Search for a heavy dark photon at future $e^{+}{e}^{-}$ colliders

Abstract

A coupling of a dark photon $A^{\prime }$ from a $U(1{)}_{A^{\prime }}$ with the standard model (SM) particles can be generated through kinetic mixing represented by a parameter $\hat{I}\mu$. A non-zero $\hat{I}\mu$ also induces a mixing between $A^{\prime }$ and $Z$ if dark photon mass $m_{A^{\prime }}$ is not zero. This mixing can be large when $m_{A^{\prime }}$ is close to $m_Z$ even if the parameter $\hat{I}\mu$ is small. Many efforts have been made to constrain the parameter $\hat{I}\mu$ for a low dark photon mass $m_{A^{\prime }}$ compared with the $Z$ boson mass $m_Z$. We study the search for dark photon in $e^{+}{e}^{-}\to {\hat{I}}^3{A}^{\prime }\to {\hat{I}}^3\hat{I}{¼}^{+}\hat{I}{¼}^{-}$ for a dark photon mass $m_{A^{\prime }}$ as large as kinematically allowed at future $e^{+}{e}^{-}$ colliders. For large $m_{A^{\prime }}$, care should be taken to properly treat possible large mixing between $A^{\prime }$ and $Z$. We obtain sensitivities to the parameter $\hat{I}\mu$ for a wide range of dark photon mass at planed $e^{+}{e}^{-}$ colliders, such as Circular Electron Positron Collider (CEPC), International Linear Collider (ILC) and Future Circular Collider (FCC-ee). For the dark photon mass $20\text{GeV}\lesssim m_{A^{\prime }}\lesssim 330\text{GeV}$, the $2\ddot{I}ƒ$ exclusion limits on the mixing parameter are $\hat{I}\mu \lesssim 10^{-3}-10^{-2}$. The CEPC with $\sqrt{s}=240\text{GeV}$ and FCC-ee with $\sqrt{s}=160\text{GeV}$ are more sensitive than the constraint from current LHCb measurement once the dark photon mass $m_{A^{\prime }}\gtrsim 50\text{GeV}$. For $m_{A^{\prime }}\gtrsim 220\text{GeV}$, the sensitivity at the FCC-ee with $\sqrt{s}=350\text{GeV}$ and $1.5{\text{ab}}^{-1}$ is better than that at the 13~TeV LHC with $300{\text{fb}}^{-1}$, while the sensitivity at the CEPC with $\sqrt{s}=240\text{GeV}$ and $5{\text{ab}}^{-1}$ can be even better than that at 13~TeV LHC with $3{\text{ab}}^{-1}$ for $m_{A^{\prime }}\gtrsim 180\text{GeV}$.

21 pages, 5 figures, 2 tables