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arXiv:1005.1241v2 [hep-ex] 23 Nov 2010
MAN/HEP/2010/2
Probing New Physics Models of Neutrinoless Double Beta Decay
with SuperNEMO
R. Arnold1, C. Augier2, J. Baker3, A.S. Barabash4, A. Basharina-Freshville5, M. Bongrand2, V. Brudanin6,
A.J. Caffrey3, S. Cebri´ an7, A. Chapon8, E. Chauveau9,10, Th. Dafni7, F.F. Deppisch11, J. Diaz12, D. Durand8,
V. Egorov6, J.J. Evans5, R. Flack5, K-I. Fushima13, I. Garc´ ıa Irastorza7, X. Garrido2, H. G´ omez7, B. Guillon8,
A. Holin5, K. Holy14, J.J. Horkley3, Ph. Hubert9,10, C. Hugon9,10, F.J. Iguaz7, N. Ishihara15, C.M. Jackson11,
S. Jullian2, M. Kauer5, O. Kochetov6, S.I. Konovalov4, V. Kovalenko1,6, T. Lamhamdi16, K. Lang17, G. Lutter9,10,
G. Luz´ on7, F. Mamedov18, Ch. Marquet9,10, F. Mauger8, F. Monrabal12, A. Nachab9,10, I. Nasteva11, I. Nemchenok6,
C.H. Nguyen9,10, M. Nomachi19, F. Nova20, H. Ohsumi21, R.B. Pahlka17, F. Perrot9,10, F. Piquemal9,10,
P.P. Povinec14, B. Richards5, J.S. Ricol9,10, C.L. Riddle3, A. Rodr´ ıguez7, R. Saakyan5, X. Sarazin2, J.K. Sedgbeer22,
L. Serra12, Yu. Shitov22, L. Simard2, F.ˇSimkovic14, S. S¨ oldner-Rembold11, I.ˇStekl18, C.S. Sutton23, Y. Tamagawa24,
J. Thomas5, V. Timkin6, V. Tretyak6, Vl.I. Tretyak25, V.I. Umatov4, I.A. Vanyushin4, R. Vasiliev6, V. Vasiliev5,
V. Vorobel26, D. Waters5, N. Yahlali12, and A.ˇZukauskas26
1IPHC, Universit´ e de Strasbourg, CNRS/IN2P3, F-67037 Strasbourg, France
2LAL, Universit´ e Paris-Sud 11, CNRS/IN2P3, F-91405 Orsay, France
3INL, Idaho Falls, Idaho 83415, USA
4Institute of Theoretical and Experimental Physics, 117259 Moscow, Russia
5University College London, WC1E 6BT London, United Kingdom
6Joint Institute for Nuclear Research, 141980 Dubna, Russia
7University of Zaragoza, C/ Pedro Cerbuna 12, 50009 Spain
8LPC Caen, ENSICAEN, Universit´ e de Caen, F-14032 Caen, France
9Universit´ e de Bordeaux, Centre d’Etudes Nucl´ eaires de Bordeaux Gradignan, UMR 5797, F-33175 Gradignan, France
10CNRS/IN2P3, Centre d’Etudes Nucl´ eaires de Bordeaux Gradignan, UMR 5797, F-33175 Gradignan, France
11University of Manchester, M13 9PL Manchester, United Kingdom
12IFIC, CSIC - Universidad de Valencia, Valencia, Spain
13Tokushima University, 770-8502, Japan
14FMFI, Comenius University, SK-842 48 Bratislava, Slovakia
15KEK,1-1 Oho, Tsukuba, Ibaraki 305-0801 Japan
16USMBA, Fes, Morocco
17University of Texas at Austin, Austin, Texas 78712-0264, USA
18IEAP, Czech Technical University in Prague, CZ-12800 Prague, Czech Republic
19Osaka University, 1-1 Machikaneyama Toyonaka, Osaka 560-0043, Japan
20Universitat Aut` onoma de Barcelona, Spain
21Saga University, Saga 840-8502, Japan
22Imperial College London, SW7 2AZ, London, United Kingdom
23MHC, South Hadley, Massachusetts 01075, USA
24Fukui University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581 Japan
25INR, MSP 03680 Kyiv, Ukraine
26Charles University, Prague, Czech Republic
Abstract. The possibility to probe new physics scenarios of light Majorana neutrino exchange and right-
handed currents at the planned next generation neutrinoless double β decay experiment SuperNEMO is
discussed. Its ability to study different isotopes and track the outgoing electrons provides the means to
discriminate different underlying mechanisms for the neutrinoless double β decay by measuring the decay
half-life and the electron angular and energy distributions.
Correspondence to: frank.deppisch@manchester.ac.uk,
chris.jackson@hep.manchester.ac.uk, soldner@fnal.gov
1 Introduction
Oscillation experiments have convincingly shown that at
least two of the three active neutrinos have a finite mass
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2 R. Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO
and that flavour is violated in the leptonic sector [1]. De-
spite this success, oscillation experiments are unable to de-
termine the absolute magnitude of neutrino masses. Upper
limits on the effective electron neutrino mass of 2.3 eV [2]
and 2.05 eV [3] can be set from the analysis of tritium β
decay experiments. Astronomical observations combined
with cosmological considerations yield an upper bound to
be set on the sum of the three neutrino masses of the or-
der of 0.7 eV [4]. However, the most sensitive probe of
the absolute mass scale of Majorana neutrinos is neutri-
noless double β decay (0νββ) [5,6,7,8]. In this process,
an atomic nucleus with Z protons decays into a nucleus
with Z + 2 protons and the same mass number A under
the emission of two electrons,
(A,Z) → (A,Z + 2) + 2e−. (1)
This process can be described by the exchange of a light
neutrino connecting two V-A weak interactions, see Fig. 1
(a). The process (1) is lepton number violating and, in
the standard picture of light neutrino exchange, it is only
possible if the neutrino is identical to its own anti-particle,
i.e. if neutrinos are Majorana particles. Combined with
the fact that neutrino masses are more than five orders of
magnitude smaller than the masses of other fermions, such
a possibility suggests that the origin of neutrino masses is
different from that of charged fermions.
Several mechanisms of mass generation have been sug-
gested in the literature, the most prominent example be-
ing the seesaw mechanism [9] in which heavy right-handed
neutrinos mix with the left-handed neutrinos and generate
light Majorana masses for the observed active neutrinos.
The Majorana character of the active neutrinos can then
be connected to a breaking of lepton number symmetry
close to the GUT scale and might be related to the baryon
asymmetry of the Universe through the baryogenesis via
leptogenesis mechanism [10].
Because of its sensitivity to the nature and magnitude
of the neutrino mass, 0νββ decay is a crucial experimen-
tal probe for physics beyond the Standard Model and its
discovery will be of the utmost importance. It will prove
lepton number to be broken, and in most models it will
also provide direct evidence that the light active neutrinos
are Majorana particles1[12]. However, the measurement
of 0νββ decay in a single isotope is not sufficient to prove
that the standard mechanism of light Majorana neutrino
exchange is the dominant source for the decay. There are a
host of other models, such as Left-Right symmetry [5], R-
parity violating Supersymmetry (SUSY) [13] or Extra Di-
mensions [11], which can provide alternative mechanisms
to trigger 0νββ decay. In some of these models, additional
sources of lepton number violation can supplement light
neutrino exchange. For example, in Left-Right symmet-
ric models, there are additional contributions from right-
handed currents and the exchange of heavy neutrinos. In
other models, such as R-parity violating SUSY, 0νββ de-
cay can be mediated by other heavy particles that are not
directly related to neutrinos.
1See [11] for a counter-example of a model where such a
conclusion is not valid.
