PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

where ˜H = iτ 2 H ∗ . The electron, up quark and down quark masses are generated from
the above equation and are respectively the following,
m e = Y e v; m u = Y u v; m d = Y d v. (1.15)
The neutrino has been considered massless in the standard model.
1.2 Problems of the Standard Model
Standard model gives a definite quantum description of the elementary particles. The
model gives many successful predictions. For example, it predicts the existence of three
massive gauge bosons which have experimentally been verified in LEP experiments at
CERN, Geneva [5]. In addition, it predicts nine massless gauge bosons and the existence
of massive quarks and leptons. Among its different successes one major success is the
top quark discovery. Standard model predicted the existence of the top quark before it
was discovered. The top quark was later observed at the Tevatron [6]. The electroweak
properties of the standard model have been verified to a large degree of accuracy in
experiments such as LEP and Tevatron [5,6]. However,there are many issues which this
theory does not explain or address. Here we list a few of them:
• Aseriesofoutstandingexperimentslikesolarandatmosphericneutrinoexperiments,
KamLAND, K2K, MINOS, CHOOZ provide information about the standard model
neutrino mass splittings and its very peculiar mixing angles. Combined with cosmological
bound specially from WMAP data, the sum of the light neutrino masses are
bounded to 0.19 eV [7], while the observed solar and atmospheric mass splitting are
∆m 2 21 ∼ 10 −5 eV 2 and ∆m 2 31 ∼ 10 −3 eV 2 respectively. This extremely small neutrino
masses (< eV) point towards a 10 12 order mass hierarchy between the top quark
and the neutrino. Other than the extremely small neutrino masses, the mixing in
the leptonic sector is also a puzzle. Unlike the mixing in the quark sector, in the
leptonic sector two of the mixing angles θ 12 and θ 23 are quite large (sin 2 θ 12 ∼ 0.32,
sin 2 θ 23 ∼ 0.46) [8] while at present there is an upper bound on the third mixing
angle θ 13 as sin 2 θ 13 < 0.05 at 3σ Confidence Level (C.L) [8]. The observed mixing
angles are in very close agreement with the tribimaximal mixing [9] pattern where
the solar mixing angle is sin 2 θ 12 = 0.33, reactor mixing angle sin 2 θ 13 = 0.0 and the
atmospheric mixing angle is maximal sin 2 θ 23 = 0.5. The maximal mixing angle θ 23
and θ 13 = 0 points towards a possible µ−τ symmetry [10] in the neutrino sector.
The standard model of particle physics does not have any neutrino mass itself. In
addition, the standard model does not shed any light if there is any fundamental
principle governing this extremely small neutrino masses as well as the peculiar
mixing. It is possible to extend the standard model by introducing gauge singlet
neutrinos and to explain the observed neutrino mass as a consequence of the Dirac
4