Quark Singlets: Implications and Constraints

Quarks whose left- and right-handed chiral components are both singlets with respect to the SU(2) weak-isospin gauge group, offer interesting physics possibilities beyond the Standard Model (SM) already studied in many contexts. We here address some further aspects. We first collect and update the constraints from present data on their masses and mixings with conventional quarks. We discuss possible effects on $b\to s\gamma$ and $Z\to b\bar b$ decays and give fresh illustrations of CP asymmetries in $B^0$ decays differing dramatically from SM expectations. We analyse singlet effects in grand unification scenarios: $d$-type singlets are most economically introduced in ${\bf 5+5^*}$ multiplets of $SU(5)$, with up to three generations, preserving gauge coupling unification with perturbative values up to the GUT scale; $u$-type singlets can arise in ${\bf 10+10^*}$ multiplets of $SU(5)$ with at most one light generation. With extra matter multiplets the gauge couplings are bigger; we give the two-loop evolution equations including exotic multiplets and a possible extra $U(1)$ symmetry. Two-loop effects can become important, threatening unification (modulo threshold effects), perturbativity and asymptotic freedom of $\alpha_3$. In the Yukawa sector, top-quark fixed-point behaviour is preserved and singlet-quark couplings have infrared fixed points too, but unification of $b$ and $\tau$ couplings is not possible in a three-generation $E_6$ model.