There are several methods proposed in the literature
to disentangle the many possible contributions or at least
to determine the class of models that give rise to the domi-
nant mechanism for 0νββ decay. Results from 0νββ decay
can be compared with other neutrino experiments and ob-
servations such as tritium decay to determine if they are
consistent. At the LHC there could also be signs of new
physics exhibiting lepton number violation that is related
to 0νββ (see [14] for such an example in R-parity violat-
ing Supersymmetry). Such analyses would compare results
for 0νββ with other experimental searches, but there are
also ways to gain more information within the realm of
0νββ decay and related nuclear processes. Possible tech-
niques include the analysis of angular and energy correla-
tions between the electrons emitted in the 0νββ decay [5,
15,16,17,18] or a comparison of results for 0νββ decay in
two or more isotopes [19,20,21,22]. These two approaches
are studied in this paper. Other proposed methods are the
comparative analysis of 0νββ decay to the ground state
with either 0νβ+β+or electron capture decay [23] and
0νββ decay to excited states [24].
Currently, the best limit on 0νββ decay comes from
the search for 0νββ decay of the isotope76Ge giving a
half-life of T1/2 > 1.9 · 1025years [25]. This results in
an upper bound on the 0νββ Majorana neutrino mass of
?mν? ≤ 300 − 600 meV. A controversial claim of obser-
vation of 0νββ decay in76Ge gives a half-life of T1/2=
(0.8−18.3)·1025y [26] and a resulting effective Majorana
neutrino mass of ?mν? = 110 − 560 meV. Next genera-
tion experiments such as CUORE, EXO, GERDA, MA-
JORANA or SuperNEMO aim to increase the half-life ex-
clusion limit by one order of magnitude and confirm or
exclude the claimed observation. The planned experiment
SuperNEMO allows the measurement of 0νββ decay in
several isotopes (82Se,150Nd and48Ca are currently be-
ing considered) to the ground and excited states, and is
able to track the trajectories of the emitted electrons and
determine their individual energies. In this respect, the
SuperNEMO experiment has a unique potential to disen-
tangle the possible mechanisms for 0νββ decay.
This paper addresses the question of how measure-
ments at SuperNEMO can be used to gain information
on the underlying physics mechanism of the 0νββ decay.
The sensitivity of SuperNEMO to new physics parame-
ters in two models is determined by performing a detailed
simulation of the SuperNEMO experimental set-up. By
analysing both the angular and energy distributions in
the standard mass mechanism and in a model incorporat-
ing right-handed currents, the prospects of discriminating
0νββ decay mechanisms are examined. The two models
are specifically chosen to represent all possible mecha-
nisms, as they maximally deviate from each other in their
angular and energy distributions.
This paper is organised as follows. In Section 2 a short
description of the theoretical framework on which the cal-
culations of the 0νββ decay rate and the angular and en-
ergy correlations are based is shown. The example physics
models are introduced and reviewed. Section 3 gives a
brief overview of the SuperNEMO experiment design and
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R. Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO3
(a)(b)
Fig. 1: Diagrams illustrating 0νββ decay through (a) the mass mechanism and (b) the right-handed current contribu-
tion via the λ parameter.
in Section 4 a detailed account of the simulation anal-
ysis and its results are presented. In Section 5, the ex-
pected constraints from SuperNEMO on new physics are
shown and the prospects of disentangling 0νββ mecha-
nisms by analysing the angular and energy distributions
and by comparing rates in different isotopes are addressed.
Our conclusions are presented in Section 6.
2 Neutrinoless Double Beta Decay
2.1 Effective Description
Contributions to 0νββ decay can be categorised as either
long-range or short-range interactions. In the first case,
the corresponding diagram involves two vertices which are
both point-like at the Fermi scale, and connected by the
exchange of a light neutrino. Such long-range interactions
are described by an effective Lagrangian [27,28]
L =GF
√2
jV −AJV −A+
L.i.
?
a,b
ǫlr
abjaJb
, (2)
where GF is the Fermi coupling constant and the leptonic
and hadronic Lorentz currents are defined as ja= ¯ eOaν
and Ja= ¯ uOad, respectively. Here, Oadenotes the corre-
sponding transition operator, with a = V −A,V +A,S −
P,S + P,TL,TR [27]. In Equation (2), the contribution
from V −A currents originating from standard weak cou-
plings has been separated off and the summation runs over
all Lorentz invariant and non-vanishing combinations of
the leptonic and hadronic currents, except for the case
a = b = V − A. The effective coupling strengths for long-
range contributions are denoted as ǫlr
For short-ranged contributions, the interactions are
represented by a single vertex which is point-like at the
Fermi scale, and they are described by the Lagrangian [28,
29]
ab.
L =G2
F
2
m−1
p
L.i.
?
a,b,c
ǫsr
abcJaJbj′
c. (3)
Here, mp denotes the proton mass and the leptonic and
hadronic currents are given by Ja = uOad and j′
eOaeC, respectively. The transition operators Oaare de-
fined as in the long-range case above, and the summation
runs over all Lorentz invariant and non-vanishing combi-
nations of the hadronic and leptonic currents. The effec-
tive coupling strengths for the short-range contributions
are denoted as ǫsr
abc.
Described by the first term in Equation (2), the ex-
change of light left-handed Majorana neutrinos leads to
the 0νββ decay rate
a=
[Tmν
1/2]−1= (?mν?/me)2G01|Mmν|2, (4)
where ?mν? is the effective Majorana neutrino mass in
which the contributions of the individual neutrino masses
mi are weighted by the squared neutrino mixing matrix
elements, U2
ei, ?mν? = |?
both long- and short-range nature, can in general be ex-
pressed as
iU2
eimi|.
Analogously, other new physics (NP) contributions, of
[TNP
1/2]−1= ǫ2
NPGNP|MNP|2, (5)
where ǫNP denotes the corresponding effective coupling
strength, i.e. is either given by ǫlr
anism or by ǫsr
abcfor a short-range mechanism. In Equa-
tions (4) and (5), the nuclear matrix elements for the mass
mechanism and alternative new physics contributions are
given by Mmνand MNP, respectively, and G01, GNP de-
note the phase space integrals of the corresponding nuclear
processes. It is assumed that one mechanism dominates
the double β decay rate.
abfor a long-range mech-
2.2 Left-Right Symmetry
The focus in this paper is on a subset of the Left-Right
symmetric model [5], which incorporates left-handed and
right-handed currents under the exchange of light and
heavy neutrinos. Left-Right symmetric models generally
predict new gauge bosons of the extra right-handed SU(2)
gauge symmetry as well as heavy right-handed neutrinos
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4R. Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO
Isotope
76Ge
82Se
150Nd
Cmm [y−1]
1.12 × 10−13
4.33 × 10−13
7.74 × 10−12
Cλλ [y−1]
1.36 × 10−13
1.01 × 10−12
2.68 × 10−11
Cmλ [y−1]
−4.11 × 10−14
−1.60 × 10−13
−3.57 × 10−12
Table 1: Coefficients used in calculating the 0νββ decay
rate [30].
which give rise to light observable neutrinos via the seesaw
mechanism.
The 0νββ decay half-life in the Left-Right symmetric
model can be written as a function of the effective param-
eters µ,η,λ [30],
[T1/2]−1= Cmmµ2+ Cλλλ2+ Cηηη2
+Cmλµλ + Cmηµη + Cηληλ,(6)
where contributions from the exchange of heavy neutrinos
are omitted. The coefficients Cmm,Cηηetc. are combina-
tions of phase space factors and nuclear matrix elements.
The first three terms give the contributions from the fol-
lowing processes:
1. Cmmµ2: Fully left-handed current neutrino exchange,
see Fig. 1 (a) (mass mechanism);
2. Cλλλ2: Right-handed leptonic and right-handed had-
ronic current neutrino exchange, see Fig. 1 (b);
3. Cηηη2: Right-handed leptonic and left-handed hadronic
current neutrino exchange.
The remaining terms in Equation (6) describe interfer-
ence effects between these three processes. The effective
parameters µ,η,λ in (6) are given in terms of the under-
lying physics parameters as
µ = m−1
e
3
?
