NLO EW corrections to tau pair production via photon fusion in Pb-Pb ultraperipheral collision

Abstract

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.

Comments: 18 pages, 6 figures, accepted for publication in PRD