Lepton flavor violating quarkonium decays

We argue that lepton flavor violating (LFV) decays $M\to {\ell }_1{\overline{\ell }}_2$ of quarkonium states $M$ with different quantum numbers could be used to put constraints on the Wilson coefficients of effective operators describing LFV interactions at low energy scales. We note that restricted kinematics of the two-body quarkonium decays allows us to select operators with particular quantum numbers, significantly reducing the reliance on the single operator dominance assumption that is prevalent in constraining parameters of the effective LFV Lagrangian. We shall also argue that studies of radiative lepton flavor violating $M\to \gamma {\ell }_1{\overline{\ell }}_2$ decays could provide important complementary access to those effective operators.

Figure 1

Feynman diagrams for $\mathcal{A}(V\to \gamma {\ell }_1{\overline{\ell }}_2)$. The black circles represent the four fermion LFV vertex, the black boxes represent the dipole LFV vertex, and the grey boxes represent the quarkonium bound state.

Figure 2

Differential decay rates as functions of photon energy $E_{\gamma }$ for axial operators. Plotted decay rates are for (a) $\mathrm{\Upsilon }(1S)\to \gamma \mu \tau$ or $\gamma e\tau$ (solid blue curve), $\mathrm{\Upsilon }(2S)\to \gamma \mu \tau$ or $\gamma e\tau$ (short-dashed gold curve), $\mathrm{\Upsilon }(3S)\to \gamma \mu \tau$ or $\gamma e\tau$ (dotted red curve), $\mathrm{\Upsilon }(1S)\to \gamma e\mu$ (dot-dashed green curve), $\mathrm{\Upsilon }(2S)\to \gamma e\mu$ and $\mathrm{\Upsilon }(3S)\to \gamma e\mu$ (long-dashed purple curve); (b) $J/\psi \to \gamma \mu \tau$ or $\gamma e\tau$ (solid blue curve), $\psi (2S)\to \gamma \mu \tau$ or $\gamma e\tau$ (short-dashed gold curve), $J/\psi \to \gamma e\mu$ (dotted red curve), $\psi (2S)\to \gamma e\mu$ (dot-dashed green curve); (c) $\rho \to \gamma e\mu$ (solid blue curve), $\omega \to \gamma e\mu$ (short-dashed gold curve), $\varphi \to \gamma e\mu$ (dotted red curve).

Figure 3

Differential decay rates as functions of photon energy $E_{\gamma }$ for scalar/pseudoscalar operators. Plotted decay rates are for (a) $\mathrm{\Upsilon }(1S)\to \gamma \mu \tau$ or $\gamma e\tau$ (solid blue curve), $\mathrm{\Upsilon }(2S)\to \gamma \mu \tau$ or $\gamma e\tau$ (short-dashed gold curve), $\mathrm{\Upsilon }(3S)\to \gamma \mu \tau$, $\gamma e\tau$, or $\gamma e\mu$ (dotted red curve), $\mathrm{\Upsilon }(1S)\to \gamma e\mu$ (dot-dashed green curve), $\mathrm{\Upsilon }(2S)\to \gamma e\mu$ (long-dashed purple curve); (b) $J/\psi \to \gamma \mu \tau$ or $\gamma e\tau$ (solid blue curve), $\psi (2S)\to \gamma \mu \tau$ or $\gamma e\tau$ (short-dashed gold curve), $J/\psi \to \gamma e\mu$ (dotted red curve), $\psi (2S)\to \gamma e\mu$ (dot-dashed green curve); (c) $\rho \to \gamma e\mu$ (solid blue curve), $\omega \to \gamma e\mu$ (short-dashed gold curve), $\varphi \to \gamma e\mu$ (dotted red curve).