Charged lepton flavor violation in supersymmetric low-scale seesaw models

We study charged lepton flavor violation in low-scale seesaw models of minimal supergravity, which realize large neutrino Yukawa couplings thanks to approximate lepton-number symmetries. There are two dominant sources of lepton flavor violation in such models. The first source originates from the usual soft supersymmetry-breaking sector, whilst the second one is entirely supersymmetric and comes from the supersymmetric neutrino Yukawa sector. Within the framework of minimal supergravity, we consider both sources of lepton flavor violation, soft and supersymmetric, and calculate a number of possible lepton-flavor-violating transitions, such as the photonic decays of muons and taus, $\mu \to e\gamma$, $\tau \to e\gamma$ and $\tau \to \mu \gamma$, their neutrinoless three-body decays, $\mu \to eee$, $\tau \to eee$, $\tau \to \mu \mu \mu$, $\tau \to ee\mu$ and $\tau \to e\mu \mu$, and the coherent $\mu \to e$ conversion in nuclei. After taking into account the exclusion bounds placed by present experiments of lepton flavor violation, we derive combined theoretical limits on the universal heavy Majorana mass scale $m_N$ and the light-to-heavy neutrino mixings. Supersymmetric low-scale seesaw models offer distinct correlated predictions for lepton-flavor-violating signatures, which might be discovered in current and projected experiments, such as MEG, COMET/PRISM, Mu2e, super-BELLE and LHCb.

Figure 1

Feynman graphs contributing to $l\to l^{\prime }\gamma$ and $Z\to l^C{l}^{\prime }$ ($l\to Z{l}^{\prime }$) amplitudes.

Figure 2

Feynman graphs contributing to the box $l\to l^{\prime }{l}_1{l}_2^C$ amplitudes.

Figure 3

Numerical estimates of $B(\mu \to e\gamma )$ [blue (solid)], $B(\mu \to eee)$ [red (dashed)], $R_{\mu e}^{\mathrm{Ti}}$ [violet (dotted)] and $R_{\mu e}^{\mathrm{Au}}$ [green (dash-dotted)], as functions of $B(\mu \to e\gamma )$ (left panels) and the Yukawa parameter $a$ (right panels), for $m_N=400\mathrm{GeV}$ and $\tan \beta =10$. The upper two panels correspond to the Yukawa texture (2.4), with $a=b$ and $c=0$, and the lower two panels to the Yukawa texture (2.5), with $a=b=c$.

Figure 4

The same as in Fig. 3, but for $m_N=1\mathrm{TeV}$.

Figure 5

Numerical estimates of $B(\tau \to e\gamma )$ [blue (solid)], $B(\tau \to eee)$ [red (dashed)] and $B(\tau \to e\mu \mu )$ [violet (dotted)], as functions of $B(\tau \to e\gamma )$ (left panels) and the Yukawa parameter $a$ (right panels), for $m_N=400\mathrm{GeV}$ and $\tan \beta =10$. The upper panels present predictions for the Yukawa texture (2.4), with $a=c$ and $b=0$, and the lower panels for the Yukawa texture (2.5), with $a=b=c$.

Figure 6

The same as in Fig. 5, but for $m_N=1\mathrm{TeV}$.

Figure 7

Numerical estimates of $B(\mu \to e\gamma )$ [blue (solid)], $B(\mu \to eee)$ [red (dashed)], $R_{\mu e}^{\mathrm{Ti}}$ [violet (dotted)] and $R_{\mu e}^{\mathrm{Au}}$ [green (dash-dotted)], as functions of $B(\mu \to e\gamma )$ (left panels) and the heavy neutrino mass scale $m_N$ (right panels). In all panels, the Yukawa parameter $a$ was kept fixed by the condition $B(\mu \to e\gamma )={10}^{-12}$ for $m_N=400\mathrm{GeV}$, and $\tan \beta =10$ was used. The upper panels display numerical values for the Yukawa texture (2.4), with $a=b$ and $c=0$, and the lower panels for the Yukawa texture (2.5), with $a=b=c$.

Figure 8

Contours of the Yukawa parameters $(a,b,c)$ versus $m_N$, for $B(\mu \to e\gamma )$ [blue (solid)], $B(\mu \to eee)$ [red (dashed)], $R_{\mu e}^{\mathrm{Ti}}$ [violet (dotted)] and $R_{\mu e}^{\mathrm{Au}}$ [green (dash-dotted)], where $a$ and $m_N$ are determined by the condition $B(\mu \to e\gamma )={10}^{-12}$. All contours are evaluated with $\tan \beta =10$ and for different Yukawa textures, as indicated by the vertical axes labels.

Figure 9

Contours of the Yukawa parameters $(a,b,c)$ versus $m_N$, for $B(\tau \to e\gamma )$ [blue (solid)], where $\tan \beta =10$ and $a$ and $m_N$ are determined by the condition $B(\tau \to e\gamma )={10}^{-9}$. No solutions have been found for $B(\tau \to eee)$ and $B(\tau \to e\mu \mu )$.

Figure 10

Numerical estimates of $B(\mu \to e\gamma )$ [blue (solid)], $B(\mu \to eee)$ [red (dashed)], $R_{\mu e}^{\mathrm{Ti}}$ [violet (dotted)] and $R_{\mu e}^{\mathrm{Au}}$ [green (dash-dotted)], as functions of $\tan \beta$. The upper panels are obtained for $m_N=400\mathrm{GeV}$ and the lower panels for $m_N=1\mathrm{TeV}$. The left panels use the Yukawa texture (2.4), with $a=b$ and $c=0$, and the right panels the Yukawa texture (2.5), with $a=b=c$. In all panels, the Yukawa parameter $a$ is determined by the condition $B(\mu \to e\gamma )={10}^{-12}$.

Figure 11

Numerical estimates of the ratios $R_2(\mu \to eee)$, $R_3^{\mathrm{Ti}}$ and $R_3^{\mathrm{Au}}$, as functions of $m_N$. The Yukawa parameter $a$ is fixed by the condition $B(\mu \to e\gamma )={10}^{-12}$, for $m_N=400\mathrm{GeV}$ and $\tan \beta =10$. In the upper panel, thick lines give the complete evaluation of $R_2(\mu \to eee)$ [blue (solid)], $R_3^{\mathrm{Ti}}$ [red (dashed)] and $R_3^{\mathrm{Au}}$ [violet (dotted)], while the respective thin lines are evaluated keeping only the magnetic dipole form factors $G_{\gamma }^L$ and $G_{\gamma }^R$. The two middle panels provide a form factor analysis of $R_2(\mu \to eee)$ and $R_3^{\mathrm{Au}}$, in terms of contributions due to $G_{\gamma }$ and $F_{\gamma }$ [blue (solid)], $F_Z$ [red (dashed)] and box form factors [violet (dotted)]. The lower two panels show the separate contributions due to heavy neutrinos $N$ [blue (solid)], sneutrinos $\tilde{N}$ [red (dashed)] and soft SUSY-breaking LFV terms [violet (dotted)]. The green (horizontal) lines in the middle and lower panels give the predicted values obtained by assuming that only the $G_{\gamma }^{L,R}$ form factors contribute to the amplitudes.