We present a comprehensive analysis of neutrino mass and lepton mixing in theories with $A_5$ modular symmetry. construct the weight 2, 4 6 forms level 5 terms Dedekind eta-functions Klein forms, their decomposition into irreducible representation $A_5$. all simplest models based on symmetry, including scenarios without flavons charged sectors. For each case, masses can be generated through either Weinberg operator or type I seesaw mechanism. perform an exhaustive numerical analysis,...

We present a comprehensive analysis of neutrino mass and lepton mixing in theories with $A_4$ modular symmetry, where the only flavon field is single modulus $\tau$, all masses Yukawa couplings are forms. Similar to previous analyses, we discuss simplest sectors arising from both Weinberg operator type I seesaw mechanism, doublets right-handed neutrinos assumed be triplets $A_4$. Unlike allow charged leptons transform as combinations $\mathbf{1}$, $\mathbf{1}'$ $\mathbf{1}''$ representations...

A bstract In the modular symmetry approach to neutrino models, flavour emerges as a finite subgroup Γ N of symmetry, broken by vacuum expec- tation value (VEV) modulus field τ . If VEV takes some special value, residual would be preserved. We derive fixed points S = i , ST ( − 1 + $$ \sqrt{3} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msqrt> <mml:mn>3</mml:mn> </mml:msqrt> </mml:math> ) / 2, TS (1 T i∞ in fundamental domain which are in-variant under transformations...

The even weight modular forms of level $N$ can be arranged into the common irreducible representations inhomogeneous finite group $\Gamma_N$ and homogeneous $\Gamma'_N$ which is double covering $\Gamma_N$, odd transform in new $\Gamma'_N$. We find that above structure naturally generate texture zeros fermion mass matrices if we properly assign weights matter fields under group. perform a comprehensive analysis for $\Gamma'_3\cong T'$ symmetry. three generations left-handed quarks are assumed...

We perform a comprehensive analysis of the homogeneous finite modular group $Γ'_4\equiv S'_4$ which is double covering $S_4$ group. The weight 1 forms level 4 are constructed in terms Dedekind eta function, and they transform as triplet $\mathbf{\hat{3}'}$ $S'_4$. integral until 6 built from tensor products forms. systematical classification $S'_4$ models for lepton masses mixing with/without generalized CP, where left-handed leptons assigned to right-handed charged singlets under $S'_4$, we...

We extend the even weight modular forms of invariant approach to general integral forms. find that weights and level $N$ can be arranged into irreducible representations homogeneous finite group $\Gamma'_N$ which is double covering $\Gamma_N$. The lowest 1 3 are constructed in terms Dedekind eta-function, they transform as a doublet $\Gamma'_3 \cong T'$. 2, 3, 4, 5 6 presented. build model lepton masses mixing based on $T'$ symmetry.

A bstract We extend the framework of modular invariant supersymmetric theories to encompass invariance under more general discrete groups Γ, that allow presence several moduli and make connection with theory automorphic forms. Moduli span a coset space G / K , where is Lie group compact subgroup modded out by Γ. For choice Γ generic matter content, we explicitly construct minimal Kähler potential superpotential, for both rigid local $$ \mathcal{N} <mml:math...

We perform a comprehensive study of the homogeneous finite modular group ${A}_{5}^{\ensuremath{'}}$ which is double covering ${A}_{5}$. The integral weight and level 5 forms have been constructed up to 6 they are decomposed into irreducible representations ${A}_{5}^{\ensuremath{'}}$. Then we systematical analysis models for lepton masses mixing. phenomenologically viable with minimal number free parameters results fit presented. find out 15 9 real can accommodate experimental data sector....

We analyze CP symmetry in symplectic modular-invariant supersymmetric theories. show that for genus $g\ge 3$ the definition of is unique, while two independent possibilities are allowed when $g\le 2$. discuss transformation properties moduli, matter multiplets and modular forms Siegel upper half plane, as well invariant subspaces. identify CP-conserving surfaces fundamental domain moduli space. make use all these elements to build a model lepton masses mixing angles, where known data...

Modular flavor symmetries provide us with a very compelling approach to the problem. It has been argued that moduli values close some special like $\tau=i$ or $\tau=\omega$ best fits data. We point out presence of hidden "matter" fields, needed uplift symmetric AdS vacua, gives rise dynamical mechanism leads such $\tau$.

We generalize the modular invariance approach to include half-integral weight forms. Accordingly group should be extended its metaplectic covering for consistency. introduce well-defined forms congruence subgroup $\mathrm{\ensuremath{\Gamma}}(4N)$ and show that they can decomposed into irreducible multiplets of finite ${\stackrel{\texttildelow{}}{\mathrm{\ensuremath{\Gamma}}}}_{4N}$. construct concrete expressions half-integral/integral $\mathrm{\ensuremath{\Gamma}}(4)$ up 6 arrange them...

