Abstract
A simple relation UPMNS=VCKM†UTB between the lepton and quark mixing matrices (UPMNS and VCKM) is speculated under an ansatz that UPMNS becomes an exact tribimaximal mixing UTB in a limit VCKM=1. By using the observed CKM mixing parameters, possible values of neutrino oscillation parameters are estimated: sin2θ13=0.024–0.028, sin22θ23=0.94–0.95 and tan2θ12=0.24–1.00 depending on phase conventions of UTB. Those values are testable soon by precision measurements in neutrino oscillation experiments.
Highlights
There has been considerable interest in the magnitude of the neutrino mixing angle θ13, because it is a key value for checking neutrino mass matrix models, and for searching CP -violation effects in the lepton sector. (For a review of models for θ13, see, for example, Ref.[1].) Recent observed neutrino oscillation data are in favor of the so-called “tribimaximal mixing” [2] which predicts θ13 = 0, tan2 θ12 = 1/2 and sin2 2θ23 = 1, since the present data yield the values tan2 θ12 = 0.47+−00..0065 [3] and sin2 2θ23 = 1.00−0.13 [4]
The observed lepton mixing UP MNS will deviate from the exact tribimaximal mixing UP MNS = UT B by additional effects which gives the deviation from VCKM = 1. ( see, e.g., Ref.[8] for a possible deviation of UP MNS from a bimaximal mixing related to VCKM .)
Uue can vary from Uue = 1 to Uue = VCKM, so that Ued varies from Ued = VCKM to Ued = 1 and Eq(12) varies from UP MNS = UT B to UP MNS = VC†KM UT B. (Here, we have considered that Uue does, at least, not take a large mixing more than VCKM and a rotation to an opposite direction, VC†KM .) we can consider that the relation (4) describes a maximal deviation of UP MNS from UT B
Summary
Fogli et al [5] have reported a sizable value sin θ13 = 0.016 ± 0.010 (1σ) from a global analysis of neutrino oscillation data Such a form with beautiful coefficients seems to be understood from a discrete symmetry of flavors [2]. We consider that the observed form of the CKM matrix VCKM is due to some additional effects (e.g. symmetry breaking effects for the flavor symmetry) If this is true, the observed lepton mixing UP MNS will deviate from the exact tribimaximal mixing UP MNS = UT B by additional effects which gives the deviation from VCKM = 1. By using a specific mass matrix model, he have discussed realistic mixings VCKM and UP MNS caused by a small breaking of the flavor symmetry.
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