CP symmetry and symplectic modular invariance

Ding, Gui-Jun; Feruglio, Ferruccio; Liu, Xiang-Gan

doi:10.21468/SciPostPhys.10.6.133

SciPost Physics

CP symmetry and symplectic modular invariance

Gui-Jun Ding, Ferruccio Feruglio, Xiang-Gan Liu

SciPost Phys. 10, 133 (2021) · published 7 June 2021

doi: 10.21468/SciPostPhys.10.6.133
pdf
Submissions/Reports

Abstract

We analyze CP symmetry in symplectic modular-invariant supersymmetric theories. We show that for genus $g\ge 3$ the definition of CP is unique, while two independent possibilities are allowed when $g\le 2$. 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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.10.6.133
TI  - CP symmetry and symplectic modular invariance
PY  - 2021/06/07
UR  - https://www.scipost.org/SciPostPhys.10.6.133
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 10
IS  - 6
SP  - 133
A1  - Ding, Gui-Jun
AU  - Feruglio, Ferruccio
AU  - Liu, Xiang-Gan
AB  - We analyze CP symmetry in symplectic modular-invariant supersymmetric theories. We show that for genus $g\ge 3$ the definition of CP is unique, while two independent possibilities are allowed when $g\le 2$. 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.
ER  -

@Article{10.21468/SciPostPhys.10.6.133,
	title={{CP symmetry and symplectic modular invariance}},
	author={Gui-Jun Ding and Ferruccio Feruglio and Xiang-Gan Liu},
	journal={SciPost Phys.},
	volume={10},
	pages={133},
	year={2021},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.10.6.133},
	url={https://scipost.org/10.21468/SciPostPhys.10.6.133},
}

