Constraints on the mixing of a fourth family of quarks

Abstract

This paper studies the constraints on the mixing of a possible fourth family of quarks. A mixing-angle convention is introduced in which $s_{\mathrm{ij}}$≡sin${\theta }_{\mathrm{ij}}$ represents to a good approximation the ij element of the quark mixing matrix (i<j). A range of parameters is found, $s_{14}$$s_{24}$$s_{14}$$s_{24}$∼${10}^{\mathrm{-}4}$–${10}^{\mathrm{-}3}$ and/or $s_{14}$ $s_{34}$≳${10}^{\mathrm{-}2}$, for which the contribution of the fourth family to the $K_L$-$K_S$ mass difference is negligible yet may lead to dominant effects in the $K^0$-K¯ ${}_{}{}^0{}_{}{}^{}$ CP-impurity parameter ε. This may be realized in a scheme in which the four quark generations are mixed mostly in pairs. A possible signature of such a scheme may be an abundant rate of same-sign dileptons at Υ(4S) if the fourth up-type quark is sufficiently heavy.