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Single top quark production cross sections at hadron colliders aretraditionally used to extract the modulus of the $V_{tb}$ element of theCabibbo-Kobayashi-Maskawa matrix under the following assumption: $|V_{tb}| \gg|V_{td}|, |V_{ts}|$. For the first time, direct limits on $|V_{td}|$ and$|V_{ts}|$ are obtained using experimental data without the assumption of theunitarity of the CKM matrix. Limits on the $|V_{td}|$, $|V_{ts}|$ and$|V_{tb}|$ are extracted from differential measurements of single top quarkcross sections in $t$-channel as a function of the rapidity and transversemomentum of the top quark and the light jet recoiling against the top quark. Wehave shown that the pseudorapidity of the forward jet in the single topproduction is one of the most powerful observables for discriminating betweenthe $|V_{td}|$ and $|V_{tb}|$ events. We perform a global fit of top quarkrelated CKM elements to experimental data from the LHC Runs I and II andTevatron. Experimental data include inclusive and differential single top crosssections in $t$-channel, inclusive tW production cross section, and top quarkbranching ratio to b quark and W boson. We present bounds on $|V_{tb}|$,$|V_{ts}|$ and $|V_{td}|$ using current data and project the results for futureLHC data sets corresponding to luminosities of 300 and 3000 \fb.

Model-independent constraints on the CKM matrix elements $|V_{tb}|$, $|V_{ts}|$ and $|V_{td}|$