Open Journal of Microphysics, 2013, 3, 5-9
doi:10.4236/ojm.2013.33B002 Published Online August 2013 (http://www.scirp.org/journal/ojm)
Neutrino Properties Probed by Lepton Number
Violating Processes
Sabin Stoica
Department of Fundamental Research, Horia Hulubei Foundation, P.O. Box MG-12, Bucharest-Magurele, Romania
Received July, 2013
ABSTRACT
Study of neutrino properties is nowadays one of the most active domains of research in physics. On the one hand, fun-
damental properties of the neutrinos like their absolute mass, their character (are they Dirac or Majorana particles?) and
the number of neutrino flavors, are still unknown. On the other hand, the knowledge of these properties are of great
importance since the neutrinos are very abundant in nature and play a key role in nuclear and particle physics, astro-
physics and cosmology. In addition, the results of the neutrino oscillation experiments have convincingly showed that
neutrinos have mass and mix, in contradiction to the initial assumptions of the Standard Model. In this context there is
an increased interest in the study of the Lepton Number Violating (LNV) processes, since they are capable to decide on
the above mentioned neutrino properties. Since recently, the neutrinoless double beta (0ββ) decay was considered the
only process able to distinguish between Dirac or Majorana neutrinos and to give a hint on the absolute mass of the
electron neutrino. At present, the increased luminosity of the LHC experiments at CERN makes it feasable the search
for LNV processes at LHC as well. Besides the neutrino character, these studies can also shed light on the existence of
other types of neutrinos (the sterile neutrinos), than the three known ones. In this paper, I make a brief review on our
present knowledge about the neutrino properties and on the way they can be probed by LNV processes at low- and
high-energies. Particularly, I refer to the 0ββ decay process and to the first attempts of searching of LNV processes in
hadron collider experiments, particularly in LHC experiments at CERN-Geneva.
Keywords: Neutrinos; Neutrino Oscillations; Double Beta Decay; Neutrino Mass; Lepton Number Violation
1. Introduction
Results of the neutrino oscillation experiments have con-
vincingly showed that neutrinos have mass and can os-
cillate from one flavor to another. They extend our un-
derstanding on the Standard Model (SM) and strongly
encourage us for searching of beyond SM physics.
However, fundamental properties of the neutrinos as
their absolute mass, their character (are they non-identi-
cal (Dirac particles) or identical (Majorana particles)
with their anti-particles?), the number of neutrino flavors,
the mechanism of their mass generation and their mass
hierarchy, are still unknown. The knowledge of these
properties is of fundamental importance for understand-
ing the formation, composition and evolution of the uni-
verse, as well as for all the processes in which the neu-
trinos take part.
In this context there is a great interest for the study of
LNV processes because they are capable to provide in-
formation on these unknown neutrino properties.
Since recently, the neutrinoless double beta decay
(0νββ) was considered the only process capable to dis-
tinguish between Dirac or Majorana neutrinos and to
give a hint on the absolute mass scale of the electron
neutrino. At present, the increased luminosity of the LHC
experiments at CERN makes it feasable the searching of
LNV processes at LHC experiments, as well. They can
bring complementary information to that which can be
extracted from low-energy neutrino studies.
In this paper, I make a brief review on our present
knowledge about the neutrino properties and on the way
they can be probed by LNV processes at low and high
energies. Particularly, I refer to the 0ββ decay process
and to the first attempts of searching of LNV processes
in hadron collider experiments, particularly in LHC ex-
periments at CERN-Geneva.
The paper is organized as follows: in the Section 2, I
shortly present the actual status of our knowledge about
the neutrino properties. In the section 3, I refer to the
0νββ process and to how one can extract the relevant
neutrino parameters from the information provided by
the study of this decay mode in connection with neutrino
oscillation experiments. Section 4 is dedicated to the
presentation of the LNV processes at high energy, and to
the first attempts for their searching at hadron colliders,

S. STOICA
6
particularly at LHC experiments at CERN. The paper
ends up with Section Conclusions, where I sum up the
importance of the study of these LNV processes and I
sketch some future prospects.
