Measuring $|V_{td}|$ at LHC

We propose a direct measurement of the CKM element $V_{td}$ at the LHC. Taking profit of the imbalance between $d$ and $\bar d$ quark content in the proton, we show that a non-zero $V_{td}$ induces a charge asymmetry in the $tW$ associated production. The main backgrounds to this process, $t\bar t$ production, and $tW$ associated production mediated by $V_{tb}$, give charge symmetric contributions at leading order in QCD. Therefore, using specific kinematic features of the signal, we construct a charge asymmetry in the di-lepton final state which, due also to a reduction of systematic uncertainties in the asymmetry, is potentially sensitive to $V_{td}$ suppressed effects. In particular, using signal and background simulations up to detector level, we show that this new observable could improve the current direct upper bound on $|V_{td}|$ already with existing LHC data. We also project that $|V_{td}|$ values down to $\sim 10$ times the Standard Model prediction could be probed in the high luminosity phase of the LHC.