A bstract We present a neutrino mass model based on modular symmetry with the fewest input parameters to date, which successfully accounts for 12 lepton masses and mixing through 6 real free including modulus. The are predicted be normal ordering, atmospheric angle θ 23 is quite close maximal value Dirac CP phase δ about 1 . 34 π also study soft supersymmetry breaking terms due modulus F -term in this minimal model, constrained non-holomorphic forms. radiative flavor violation process μ → eγ...

The K\"ahler potentials of modular symmetry models receive unsuppressed contributions which may be controlled by a flavor symmetry, where the combination two types is referred to as eclectic symmetry. After briefly reviewing consistency conditions models, including with generalised (g)CP, we perform comprehensive bottom-up study based on $\Omega(1)\cong \Delta(27)\rtimes T^\prime$, consisting $\Delta(27)$ in semi-direct product $T^\prime$. transformations different multiplets are given...

A bstract We analyze a general class of locally supersymmetric, CP and modular invariant models lepton masses depending on two complex moduli taking values in the vicinity fixed point, where theory enjoys residual symmetry under finite group. Like that depend single modulus, we find all physical quantities exhibit universal scaling with distance from point. There is no dependence level construction, weights matter multiplets their representations, only restriction electroweak doublets...

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

A bstract We propose to construct the finite modular groups from quotient of two principal congruence subgroups as Γ( N′ )/Γ( N″ ), and group SL(2 , ℤ) is ex- tended a subgroup ). The original invariant theory reproduced when = 1. perform comprehensive study $$ {\Gamma}_6^{\prime } <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>Γ</mml:mi> <mml:mn>6</mml:mn> <mml:mo>′</mml:mo> </mml:msubsup> </mml:math> symmetry corresponding 1 6, five types models for lepton...

A bstract We have investigated the modular binary octahedral group 2 O as a flavor symmetry to explain structure of Standard Model. The vector-valued forms in all irreducible representations this are constructed. classified possible fermion mass models based on . comprehensive numerical analysis is performed, and we present some benchmark quark/lepton good agreement with experimental data. Notably find minimal invariant model for leptons quarks, which able simultaneously masses mixing...

A bstract Inspired by the structure of top-down derived models endowed with modular flavor symmetries, we investigate yet phenomenologically unexplored binary dihedral group 2 D 3 . After building vector-valued forms in representations small weights, systematically classify all (Dirac and Majorana) mass textures fermions fractional weights possible + 1-family structures. This allows us to explore parameter space fermion based on , aiming at a description both quarks leptons minimal number...

We have performed a systematical analysis of lepton and quark mass models based on ${\mathrm{\ensuremath{\Gamma}}}_{4}\ensuremath{\cong}{S}_{4}$ modular symmetry with generalized $CP$ symmetry. considered both cases; neutrinos are Majorana particles Dirac particles. All possible nontrivial representation assignments matter fields considered, the most general form fermion matrices given. The phenomenologically viable lowest number free parameters together results fit presented. find out nine...

We revisit the modular flavor symmetry from a more general perspective. The scalar forms of principal congruence subgroups are extended to vector-valued forms, then we have possible finite groups including $\Gamma_N$ and $\Gamma'_N$ as symmetry. theory provide method differential equation construct multiplets, it also reveals simple structure invariant mass models. review give results for lower dimensional forms. listed up order 72. apply formalism two new lepton models based on $A_4\times...

In modular invariant models of flavor, observables must be invariant. The discussed so far in the literature are functions modulus τ and its conjugate, τ¯. We point out that certain combinations depend only on τ, i.e. meromorphic, some cases even holomorphic τ. These functions, which we dub "invariants" this Letter, highly constrained, renormalization group invariant, allow us to derive many models' features without need for extensive parameter scans. illustrate robustness these invariants...

In modular invariant models of flavor, observables must be invariant. The discussed so far in the literature are functions modulus $\tau$ and its conjugate, $\bar\tau$. We point out that certain combinations depend only on $\tau$, i.e. meromorphic, some cases even holomorphic $\tau$. These functions, which we dub ``invariants'' this Letter, highly constrained, renormalization group invariant, allow us to derive many models' features without need for extensive parameter scans. illustrate...

We analyze a general class of locally supersymmetric, CP and modular invariant models lepton masses depending on two complex moduli taking values in the vicinity fixed point, where theory enjoys residual symmetry under finite group. Like that depend single modulus, we find all physical quantities exhibit universal scaling with distance from point. There is no dependence level construction, weights matter multiplets their representations, only restriction electroweak doublets transform as...