Generalised CP symmetry in modular-invariant models of flavour

Novichkov, P. P.; Penedo, J. T.; Petcov, S.T.; Titov, Arsenii

doi:10.1007/jhep07(2019)165

Cited by 165 publications

(194 citation statements)

References 51 publications

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“…This observation was reported in our earlier paper[17] and was subsequently incorporated in an explicit bottom-up flavor construction in[25].…”

supporting

confidence: 71%

“…The main focus there was on the description of the flavor structure of the lepton sector of the Standard Model (based on the finite modular groups Γ N for N = 2, 3, 4, 5), where modular transformations seem to be particularly successful. There has been less work on the quark sector [46,47,52,55] and the question of CP symmetries has usually not been discussed (with the recent exception of [25]). Time has come to analyze possible connections of the bottom-up constructions with the rules and lessons from string theory presented in this paper.…”

Section: Discussionmentioning

confidence: 99%

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A string theory of flavor and CP

et al. 2019

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Modular transformations of string theory (including the well-known stringy dualities) play a crucial role in the discussion of discrete flavor symmetries in the Standard Model. They are at the origin of CP-transformations and provide a unification of CP with traditional flavor symmetries. Here, we present a novel, fully systematic method to reliably compute the unified flavor symmetry of the low-energy effective theory, including enhancements from the modular transformations of string theory. The unified flavor group is non-universal in moduli space and exhibits the phenomenon of "Local Flavor Unification" where different sectors of the theory can be subject to different flavor structures.

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“…This observation was reported in our earlier paper[17] and was subsequently incorporated in an explicit bottom-up flavor construction in[25].…”

supporting

confidence: 71%

Section: Discussionmentioning

confidence: 99%

A string theory of flavor and CP

et al. 2019

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“…10 in Appendix C), where CP is conserved. This result strongly supports the indication that, in a CP invariant model, even a tiny departure from the region of moduli space where CP is preserved can cause large observable CP -violating effects [11]. We also notice that all the components of the multiplet ϕ are of the same order, indicating that the charged lepton mass matrix is far from the diagonal form, related to ϕ ∝ (1, 0, 0).…”

Section: Numerical Results At Levelsupporting

confidence: 85%

Modular invariant models of lepton masses at levels 4 and 5

Criado

Feruglio

King

2020

J. High Energ. Phys.

111

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We explore alternative descriptions of the charged lepton sector in modular invariant models of lepton masses and mixing angles. In addition to the modulus, the symmetry breaking sector of our models includes ordinary flavons. Neutrino mass terms depend only on the modulus and are tailored to minimize the number of free parameters. The charged lepton Yukawa couplings rely upon the flavons alone. We build modular invariant models at levels 4 and 5, where neutrino masses are described both in terms of the Weinberg operator or through a type I seesaw mechanism. At level 4, our models reproduce the hierarchy among electron, muon and tau masses by letting the weights play the role of Froggatt-Nielsen charges. At level 5, our setup allows the treatment of left and right handed charged leptons on the same footing. We have optimized the free parameters of our models in order to match the experimental data, obtaining a good degree of compatibility and predictions for the absolute neutrino masses and the CP violating phases. At a more fundamental level, the whole lepton sector could be correctly described by the simultaneous presence of several moduli. Our examples are meant to make a first step in this direction. arXiv:1908.11867v1 [hep-ph] 30 Aug 2019 Recently, modular invariance has been invoked as candidate flavour symmetry [10]. In its simplest implementation a unique complex field, the modulus, acts as symmetry breaking parameter, thus simplifying the vacuum alignment problem. Modular invariance, in the limit of exact supersymmetry, completely determines the Yukawa couplings, to any order of the expansion in powers of the modulus. Moreover, neutrino masses, mixing angles and phases are all related to each other and, in minimal models, depend only on a few parameters. The formalism has been extended to consistently include CP transformations [11] 1 and it can involve several moduli [16,17]. The idea that Yukawa couplings are determined by a set of moduli is clearly not new, and has been naturally realized in the context of string theory [18][19][20][21][22], in D-brane compactification [23][24][25][26][27][28][29], in magnetized extra dimensions [30][31][32], and in orbifold compactification [33][34][35][36]. Modular invariance has also been incorporated in early flavour models [37][38][39][40][41]. However, the main advantage of the recent approach is that it can be implemented in a bottom-up perspective, relying on the group transformation properties of modular forms of given weight and level. Several models of lepton masses and mixing angles have been built at level 2 [42, 43], 3 [10, 44-47], 4 [48-50] and 5 [51,52]. Extensions to quarks [53,54] and to grand unified theories [55,56] have also been proposed. In most of the existing constructions, there is a unique symmetry breaking parameter: the modulus itself. While this scenario is certainly appealing since it minimizes the symmetry breaking sector, it does not yet provide a convincing explanation of the charged lepton masses. The mass hierarchy is achieved by...

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“…The formalism with a single complex modulus field τ has also been extended to the case of multiple moduli fields τ i [41]. The generalized CP symmetry in modular invariant models are studied in [42]. The formalism of modular invariant approach has extended to include odd weight modular forms [43].…”

Section: Introductionmentioning

confidence: 99%

Modular A4 symmetry models of neutrinos and charged leptons

Ding

King

Liu

2019

J. High Energ. Phys.

122

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We present a comprehensive analysis of neutrino mass and lepton mixing in theories with A 4 modular symmetry, where the only flavon field is the single modulus field τ , and all masses and Yukawa couplings are modular forms. Similar to previous analyses, we discuss all the simplest neutrino sectors arising from both the Weinberg operator and the type I seesaw mechanism, with lepton doublets and right-handed neutrinos assumed to be triplets of A 4 . Unlike previous analyses, we allow right-handed charged leptons to transform as all combinations of 1, 1 and 1 representations of A 4 , using the simplest different modular weights to break the degeneracy, leading to ten different charged lepton Yukawa matrices, instead of the usual one. This implies ten different Weinberg models and thirty different type I seesaw models, which we analyse in detail. We find that fourteen models for both NO and IO neutrino mass ordering can accommodate the data, as compared to one in previous analyses, providing many new possibilities. *

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Generalised CP symmetry in modular-invariant models of flavour

Cited by 165 publications

References 51 publications

A string theory of flavor and CP

A string theory of flavor and CP

Modular invariant models of lepton masses at levels 4 and 5

Modular A4 symmetry models of neutrinos and charged leptons

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