Modular invariance and the QCD angle

Feruglio, Ferruccio; Струмиа, Алессандро; Titov, Arsenii

doi:10.1007/jhep07(2023)027

Cited by 18 publications

(5 citation statements)

References 75 publications

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“…Radiative corrections and supersymmetry breaking effects are negligible in a large portion of the parameter space [4]. Invariance under the modular group offers a simple, axion-free solution to the strong CP problem [5]. Moreover, such a framework is intimately related to the basic properties of superstring compactifications , allowing the bottom-up and top-down approaches to reinforce each other [28].…”

Section: Introductionmentioning

confidence: 99%

CP symmetry and symplectic modular invariance

2021

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

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Section: Introductionmentioning

confidence: 99%

CP symmetry and symplectic modular invariance

2021

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“…(3.2). Imposing gCP, all α i are made real 9 and the number of real parameter matches the number of observables, as previously commented: (4 × 2) + 2 = 10, independently of whether Q or q c is a triplet. Lifting the requirement of gCP in the case Q ∼ 3 * generically leads to one extra physical phase in each matrix, since the u c β and d c β can be rephased independently to absorb all arg(α 1,2,3 ).…”

Section: Jhep09(2023)196mentioning

confidence: 89%

“…1 Modular invariance may also play a role in solving the strong CP problem [9]. 2 In the case of the finite groups Γ ′ N , an extra residual Z R 2 is preserved [14].…”

Section: Introductionmentioning

confidence: 99%

Quarks at the modular S4 cusp

de Medeiros Varzielas,

Levy,

Penedo

et al. 2023

J. High Energ. Phys.

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We analyse the possibility of describing quark masses, mixing and CP violation in $$ {S}_4^{\prime } $$ S 4 ′ modular flavour models without flavons. We focus on the case where the closeness of the modulus to the point of residual $$ {\mathbb{Z}}_3^{ST} $$ ℤ 3 ST symmetry (the cusp) plays a role in generating quark mass hierarchies and discuss the role modular form normalisations play in such constructions. We find that fitting quark data requires explicit CP breaking, unless a second modulus is introduced.

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“…Hence the modular invariant models could involve a small number of free parameters, and they can predict not only the lepton mixing but also lepton masses. Moreover, modular symmetry has been used to address the strong CP problem [279,280], and it is also exploited to new physics beyond SM [281][282][283][284][285][286][287][288][289][290][291][292][293]. The 28 The representation ρφ and weight kφ of matter fields can be freely assigned in bottom-up models, while they could possibly be fixed in the top-down approach [156,157,239,240,278].…”

Section: General Model Building Considerations and Overview Of Modelsmentioning

confidence: 99%

Neutrino mass and mixing with modular symmetry

Ding,

King

2024

Rep. Prog. Phys.

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This is a review article about neutrino mass and mixing and flavour model building strategies based on modular symmetry. After an introduction to neutrino mass and lepton mixing, we then turn to the main subject of this review, namely a pedagogical introduction to modular symmetry as a candidate for family symmetry, from the bottom-up point of view. After an informal introduction to modular symmetry, we introduce the modular group, and discuss its fixed points and residual symmetry, assuming supersymmetry throughout. We then introduce finite modular groups of level N and modular forms with integer or rational modular weights, corresponding to simple geometric groups or their double or metaplectic covers, including the most general finite modular groups and vector-valued modular forms, with detailed results for N=2,3,4,5. The interplay between modular symmetry and generalized CP symmetry is discussed, deriving CP transformations on matter multiplets and modular forms, highlighting the CP fixed points and their implications. In general, compactification of extra dimensions generally leads to a number of moduli, and modular invariance with factorizable and non-factorizable multiple moduli based on symplectic modular invariance and automorphic forms is reviewed. Modular strategies for understanding fermion mass hierarchies are discussed, including the weighton mechanism, small deviations from fixed points, and texture zeroes. Then examples of modular models are discussed based on single modulus A4 models, a minimal S′4 model of leptons (and quarks), and a multiple moduli model based on three S4 groups capable of reproducing the Littlest Seesaw model. We then extend the discussion to include Grand Unified Theories (GUTs) based on modular (flipped) SU(5) and SO(10). Finally we discuss top-down approaches, including eclectic flavour symmetry and moduli stabilisation.

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Modular invariance and the QCD angle

Cited by 18 publications

References 75 publications

CP symmetry and symplectic modular invariance

CP symmetry and symplectic modular invariance

Quarks at the modular S4 cusp

Neutrino mass and mixing with modular symmetry

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