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 ($iii$) $M_d^{†}=M_d$. 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 $V_{PMNS}^0=V^{T}V$. $V$ 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 $V_{PMNS}^0$. We find that if the correction matrix equals the CKM matrix, the resulting lepton mixing agrees well with data and predicts $\sin {\theta }_{13}>0.08$. 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 $V_{PMNS}{V}_{CKM}=V^{T}V$ in the lowest order.

Comments: 22 pages, 2 figures; references added; abstract slightly modified