Light flavon signals at electron-photon colliders

Flavor symmetries are useful to realize fermion flavor structures in the standard model (SM). In particular, the discrete $A_4$ symmetry is used to realize lepton flavor structures, and some scalars—called flavons—are introduced to break this symmetry. In many models, flavons are assumed to be much heavier than the electroweak scale. However, our previous work showed that a flavon mass around 100 GeV is allowed by experimental constraints in the $A_4$ symmetric model with a residual $Z_3$ symmetry. In this paper, we discuss collider searches for such a light flavon ${\phi }_T$. We find that electron-photon collisions at the International Linear Collider have advantages for searching for these signals. In electron-photon collisions, flavons are produced as $e^{-}\gamma \to l^{-}{\phi }_T$ and decay into two charged leptons. Then, we analyze signals of the flavor-conserving final state ${\tau }^{+}{\tau }^{-}{e}^{-}$ and the flavor-violating final states ${\tau }^{+}{\mu }^{-}{\mu }^{-}$ and ${\mu }^{+}{\tau }^{-}{\tau }^{-}$ by carrying out numerical simulations. For the former final state, SM background can be strongly suppressed by imposing cuts on the invariant masses of final-state leptons. For the latter final states, SM background is extremely small, because in the SM there are no such flavor-violating final states. We then find that sufficient discovery significance can be obtained, even if flavons are heavier than the lower limits from flavor physics.

Figure 1

One of the diagrams which produces the flavon ${\phi }_{T1}$ at an electron-positron collider (left) and an electron-photon collider (right).

Figure 2

The $m_{{\tau }_h^{-}{\tau }_h^{+}}$ distribution after the first selection (left) and the distribution, where the horizontal axis is the transverse momentum of an antitau lepton $p_T({\tau }^{+})$ and the vertical axis is the $m_{{\tau }^{-}{\tau }^{+}}$ in a parton-level simulation (right). In these calculations we consider only the signal process and generate 10 times the expected number of events at the ILC.

Figure 3

The $m_{e^{-}{\tau }_h^{+}}$ distribution after the second selection rule for the beam energies $250\times 200{\mathrm{GeV}}^2$ (left) and $125\times 100{\mathrm{GeV}}^2$ (right) at the ILC. The red solid histograms are for both the SM and flavon processes, while the black dashed histograms are for only the SM process. In this calculation we fix the flavon masses to be $v_T=2m_{{\phi }_{T1}}=m_{{\phi }_{T2}}=m_{{\phi }_{T3}}=65\mathrm{GeV}$.

Figure 4

The $m_{e^{-}{\tau }_h^{+}}$ distribution where the beam energy is $500\times 400{\mathrm{GeV}}^2$ at the upgraded ILC. The red solid histograms indicate the number of events which come from the SM and flavon interactions, and the black dashed histograms indicate the number of events which come from only the SM interactions. In this calculation the flavon masses are $v_T=2m_{{\phi }_{T1}}=m_{{\phi }_{T2}}=m_{{\phi }_{T3}}=65\mathrm{GeV}$.

Figure 5

The $m_{e^{-}{\tau }_h^{+}}$ distribution where the beam energies are $250\times 200{\mathrm{GeV}}^2$ (left) and $125\times 100{\mathrm{GeV}}^2$ (right) at the upgraded ILC. The red solid histograms indicate the number of events which come from the SM and flavon interactions, and the black dashed histograms indicate the number of events which come from only the SM interactions. In this calculation the flavon masses are $v_T=2m_{{\phi }_{T1}}=m_{{\phi }_{T2}}=m_{{\phi }_{T3}}=150\mathrm{GeV}$ (left) and 100 GeV (right).

Figure 6

The flavon mass dependence for the event number of the lepton-flavor-violating process where the beam energy and luminosity is $250\times 200{\mathrm{GeV}}^2$ at the ILC (black solid line), $125\times 100{\mathrm{GeV}}^2$ at the ILC (red solid line), $250\times 200{\mathrm{GeV}}^2$ at the upgraded ILC (black dashed line), and $125\times 100{\mathrm{GeV}}^2$ at the upgraded ILC (red dashed line).