Quark-Lepton universality and large leptonic mixing

Abstract

A unified description of fermionic mixing is proposed which assumes that in certain basis ($i$) a single complex unitary matrix $V$ diagonalizes mass matrices of all fermions to the leading order, ($ii$) the SU(5) relation $M_d=M_l^T$ exists between the mass matrices of the down quarks and the charged leptons, and ($iii$) $M_d^\dagger=M_d$. These assumptions automatically lead to different mixing patterns for quarks and leptons: quarks remain unmixed to leading order ($i. e. V_{CKM}=1$) while leptons have non-trivial mixing given by a symmetric unitary matrix $V^0_{PMNS} = V^T V$. $V$ depends on two physical mixing angles and for values of these angles $\sim 20^\circ-25 ^\circ$ it reproduces the observed mixing patterns rather well. We identify conditions under which the universal mixing $V$ follows from the universal mass matrices of fermions. Relatively small perturbations to the leading order structure lead to the CKM mixing and corrections to $V^0_{PMNS}$. We find that if the correction matrix equals the CKM matrix, the resulting lepton mixing agrees well with data and predicts $\sin θ_{13} > 0.08$. In a more general context, the assumption of partial universality ($i.e.$, different mixing for the up and the down components of doublets) is shown to lead to a complementarity relation $V_{PMNS}V_{CKM}=V^TV$ in the lowest order.