Physics Letters B 742 (2015) 99–106
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Relating quarks and leptons with the T
7
flavour group
Cesar Bonilla
a,∗
, Stefano Morisi
b
, Eduardo Peinado
c
, J.W.F. Valle
a
a
Instituto de Física Corpuscular (CSIC-Universitat de València), Apdo. 22085, E-46071 Valencia, Spain
b
DESY, Platanenallee 6, D-15735 Zeuthen, Germany
c
Instituto de Física, Universidad Nacional Autónoma de México, A.P. 20-364, México D. F. 01000, Mexico
a r t i c l e i n f o a b s t r a c t
Article history:
Received
24 November 2014
Received
in revised form 9 January 2015
Accepted
13 January 2015
Available
online 15 January 2015
Editor:
A. Ringwald
In this letter we present a model for quarks and leptons based on T
7
as flavour symmetry, predicting
a canonical mass relation between charged leptons and down-type quarks proposed earlier. Neutrino
masses are generated through a Type-I seesaw mechanism, with predicted correlations between the
atmospheric mixing angle and neutrino masses. Compatibility with oscillation results leads to lower
bounds for the lightest neutrino mass as well as for the neutrinoless double beta decay rates, even for
normal neutrino mass hierarchy.
© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
Ever since the discovery of the muon in the thirties particle physicists have wondered about a possible simple understanding of fermion
mass and mixing patterns. The experimental confirmation of neutrino oscillations [1–4] has brought again the issue into the spotlight. Yet
despite many attempts, so far the origin of neutrino mass and its detailed flavour structure remains one of the most well-kept secrets of
nature. In particular the observed values of neutrino oscillation parameters [5] pose the challenge to figure out why lepton mixing angles
are so different from those of quarks. Indeed the sharp differences between the flavour mixing parameters characterising the quark and
lepton sectors escalate the complexity of the flavour problem. Many extensions of the Standard Model (SM) have been proposed in order
to induce nonzero neutrino masses [6] and to predict the oscillation parameters such as the neutrino mass ordering, the octant of the
atmospheric mixing angle and the value of the CP-violating phase in the lepton sector.
A
popular approach to tackle these issues is the use of discrete non-Abelian flavour symmetries which are known to be far more
restrictive than Abelian ones [7]. In the literature there are many models based on, for instance, A
4
(the group of even permutations of
a tetrahedron) whose simplest realisations predict zero reactor mixing angle and maximal atmospheric angle [8–10]. However, this nice
prediction has now been experimentally ruled out [1–4] so that the corresponding models need to be revamped in order to account for
observations [11].
A
variety of possible predictions of flavour symmetry based models can be found, for instance [12]:
i) neutrino
mass sum rules leading to restrictions on the effective mass parameter |m
ee
| characterising neutrinoless double beta decay
(0νββ) processes [13–16];
ii) neutrino
mixing sum rules [17].
Here
we concentrate on the alternative possibility of having mass relations in the charged fermion sector. For definiteness we focus on the
relation in Eq. (1),
m
b
√
m
d
m
s
≈
m
τ
√
m
e
m
μ
. (1)
*
Corresponding author.
E-mail
addresses: cesar.bonilla@ific.uv.es (C. Bonilla), stefano.morisi@gmail.com (S. Morisi), epeinado@fisica.unam.mx (E. Peinado), valle@ific.uv.es (J.W.F. Valle).
http://dx.doi.org/10.1016/j.physletb.2015.01.017
0370-2693/
© 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.