analysis of the Z' production at the LHC run II is performed.
To be added later
In many flavour models, the vacuum expectation values of flavon multiplets
form the fermion mass matrices. The VEVs and their symmetries lead to
constraints among the masses and the mixing observables. The presence of
coupling constants (corresponding to various flavon multiplets) leaves
some degrees of freedom of the mass matrices unconstrained. Recently we
introduced a single sextet of Sigma(72x3) as a convenient flavon multiplet
to represent the entire complex symmetric Majorana neutrino mass matrix.
In this scenario, the flavon VEV fully constrains the mass matrix. In
2012, we introduced a set of four Majorana neutrino mass matrices which
give rise to non-zero theta_13 (consistent with the Daya Bay results).
Being fully constrained, these mass matrices also predicted the neutrino
mass ratios. Here we use the framework of the Sigma(72x3)-sextet to
construct a model which reproduces the above set of Majorana mass
matrices.
More than eighty years after they were first proposed, neutrinos still remain an enigma. Although they are an integral part of Standard Model, still we know very little about them. In particular, the Dirac or Majorana nature of neutrinos remains a mystery. For a long time theoretical particle physicists believed that neutrinos must be Majorana in nature and several elegant mass generation mechanisms have been proposed for Majorana neutrinos. In this talk, I will discuss many ways in which naturally small Dirac neutrino masses can be generated. I will also discuss the various interesting and sometimes surprising connections between Dirac nature of neutrinos and Dark Matter stability, proton decay etc.
We describe the many pathways to generate Dirac neutrino mass through generalized dimension-5 operators a la Weinberg and dimension 6 operators. The presence of new scalars beyond the Standard Model Higgs doublet implies new possible field contractions, which are required in the case of Dirac neutrinos. We also notice that the extra symmetries needed to ensure the Dirac nature of neutrinos can also be made responsible for stability of dark matter.
We systematically analyze the $d=5$ Weinberg operator at 3-loop order. From all possible topologies only a small number of them can generate a genuine 3-loop neutrino mass for which $d=5$ tree-level, 1-loop and 2-loop, as well as $d=7$ up to 1-loop, are guaranteed to be absent. Moreover, from the large list of all possible genuine neutrino mass diagrams, we find that they consist of variations of only 18 diagrams, that can be written in terms of 5 three-loop integrals. Finally, we show how our results can be consistently used to construct 3-loop neutrino mass models.
Some novel notions of lepton and baryon numbers are discussed, with applications to dark matter as well as the strong CP problem.
The first part of my talk is devoted to the discussion of the first model where the SM fermion mass hierarchy is generated by a sequential loop suppression mechanism: tree-level top quark mass; 1-loop bottom, charm, tau and muon masses; 2-loop masses for the light up, down and strange quarks as well as for the electron; and 4-loop masses for the light active neutrinos. The model features viable dark matter candidates. In the second part of my talk, I will discuss the first renormalizable extension of the SU(3)CxSU(3)LxU(1)X model, which explains the SM charged fermion mass hierarchy by a sequential loop suppression mechanism. In that model the light active neutrino masses are generated from a combination of linear and inverse seesaw mechanisms at two loop level. The model has viable dark matter candidates.
We show how an accidental U(1) Peccei-Quinn (PQ) symmetry can arise in a realistic Pati-Salam unified theory of flavour. A QCD axion arises from a linear combination of A4 triplet favons, which are responsible for fermion flavour structures and thus specific flavour-violating couplings of the axion are predicted. We also discuss the prospect of probing such a flavourful axion in future experiments.
We present the study of processes in current experiments to search for heavy sterile neutrinos, particles which appear as natural extensions of the Standard Model spectrum, whose presence will explain the tiny masses of the known neutrinos. While the simplest explanation of these tiny masses is by a seesaw mechanism where extra neutral leptons have masses way up to GUT scales, there are many versions that imply masses within the reach of current experiments. The Majorana vs. Dirac character of these heavy neutrals, another essential piece of information that helps elucidate the type of seesaw mechanism, is also explored in these studies.
We consider a version of the low-scale type I seesaw mechanism for generating small neutrino masses, as an alternative to the standard seesaw scenario. It involves two right-handed (RH) neutrinos $\nu_{1R}$ and $\nu_{2R}$ having a Majorana mass term with mass $M$, which conserves the lepton charge $L$. The RH neutrino $\nu_{2R}$ has lepton-charge conserving Yukawa couplings $g_{\ell 2}$ to the lepton and Higgs doublet fields, while small lepton-charge breaking effects are assumed to induce tiny lepton-charge violating Yukawa couplings $g_{\ell 1}$ for $\nu_{1R}$, $l=e,\mu,\tau$. In this approach the smallness of neutrino masses is related to the smallness of the Yukawa coupling of $\nu_{1R}$ and not to the large value of $M$: the RH neutrinos can have masses in the few GeV to a few TeV range. The Yukawa couplings $|g_{\ell 2}|$ can be much larger than $|g_{\ell 1}|$, of the order $|g_{\ell 2}| \sim 10^{-4} - 10^{-2}$, leading to interesting low-energy phenomenology. We consider a specific realisation of this scenario within the Froggatt-Nielsen approach to fermion masses. In this model the Dirac CP violation phase $\delta$ is predicted to have approximately one of the values $\delta \simeq \pi/4,\, 3\pi/4$, or $5\pi/4,\, 7\pi/4$, or to lie in a narrow interval around one of these values. The low-energy phenomenology of the considered low-scale seesaw scenario of neutrino mass generation is also briefly discussed.
