Neutrino masses and mixing parameters in a left-right model with mirror fermions

Abstract

In this work we consider a left-right model containing mirror fermions with gauge group SU(3)$_{C} \otimes SU(2)_{L} \otimes SU(2)_{R} \otimes U(1)_{Y^\prime}$. The model has several free parameters which here we have calculated by using the recent values for the squared-neutrino mass differences. Lower bound for the mirror vacuum expectation value helped us to obtain crude estimations for some of these parameters. Also we estimate the order of magnitude of the masses of the standard and mirror neutrinos. Comment: 13 pages, version submitted to European Physical Journal C

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arXiv:hep-ph/0605249v1 23 May 2006
Neutrino masses and mixing parameters in a
left-right model with mirror fermions
R. Gait´ an2, A. Hern´ andez-Galeana1∗, J. M. Rivera-Rebolledo1†
and P. Fern´ andez de C´ ordoba3
”Interdisciplinary Modeling Group, InterTech.”
1. Departamento de F´ ısica,
Escuela Superior de F´ ısica y Matem´ atica, I.P.N.,
U.P. Adolfo L. Mateos, M´ exico D.F., 07738, M´ exico
2. Centro de Investigaciones Te´ oricas, FES, UNAM,
Apartado Postal 142, Cuatitl´ an-Izcalli, Estado de M´ exico,
C´ odigo postal 54700, M´ exico.
3. Departamento de Matem´ atica Aplicada, Universidad Polit´ ecnica de Valencia,
Valencia, Spain.
Abstract
In this work we consider a left-right model containing mirror fermions
with gauge group SU(3)C⊗SU(2)L⊗SU(2)R⊗U(1)Y′. The model has
several free parameters which here we have calculated by using the
recent values for the squared-neutrino mass differences. Lower bound
for the mirror vacuum expectation value helped us to obtain crude
estimations for some of these parameters. Also we estimate the order
of magnitude of the masses of the standard and mirror neutrinos.
∗With support from EDI, COFAA and SNI
†With support from COFAA-IPN, EDD and SNI
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1 Introduction
The understanding of the properties of neutrinos is a problem that has re-
quired an immense experimental and theoretical effort. There is now convinc-
ing evidence that neutrinos have non-standard properties: they have masses
and their flavor states mix, leading to processes like neutrino oscillations.
There are various features that make neutrinos specially interesting. The
smallness of neutrino masses is probably related to the fact that neutrinos
are completely neutral, i.e., they carry no electric charge which is exactly
conserved, and are Majorana particles with masses inversely proportional to
the large scale where lepton number (L) conservation is violated. [1] The
relation with L non-conservation and the fact that the observed neutrino os-
cillation frequencies are compatible with a large scale for L non-conservation,
establish connection with Grand Unified Theories (GUT’s). Then, neutrino
masses and mixing offer a different perspective on the problem of flavor and
the origin of fermion masses.
Another modern interest in neutrinos arises from their significance in
astrophysics and cosmology [2] and the possible non-negligible contribution
of neutrinos to hot dark matter in the Universe.
An alternative explanation of small neutrino masses comes from the con-
cept of extra dimensions beyond the three ones that we know [3]. It has
been suggested that right-handed neutrinos (but not other particles of the
Standard Model) experience one or more of these extra dimensions. The
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right-handed neutrinos then only spend part of their time in our world, lead-
ing to apparently small neutrino masses.
From the experimental study of atmospheric and solar neutrinos we have
considerably improved our knowledge. The idea of neutrino oscillations have
gained support from the Japanese experiment Super-Kamiokande [4] which in
1998 showed that there was a deficit of muon neutrinos reaching Earth when
cosmic rays strike the upper atmosphere. These results were interpreted as
muon neutrinos oscillating into tau neutrinos, but they were not detected.
Recently The Sudbury Neutrino Observatory (SNO)[5] in Canada had
confirmed that the solar neutrino deficit is due to neutrino oscillations and
not to a flaw in the model of the Sun: the total neutrino flux is in agreement
with the solar model but only about one third arrives on Earth as νe, while
the remaining part consists of other kinds of neutrinos, presumably νµand
ντ.
The KamLAND experiment has established that ¯ νefrom reactors show
oscillations over an average distance of about 180 Km which are perfectly
compatible with the frequency and mixing angle corresponding to one of the
solutions of the solar neutrino problem (the Large Angle solution) [6].
In this paper we use a model with gauge group SU(3)C⊗SU(2)L⊗SU(2)R
⊗U(1)Y′ which contains mirror fermions. In Section 1 we give an introduction
to the problem that we deal with; in Sec. 2 we present the model and discuss
the symmetry breaking part with the help of two scalar doublets. Sec. 3 is
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devoted to write the Yukawa couplings for Majorana and Dirac neutrinos,
although we consider only these last ones in calculations; the neutrino mass
matrix is shown in terms of three parameters; we diagonalise it and get
expressions for the physical neutrino masses. The use of their experimental
values and bounds gives us approximate numbers for the involved parameters.
2 The model
The gauge group symmetry is [7] G = SU(3)C⊗SU(2)L⊗SU(2)R⊗U(1)Y′ and
the content of fermions assumes the ordinary quarks and leptons including
the mirror counterpart, where the leptonic sector is assigned under the group
G in the form:
liL∼ (1,2,1,−1)L,
νiR∼ (1,1,1,0)R,
eiR∼ (1,1,1,−2)R,
ˆ νiL∼ (1,1,1,0)L,
ˆ eiL∼ (1,1,1,−2)L,
ˆliR∼ (1,1,2,−1)R,
where i = 1,2,3 is the family index, the numbers in parenthesis are the
quantum numbers of the fermionic fields under the groups SU(3)C, SU(2)L,
SU(2)R, and U(1)Y′, respectively; the last entry corresponds to the hyper-
charge (Y′), with the electric charge defined by Q = T3L+ T3R+Y′
2.
The ”Spontaneous Symmetry Breaking” (SSB) is proposed to be achieved
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in the stages
G −→ GSM−→ SU(3)C⊗ U(1)Q
(1)
where GSM= SU(3)C⊗SU(2)L⊗U(1)Y is the ”Standard Model” group sym-
metry, andY
2= T3R+Y′
2.
The Higgs sector used to induce the SSB in eq.(1) involves the scalar
fields
Φ = (1,2,1,1)(2)
ˆΦ = (1,1,2,1)(3)
where the entries correspond to the transformation properties under the sym-
metries of the group G, with the ”Vacuum Expectation Values” (VEV’s)
< Φ >=
1
√2
?
0
v
?
,
(4)
<ˆΦ >=
1
√2
?
0
ˆ v
?
(5)
Here the VEV’s v and ˆ v are related to the masses of the charged gauge
bosons W andˆ W through MW =1
2gLv; Mˆ W=1
2gRˆ v, with gLand gRbeing
the coupling constants of SU(2)Land SU(2)R, and gL= gRif we demand
L-R symmetry.
5