Precision Diboson Observables for the LHC

Motivated by the restoration of $SU(2)\times U(1)$ at high energy, we suggest that certain ratios of diboson differential cross sections can be used as high-precision observables at the LHC. We rewrite leading-order diboson partonic cross sections in a form that makes their $SU(2)\times U(1)$ and custodial $SU(2)$ structure more explicit than in previous literature, and identify important aspects of this structure that survive even in hadronic cross sections. We then focus on higher-order corrections to ratios of $\gamma\gamma$, $Z\gamma$ and $ZZ$ processes, including full next-to-leading-order corrections and $gg$ initial-state contributions, and argue that these ratios can likely be predicted to better than $5\%$, which should make them useful in searches for new phenomena. The ratio of $Z\gamma$ to $\gamma\gamma$ is especially promising in the near term, due to large rates and to exceptional cancellations of QCD-related uncertainties. We argue that electroweak corrections are moderate in size, have small uncertainties, and can potentially be observed in these ratios in the long run.