We study the next-to-leading order (NLO) electroweak (EW) corrections to the $\gamma \gamma \to \tau^+ \tau^-$ process in Pb-Pb ultraperipheral collision (UPC). We find that the EW correction $\delta \sigma_{ \mathrm{ EW}}$ decreases the total cross section $\sigma_{ \mathrm{ NLO}} = \sigma_{ \mathrm{ LO}} + \delta \sigma_{ \mathrm{ EW}}$ by -3\% at Pb-Pb center-of-mass energy $\sqrt{ s_{ NN}}=5.02$ TeV. The weak correction plays significant role whose contribution is about -4 times of that of QED. The CMS and ATLAS collaborations use the reaction $\gamma\gamma \to \tau^+ \tau^-$ in Pb-Pb and proton-proton UPC to constrain tau's anomalous magnetic moment $a_\tau$. By parameterizing the $\gamma \tau \tau$ vertex with two form factors $F_{ 1,2}$, the cross section can be written as $\sigma_{ a_\tau} = \sigma_{ \mathrm{ LO}} + \delta \sigma_{ a_\tau}$, where $\delta \sigma_{ a_\tau}$ is proportional to $a_\tau$. The impact of NLO EW corrections on $a_\tau$ bounds in Pb-Pb UPC is limited, as the current experimental bounds are loose. We also find that various differential distributions of the two ratios $\mathrm{ d} \sigma_{ \mathrm{ NLO}}/ \mathrm{ d} \sigma_{ \mathrm{ LO}}$ and $\mathrm{ d} \sigma_{ a_\tau}/ \mathrm{ d} \sigma_{ \mathrm{ LO}}$ have different lineshapes. This work is significant to precisely study the interaction of $\gamma \tau \tau$ via $\gamma \gamma \to \tau^+ \tau^-$ process.
Categories: hep-ph