Search for C-parity violation in $J\mathrm{/}\psi \to \gamma \gamma$ and $\gamma \varphi$

Using $1.06\times {10}^8$ $\psi (3686)$ events recorded in $e^{+}{e}^{-}$ collisions at $\sqrt{s}=$ 3.686 GeV with the BESIII at the BEPCII collider, we present searches for C-parity violation in $J\mathrm{/}\psi \to \gamma \gamma$ and $\gamma \varphi$ decays via $\psi (3686)\to J\mathrm{/}\psi {\pi }^{+}{\pi }^{-}$. No significant signals are observed in either channel. Upper limits on the branching fractions are set to be $\mathcal{B}(J\mathrm{/}\psi \to \gamma \gamma )<2.7\times {10}^{-7}$ and $\mathcal{B}(J\mathrm{/}\psi \to \gamma \varphi )<1.4\times {10}^{-6}$ at the 90% confidence level. The former is one order of magnitude more stringent than the previous upper limit, and the latter represents the first limit on this decay channel.