3
?
i=1
?U11
U11
ei
?2mνi=?mν?
me
, (7)
η = tanζ
i=1
eiU12
ei, (8)
λ =
?MWL
MWR
?2
3
?
i=1
U11
eiU12
ei, (9)
with the electron mass me, the left- and right-handed W
boson masses MWLand MWR, respectively, and the mix-
ing angle ζ between the W bosons. The 3 × 3 matrices
U11and U12connect the weak eigenstates (νe,νµ,ντ) of
the light neutrinos with the mass eigenstates of the light
neutrinos (ν1,ν2,ν3), and heavy neutrinos, (N1,N2,N3),
respectively. We assume that the neutrino sector consists
of three light neutrino states, mνi≪ me, and three heavy
neutrino states, MNi≫ mp, i = 1,2,3. Consequently, the
summations in (7, 8, 9) are only over the light neutrino
states. For a simple estimate of the sensitivity of 0νββ de-
cay to the model parameters, we neglect the flavour struc-
ture in U11and U12; using the assumption that the ele-
ments in U11are of order unity (almost unitary mixing),
and those in U12are of order mD/MR∼
the effective magnitude mD of the neutrino Dirac mass
?mν/MR, with
matrix, and the light and heavy neutrino mass scales, mν
and MR, leads to the approximate relations:
µ ≈mν
me, (10)
η ≈ tanζ
?mν
?2?mν
MR,(11)
λ ≈
?MWL
MWR
MR. (12)
In the following analysis a simplified model incorporating
only an admixture of mass mechanism (MM) due to a neu-
trino mass term µ = ?mν?/me and right-handed current
due to the λ term (RHCλ) is considered:
[T1/2]−1= Cmmµ2+ Cλλλ2+ Cmλµλ.(13)
As we will see in Section 2.4, these two mechanisms exhibit
maximally different angular and energy distributions, and
with an admixture between them, to a good approxima-
tion any possible angular and energy distribution can be
produced. In our numerical calculation we use the values
as given in Table 1 for the coefficients Cmm, Cλλand Cmλ
in Equation (13). Furthermore, we assume that the pa-
rameter µ is real-valued positive and λ is real-valued.
2.3 Nuclear Matrix Elements
As demonstrated in Equations (4) and (5), a calculation of
the nuclear matrix elements (NMEs) is required to convert
the measured half-life rates or limits into new physics pa-
rameters. Exact solutions for the NMEs do not exist, and
approximations have to be used. Calculations using the
nuclear shell model exist for lighter nuclei such as76Ge
and82Se, though the only reliable results are for48Ca.
Quasi-particle random phase approximation (QRPA) cal-
culations are applied for most isotopes as a greater num-
ber of intermediate states can be included. In this paper,
a comparison between two possible SuperNEMO isotopes
(82Se and150Nd) and the isotope that gives the current
best limit (76Ge) is made. Consistent calculations of the
NMEs for these three isotopes in both the MM and RHC
are rare (only [30] and [31]). All the results are shown
using NMEs from [30], displayed in Table 1.
Recent work on the calculation of NMEs for the heavy
isotope150Nd suggests that nuclear deformation must be
included, as QRPA calculations usually consider the nu-
cleus to be spherical. To compensate for this a suppres-
sion factor of 2.7 is introduced into the NME due to an
approximation arising from the BCS overlap factor [32],
M(150Nd)/2.7. This gives a suppression Cmm,λλ,mλ/(2.7)2
in Table 1. The82Se nuclei are assumed to be spherical
and no correction is added in this paper.
The NMEs are a significant source of uncertainty in
double β decay physics and quantitative results in this
paper could change with different calculations (particu-
larly for150Nd). For example, more recent studies [33]
suggest the NMEs from150Nd for the MM are an addi-
tional factor 1.3-1.7 smaller. In our analysis we assume a
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R. Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO5
theoretical uncertainty of 30% in the NMEs of all isotopes
and mechanisms considered throughout. Even though the
choice of NME changes quantitative results for the ex-
tracted physics parameters, the conclusions about the ad-
vantages of using different kinematic variables will not be
affected.
2.4 Angular and Energy Distributions in the Left-Right
Symmetric Model
For our event simulation, the three-dimensional distribu-
tion of the 0νββ decay rate in terms of the kinetic energies
t1,2of the two emitted electrons and the cosine of the angle
between the electrons cosθ12is used:
ρ(t1,t2,cosθ12) =
dΓ
dt1dt2dcosθ12. (14)
The distributions for the MM and for the RHCλmecha-
nism are given by
ρMM(t1,t2,cosθ12) =
c1× (t1+ 1)p1(t2+ 1)p2F(t1,Z)F(t2,Z)
×δ(Q − t1− t2)(1 − β1β2cosθ12),
ρRHC(t1,t2,cosθ12) =
c2× (t1+ 1)p1(t2+ 1)p2F(t1,Z)F(t2,Z)(t1− t2)2
×δ(Q − t1− t2)(1 + β1β2cosθ12),
(15)
(16)
with the electron momenta pi=
βi= pi/(ti+ 1), and the mass difference Q between the
mother and daughter nucleus. All energies and momenta
are expressed in units of the electron mass and c1 and
c2 are normalisation constants. The Fermi function F is
given by
?ti(ti+ 2) and velocities
F(t,Z) = c3× p2s−2eπu|Γ(s + iu)|2,
?1 − (αZ)2, u = αZ(t + 1)/p, α = 1/137.036,
stant. Here, Z is the atomic number of the daughter nu-
cleus. The normalisation of the distributions is irrelevant
when discussing energy and angular correlations.
Using Equations (15) and (16), the differential decay
widths with respect to the cosine of the angle θ12,
(17)
where s =
Γ is the Gamma function and c3is a normalisation con-
dΓ
dcosθ12
=
?Q
0
dt1ρ(t1,Q − t1,cosθ12), (18)
and the energy difference ∆t = t1− t2,
dΓ
d(∆t)=
−1
?1
dcosθ12ρ
?Q + ∆t
2
,Q − ∆t
2
,cosθ12
?
,
(19)
may be determined.
The differential width in Equation (18) can be written
as [5,18]
dΓ
dcosθ12
=Γ
2(1 − kθcosθ12), (20)
with the total decay width Γ. The distribution shape is
linear in cosθ12, with the slope determined by the param-
eter kθwhich can range between −1 ≤ kθ≤ 1, depending
on the underlying decay mechanism. Assuming the domi-
nance of one scenario, the shape does not depend on the
precise values of new physic parameters (mass scales, cou-
pling constants) but is a model specific signature of the
mechanism. For the MM and RHCλmechanisms, the the-
oretically predicted kθis found from Equation (18) and is
given by
kSe
θMM= +0.88,
kSe
θRHC= −0.79,
kNd
θMM= +0.89,
kNd
θRHC= −0.80.
(21)
(22)
The correlation coefficient kθis modified when taking into
account nuclear physics effects and exhibits only a small
dependence on the type of nucleus. The MM and the
RHCλmechanisms give the maximally and minimally pos-
sible values for the angular correlation coefficient kθin a
given isotope, respectively.
Experimentally, kθcan be determined via the forward-
backward asymmetry of the decay distribution,
Aθ≡
??0
N+− N−
N++ N−
−1
dΓ
dcosθdcosθ −
=kθ
?1
0
dΓ
dcosθdcosθ
?
/Γ =
2.(23)
Here, N+(N−) counts the number of signal events with
the angle θ12larger (smaller) than 90◦.
Analogously, the MM and RHCλmechanism also differ
in the shape of the electron energy difference distribution,
Equation (19). For the isotopes82Se and150Nd, these dis-
tributions are shown in Fig. 2. Again, the shape is largely
independent of the isotope under inspection. The following
asymmetry in the electron energy-difference distribution
is determined,
AE≡
??Q/2
N+− N−
N++ N−
0
dΓ
d(∆t)d(∆t) −
?Q
Q/2
dΓ
d(∆t)d(∆t)
?
