On the corner elements of the CKM and PMNS matrices

¹ Departament Fisica Teorica and IFIC, Centro Mixto CSIC, Universitat de Valencia - Calle Dr. Moliner 50, E-46100 Burjassot (Valencia), Spain, EU
² Rutherford Appleton Laboratory - Chilton, Didcot, Oxon, OX11 0QX, UK, EU
³ Mathematical Institute, University of Oxford - 24-29 St. Giles', Oxford, OX1 3LB, UK, EU

Received: 7 April 2013
Accepted: 15 May 2013

Abstract

Recent experiments show that the top-right corner element (U_e3) of the PMNS matrix is small but nonzero, and suggest further via unitarity that it is smaller than the bottom-left corner element (U_τ1). Here, it is shown that if to the assumption of a universal rank-one mass matrix, long favoured by phenomenologists, one adds that this matrix rotates with scale, then it follows that A) by inputting the mass ratios m_c/m_t,m_s/m_b,m_μ/m_τ, and m₂/m₃, i) the corner elements are small but nonzero, ii) V _ub < V _td, U_e3 < U_τ1, iii) estimates result for the ratios V _ub/V _td and U_e3/U_τ1, and B) by inputting further the experimental values of V _us,V _tb and U_e2, U_μ3, iv) estimates result for the values of the corner elements themselves. All the inequalities and estimates obtained are consistent with present data within expectation for the approximations made.