MINISTRY OF EDUCATION
AND TRAINING
VIETNAM ACADEMY
OF SCIENCE AND TECHNOLOGY
GRADUATE UNIVERSITY SCIENCE AND TECHNOLOGY
……..….***…………
PHI QUANG VAN
CONSTRUCTION AND INVESTIGATION OF A
NEUTRINO MASS MODEL WITH A4 FLAVOUR SYMMETRY
BY PERTUBATION METHOD
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Speciality: Theoretical and mathematical physics
Code: 62 44 01 03
SUMMARY OF THE PHD THESIS
Hanoi – 2017
This thesis was compled at the Graduate University Science and
Technology, Viet Nam Academy of Science and Technology.
Supervisors: Assoc. Prof. Dr. Nguyen Anh Ky
Institute of Physics, Viet Nam Academy of S cience and Technology.
Referee 1: Prof. Dr. Dang Van Soa
Referee 2: Assoc. Prof. Dr. Nguyen Ai Viet
Referee 3: Dr. Tran Minh Hieu
This dissertation will be defended in front of the evaluating assembly
at academy level, Place of defending: meeting room, Graduate
University Science and Technology, Viet Nam Academy of Science
and Technology.
This thesis can be studied at:
- The Vietnam National Library
- Library of the National Academy of Public Administration
Introduction
Motivation of thesis topic
Neutrino masses and oscillations are always a challenge in elementary particle physics.
We have seen in the standard model (SM) that neutrinos do not have mass, but the
experiment has shown that neutrinos have mass. The problem of neutrino masses
and mixings is among the problems beyond the SM. This problem is important for not
only particle physics but also nuclear physics, astrophysics and cosmology, therefore,
it has attracted much interest. At present, there are many standard model extensions
to studying neutrino masses and oscillations: the supersymmetry model, the grand
unified theory, the left-right symmetry model, the 3-3-1 model, the mirror symmetry
model, Zee model, Zee-Babu model, the flavour symmetry model, etc.
One of the standard model extentions to explain neutrino mass is to add a flavor
symmetry to the SM symmetry, such as SU(3)C×SU(2)L×U(1)Y×GF, in which
GFis a flavour symmetry group, for example S3, S4, A4, A5, T 7,∆(27) [1],... A popular
flavour symmetry intensively investigated in the literature is that described by the
group A4(see, for instance, [2,3]) allowing obtaining a tribi-maximal (TBM) neutrino
mixing corresponding to the mixing angles θ12 ≈35.26◦(sin2θ12 = 1/3), θ13 = 0◦and
θ23 = 45◦. The recent experimental data that showing a non-zero mixing angle θ13
and a possible non-zero Dirac CP-violation (CPV) phase δCP , rejects, however, the
TBM scheme [4,5]. There have been many attempts to explain these experimental
phenomena. In particular, for this purpose, various models with a discrete flavour
symmetry [1], including an A4flavor symmetry, have been suggested [1–3].
The objectives of the thesis
The thesis is devoted to constructing and evaluating versions of the SM extended
with an A4 symmetry to explain some of the problems of neutrino physics. Within
these extended models, the results on neutrino masses and mixing, derived by the
perturbation method, are very closed to the global fit [4,5]. In two models, a relation
between the Dirac CPV phase and the mixing angles is established. In particular, the
models predict Dirac CPV phase δCP and effective mass of neutrinoless double beta
decay |hmeei| in good agreement with the current experimental data.
1
Introduction
The main contents of the thesis
In general, the models, based on A4flavour symmetry, have extended lepton and scalar
sectors containing new fields in additions to the SM ones which now may have an A4
symmetry structure. Therefore, base on an A4flavour symmetry, these fields may also
transform under A4. At the beginning, the A4based models were build to describe a
TBM neutrino mixing (see, for example, [2]) but later many attempts, such as those
in [1,3,6], to find a model fitting the non-TBM phenomenology, have been made. On
these models, however, are often imposed some assumptions, for example, the vacuum
expectation values (VEV’s) of some of the fields, especially those generating neutrino
masses, have a particular alignment. These assumptions may lead to a simpler diag-
onalization of a mass matrix but restrict the generality of the model. Since, according
to the current experimental data, the discrepancy of a phenomenological model from
a TBM model is quite small, we can think about a perturbation approach to building
a new, realistic, model [7,8].
The perturbative approach has been used by several authors (see for example, [9])
but their methods mostly are model-independent, that is, no model realizing the ex-
perimentally established neutrino mixing has been shown. On the other hand, most
of the A4-based models are analyzed in a non-perturbative way. There are a few cases
such as [10] where the perturbative method is applied but their approach is different
from ours and their analysis, sometimes, is not precise (for example, the conditions
imposed in section IV of [10] are not always possible). Besides that, in many works
done so far, the neutrino mixing has been investigated with a less general vacuum
structure of scalar fields.
In this thesis we will introduce two versions of A4flavor symmetric standard model,
which can generate a neutrino mixing, deviating from the TBM scheme slightly, as
requested and explained above. Since the deviation is small we can use a perturbation
method in elaborating such a non-TBM neutrino mixing model. The corresponding
neutrino mass matrix can be developed perturbatively around a neutrino mass matrix
diagonalizable by a TBM mixing matrix. As a consequence, a relation between the
Dirac CPV phase δCP and the mixing angles θij,i, j = 1,2,3(for a three-neutrino
mixing model) are established. Based on the experimental data of the mixing angles,
this relation allows us to determine δCP numerically in both normal odering (NO)
and inverse ordering (IO). It is very important as the existence of a Dirac CPV phase
indicates a difference between the probabilities P(νl→νl′)and P(¯νl→¯νl′),l6=l′,
of the neutrino- and antineutrino transitions (oscillations) in vacuum νl→νl′and
¯νl→¯νl′, respectively, thus, a CP violation in the neutrino subsector of the lepton
sector. We should note that for a three-neutrino mixing model, as considered in this
paper, the mixing matrix in general has one Dirac- and two Majorana CPV phases.
Since the Majorana CPV phases do not effect these transition probabilities they are
not a subject of a detailed analysis here.
In the framework of the suggested models and the perturbation method our ap-
proach allows us to obtain δCP , within the 1σregion of the best fit value [5]. Further,
2
Introduction
knowing δCP we can determine the Jarlskog parameter (JCP ) measuring a CP viola-
tion. The determination of δCP and JCP represents an application of the present model
and, in this way, verifies the latter (of course, it is not a complete verification).
Structure of thesis
Chapter 1 presents the basis of the standard model and the problem of neutrino mass.
Chapters 2 and 3 are designed for constructing and evaluating the two models A(1)
4
and A(10)
4for neutrino masses and mixing. Both models are constructed perturbatively
around a TBM model but objects of perturbation are different: vacuums in A1
4and
Yukawa coupling coefficients in A10
4. In each model, physical quantities such as neu-
trino mass, mixing angles θij ,δCP ,JCP , and the relation between δCP with angle θij
are investigated and calculated. Conclusions and discussion of the thesis’s results are
presented in the final chapter.
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