2. Neutrino Properties
From neutrino oscillation experiments we know that
neutrinos have a non-zero mass and they can oscillate
from one flavor to another, in contradiction with the ini-
tial assumtions of the SM. The squared mass differences
between mass eigenstates and the mixing angles ( θ12, θ23,
θ13 ) are measured within a few percentage accuracy by
various experiments running in both terestrial and under-
ground laboratories, and measuring neutrinos produced
in Sun, Earth atmosphere, accelerators and reactors [1-8].
The actual values of these parameters are: 1) Δm2
12 =
Δm2
sol ~ 7.58 x 10-5 eV2; tan2θ12 ~ 0.484 → θ12~350 -
measured in solar neutrino (underground) + KamLAND
(reactor) experiments; 2) |Δm2
13| = |Δm2 32| = Δm2 atm ~
2.40 x10-3 eV2; sin2 2θ23 ~ 1.02 → θ23 ~ 450 – measured in
atmospheric (underground) + K2K (reactor) + MINOS
(accelerator) experiments; 3) sin2 2θ13 ~ 0.092; θ13 ~ 90 -
Daya Bay (reactor) experiment. This last measurement
(with 5.2σ statistical significance) allows an unambigous
differentiation between oscillation 1-3 and the anomalous
disappearance of anti-electron neutrinos from the reactor
ν flux at RENO and Double-Chooz experiments, strengh
tening the argument for existence of a sterile neutrino.
Future expected measurements at T2K, RENO, MINOS,
etc. Experiments are expected to start in the next future
to measure the imbalance matter-antimatter. An impor-
tant remark is the following: while the sign of Δm2
12 can
be measured due to matter effects of the neutrino propa-
gation from sun, the sign of Δm2
13 can not be measured.
In a three flavor neutrino analysis this leads to two possi-
ble scenarios for the neutrino mass hierarchy, the so-
called “normal” (m1<m2<<m3) and “inverted” (m3<<m1<
m2) hierarchies, which are shown in Figure 1. As we
mentioned above, there remain still unknown issues as:
the absolute mass of the neutrinos, the mechanism of
mass generation, their mass hierarchy, if neutrinos are
Majorana or Dirac particles?), are there “sterile” neutri-
nos, is the CP symmetry violated in the lepton sector, and
if yes, how much? Information on all these issues can be
provided by the study of LNV processes.
3. Lepton Number Violating Processes at
Low-Energy
Lepton number (LN) conservation is a symmetry that is
experimentally verified to a very high precision, and it is
assumed within the SM. However, it is not a conse-
quence of a known gauge symmetry, thus other theories
more general than the SM allow the non-conservation of
this quantum number. Lepton number violation was first
invoked to argue the possible existence of the 0νββ decay
mode, a process which could probe the Dirac or Majo-
rana character of neutrinos. More detailed information
about its study can be found in some recent publications
[9-12]. The Double beta decay (DBD) is a nuclear natu-
ral decay by which an even-even nucleus transforms an
even-even nucleus into another even-even nucleus with
the same mass but the nuclear charge changed by two
units. It occurs whatever single  decay can not occur
due to energetical reasons, or it is highly forbidden by
angular momentum selection rules. Figure 2 illustrates
such a situation. Within the SM this process occurs with
the emission of two electrons and two anti-neutrinos, and
this decay mode (2νββ) was already measured for eleven
isotopes. However, within theories that go beyond SM
(BSM), in which LNV is permitted, the DBD process
may occur without emission of neutrinos. This implies
that neutrino is a Majorana particle with mass different
from zero. Considering the most common mechanism of
occurrence, i.e. exchange of light Majorana neutrinos
between two nucleons inside the nucleus and in the
presence of only left-handed (LH) weak interactions, the
half-life of this decay mode can be expressed as a prod-
uct of three factors:
Figure 1. Hierarchical neutrino mass scheme: (a) normal
hierarchy; (b) inverted hierarchy.
