Speaker
Description
The anarchy principle leading to the seesaw ensemble is studied analytically with
the usual tools of random matrix theory. The probability density function for the
seesaw ensemble of N × N matrices is obtained in terms of a multidimensional
integral. This probability density functions is then used to extract information
on the relevant physical parameters of the neutrino sector of a seesaw-extended
Standard Model. For N = 2 and N = 3, the distributions of the light neutrino
masses, as well as the mixing angles and phases, are obtained using numeri-
cal integration methods. A systematic comparison with the much simpler type
II seesaw ensemble is also performed to point out the fundamental differences
between the two ensembles. It is found that the type I-III seesaw ensemble is
better suited to accommodate experimental data. Moreover, the results indi-
cate a strong preference for the mass splitting associated to normal hierarchy.
However, because of the decoupling of the probability density function for the
light neutrino masses and the neutrino mixings, which implies no correlation
between the neutrino mass eigenstates and the neutrino mixing matrix, every
permutations of the singular values are found to be equally probable for a par-
ticular mass splitting. This leads to a loss of predictive power when comparing
with observations as predictions regarding the hierarchy of the mass spectrum
remains out of reach in the framework of anarchy.
