Examining a right-handed quark mixing matrix with $b$-tags at the LHC

Encouraged by a hint in a search for right-handed $W$ bosons at the LHC, we investigate whether the unitarity of a right-handed quark mixing matrix and the equality of the left- and right-handed quark mixing matrices could be tested at the LHC. We propose a particular test, involving counting the numbers of $b$-tags in the final state, and simulate the test at the event level with Monte-Carlo tools for the forthcoming $\sqrt{s}=13$ TeV LHC run. We find that testing unitarity with 20/fb will be challenging; our test successfully rejects unitarity if the right-handed quark mixing matrix is non-unitary, but only in particular cases. On the other hand, our test may provide the first opportunity to test the unitarity of a right-handed quark mixing matrix and with 3000/fb severely constrains possible departures from unitarity in the latter. We refine our previous work, testing the equality of quark mixing matrices, with full collider simulation. With 20/fb, we are sensitive to mixing angles as small as $30^\circ$, and with 3000/fb, angles as small as $7.5^\circ$, confirming our preliminary analysis. We briefly investigate testing the unitarity of the SM CKM matrix with a similar method by studying semileptonic $t\bar t$ production, concluding that systematics make it particularly difficult.