Figure 2. Illustration of a DBD process: nuclei (a) and (d)
are stable against  decay, but unstable against  decay:
- - for (a) and ++ for (d).

S. STOICA 7
[T0ν
1/2]-1 = G0ν(Qββ,Z) |M0ν|2 <mν2>/me (1)
where G0ν is a phase space depending on the energy Qββ
released in the decay and on the nuclear charge Z, and
M0ν are the nuclear matrix elements (NMEs) which de-
pend on the nuclear structure of the isotope that decays.
The third factor <mν> appearing in Equation (1) is a
BSM parameter, that can be expressed in terms of neu-
trino mass eigenstates and neutrino mixing matrix U:
<m>2 = | i U
ei
2 m
i|2=| i |Uei|2 e
i m
i|2, i=1,2,3 (2)
Experimentally one can distinguish the two DBD
modes by measuring the sum of the electron energies: for
the 2νββ mode the number of DBD events versus the
sum of the electron energies is a function that looks like a
gaussian (the electrons share their energy with the two
neutrinos), while in the case of 0νββ mode this function
is a single line at the energy Qββ (all the energy released
in the decay is taken by the two electrons).
The extraction of the neutrino parameters is a very
important issue. As one can see from the Equations (1)
and (2) it is subject of the measured half-lives and of the
precise calculation of the NMEs. Their accurate calcula-
tion is a challenge for the study of 0νββ. A measurement
of the 0νββ decay rate combined with neutrino oscillation
data and a reliable calculation of the NMEs, would yield
insight into all three neutrino mass eigenstates. In the
following we show how the neutrino mass parameter can
be extracted in the case that one (dominant) mechanism
is responsible for the occurrence of 0νββ decay. This is
done separately for the two mass hierarchy scenarios.
i) normal hierarchy:
|<m

>| = |c2
13 s2 12 (∆m2 sun)½ + s2 13(∆m2 atm)½ e2i
≤ 4 · 10-3 eV (3)
ii) inverted hierarchy:
|<m

>| = |c2
13 s2 12(∆m2 sun)½ + (∆m2 atm)½ s2 13(1-sin22θ12
sinα12)½| → 1.5 ·10-2eV ≤ |<m

>| ≤ 5.0·10-2 eV (4)
where cij = cosθij and s
ij = sinθij are the neutrino mix-
ing parameters, θij being the mixing angle between neu-
trino species i and j. It is worth to mention that while in
the case of normal hierarchy there is no lower limit for
the electron neutrino mass, so an exact cancellation be-
tween the terms in Equation (3) can occur. By contrary,
in the case of inverted hierarchy there is a lower limit for
the electron neutrino mass and this will be checked by
the next generation of the DBD experiments. This is an
important experimental challenge in the study of this
process. Theoretically, the main challenge is the accurate
calculation of the NMEs involved in DBD. Then, if the
0νββ will be discovered, an important issue will be to
establish the (dominant) mechanism of its occurrence. In
case when more mechanisms contribute to the 0νββ oc-
currence, the expression of the half-life is modified ac-
cordingly. An interesting case is that when two mecha-
nisms dominate: exchange of light (active) and heavy
(sterile) Majorana neutrinos. Recently, it has shown that
in spite of the naive expectation that the light neutrinos
give the dominant contribution, heavy sterile neutrinos
can saturate the present experimental bound of 0νββ de-
cay process. In this case, under the assumtion that only
one flavour (N) of heavy neutrino exist, the expression of
the half-life reads:
(T0
1/2
)-1 = G0ν (Mν ην + MN ηN)2 , with
η = <m>3/me = i Uei
2 mi/me and
ηN = <m>4/MN = UeN
2 m
p /MN (5)
and
<m>3+1 = |c2
12 c2 13 c2 14 e2i1 m1 + c2 13 c2 14 s2 12 e2i2 m2
+ s2
13 c
2
14 e
2i3 m
3 + s2 14MN (6)
In this scenario one can extract information about the
neutrino parameters if we have data from 0νββ decay
of at least two different nuclei.
