Constraints on the four-generation quark mixing matrix from a fit to flavor-physics data

Abstract

In the scenario with four quark generations, we perform a fit using flavor-physics data and determine the allowed values---preferred central values and errors---of all of the elements of the $4\ifmmode\times\else\texttimes\fi{}4$ quark-mixing matrix. In addition to the direct measurements of some of the elements, we include in the fit the present measurements of several flavor-changing observables in the $K$ and $B$ systems that have small hadronic uncertainties, and also consider the constraints from the vertex corrections to $Z\ensuremath{\rightarrow}b\overline{b}$. The values taken for the masses of the fourth-generation quarks are consistent with the measurements of the oblique parameters and perturbativity of the Yukawa couplings. We find that $|{\stackrel{\texttildelow{}}{V}}_{tb}|\ensuremath{\ge}0.98$ at $3\ensuremath{\sigma}$, so that a fourth generation cannot account for any large deviation of $|{V}_{tb}|$ from unity. The fit also indicates that all the new-physics parameters are consistent with zero, and the mixing of the fourth generation with the other three is constrained to be small: we obtain $|{\stackrel{\texttildelow{}}{V}}_{u{b}^{\ensuremath{'}}}|<0.06$, $|{\stackrel{\texttildelow{}}{V}}_{c{b}^{\ensuremath{'}}}|<0.027$, and $|{\stackrel{\texttildelow{}}{V}}_{t{b}^{\ensuremath{'}}}|<0.31$ at $3\ensuremath{\sigma}$. Still, this does allow for the possibility of new-physics signals in ${B}_{d}$, ${B}_{s}$ and rare $K$ decays.