Lepton sector in modular \(A_4\) and gauged \(U(1)_R\) symmetry

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Abstract: We propose a lepton model under modular

A_{4}

and gauged

U (1)_{R}

symmetries, in which the neutrino masses are induced at one-loop level. Thanks to the modular

A_{4}

symmetry, we have several predictions on the lepton sector, especially, on fixed points of

a u = i, o m e g a e q u i v e^{2 p i i / 3}, i i m e s i n f t y

each of which has remnant symmetry;

Z_{2}

for

a u = i

and

Z_{3}

for

a u = o m e g a, i i n f t y

. These points are favored by a string theory and phenomenologically interesting.

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