/Γ =
=kE
2,(24)
thereby defining an energy correlationcoefficient kE, where
Q is the energy release of the decay. The rate N+ (N−)
counts the number of signal events with an electron en-
ergy difference smaller (larger) than Q/2. For the MM and
RHCλmechanism, the theoretical kE parameter may be
found from Equation (19) and is given by
kSe
EMM= +0.66,
kSe
ERHC= −1.07,
kNd
EMM= +0.64,
kNd
ERHC= −1.09,
(25)
(26)
in the isotopes82Se and150Nd. As can be seen in Fig. 2,
the MM and RHCλ mechanisms correspond to different
shapes of the energy difference distribution. Analogous to
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6R. Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO
0.0 0.20.4
??t? ? Q
0.60.81.0
0.0
0.5
1.0
1.5
??1d??d???t??Q?
MM
RHCΛ
Fig. 2: Normalised 0νββ decay distribution with respect to
the electron energy difference in the MM (red) and RHCλ
mechanism (blue) for the isotopes82Se (solid curves) and
150Nd (dashed curves).
the angular distribution, the corresponding energy corre-
lation coefficients in the two mechanisms considered are,
to a good approximation, at their upper and lower limits
in a given isotope.
3 SuperNEMO
SuperNEMO is a next generation experiment building on
technology used by the currently running NEMO-III ex-
periment [34,35,36,37,38,39,40]. The design of the de-
tector consists of 20 modules each containing approxi-
mately 5 kg of enriched and purified double β emitting
isotope in the form of a thin foil (with a surface density
of 40 mg/cm2). Isotopes under consideration for Super-
NEMO are82Se,150Nd and48Ca.
The foil is surrounded by a tracking chamber compris-
ing nine planes of drift cells (44 mm diameter) on each
side operating in Geiger mode in a magnetic field of 25
Gauss. The tracking chamber has overall dimensions of 4
m height (parallel to the drift cells), 5 m length and 1 m
width (perpendicular to the foil); the foil is centred in this
volume with dimensions of 3 m height and 4.5 m length.
The tracking allows particle identification (e−,e+,γ,α)
and vertex reconstruction to improve background rejec-
tion and to allow measurement of double β decay angular
correlations.
Calorimetry consisting of 25×25cm2square blocks of 5
cm thickness scintillating material connected to low activ-
ity photomultiplier tubes (PMTs) surrounds the detector
on four sides. An energy resolution of 7% (FWHM) and
time resolution of 250 ps (Gaussian σ) at 1 MeV for the
blocks is required. The granularity of the calorimetry al-
lows the energy of individual particles to be measured. Ad-
ditional γ-veto calorimetry to identify photons from back-
ground events of thickness 10 cm surrounds the detector
on all sides. The modules are contained in shared back-
ground shielding and will be housed in an underground
laboratory to reduce the cosmic ray flux. A diagram of the
planned SuperNEMO module design is shown in Fig. 3.
4 Simulation
4.1 Simulation Description
A full simulation of the SuperNEMO detector was per-
formed including realistic digitisation, tracking and event
selection. Signals for two mechanisms of 0νββ decay (mass
mechanism MM and right-handed current via the λ pa-
rameter RHCλ) and the principal internal backgrounds
were generated using DECAY0 [41]. This models the full
event kinematics, including angular and energy distribu-
tions.
A GEANT-4 Monte Carlo simulation of the detector
was constructed. Digitisation of the hits in cells was ob-
tained by assuming a Geiger hit model validated with
NEMO-III with a transverse resolution of 0.6 mm and a
longitudinal resolution of 0.3 cm. The calorimeter response
was simulated assuming a Gaussian energy resolution of
7%/√E (FWHM) and timing resolution of 250 ps (Gaus-
sian σ at 1 MeV). Inactive material in front of the γ-veto
was partially simulated.
Full tracking was developed consisting of pattern recog-
nition and helical track fitting. The pattern recognition
uses a cellular automaton to select adjacent hits in the
tracking layers. Helical tracks are fitted to the particles.
Tracks are extrapolated into the foil to find an appropriate
event origin and into the calorimeter where they may be
associated with calorimeter energy deposits. The realistic
event selection (validated using NEMO-III) was optimised
for double β decay electrons (two electrons with a common
vertex in the foil). The selection criteria are:
– events must include only two negatively charged par-
ticles each associated with one calorimeter hit;
– event vertices must be within the foil and the tracks
must have a common vertex of <10 standard devia-
tions between intersection points in the plane of the
source foil;
– the time of flight of the electrons in the detector must
be consistent with the hypothesis of the electrons orig-
inating in the source foil;
– the number of Geiger drift cell hits unassociated with
a track must be less than 3;
– the energy deposited in individual calorimeter blocks
must be > 50 keV;
– there are zero calorimeter hits not associated with a
track;
– tracks must have hits in at least one of the first three
and one of the last three planes of Geiger drift cells;
Page 7
R. Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO7
Fig. 3: A SuperNEMO module. The source foil (not shown) sits in the centre of a tracking volume consisting of drift
cells operating in Geiger mode. This is surrounded by calorimetry consisting of scintillator blocks connected to PMTs
(grey). The support frame is shown in red.
– the number of delayed Geiger drift cell hits due to α
particles from214Bi-214Po events must be zero;
– there are no hits in the γ-veto detectors with energy
> 50 keV.
Using these experimental selection criteria the signal
efficiency was found to be 28.2% for the MM and 17.0%
for the RHCλin82Se and 29.1% for the MM and 17.3%
for the RHCλin150Nd. This is higher than the efficiency
for MM detection in100Mo decays in NEMO-III of 17.4%
(in the electron energy sum range 2-3.2 MeV) [40].
The variables reconstructed from the simulation are
the energy sum, where a peak is expected at the energy
release, Q, of the 0νββ decay, the energy difference and
the cosine of the opening angle of the two electrons. Sim-
ulations of the angular and energy difference distributions
of the two electrons in a signal sample are shown in Fig. 4
for the isotope82Se (similar results hold for150Nd). The
reconstructed distributions, normalised to the theoretical
distributions, show detector effects which arise due to mul-
tiple scattering in the source foil, compared to the theo-
retically predicted distributions based on Equations (18)
and (19). This influence is particularly strong in the right-
handed current as one electron usually has low energy so
the shape of the distribution is changed (on average a
30◦deviation from the generated distribution). The recon-
struction efficiency is also low for small angular separation
between the electrons when they travel through the same
drift cells.
The backgrounds were processed by the same detector
simulation and reconstruction programs as the signal. The
dominant two neutrino double β decay (2νββ) background
and the background due to foil contamination were nor-
malised assuming a detector exposure of 500 kg y. Due to
the high decay energy Q for 0νββ in150Nd, the214Bi back-
ground may be neglected. The activities were assumed to
be 2 µBq/kg for208Tl and 10 µBq/kg for214Bi. These
are the target radioactive background levels in the base-
line SuperNEMO design. Reconstructed distributions of
the experimental variables including background events
for the MM at an example signal half-life of 1025y are
shown in Figure 5.
4.2 Limit Setting
To determine the longest half-life that can be probed with
SuperNEMO, exclusion limits at 90% CL on the half-
life using the distribution of the sum of electron ener-
gies (Fig. 5 (a)) were set using a Modified Frequentist
(CLs) [42] method. This method uses a log-likelihood ra-
tio (LLR) of the signal-plus-background hypothesis and
the background-only hypothesis, where the signal is due
to the 0νββ process. The effect of varying the214Bi back-
ground activities on the expected limit to the MM is shown
in Fig. 6. The expected limit is given by the median of
the distribution of the LLR and the widths of the bands
shown represent one and two standard deviations of the
LLR distributions for a given
parison, the NEMO-III internal214Bi background is <
100 µBq/kg in100Mo and 530±180 µBq/kg in82Se. The
NEMO-III internal208Tl background is 110 ± 10 µBq/kg
in100Mo, 340±50 µBq/kg in82Se and 9320±320 µBq/kg
in150Nd [39]. The γ-veto used reduces the number of ra-
dioactive background events by 30% for214Bi in the elec-
tron energy sum window > 2.7 MeV.