4. Lepton Number Niolating Processes at
High-Energies
In the extensions of the SM where a Majorana mass term
is introduced, the LN is violated by two units. Thus, any
such a LNV process can probe the Majorana character of
the neutrino. At present the increase of the integrated
luminosity at the LHC and superB experiments makes
feasible the study of LNV processes at high energy, as
well. There are many possible decay channels where the
LN is violated by two units. The common experimental
signature of these channels is the presence of same sign
di-leptons in the decay products. Below, we give a list of
such possible decay channels. There are baryon, meson,
tau, top quark, double Higgs possible decays, with
3-body or 4-body products in the final states.
i) baryon decays: B → B l1
± l2 ±
ii) hyperon decays: Σ- → Σ+ e-e- ; Ξ- → p - 
Ξ+
c → Ξ- + + , etc.
iii) meson decays: M± → M-/+ l1
± l2 ± (3-body decays)
M
0 →l1
- l2 - M1 + M2 + (4-body decays)
iv) tau decays:
- → μ+ μ- μ- ; - → p μ− μ− - →  l- l- X+
v) same sign di-leptonic production: pp → l1
+ l2 + X
vi) top-quark decay: t → b 11
+ l2 + W- W-
vii) double-charged Higgs decays: H±± → l1
± l2 ±X
The decay sensitivity of different heavy flavor LNV
processes is determined by comparing the scale of the
neutrino mass with the energies of the decay process [13].
We have three different cases: 1) exchange of light neu-
trinos (m
2 << q2). In this case the decay rate R ~ <mll’>
= ΣiUliUl’imi (Uli – mixing parameters of the active
neutrinos); 2) exchange of heavy neutrinos (m
2 >> q2),
and in this case the decay rate → R ~ <mll’> = ΣNVlNVl’N

S. STOICA
8
/ mN (VlN – mixing parameters between light (active) and
heavy (sterile) neutrinos); and 3) exchange of neutrinos
with mass of the of the order of the energy decay process
(mN
2 ~ q2). In this case they can be produced on their
mass shell and the decay rates are enhanced due to the
resonant effect associated to their decay widths ΓN → R
~ ΣNVlNVl’N/ ΓN. For the first two cases the decay rates
are quite small: in the first case due to the smallness of
both the mixing parameters between the active neutrinos
and of the neutrino mass (of ~ 1 eV), and in the second
case due to the smallness of the mixing parameters be-
tween the ligh (active) and heavy (sterile) neutrinos di-
vided by the large mass of the heavy neutrino. The
branching ratios (Br) in these cases are of the order of
10-20 -10-31 and, at the present LHC luminosities, they can
not be detected. The third case is quite interesting since
the theoretical predictions for the Br for these resonant
decay processes become at reach of the present and next
future high energy experiments.
Until now several LNV processes at high energy have
already been investigated. Their non-observation has set
bounds on the corresponding Br and, further, on the neu-
trino mixing parameters. In the following we shortly
present the most important such investigations performed
at LHC experiments at CERN.
ATLAS experiment [14] has performed an inclusive
search of events with two isolated leptons (e or μ) having
the same electric charge. The data are selected from
events collected from pp collisions at sqrt(s) = 7 TeV by
the ATLAS detector and correspond to an integrated lu-
minosity of 34 pb-1. The spectra in dilepton invariant
mass are compared to SM predictions. No evidence is
found for contributions beyond those of the SM. Limits
are set on the cross-section in a fiducial region for new
sources of same-sign high-mass dilepton events in the ee,
e and  channels. Four models predicting same-sign
dilepton signals are constrained: two descriptions of Ma-
jorana neutrinos, a cascade topology similar to super-
symmetry or universal extra dimensions, and fourth gen-
eration down-type quarks. Assuming a new physics scale
of 1 TeV, Majorana neutrinos produced by an effective
operator V with masses below 460 GeV are excluded at
95% CL. A lower limit of 290 GeV is set at 95% CL on
the mass of fourth generation down type quarks.
