A Constraint on Yukawa-Coupling Unification from Lepton-Flavor Violating Processes

Abstract

We present a new constraint on a lepton mixing matrix $V$ from lepton-flavor violating (LFV) processes in supersymmetric standard models with massive neutrinos. Here, we assume Yukawa-coupling unification $f_{\nu 3}\simeq f_{\mathrm{top}}$, in which $\tau$-neutrino Yukawa coupling $f_{\nu 3}$ is unified into top-quark Yukawa coupling $f_{\mathrm{top}}$ at the unification scale $M_{\ast }\simeq 3\times 10^{16}$ GeV. We show that the present experimental bound on $\mu \to e\gamma$ decay already gives a stringent limit on the lepton mixing (typically $V_{13}<0.02$ for $V_{23}=1/\sqrt{2}$). Therefore, many existing neutrino-mass models are strongly constrained. Future improvement of bounds on LFV processes will provide a more significant impact on the models with the Yukawa-coupling unification. We also stress that a precise measurement of a neutrino mixing $(V_{MNS}{)}_{e3}$ in future neutrino experiments would be very important, since the observation of non-zero $(V_{MNS}{)}_{e3}$, together with negative experimental results for the LFV processes, have a robust potential to exclude a large class of SUSY standard models with the Yukawa-coupling unification.

12 pages, 3 figures

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