All external backgrounds from outside the foil, apart
from radon in the tracking volume, are expected to be
negligible and were not simulated. The energy distribu-
tion of the external radon background is similar to the
internal background. Simulations have shown that a con-
tamination of 10 µBq/kg of214Bi in the foil is equivalent
to 280 µBq/m3of214Bi in the gas volume and 2 µBq/kg
of208Tl in the foil is equivalent to 26 µBq/m3of208Tl in
the gas volume. Figure 6 shows that this level of external
background would lead to a ∼ 15% reduction in the half-
life limit. The dominant 2νββ background is measured by
SuperNEMO and statistical uncertainties on its half-life
214Bi activity. For com-
Page 8
8 R. Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO
Cosine of angle between electronsCosine of angle between electrons
-1-1-0.8 -0.6 -0.4 -0.2 -0.8 -0.6 -0.4 -0.200 0.2 0.4 0.2 0.40.6 0.8 0.6 0.811
Events
0.2 0.2
0.4 0.4
0.60.6
0.80.8
11
Events
Mass Mechanism
Theoretical distribution
Reconstructed distribution
(a)
Cosine of angle between electronsCosine of angle between electrons
-1 -1 -0.8 -0.6 -0.4 -0.2-0.8 -0.6 -0.4 -0.200 0.2 0.4 0.2 0.40.6 0.8 0.6 0.811
Events
00
0.20.2
0.4 0.4
0.6 0.6
0.8 0.8
11
Events
Right Handed Current
Theoretical distribution
Reconstructed distribution
(b)
Difference in energy of electrons (MeV)Difference in energy of electrons (MeV)
00 0.50.5111.5 1.5222.5 2.533
Events
00
0.20.2
0.40.4
0.60.6
0.8 0.8
11
Events
Mass Mechanism
Theoretical distribution
Reconstructed distribution
(c)
Difference in energy of electrons (MeV) Difference in energy of electrons (MeV)
00 0.5 0.511 1.51.522 2.52.533
Events
00
0.20.2
0.40.4
0.6 0.6
0.8 0.8
11
Events
Right Handed Current
Theoretical distribution
Reconstructed distribution
(d)
Fig. 4: Theoretical and experimental electron angular distributions for (a) MM and (b) RHCλ. Theoretical and
experimental electron energy difference distributions for (c) MM and (d) RHCλ. All distributions are shown for the
isotope82Se and the reconstructed distributions are normalised to the theoretical distribution to show signal efficiency.
are expected to be negligible. Inclusion of an estimated
7% correlated systematic uncertainty on the signal and
background distributions [35] leads to a ∼ 5% reduction in
the MM half-life limit. The effects of external background
and of systematic uncertainties on the 2νββ background
are not included in the results of this paper.
Expected exclusion limits at 90% confidence level on
the half-life are shown in Fig. 7. Results are displayed as a
function of RHCλadmixture, where the signal distribution
is produced by combining weighted combinations per bin
of the MM and RHCλcontributions at the event level. An
admixture of 0% corresponds to a pure MM contribution,
and an admixture of 100% to pure RHCλ. Interference
terms are assumed to be small and are neglected in the
experimental simulation. The lower efficiency in the case
of RHCλ results in a lower limit for larger admixtures.
The half-life limit is approximately twice as sensitive in
measurements of82Se due to the lower mass number and
higher 2νββ decay half-life, though this is compensated
in150Nd by more favourable phase space when convert-
ing into physics parameter space. In the case where one
mechanism dominates SuperNEMO is expected to be able
to exclude 0νββ half-lives up to 1.2 · 1026y (MM) and
6.1 · 1025y (RHCλ) for82Se, and 5.1 · 1025y (MM) and
2.6 · 1025y (RHCλ) for150Nd.
4.3 Observation
A 0νββ signal rate with significant excess over the back-
ground expectation, as for example shown in Fig. 5, would
lead to an observation. The expected experimental sta-
tistical uncertainties on the decay half-life are calculated
from the Gaussian uncertainties on the observed number
Page 9
R. Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO9
Electron energy sum (MeV) Electron energy sum (MeV)
2.7 2.72.8 2.8 2.9 2.933 3.1 3.13.2 3.2 3.3 3.33.43.4
Events
00
55
10 10
15 15
20 20
25 25
3030
35 35
40 40
Events
Mass Mechanism (500 kg y)
y)
25
(10
ββν
0
ββν
2
Bi
214
Tl
208
(a)
Difference in energy of electrons (MeV)Difference in energy of electrons (MeV)
00 0.5 0.511 1.51.522 2.5 2.533
Events
00
22
44
66
88
10 10
1212
1414
1616
1818
Events
Mass Mechanism (500 kg y)
y)
25
(10
ββν
0
ββν
2
Bi
214
Tl
208
(b)
Cosine of angle between electronsCosine of angle between electrons
-1 -1-0.8 -0.8-0.6-0.6 -0.4-0.4 -0.2-0.200 0.2 0.20.4 0.40.6 0.60.8 0.811
Events
00
22
44
66
88
10 10
1212
14 14
Events
Mass Mechanism (500 kg y)
y)
25
(10
ββν
0
ββν
2
Bi
214
Tl
208
(c)
Fig. 5: Expected number of MM signal (half-life of 1025y) and background events in82Se after 500 kg y exposure
shown for (a) electron energy sum, (b) electron energy difference and (c) cosine of angle between electrons.
Bq/kg)Bq/kg)
µµ
Bi (Bi (
214214
Background Activity Background Activity
111010
22
1010
y)
25
Half-life limit (10
00
55
10 10
1515
2020
25 25
30 30
Se (500 kg y)Se (500 kg y)
82 82
Expected half-life limit for Expected half-life limit for
90% CL limit
1 sigma1 sigma
2 sigma2 sigma
90% CL limit
y)
25
Half-life limit (10
Fig. 6: Expected limit on the 0νββ half-life due to the MM for SuperNEMO under the background-only hypothesis.
The expected limit with the one and two standard deviation bands is shown as a function of background activity for
214Bi in82Se (a208Tl activity of 2 µBq/kg is assumed).
of signal and background events in the simulation. Fig-
ure 8 shows the results for82Se and150Nd as a function
of the admixture of RHCλ. Acceptance effects cause the
uncertainty to increase with admixture of RHCλ. The sta-
tistical uncertainty increases significantly for large admix-
tures of RHCλ at T1/2 = 1026y which go beyond the
exclusion limit of SuperNEMO.
Page 10
10R. Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO
Admixture of right-handed current (%)
0204060 80100
yrs)
25
Half-life limit (10
0
5
10
15
20
25
Se (500 kg y)
82
Expected half-life limit for
90% CL limit
1 sigma
2 sigma
(a)
Admixture of right-handed current (%)
020 40 6080 100
yrs)
25
Half-life limit (10
0
5
10
15
20
25
Nd (500 kg y)
150
Expected half-life limit for
90% CL limit
1 sigma
2 sigma
(b)
Fig. 7: Expected limit on the 0νββ half-life for SuperNEMO under the background-only hypothesis. The expected
limit with the one and two standard deviation bands is shown as a function of admixture of the RHCλmechanism for
(a)82Se and (b)150Nd.
