Anarchy and hierarchy: An approach to study models of fermion masses and mixings

Abstract

We advocate a new approach to study models of fermion masses and mixings, namely anarchy proposed in Ref. [1]. In this approach, we scan the O(1) coefficients randomly. We argue that this is the correct approach when the fundamental theory is sufficiently complicated. Assuming there is no physical distinction among three generations of neutrinos, the probability distributions in MNS mixing angles can be predicted independent of the choice of the measure. This is because the mixing angles are distributed according to the Haar measure of the Lie groups whose elements diagonalize the mass matrices. The near-maximal mixings, as observed in the atmospheric neutrino data and as required in the LMA solution to the solar neutrino problem, are highly probable. A small hierarchy between the ∆m 2 for the atmospheric and the solar neutrinos is obtained very easily; the complex seesaw case gives a hierarchy of a factor of 20 as the most probable one, even though this conclusion is more measuredependent. U e3 has to be just below the current limit from the CHOOZ experiment. The CP-violating parameter sin δ is preferred to be maximal. We present a simple SU (5)-like extension of anarchy to the charged-lepton and quark sectors which works well phenomenologically.

(S)fermion masses in the fat brane scenario

“…The above mass matrices and flavor mixings are roughly consistent with the experimental data, and explicit values of O (1) coefficients of mass matrices can really induce the suitable magnitudes of fermion masses and flavor mixing angles [18]. The random coefficients have suggested the probabilities of fermion masses and flavor mixings [20][21]. If we would like to obtain the suitably large (small) Cabibbo angle (U e3 ), and small m d,e , of order the power of λ, the matter configuration should be modified.…”

Statistical understanding of quark and lepton masses in Gaussian landscapes

“…We refer to this as the ''generation structure'' of the standard model. Mixing angles near =2 maximally violate this generation structure; for example, the set of angles 12 …”

“…Figure 3 shows the distributions of mixing angles in the quark sector that result from a numerical simulation where each element of both the up-type and down-type Yukawa matrices is assumed to follow the distribution (4) independently. 3 The probability distribution functions of the mixing angles are shown against the axes of d 12 , d 23 , and d sin 13 because the invariant measure 4 of SO(3) mixing matrices is d 12d 23^d sin 13 . Since in this model the Yukawa couplings are all real valued and positive valued, the CKM quark mixing matrices are SO(3) matrices.…”

“…where e min;max and C min;max are of order unity (for more details see [8,12]). Such an absolute anarchy of lepton couplings tends to result in comparable mass eigenvalues.…”

Probing the Planck scale with proton decay

“…Here we see that z = 0 corresponds to an "anarchical" MNS matrix [18,19], whereas z = 1 corresponds to a "semi-anarchical" MNS matrix [20]. The minimalist approach is to add only two righthanded neutrinos.…”