A neutrino mass-mixing sum rule from SO(10) and neutrinoless double beta decay
Received: January
mass-mixing sum rule from SO(10) and neutrinoless double beta decay
Complesso Univ. Monte S. Angelo
I-
Napoli
Italy
Open Access
c The Authors.
Complesso Univ. Monte S. Angelo, I-80126 Napoli, Italy
0 INFN , Sezione di Napoli
P. Santorellia;b for neutrino mass patterns and mixing. These are the outcome of the interplay of several features, namely: i) the seesaw mechanism; ii) the presence of an intermediate scale where B-L gauge symmetry is broken and the right-handed neutrinos acquire a Majorana mass; iii) a symmetric Dirac neutrino mass matrix whose pattern is close to the up-type quark one. In this framework two natural characteristics emerge. Normal neutrino mass hierarchy is the only allowed, and there is an approximate relation involving both light-neutrino masses and mixing parameters. This di ers from what occurring when horizontal avour symmetries are invoked. In this case, in fact, neutrino mixing or mass relations have been separately obtained in literature. In this paper we discuss an example of such comprehensive mixingmass relation in a speci c realization of SO(10) and, in particular, analyse its impact on the expected neutrinoless double beta decay e ective mass parameter hmeei, and on the neutrino mass scale. Remarkably a lower limit for the lightest neutrino mass is obtained (mlightest & 7:5
bDipartimento di Fisica Ettore Pancini; Universita di Napoli Federico II
1 Introduction
Mass-mixing sum rule from SO(10)
Results on neutrinoless double beta decay
Grand Uni ed Theories (GUT) embed the Standard Model (SM) gauge group into (semi)
simple groups of higher dimension, and provide remarkable insights on issues which are
left unsolved by the - yet extremely successful - SU(3)c SU(2)L
U(1)Y theory. Examples
of these phenomenological features are the explanation of electric charge quantization,
uni cation of the gauge couplings at some large mass scale and a prediction for the value
of the Weinberg angle. Furthermore, GUTs have a smaller set of free parameters with
respect to SM, and provide nice relations among fermion masses and mixing. Finally, they
share the property that all matter
elds, for each generation, can be allocated in just a
few of irreducible group representations (IRR): only two in case of SU(5) [1] and
PatiSalam [2, 3] groups, and a single 16-dimensional spinorial representation for SO(10) [4, 5]
(for a review see ref. [6]).
In this paper we focus on the SO(10) GUTs, pointing out that, adopting minimal and
reasonable assumptions that will be discussed in the following, two interesting
phenomenological implications about neutrino masses and mixing emerge:
mass ordering is allowed [7, 8];
there is a mixing dependent
mass sum rule that constraints the allowed region
in the plane lightest neutrino mass eigenstate (mlightest) vs e ective mass parameter
(hmeei). This eventually a ects the neutrinoless double beta decay rates.
We know from neutrino oscillations experiments, that at least two of the three active
neutrinos are massive. However, the absolute neutrino mass scale is still unknown, as well
as the mass ordering. In fact, both Normal Hierarchy (NH) (m1 < m2
m3) and Inverted
Hierarchy (IH) (m3
m1 < m2) are still allowed by present data [9{11], where by de nition
the mass eigenstate m3 is the one that maximally mixes with avour eigenstates
Indeed, it is the whole paradigm of fermion mass pattern and mixing parameters
hierarchies that remains a mystery, a deep question in particle physics known as the avour
problem. In the last decades, many ideas have been put forward as attempts to address
this problem, within GUTs or in di erent schemes. One interesting possibility is based
on the idea of extending the SM gauge group to include a symmetry acting between the
three families, known as horizontal or
avour symmetries. Such a symmetry could be
abelian continuous [12] or discrete [14], and non-abelian continuous [13] or discrete [15, 16].
Some years ago, it became very popular to exploit non-abelian discrete symmetry after
preliminary experimental indications supporting an almost maximal atmospheric neutrino
mixing angle 23 and a small reactor angle 13 at the same time (see for instance ref. [17]
and references therein). However, recent experimental data show a clear deviation from
the maximality for the atmospheric angle, and indicate a not vanishing sin 13
0:23 denoting the sinus of the Cabibbo angle [18]. In view of this, non-abelian
avour symmetries at the present seem to be quite disfavoured [19].
avour symmetries lead to simple relations among neutrino parameters,
known as the mass and mixing sum rules. The presence of neutrino mass sum rules was
rst observed in ref. [20] and then studied in ref. [21]. A phenomenological classi cation
was given in ref. [22] while a more extensive analysis based on the possible neutrino mass
mechanism can be found in ref. [23] (for a review on this issue see also ref. [24]). On the
other hand, mixing sum rules have (...truncated)