Admixture of right-handed current (%)Admixture of right-handed current (%)
00 2020 404060 6080 80100100
Observed half-life (y)
23 23
1010
24 24
1010
2525
10 10
26 26
1010
27 27
10 10
Observed half-life (y)
Se
82
Experimental statistical uncertainty
= 10
1/2
T
= 10
1/2
T
= 10
1/2
T
yr
26
yr
25
yr
24
(a)
Admixture of right-handed current (%)Admixture of right-handed current (%)
00 20 2040 4060 608080100 100
Observed half-life (y)
23 23
10 10
24 24
1010
2525
1010
26 26
10 10
27 27
1010
Observed half-life (y)
Nd
150
Experimental statistical uncertainty
yr
25
= 10
1/2
T
yr
24
= 10
1/2
T
(b)
Fig. 8: One standard deviation statistical uncertainties in the measurement of double β decay half-lives at SuperNEMO
as a function of admixture of the RHCλmechanism represented as band thickness for (a)82Se and (b)150Nd.
The angular asymmetry parameter kθin Equation (23)
is experimentally accessible by defining N+as the number
of events with measured angle cosθ < 0 and N− as the
number of events with cosθ > 0. Similarly, an energy dif-
ference asymmetry kE can be obtained where N+ is the
number of events with energy difference < Q/2 (half the
energy of the 0νββ decay) and N−is the number of events
with energy difference > Q/2. The electron energy sum is
required to be greater than 2.7 MeV for82Se and 3.1 MeV
for150Nd to maximise signal to background ratio. This re-
sults in signal efficiencies of 23.2% for the MM and 13.2%
for the RHCλin82Se and 19.1% for the MM and 10.4%
for the RHCλin150Nd.
Experimentally, the distributions are only available as
a sum of signal plus background so the measured values
differ from the theoretically expected values due to the
background distributions. This generally results in recon-
structed correlation factors that are biased towards pos-
itive values. The measured values of kθ,E are shown in
Fig. 9 for a number of half-lives in the two isotopes. Sta-
tistical uncertainties are shown as the width of the bands.
All reconstructed kθ,Evalues are displayed as a function of
the corresponding theoretical kT
a model independent generalisation. It can be seen that
the energy difference distribution allows stronger model
discrimination than the angular distribution.
θ,Eparameter, to allow for
5 Probing New Physics
5.1 Model Parameter Constraints
Having performed a detailed experimental analysis includ-
ing a realistic simulation of the detector setup, the re-
sults are interpreted in terms of the expected reach of the
SuperNEMO experiment to new physics parameters of the
combined MM and RHCλmodel of 0νββ decay.
Using Equation (13) for the 0νββ decay half-life to-
gether with the coefficients listed in Table 1, the expected
90% CL limit on T1/2shown in Fig. 7 can be translated
into a constraint on the model parameters mνand λ. As-
suming all other contributions are negligible this is shown
Page 11
R. Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO 11
T
θ
Theoretical k
-1-0.8 -0.6-0.4-0.20 0.20.4 0.60.81
θ
Reconstructed k
0
0.2
0.4
0.6
0.8
1
1.2
Se
82
parameter for
T
T
T
θ
k
yr
yr
yr
24
= 10
= 10
= 10
1/2
25
1/2
26
1/2
(a)
T
θ
Theoretical k
-1 -0.8-0.6 -0.4-0.200.2 0.40.60.81
θ
Reconstructed k
0
0.2
0.4
0.6
0.8
1
1.2
Nd
150
parameter for
θ
k
yr
24
= 10
1/2
T
yr
25
= 10
1/2
T
(b)
T
E
Theoretical k
-1.2 -1-0.8 -0.6 -0.4 -0.200.2 0.4 0.60.8
E
Reconstructed k
-1
-0.5
0
0.5
1
1.5
Se
82
parameter for
E
T
T
T
k
yr
yr
yr
24
= 10
1/2
= 10
1/2
= 10
1/2
25
26
(c)
T
E
Theoretical k
-1.2-1-0.8-0.6-0.4 -0.20 0.20.40.60.8
E
Reconstructed k
-1
-0.5
0
0.5
1
1.5
Nd
150
parameter for
E
k
yr
24
= 10
1/2
T
yr
25
= 10
1/2
T
(d)
Fig. 9: Simulation of the correlation coefficients kθand kEas a function of theoretical kT
one standard deviation statistical uncertainties. Shown are the angular correlation factor kθ for82Se (a) and150Nd
(b) and the energy difference correlation factor kEfor82Se (c) and150Nd (d).
θ,E. The bands represent the
in Fig. 10 (a), as a contour in the mν−λ parameter plane.
In the case SuperNEMO does not see a signal these pa-
rameters would be constrained to be located within the
coloured contour. The odd shape of the coloured contour
is a direct consequence of the SuperNEMO 90% CL exclu-
sion limit as a function of the specific admixture between
the MM and the RHCλ shown in Fig. 7. The small in-
terference term, though not included in the experimental
simulation, is taken into account through Equation (13) in
this figure and results in the asymmetry of the distribution
with respect to the sign of the parameter λ.
As shown in Section 4, SuperNEMO is expected to
be more sensitive to the 0νββ half-life when using the
isotope82Se, but this is compensated by the larger phase
space of150Nd. As a result, the constraint on the model
parameters is slightly stronger for150Nd. Due to the large
uncertainty in the NMEs, this might be different for other
NME calculations. To demonstrate the improvement over
existing experimental bounds, the parameter constraints
are shown in Fig. 10 (b) on a logarithmic scale (for positive
values of λ), comparing the expected SuperNEMO reach
with the current constraints from the 0νββ experiments
NEMO-III [40,38] and Heidelberg Moscow [25].
Figure 10 shows that SuperNEMO is expected to con-
strain model parameters at 90% CL down to ?mν?=70-73
meV and λ=(1-1.3)·10−7. This would be an improvement
by a factor 5-6 over the current best limit from the Heidel-
berg Moscow experiment and more than an order of mag-
nitude compared to the NEMO-III results.
5.2 Angular and Energy Correlations
As a more intriguing scenario it is now assumed that
SuperNEMO actually observes a 0νββ decay signal in82Se
or150Nd. Because of the tracking abilities described in
Section 4 this opens up the additional possibility of mea-
suring the angular and energy distribution of the decays.
Depending on the number of signal events detected, this
can be crucial in distinguishing between different 0νββ
decay mechanisms. In the analysis a reconstruction of the
angular and energy correlation coefficients kθ and kE is
used to determine the theoretical coefficients, and thereby
Page 12
12R. Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO
?2
?1012
0
20
40
60
80
Λ ?10?7?
?mΝ? ?meV?
82Se
150Nd
(a)
10?8
10?7
10?6
10?5
100
101
102
103
104
Λ
?mΝ? ?meV?
150Ndexp
82Seexp
76Geexp
82Se
150Nd
(b)
Fig. 10: (a) Expected SuperNEMO constraints on the model parameters (mν,λ) for the isotopes82Se (light blue
contour) and150Nd (dark blue contour). (b) Comparison with current bounds on 0νββ half-lives of the isotopes82Se
(NEMO-III [40]),150Nd (NEMO-III [38]) and76Ge (Heidelberg Moscow [25]). The contours show the 90% CL exclusion
region.
the admixture between the left- and right-handed currents
in the combined MM and RHCλmodel.
For the isotope82Se, this is shown in Fig. 11 for dif-
ferent RHCλadmixtures. The two blue elliptical contours
correspond to the allowed one standard deviation (mν−λ)
parameter space at SuperNEMO when observing a signal
at T1/2= 1025y and T1/2= 1026y, respectively. This
takes into account a nominal theoretical uncertainty on
the NME of 30% and a one standard deviation statistical
uncertainty on the measurement determined from the sim-
ulation (Fig. 8). The blue elliptical error bands therefore
give the allowed parameter region when only considering
the total 0νββ rate, which does not allow to distinguish
between the MM and RHCλcontributions.