Cited by 38

Liu et al., Modular flavor symmetry and vector-valued modular forms
J. High Energ. Phys. 2022, 123 (2022) [Crossref]
Kobayashi et al., Lepton flavor violation, lepton (g − 2)μ, e and electron EDM in the modular symmetry
J. High Energ. Phys. 2022, 13 (2022) [Crossref]
Feruglio,
396, 449 (2022) [Crossref]
Ding et al., Neutrino mass and mixing models with eclectic flavor symmetry ∆(27) ⋊ T′
J. High Energ. Phys. 2023, 144 (2023) [Crossref]
Petcov et al., A4 modular flavour model of quark mass hierarchies close to the fixed point τ = i∞
J. High Energ. Phys. 2023, 86 (2023) [Crossref]
Qu et al., Flavor mixing and CP violation from the interplay of an S4 modular group and a generalized CP symmetry
Phys. Rev. D 104, 076001 (2021) [Crossref]
Ding et al., SO(10) models with A4 modular symmetry
J. High Energ. Phys. 2021, 7 (2021) [Crossref]
Nomura et al., Linear seesaw model with a modular S 4 flavor symmetry *
Chinese Phys. C 46, 053101 (2022) [Crossref]
Ding et al., A minimal modular invariant neutrino model
J. High Energ. Phys. 2023, 125 (2023) [Crossref]
Novichkov et al., Modular invariance approach to the flavour problem (from bottom up)
Int. J. Mod. Phys. A 39, 2441011 (2024) [Crossref]
de Medeiros Varzielas et al., Quarks at the modular S4 cusp
J. High Energ. Phys. 2023, 196 (2023) [Crossref]
Baur et al., Top-down anatomy of flavor symmetry breakdown
Phys. Rev. D 105, 055018 (2022) [Crossref]
Novichkov et al., Modular flavour symmetries and modulus stabilisation
J. High Energ. Phys. 2022, 149 (2022) [Crossref]
Li et al., Eclectic flavor group ∆(27) ⋊ S3 and lepton model building
J. High Energ. Phys. 2024, 54 (2024) [Crossref]
Petcov et al., $$A_4$$ modular flavour model of quark mass hierarchies close to the fixed point $$\tau = \omega $$
Eur. Phys. J. C 83, 579 (2023) [Crossref]
Qu et al., Non-holomorphic modular flavor symmetry
J. High Energ. Phys. 2024, 136 (2024) [Crossref]
Li et al., Modular symmetry at level 6 and a new route towards finite modular groups
J. High Energ. Phys. 2021, 238 (2021) [Crossref]
Petcov et al., $$A_4$$ modular invariance and the strong CP problem
Eur. Phys. J. C 84, 914 (2024) [Crossref]
Kobayashi et al., Modular flavor symmetric models
Int. J. Mod. Phys. A 39, 2441012 (2024) [Crossref]
Kikuchi et al., Zero-modes in magnetized T6/ZN orbifold models through Sp(6,Z) modular symmetry
Phys. Rev. D 108, 036005 (2023) [Crossref]
Nomura et al., Quark and lepton flavor model with leptoquarks in a modular $$A_4$$ symmetry
Eur. Phys. J. C 81, 947 (2021) [Crossref]
Singh et al., Minimal type-I Dirac seesaw and leptogenesis under A4 modular invariance
Nuclear Physics B 1007, 116666 116666 (2024) [Crossref]
Tanimoto et al., Electron EDM arising from modulus τ in the supersymmetric modular invariant flavor models
J. High Energ. Phys. 2021, 183 (2021) [Crossref]
Ding et al., Universal predictions of Siegel modular invariant theories near the fixed points
J. High Energ. Phys. 2024, 52 (2024) [Crossref]
Knapp-Pérez et al., Matter matters in moduli fixing and modular flavor symmetries
Physics Letters B 844, 138106 138106 (2023) [Crossref]
Nilles et al., Orbifolds from Sp(4,Z) and their modular symmetries
Nuclear Physics B 971, 115534 115534 (2021) [Crossref]
Nagao et al., Modular A4 symmetry and light dark matter with gauged U(1)B−L
Physics of the Dark Universe 36, 101039 101039 (2022) [Crossref]
Feruglio, Fermion masses, critical behavior and universality
J. High Energ. Phys. 2023, 236 (2023) [Crossref]
Arriaga-Osante et al., Quark and lepton modular models from the binary dihedral flavor symmetry
J. High Energ. Phys. 2024, 119 (2024) [Crossref]
Ding et al., Modular binary octahedral symmetry for flavor structure of Standard Model
J. High Energ. Phys. 2023, 83 (2023) [Crossref]
Ding et al., Modular S4×SU(5) GUT
Phys. Rev. D 104, 055034 (2021) [Crossref]
Okada et al., Lepton mass matrix from double covering of A 4 modular flavor symmetry*
Chinese Phys. C 46, 123108 (2022) [Crossref]
Ding et al., Leptogenesis in SO(10) models with A4 modular symmetry
J. High Energ. Phys. 2022, 71 (2022) [Crossref]
Kikuchi et al., Modular symmetry in magnetized T2g torus and orbifold models
Phys. Rev. D 109, 065011 (2024) [Crossref]
Okada et al., Modulus τ linking leptonic CP violation to baryon asymmetry in A4 modular invariant flavor model
J. High Energ. Phys. 2021, 184 (2021) [Crossref]
Kobayashi et al., Dark matter stability at fixed points in a modular A4 symmetry
Physics of the Dark Universe 37, 101080 101080 (2022) [Crossref]
Baur et al., Completing the eclectic flavor scheme of the ℤ2 orbifold
J. High Energ. Phys. 2021, 110 (2021) [Crossref]
Kikuchi et al., Number of zero-modes on magnetized T4/ZN orbifolds analyzed by modular transformation
J. High Energ. Phys. 2023, 13 (2023) [Crossref]

Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.

¹ ² Gui-Jun Ding,
³ ⁴ Ferruccio Feruglio,
¹ ² Xiang-Gan Liu

Funders for the research work leading to this publication

Horizon 2020 (through Organization: European Commission [EC])
Instituto Nazionale di Fisica Nucleare (INFN) (through Organization: Istituto Nazionale di Fisica Nucleare / National Institute for Nuclear Physics [INFN])
National Natural Science Foundation of China [NSFC]