CMS experiment [15] has searched for events with
same-sign isolated dileptons (ee, e, , 
 ,  ). The
searches used an integrated luminosity of 35 pb-1 of pp
collision data at a ECM of 7 TeV collected by the CMS
experiment at the LHC. The observed numbers of events
agree with the SM predictions, and no evidence for new
physics was found. To facilitate the interpretation of the
data in a broader range of new physics scenarios, infor-
mation on the event selection, detector response, and
efficiencies is provided.
LHCb experiment has investigated several LNV proc-
esses of meson and tau decays. A first search of same
sign dileptons was performed in the decays of B+ → K-
(π-) μ+μ+ at an integrated luminosity of 36pb-1 [16]. No
signal was observed in either channels. They set limits of
the Br for the two channels as follows: Br(B+ → K- μ+ μ+ )
< 5.4·10-8 and Br( B+ → π- μ+ μ+ ) < 5.8 · 10-8 at 95% CL,
which improves the previous existed limits by factors of
40, 30, respectively. Another analysis was performed for
the B- decays into same sign di-muon channels at an in-
tegrated luminosity of 380 pb-1 [17]. Also, no signal was
observed beyond the SM and limits were set for the
channels Br(B- → D+ μ- μ-) < 5.6·10-7 and B(B- → D*+ μ-
μ- ) < 4.1 x 10-6 at 90% CL. Besides these B meson
channels a first search for tau decays was also performed
[18]. Particularly, such an investigated process was - →
μ+ μ- μ-, which is in the same time a Lepton Flavor Vio-
lating process. The analysis was done using 1.0 fb-1 of
data collected in 2011 at (s)1/2 = 7 TeV. The upper limit
for the Br was Br < 7.8 ·10-8 at 95% CL. These studies
performed at LHC experiments will be certainly im-
proved in the next future with a new set of data at an in-
creased luminosity. Besides these already investigated
channels, there are many others that merit to be investi-
gated, according to theoretical estimations for the Br. For
example, the hyperon decay channels are at present
weakly constraint (Br ~ 10-3 – 10-4). In addition, there are
very recent theoretical estimations which show that
4-body decay channels, like decays of neutral mesons (B,
D), or the tau decay channel - →  μ- μ- π+ can provide
us with even more stringent bounds on Br and neutrino
mixing parameters between muon flavor and sterile fla-
vor (N) [19]. Thus, the study of the LNV channels at
high energies opens an interesting direction of investiga-
tion at LHC experiments and superB factories in the next
future.
5. Conclusions
Recent neutrino oscillation experiments have convinc-
ingly shown that neutrinos are massive particles and they
mix. This is the first evidence that extends our under-
standing on the SM and encourages us to search for BSM
physics. The large majority of BSM theories involve
massive Majorana neutrinos which imply non-conserva-
tion of the LN. Concerning the neutrino properties we
still do not know important issues as the scale of their
absolute mass and the mass hierarchy, the mechanism of
their mass generation, the nature of neutrinos (are they
Dirac or Majorana particles?), the number of neutrino
flavors, etc. The LNV processes can shed light on these
issues, that is why there is a great interest to search for
such processes. At low energy there is the 0ββ decay, a
process which is intensively studied both theoretically
and experimentally. Theoretically, a key challenge is to

S. STOICA
9
accurately compute the NMEs involved in DBD by de-
veloping of nuclear structure methods for their calcula-
tion. Experimentally, there are several running experi-
ments, and others are planned to start in the next future.
The expectation is to explore the entire region of neutrino
masses associated with the inverted mass hierarchy sce-
nario. If the 0ββ will be discovered, the next challenge
will be to find the dominant mechanism(s) which con-
tributes to its occurrence. At present, a new opportunity
appears: the search of LNV processes at high energies.