When taking into account the information provided
by the angular and energy difference distribution shape,
the parameter space can be constrained significantly. This
is shown using the green contours in Fig. 11 for (a) a
pure MM model, (b) a RHCλ admixture of 30%, corre-
sponding to an angular correlation of kθ ≈ 0.4 and (c)
a pure RHCλ model. This fixes two specific directions
in the mν− λ plane (one for positive and one for neg-
ative λ). The widths of the contours are determined by
the uncertainty in determining the theoretical correlation
and admixture from the apparent distribution shape, see
Fig. 9. The outer (light green) contours in Fig. 11 give
the one standard deviation uncertainty on the parame-
ters from reconstructing the angular distribution, while
the inner (darker green) contour gives the one standard
deviation uncertainty when using the distributions of the
electron energy difference. As was outlined in Section 4,
the energy difference distribution is expected to be easier
to reconstruct and therefore gives a better determination
of the RHCλadmixture and a better constraint. While in-
terference between MM and RHCλis neglected in the sim-
ulation, it is taken into account in Equation (13) through
the term Cmλµλ resulting in the slightly tilted elliptical
contours and the asymmetry for λ ↔ −λ. Finally, the red
contours in Fig. 11 show the constraints on the model
parameters when combining both the determination of
the 0νββ decay rate and the decay energy distribution.
This demonstrates that such a successful combination can
make it possible to determine the mechanism (i.e. the de-
gree of MM and RHCλadmixture in this case), and pro-
vide a better constraint on the model parameters. From
Fig. 11 (a), the Majorana mass term can be determined at
?mν? = 245+56
to be −0.87·10−7< λ < 0.92· 10−7in the case of a mea-
sured 0νββ decay half-life of82Se of T1/2= 1025y. For a
82Se half-life of T1/2= 1026y, the uncertainty on the decay
rate increases as SuperNEMO reaches its exclusion limit
for RHCλadmixtures. It is therefore only possible to ex-
tract upper limits on the model parameters from Fig. 11
for T1/2= 1026y. However, the shape information pro-
vides additional constraints on the parameter space. In
Fig. 12 we show the analogous plots for the isotope150Nd
assuming a decay half-life of T1/2= 1025y.
−41meV while the λ parameter is constrained
Page 13
R. Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO13
?4
?2024
0
50
100
150
200
250
300
Λ ?10?7?
?mΝ? ?meV?
(a)
?4
?2024
0
50
100
150
200
250
300
Λ ?10?7?
?mΝ? ?meV?
(b)
?4
?2024
0
50
100
150
200
250
300
Λ ?10?7?
?mΝ? ?meV?
(c)
Fig. 11: Constraints at one standard deviation on the model parameters mν and λ for82Se from: (1) an observation
of 0νββ decay half-life at T1/2= 1025y (outer blue elliptical contour) and 1026y (inner blue elliptical contour); (2)
reconstruction of the angular (outer, lighter green) and energy difference (inner, darker green) distribution shape; (3)
combined analysis of (1) and (2) using decay rate and energy distribution shape reconstruction (red contours). The
admixture of the MM and RHCλcontributions is assumed to be: (a) pure MM contribution; (b) 30% RHCλadmixture;
and (c) pure RHCλcontribution. NME uncertainties are assumed to be 30% and experimental statistical uncertainties
are determined from the simulation.
?4
?2024
0
50
100
150
200
250
300
Λ ?10?7?
?mΝ? ?meV?
(a)
?4
?2024
0
50
100
150
200
250
300
Λ ?10?7?
?mΝ? ?meV?
(b)
?4
?2024
0
50
100
150
200
250
300
Λ ?10?7?
?mΝ? ?meV?
(c)
Fig. 12: As Fig. 11 but for the isotope150Nd with a decay half-life of T1/2= 1025y.
5.3 Rate Comparison of150Nd and82Se
While reconstruction of the decay distribution can be an
ideal way to distinguish between different mechanisms, it
might be of little help if 0νββ decay is observed close to
the exclusion limit of SuperNEMO, or not at all. This is
demonstrated in Fig. 11 where, for a half-life of T1/2=
1026y, the reconstruction of the energy difference distri-
bution will be problematic due to the low number of events
(compare Fig. 9). As an alternative, it is possible to com-
pare the 0νββ rate in different isotopes. This method,
which could provide crucial information close to the ex-
clusion limit, is especially relevant for SuperNEMO which
could potentially measure 0νββ decay in two (or more)
isotopes. Such a comparative analysis was used in [21]
to distinguish between several new physics mechanisms.
A combined analysis of several isotopes, potentially mea-
sured in other experiments, will improve the statistical
significance [22].
The possibility of sharing the two isotopes equally in
SuperNEMO, each with a total exposure of 250 kg y, is
now considered. In the cases where the MM or the RHCλ
contributions dominate, the following half-life ratios can
be found:
MM :
T
82Se
1/2
T
150Nd
1/2
=
C
150Nd
mm
(2.7)2· C
82Se
mm
= 2.45, (27)
Page 14
14R. Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO
RHCλ:
T
82Se
1/2
T
150Nd
1/2
=
C
150Nd
λλ
(2.7)2· C
82Se
λλ
= 3.64. (28)
These ratios and their uncertainties are determined by the
0νββ decay NMEs and phase spaces. The factor 2.7 is the
correction added to the150Nd NMEs as described in Sec-
tion 2.3. It has recently been suggested that uncertainties
in NME calculations are highly correlated [43] so mea-
surements made with two or more isotopes could reduce
the uncertainty on the physics parameters significantly.
Additionally, most experimental systematic uncertainties
would cancel if different isotopes are studied in a single
experiment such as SuperNEMO. This would not be pos-
sible when comparing results with other experiments. The
statistical uncertainties are naturally greater than in the
single-isotope case, due to the exposure being halved for
each isotope.
The results of the combined NME and statistical un-
certainties analysis, including a possible correlation of the
NMEs, are illustrated in Fig. 13. It shows the 0νββ half-
life of150Nd as a function of the half-life in82Se assuming
a pure MM model, with the coloured contours giving the
deviation from the hypothesis that the mass mechanism
is the single source of 0νββ decay in both isotopes at the
1, 2 and 5 standard deviation level. The statistical uncer-
tainties used in Fig. 13 are derived from our experimental
simulation and the standard 30% NME uncertainties are
applied. The effect of a possible correlation of the NMEs
is shown by assuming the covariance coefficient between
the NME uncertainties of82Se and150Nd to be (a) zero
(no correlation), (b) 0.7 and (c) 1.0 (full correlation). The
experimental uncertainties and expected sensitivity (90%
CL exclusion) limits are calculated for 250 kg y of ex-
posure of each isotope and assume a 50%82Se and 50%
150Nd option for SuperNEMO. The red line shows the re-
lationship for the half-life ratio in the pure RHCλmodel
(Equation (28)). It can be seen that an exclusion at two
standard deviations is possible if the NME errors are per-
fectly correlated and at the one standard deviation level if
the correlation is 70%, which is a more realistic assump-
tion.
Other mechanisms have different half-life ratios [21]
so they could be excluded with different CLs at Super-
NEMO. One important advantage of this method is that
it provides a possibility to falsify the mass mechanism as
the sole source for 0νββ. A measurement within the blue
contour would indicate that the pure MM model can be
excluded at the 5 standard deviation level and new physics
is required to explain the measured half-lives.
5.4 Combined Energy and Rate Comparison of150Nd
and82Se
In the most favourable case, signal event rates in two iso-
topes could be high enough (0νββ decay half-lives small
enough) that the distribution method and the two iso-
tope rate analysis can be combined to put further con-
straints on the parameter space. The effect of such a com-
bined analysis on the allowed parameter space is shown
in Fig. 14, where the 50%150Nd - 50%82Se two-isotope
option (red contours) is compared to the single-isotope op-
tions 100%82Se (green contours) and 100%150Nd (blue
contours). The 0νββ decay half-life of82Se is assumed
to be 1025y, and the half-life of
by the respective MM-RHCλ admixture, i.e. (a) TNd
1025/2.45 y, (b) 1025/2.73 y and (c) 1025/3.64 y. The NME
uncertainties are assumed to be 30% with a 0.7 covariance
between the uncertainties of the NMEs of82Se and150Nd.