Neutrinoless double beta (0vbb) decay is the most powerful tool to probe not only for Majorana neutrino masses but for lepton number violating physics in general. I will discuss the connections between lepton number violation, double beta decay and neutrino mass, highlighting recent experimental and theoretical efforts. Extending the standard picture of light neutrino exchange, I will review a general Lorentz invariant parametrization of the 0vbb decay rate and the resulting constraints on new physics models. Finally, I will discuss the relation between 0vbb decay and models of baryogenesis.
I discuss examples of correlations of leptonic CP phases at low and high energies and of CP phases in the lepton and in the quark sector that are achieved with the help of flavour and CP symmetries.
We discuss the correlation between the CP violating Dirac phase and the baryon asymmetry of the universe based on the leptogenesis in the minimal seesaw model.
In our model, we introduce two right-handed Majorana neutrinos and consider the trimaximal mixing matrix in the neutrino flavors. Because there is only one phase parameter in our model, the sign of the CP violating Dirac phase at low energy is fixed by the observed baryon asymmetry of the universe. According to the recent T2K and NOvA data of the CP violation, the Dirac neutrino mass matrix of our model is fixed only for the normal hierarchy of neutrino masses.
TBA
We answer the following question: what are the flavour groups and representations providing, in the symmetric limit, an approximate description of lepton masses and mixings? We assume that neutrinos masses are described by the Weinberg operator. We find that in all cases the neutrinos are either anarchical or have an inverted hierarchical spectrum. In the context of SU(5) unification, only the anarchical option is allowed. Therefore, if the hint of a normal hierarchical spectrum were confirmed, we would conclude that symmetry breaking effects must play a primary role in the understanding of neutrino flavour observables.
We investigate the structure of different softs terms in the context of an A4xSU(5) SUSY GUT model. While starting from a minimal flavour violation (MFV) benchmark point which lies in the correct region for dark matter constraint and giving the experimental value of muon g-2, we perform a scan over the different off-diagonal soft terms and study the impact of the flavour and dark matter constraint on the flavour violating parameters. Since SU(5) enforces relations between the hadronic and leptonic parameters, interesting restrictions can arise from both sectors. This study shows how flavoured SUSY GUTs may be distinguished via their flavour predictions.
Constrained Sequential neutrino Dominance of type 2 (referred to as CSD2) is an attractive building block for Grand Unified Theory (GUT) flavour models because it predicts a non-zero leptonic mixing angle $\theta_{13}^{PMNS}$, a deviation of $\theta_{23}^{PMNS}$ from $\pi /4$, as well as a leptonic Dirac CP phase $\delta^{PMNS}$ which is directly linked to the CP violation relevant for generating the baryon asymmetry via the leptogenesis mechanism. When embedded into GUT flavour models, these predictions are modified in a predictive way, depending on which GUT operators are responsible for generating the fermion Yukawa matrices. In this paper, we systematically investigate and classify the resulting predictions from $\mathrm{SU}(5)$ based flavour models, in order to select the most promising routes for future model building.
I will discuss a simple $U(2)$ flavor model compatible with an $SU(5)$ GUT structure. All hierarchies in fermion masses and mixings arise from powers of two small parameters that control the $U(2)$ breaking pattern. In contrast to previous $U(2)$ models this setup can be realized without supersymmetry and provide an excellent fit to all SM flavor observables including neutrinos, thus predicting an upper bound on the neutrino mass scale below current cosmological bounds. A variant of this model is based on a $D_6 \times U(1)_F$ flavor symmetry, which closely resembles the $U(2)$ structure, but allows for Majorana neutrino masses from the Weinberg operator. Remarkably, in this case the structure of neutrino masses is closely tied to the quark sector, and one naturally obtains large mixing in the lepton sector from small mixing in the quark sector. Finally the model offers a natural option for adressing the Strong CP Problem and Dark Matter by identifying the Goldstone boson of the $U(1)_F$ factor as the QCD axion.
The Standard Model (SM) of particle physics is a big success. However, it lacks
an explanation of cosmic inflation, of the matter-anti-matter asymmetry of the Universe, of dark matter, of neutrino oscillations, and of the feebleness of strong CP violation. The latter may be explained by an extension of the Standard Model by a complex scalar field charged under a spontaneously broken global U(1) Peccei-Quinn (PQ) symmetry. Moreover, the pseudo Nambu-Goldstone boson of this breaking - the axion - may play the role of dark matter. Furthermore, the PQ scalar can feature as a viable inflaton candidate if its possible non-minimal coupling to the Ricci scalar is taken into account. Finally, adding three extra SM-singlet neutrinos, the model dubbed SMASH -- for SM-Axion-Seesaw-Higgs portal inflation -- solves all the five problems mentioned above at one stroke. It can be probed decisively by upcoming cosmic microwave background and dark matter experiments.
