A Method to Determine $|V_{cb}|$ at the Weak Scale in Top Decays at the LHC

Until now, the Cabibbo Kobayashi Maskawa matrix element, $|V_{cb}|$, has always been measured in $B$ decays, i.e.~at an energy scale $q_b\sim \frac{m_b}{2}$, far below the weak scale. We consider here the possibility of measuring it close to the weak scale, at $q_W\sim m_W$, in top decays at the Large Hadron Collider (LHC). Our proposed method would use data from the LHC experiments in hadronic top decays $t\rightarrow bW\rightarrow b\overline{b} c$, tagged by the semileptonic decay of the associated top. We estimate the uncertainty of such a measurement, as a function of present and potential future experimental jet flavour-tagging performances, and conclude that first measurements using the data collected during 2016 - 2018 could yield a fractional error on \Vcb\ of order 7\% per experiment. We also give projected performances at higher luminosities, which could yield sensitivity to any Standard Model running of \Vcb\ below the weak scale, if present.