As can be seen in Fig. 14, the two-isotope option can im-
prove the constraints on the parameter space along the
radial direction, e.g. it allows a more accurate determina-
tion of the MM neutrino mass mν in Fig. 14 (a). On the
other hand, the accuracy in the lateral direction (the pa-
rameter λ in Fig. 14 (a)) becomes worse compared to the
best single-isotope option due to the reduced statistics for
a given isotope.
150Nd is determined
1/2=
6 Conclusion
The 0νββ decay is a crucial process for physics beyond the
Standard Model, and the next generation SuperNEMO ex-
periment is designed to be a sensitive probe of this lepton
number violating observable. In addition to being able to
measure the 0νββ half-life of one or more isotopes, it also
allows the determination of the angular and energy differ-
ence distributions of the outgoing electrons.
In this paper we have focussed on the sensitivity of
SuperNEMO to new physics and its ability to discriminate
between different 0νββ mechanisms. This was achieved by
a detailed analysis of two important models, namely the
standard mass mechanism via light left-handed Majorana
neutrino exchange and a contribution from right-handed
current via the effective λ parameter stemming from Left-
Right symmetry. The study included a full simulation of
the process and the SuperNEMO detector at the event
level, allowing a realistic estimation of the experimental
90% CL exclusion limit and statistical uncertainties.
SuperNEMO is expected to exclude 0νββ half-lives up
to 1.2·1026y (MM) and 6.1·1025y (RHCλ) for82Se and
5.1·1025y (MM) and 2.6·1025y (RHCλ) for150Nd at 90%
CL with a detector exposure of 500 kg y. This corresponds
to a Majorana neutrino mass of mν ≈ 70 meV and a λ
parameter of λ ≈ 10−7, giving an improvement of more
than one order of magnitude compared to the NEMO-III
experiment.
It has been shown that the angular and electron en-
ergy difference distributions can be used to discriminate
new physics scenarios. In the framework of the two mecha-
nisms analysed, it was demonstrated that using this tech-
nique the individual new physics model parameters can be
determined. For a half-life of T1/2= 1025y with an expo-
sure of 500 kg y, the Majorana neutrino mass can be de-
termined to be 245 meV with an uncertainty of 30% while
the λ parameter can be constrained at the same time to
be smaller than |λ| < 0.9·10−7. Such a decay distribution
analysis could be easily extended further to include other
new physics scenarios with distinct distributions and the
Page 15
R. Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO15
1024
1025
T1?2
1026
1024
1025
1026
Se?y?
T1?2
Nd?y?
1Σ
2Σ
5Σ
Sensitivity limit
Sensitivity limit
(a)
1024
1025
T1?2
1026
1024
1025
1026
Se?y?
T1?2
Nd?y?
1Σ
2Σ
5Σ
Sensitivity limit
Sensitivity limit
(b)
1024
1025
T1?2
1026
1024
1025
1026
Se?y?
T1?2
Nd?y?
1Σ
2Σ
5Σ
Sensitivity limit
Sensitivity limit
(c)
Fig. 13: The 0νββ half-life of150Nd as a function of measured half-life in82Se for the hypothesis that the MM
is the single 0νββ decay source. The contours show the 1, 2 and 5 standard deviation levels assuming statistical
uncertainties derived from the experimental simulation and 30% NME errors assumed to have (a) no, (b) 0.7 and (c)
perfect correlation. The experimental uncertainties and expected sensitivity (90% CL exclusion) limit are calculated
for 250 kg y of exposure (assuming a 50%82Se and 50%150Nd option). The red line shows the relationship for the
RHCλ. The blue contour shows the 5σ exclusion of the MM.
?4
?2024
0
50
100
150
200
250
300
Λ ?10?7?
?mΝ? ?meV?
(a)
?4
?2024
0
50
100
150
200
250
300
Λ ?10?7?
?mΝ? ?meV?
(b)
?4
?2024
0
50
100
150
200
250
300
Λ ?10?7?
?mΝ? ?meV?
(c)
Fig. 14: Constraints at one standard deviation on the model parameters mν and λ from: (1) an observation of 0νββ
decay half-life of82Se at T1/2= 1025y with 500 kg y exposure and reconstruction of the energy difference distribution
(outer green contour); (2) an observation of 0νββ decay half-life of150Nd at a half-life corresponding to T1/2= 1025y
in82Se with an exposure of 500 kg y and reconstruction of the energy difference distribution (inner blue contour);
(3) combined analysis of (1) and (2) with an exposure of 250 kg y in82Se and150Nd (red contour). The admixture
of the MM and RHCλcontributions is assumed to be: (a) pure MM contribution; (b) 30% RHCλadmixture; and (c)
pure RHCλcontribution. NME uncertainties are assumed to be 30% with a correlation of the uncertainties of 0.7, and
experimental statistical uncertainties are determined from the simulation.
results are quoted in terms of a generalised distribution
asymmetry parameter to allow new physics scenarios to
be compared. As the two example mechanisms considered
exhibit maximally different angular and energy distribu-
tion shapes, they serve as representative scenarios cover-
ing a large spectrum of the model space. For example,
the right-handed current contribution due the effective η
parameter, also arising in Left-Right symmetrical models,
can be distinguished from the mass mechanism and the
right-handed current λ contribution by looking at both
the angular and energy difference decay distribution. This
would allow a determination of all three model parameters
mν, λ and η by looking at the total rate and the angular
and energy difference distribution shapes.
Further insight into the mechanism of 0νββ can be
gained by using multiple isotopes within the SuperNEMO
Page 16
16R. Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO
setup. This possibility was explored by studying the op-
tion of having 50%150Nd and 50%82Se, each with an
exposure of 250 kg y. While the statistics per isotope is re-
duced compared to the individual 100% options, the abil-
ity to measure the ratio between the half-lives of the two
isotopes can be used as additional information on the un-
derlying physics mechanism responsible for 0νββ decay.
As was shown for the isotopes82Se and150Nd at Super-
NEMO, this could be a powerful method to falsify the
mass mechanism as the dominant 0νββ mechanism. A cor-
relation between the uncertainties of nuclear matrix ele-
ments, which is generally expected on theoretical grounds,
has proven to be of importance and its impact on the falsi-
fication potential was analysed. Within SuperNEMO such
a correlation could also be found between the systematic
uncertainties in the measurements of different isotopes.
SuperNEMO also has a number of other possibilities
to disentangle the underlying physics. The detection tech-
nology is not dependent on one particular isotope and any
double β emitting source could be studied in the detector.
In this paper82Se and150Nd have been considered but
other isotopes such as48Ca or100Mo are feasible. The
analysis can be extended to cover more than two isotopes
thereby achieving a higher significance and a comparison
with other experimental results will provide additional in-
formation. SuperNEMO is also able to measure a 0νββ
decay to an excited state, by measuring two electrons and
an accompanying photon. This again could be used to aid
the analysis to discriminate between new physics mecha-
nisms.
A combination of the above methods makes Super-
NEMO an exciting test of new physics. These methods
would prove invaluable in excluding or confirming domi-
nating mechanisms of lepton number violation in the reach
of the next generation 0νββ experiments.
The authors would like to thank H. P¨ as, M. Hirsch, E. Lisi,
V. Rodin and A. Faessler for useful discussions. We acknowl-
edge support by the Grants Agencies of France, the Czech Re-
public, RFBR (Russia), STFC (UK), MICINN (Spain), NSF,
DOE, and DOD (USA). We acknowledge technical support
from the staff of the Modane Underground Laboratory (LSM).
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