To be filled later
The hope of relating fermion masses and mixing angles to
some fundamental underlying principle, has fostered an intense activity
aimed at identifying possible symmetry patterns in the data.
Neutrino masses and lepton mixing angles have played an important
role in such attempts. In this talk I will illustrate a new class of models where
the role of flavour symmetry is played by the modular invariance.
Modular invariance is ubiquitous in string theory and in condense matter
systems. I will explain how it can be exploited to constrain neutrino masses
and mixing angles and I will illustrate its remarkable and unique properties
in this context.
In this talk, we fully discuss the old idea of parametrizing fermion mixing through the corresponding fermion masses. We begin by showing how 't Hooft's criteria for naturalness could be employed to build a new mixing parametrization with the right behaviour to allow the emergence of new symmetries, whenever considering either the first or the first two lightest families equal to zero. Thereafter, by virtue of these limits, a rough estimation of quark mixing is obtained in well agreement to its present experimental values. We end by discussing a particular parametrization where such relations between mixing angles and only mass ratios were achieved, that, however, do not fulfill all the conditions that naturalness imply.
It is well known that a mass relation for the charged leptons,
$(m_e +m_\mu + m_\tau)/(\sqrt{m_e} +\sqrt{m_\mu} +\sqrt{m_\tau})^2
=2/3$, is excellently satisfied by the observed masses (pole mass).
However, this excellent coincidence is just a big problem, because
``mass" in a field theoretical model means a running mass, not
pole mass. For this problem, Sumino has proposed a way out by
introducing family gauge bosons. But his model is a model with
non-anomaly free, so that the model is not so attractive.
A model with anomaly free
proposed by Yamashita and Y.K. is
reviewed together with recent progress.
The recent data of both T2K and NOνA indicate the atmospheric neutrino mixing angle θ23 to be near the maximal angle 45◦. The closer the observed θ23 is to the maximal mixing, the more likely some ﬂavor symmetry behind it. In order to confirm the flavor symmetry, it is advantageous to consider the minimum number of parameters needed for reproducing the neutrino mixing angles and CP violating phases completely. We dicuss the flavor model with A4 symmetry in the minimal scheme of flavons focusing on the CP violation. We also discuss the A4 symmetry as the modular group.
We consider the $A_4$, $S_4$ and $A_5$
discrete lepton flavour symmetries
in the case of 3-neutrino mixing,
broken down to non-trivial residual symmetries in
the charged lepton and neutrino sectors in such a way that
at least one of them is a $Z_2$.
Such symmetry breaking patterns lead to predictions
for some of the three neutrino mixing angles and/or
the leptonic Dirac CP violation phase $\delta$
of the neutrino mixing matrix.
We assess the viability of these predictions by
performing a statistical analysis
which uses as an input the latest
global data on the neutrino mixing parameters.
We find 14 phenomenologically viable cases
providing distinct predictions for some of the mixing angles
and/or the Dirac phase δ.
Employing the current best fit values of the
three neutrino mixing angles,
we perform a statistical analysis of these cases
taking into account the prospective uncertainties
in the determination of the mixing angles,
planned to be achieved in currently running (Daya Bay)
and the next generation (JUNO, T2HK, DUNE) of neutrino oscillation experiments.
We find that only six cases would be compatible with these prospective data.
We show that this number is likely to be further reduced
by a precision measurement of $\delta$.
We study the lepton flavor models, whose flavor symmetries are finite
subgroups of the modular group such as S3 and A4.
In our models, couplings are also non-trivial representations of these
groups and modular functions of the modulus.
We study the possibilities that these models realize realistic values of
neutrino masses and lepton mixing angles.
This talk is based on our paper arXiv:1803.10391 and additional study.
Flavor symmetries à la Froggatt-Nielsen (FN) provide a compelling way to explain the hierarchies of fermionic masses and mixing angles in the Yukawa sector. In Supersymmetric (SUSY) extensions of the Standard Model where the mediation of SUSY breaking occurs at scales larger than the breaking of flavor, this symmetry must be respected not only by the Yukawas of the superpotential, but by the soft-breaking masses and trilinear terms as well. Here, I will show that contrary to naive expectations, even starting with completely flavor blind soft-breaking in the full theory at high scales, the low-energy sfermion mass matrices and trilinear terms of the effective theory, obtained upon integrating out the heavy mediator ?fields, are strongly non-universal.
Supersymmetric theories supplemented by an underlying flavor-symmetry provide a rich playground for model building aimed at explaining the flavor structure of the Standard Model. In the case where supersymmetry breaking is mediated by gravity, the soft-breaking Lagrangian typically exhibits large tree-level flavor violating effects, even if it stems from an ultraviolet flavor-conserving origin. Here, I will show the results of our phenomenological analysis of these models with a particular emphasis on the leptonic flavor observables. We consider some representative models which aim to explain the flavor structure of the lepton sector.
Will be added later