The very large “effective luminosity” of 0ββ decay ex-
periments becomes now to be compensated by the in-
creased luminosity at LHC and superB factories. Thus,
the search of these processes at high energies becomes
another interesting avenue of research. Also, the com-
bined information from low- and high-energy experi-
ments will be of help in the study of LNV processes with
consequences on the better understanding of the neutrino
properties.
6. Acknowledgements
This work was supported by a grant of the Romanian
National Authority for Scientific Research, CNCS – UE-
FISCDI, project no. PN-II-ID-PCE-2011-3-0318.
REFERENCES
[1] Y. Ashie et al. (SK collaboration), “Measurement of
Atmospheric Neutrino Oscillation Parameters by
Super-Kamiokande I,” Physical Review D, Vol. 71, No.
11, 2005. doi:10.1103/PhysRevD.71.112005
[2] T. Araki et al., “Measurement of Neutrino Oscillation
with KamLAND: Evidence of Spectral Distortion,”
Physical Review Letters, Vol. 94, No. 8, 2005,
081801.doi:10.1103/PhysRevLett.94.081801
[3] M. H. Ahn et al., “Measurement of Neutrino Oscillation
by the K2K Experiment,” Physical Review D, Vol. 74, No.
7, 072003, 2006. doi:10.1103/PhysRevD.74.072003
[4] P. Adamson et al., (MINOS collaboration), “Measure-
ment of the Neutrino Mass Splitting and Flavor Mixing
by Minos,” Physical Review Letters, Vol. 106, 181801,
2011. doi:10.1103/PhysRevLett.106.181801
[5] Daya Bay Collaboration, Physical Review Letters, “Ob-
servation of Electron-Antineutrino Disappearance at Daya
Bay,” Vol. 108, 171803, 2012.
doi:10.1103/PhysRevLett.108.171803
[6] J. Ahn et al., (RENO collaboration), “Observation of
Reactor Electron Antineutrinos Disappearance in the
RENO Experiment,” Physical Review Letters, Vol. 108,
191802, 2012. doi:10.1103/PhysRevLett.108.191802
[7] Y. Abe et al., (Double Chooz collaboration), “Indication
of Reactor ν̅ e Disappearance in the Double Chooz
Experimen,” Physical Review Letters, Vol. 108, 131801,
2012. doi:10.1103/PhysRevLett.108.131801
[8] K. Abe et al., (T2K Collaboration), Physical Review D,
Vol. 85, No. 3, 031103 2012.
doi:10.1103/PhysRevD.85.031103
[9] J. D. Vergados, H. Ejiri and F. Simkovic, arXiv:
1205.0649.
[10] A. Faessler, arXiv:1203. 3648.
[11] Werner Rodejohann, International Journal of Modern
Physics E, Vol. 20, No. 09, 2011, 1833.
doi:10.1142/S0218301311020186
[12] M. Horoi and S. Stoica. Physical Review C, Vol. 81,
024321, 2010; A. Neascu, S. Stoica and M. Horoi,
Physical Review C, Vol. 86, 067304, 2012.
[13] A. Atre, T. Han, S. Pascoli and B. Zhang, JHEP, Vol. 05,
030 (2009).
[14] ATLAS collaboration, JHEP, Vol. 10, 107 (2011).
[15] CMS collaboration, JHEP, Vol. 06, 077 (2011).
[16] LHCb Collaboration, “Search for Lepton Number
Violating Decays B+→π-μ+μ+ and B+→K-μ+μ+,”
Physical Review Letters, Vol. 108, 101601, 2012.
doi:10.1103/PhysRevLett.108.101601
[17] LHCb collaboration, Phys. Rev.85,112004 (2012).
[18] LHCb collaboration: J.Harrison, Nucl. Phys. B, Proceed-
ings Supplement, 2012; LHCb collaboration: P. Seyfert,
arXiv: 1209; 4939v1 [hep-ex] and FPCP 2012, Hefei,
China.
[19] G. Lopez-Castro, N. Quinteros, arXiv: 1212.0037 [hep-
ph].