Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Sterile Neutrinos



This was posted on another Physics List. Perhaps it may be of interest on
this list also.

The LSND neutrino experimental data, if correct, has revealed anomalous
mixing between the muon and tau neutrinos. This is surprising because atmospheric
neutrino mixing data strongly supports maximal mixing between the muon and tau
neutrino flavors. This perhaps, may be the reason that many physicists view
the LSND as suspect, perhaps due to some yet to be identified systematic error.
In fact, Sheldon Glashow has expressed this exact opinion to me in private
correspondence. Nevertheless, this post will make the assumption that in fact the
LSND data is correct and will be vindicated in the upcoming and more accurate
BooNE experiment.
The most parsimonious explanation of the LSND results, which conform
to the collective data from other neutrino experiments, is the existence of a
light sterile neutrino. As we shall see, the existence of such a neutrino
presents a challenge to existing neutrino theory.


Sterile Neutrinos in the Standard Model

The simplest explanation for the origin of sterile neutrinos is as uncharged
lepton singlets. The group structure for the Standard model (SM) is

G_sm=SU(3)_c X SU(2)_L X U(1)_Y


Where (First Family)

Q_L = (3,2,1/3) U_R=(3,1,4/3) d_R= (3,1,-2/3)

Le_L = (1,2,-1) e_R=(1,1,-2) v_R= (1,1,0)

And for the Higgs quantization

theta= (1,2,1)

Here theta is the Higgs Doublet.


Until the discovery of neutrino mixing revealed a nonzero rest mass for
neutrinos, the v_R were considered a missing entry. If in fact neutrinos do have
mass then like all the other Fermions they should have a right handed helicity
amplitude. These right handed neutrinos would be sterile since the weak force
only couples to left handed Fermions.
However, the generation of neutrinos rest mass presents a problem.
Given the very low masses of the active neutrino flavors the straight forward idea
of Higgs field coupling to generate the rest mass of these particles seems
unlikely in its simplest form. The currently best accepted mechanism for active
neutrino mass generation is the See Saw Mechanism, first proposed by Glashow
and others. This would require a Majorana mass for the neutrino singlet which
would be on the order of the GUT scale.

L_sm=v”_L*M_D*v”^c_L+v”^c_R*M^T_D*v_R

Where v”=v^dag*gamma_0

M_D is the Dirac mass matrix and M is the Majorana mass matrix.



Accepting the See Saw mass generation mechanism would seem to prelude light
sterile neutrinos in the standard model.


Beyond The SM, Left Right Symmetry.

An interesting idea which predicts the existence of sterile neutrinos is the
left right symmetric model. This has the group structure;


G_LR=SU(3)_c X SU(2)_L X SU(2)_R X U(1)_B-Le


Here we postulate a new symmetry which requires addition gauge bosons, the
very massive charged Wprime bosons and a neutral boson which we call Zprime. In
this case our sterile neutrinos are weakly sterile rather than fully sterile.
That is they do have gauge fields they can couple to but only over a very
short range.

Here in the Fermion sector we get.

Q_L=( 3 2,1,1/3) Q_R=( 3,1,2,1/3)

L_e_L = ( 1,2,1,-1) Le_R=(1,1,2,-1)

In the Higgs sector we get.

Theta=(1,2,2,0) Theta_L= (1,2,1,2) Theta_R=(1,1,2,2)


This gives us three Higgs Doublets.

Another left right symmetry model which gives us both weakly sterile
neutrinos and fully sterile neutrinos is achieved with a modified Higgs sector.

Theta=( 1,2,2,0) chi=(1,1,2,1)

This gives us.

L_LR=v”_L*theta*v_R+v_R*theta*v_L^c+v”^c*chi*S^c_L+S’^c*chi*v_R+S”_L*M*S^c_L

Here S_L and v_r are the fully sterile and weakly sterile neutrinos
respectively.

However, as with the SM sterile neutrinos, the left-right symmetry model's
uses the See Saw mechanism to generate the neutrino masses, making light sterile
neutrinos impossible. Of course this is no way precludes the possibility
that a different neutrino mass generation mechanism may exist which can generate
light sterile neutrinos. Nevertheless no such mechanism has been theorized
which has wide acceptance in the theoretical community.

Mirror Fermions.

Another theoretical extension of the SM. which predicts sterile neutrinos is
the Mirror Fermion proposal. This idea restores left right symmetry for
Fermions by postulating a complete set of Fermions with opposite handiness with
their own gauge couplings which as the name implies mirrors the gauge couplings of
the standard model.

This gives us a squared group structure

G_unv=G_sm X G’_sm

G_sm= SU(3)_c X SU(2)_L X U(1)_Y

G’_sm= SU(3)_c X SU(2)_R X U(1)_Y


In this scheme there is mixing between the singlets of both G_sm and G’_sm
where the singlet flavor eigenstate is

V(+)= (1/sqrt2)* (v+v’)

V(-)=(1/sqrt2)*(v-v’)


Where v is mostly v_L and v’ is mostly v’_R

This mixing keeps the sterile neutrino mass light for the same reason that
the masses of the active neutrinos are light. Effectively the right handed
neutrinos have mirror neutrino amplitude which suppresses the neutrino masses and
visa versa. However, all is not rosy here either. This model seems to predict
maximal active-sterile neutrino mixing which has been ruled out by both the
solar and atmospheric neutrino mixing data.
Therefore we have several models which predict sterile neutrinos
which aren't ruled out in terms of observed atmospheric and solar neutrino mixing
ratios but seem to require an unacceptably large mass splitting between active
and sterile neutrinos, and we have a model which gives us acceptable values
of active-passive mass splitting but predicts active-sterile mixing angles
precluded by the observed atmospheric and solar neutrino mixing ratios. Of course
we shouldn't assume that the See Saw neutrino mass generation will be the last
word. In fact assuming BooNE confirms the LSND data, we can expect this to
stimulate the pursuit of alternate mass generation mechanism. Also possibly, new
factors may be found which would suppress the maximal active-sterile neutrino
mixing predicted by the current mirror Fermion model. In any case the
confirmation of the existence of sterile neutrinos would be an important addition to
our description of the particles which make up all the visible matter in our
Universe.


Bob Zannelli