# Probing new physics models of neutrinoless double beta decay with SuperNEMO

**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.

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- J.W. Beeman, F. bellini, P. Benetti, L. Cardani, N. Casali, D. Chiesa, M. Clemenza, I. Dafinei, S. Di Domizio, F. Ferroni, [......], F. Orio, L. Pattavina, G. pessina, G. Piperno, S. Pirro, E. Previtali, C. Rusconi, M. Tenconi, C. Tomei, M. Vignati[Show abstract] [Hide abstract]

**ABSTRACT:**In the field of fundamental particle physics, the neutrino has become more and more important in the last few years, since the discovery of its mass. In particular, the ultimate nature of the neutrino (if it is a Dirac or a Majorana particle) plays a crucial role not only in neutrino physics, but also in the overall framework of fundamental particle interactions and in cosmology. The only way to disentangle its ultimate nature is to search for the neutrinoless double beta decay. The idea of LUCIFER is to combine the bolometric technique proposed for the CUORE experiment with the bolometric light detection technique used in cryogenic dark matter experiments. The bolometric technique allows an extremely good energy resolution while its combination with the scintillation detection offers an ultimate tool for background rejection. The goal of LUCIFER is not only to build a background-free small-scale experiment but also to directly prove the potentiality of this technique. Preliminary tests on several detectors containing different interesting DBD emitters have clearly demonstrated the excellent background rejection capabilities that arise from the simultaneous, independent, double readout of heat and scintillation light.Advances in High Energy Physics 09/2013; · 3.50 Impact Factor -
##### Article: The Potential of Hybrid Pixel Detectors in the Search for the Neutrinoless Double-Beta Decay of

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**ABSTRACT:**We investigated the potential of the energy resolving hybrid pixel detector Timepix contacted to a CdTe sensor layer for the search for the neutrinoless double-beta decay of . We found that a CdTe sensor layer with 3 mm thickness and 165 μm pixel pitch is optimal with respect to the effective Majorana neutrino mass () sensitivity. In simulations, we were able to demonstrate a possible reduction of the background level caused by single electrons by approximately 75% at a specific background rate of 10−3 counts/() at a detection efficiency reduction of about 23% with track analysis employing random decision forests. Exploitation of the imaging properties with track analysis leads to an improvement in sensitivity to by about 22%. After 5 years of measuring time, the sensitivity to of a 420 kg CdTe experiment (90% enrichment) would be 59 meV on a 90% confidence level for a specific single-electron background rate of 10−3 counts/(). The α-particle background can be suppressed by at least about six orders of magnitude. The benefit of the hybrid pixel detector technology might be increased significantly if drift-time difference measurements would allow reconstruction of tracks in three dimensions.Advances in High Energy Physics 11/2013; 2013. · 2.62 Impact Factor - V. B. Brudanin, V. G. Egorov, A. A. Klimenko, A. Kovalík, N. I. Rukhadze, V. V. Timkin, P. Čermák, J. Čermák, J. M. Jose, F. Mamedov, E. Rukhadze, I. Štekl, Ch. Briançon, F. Šimkovic, Yu. Shitov, A. M. Bakalyarov, V. I. Lebedev, S. V. Zhukov, T. M. Bolotskaya[Show abstract] [Hide abstract]

**ABSTRACT:**The collaboration TGV has finished measurement of 2νEC/EC decay of 106Cd with 10 g (Phase I) and 13.6 g (Phase II) samples (with enrichment of 75%), respectively. The times of measurements were 8687h (Phase I) and 12900h (Phase II). The half-life limits (at 90% CL) were obtained for 2νEC/EC decay of 106Cd to the ground state of 106Pd as T1/2>3.0×1020 y (Phase I) and T1/2>4.2×1020 y (Phase II). The collaboration decided to continue with the study of 2νEC/EC decay of 106Cd using 23 g of an isotope enriched to 98.4%. We plan to use the TGV II spectrometer for this measurement and also Si pixel detectors for further study of double beta decay (ββ) processes.12/2011;

Page 1

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

Page 2

2R. 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

Page 3

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

Page 4

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

Page 5

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

Page 6

6R. Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO

0.00.20.4

??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

8R. 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 -0.2000.2 0.40.2 0.40.6 0.80.6 0.811

Events

0.20.2

0.40.4

0.6 0.6

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 -0.2000.2 0.4 0.2 0.40.6 0.80.6 0.811

Events

00

0.2 0.2

0.40.4

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 0.50.511 1.51.5222.52.533

Events

00

0.2 0.2

0.40.4

0.60.6

0.80.8

11

Events

Mass Mechanism

Theoretical distribution

Reconstructed distribution

(c)

Difference in energy of electrons (MeV)Difference in energy of electrons (MeV)

000.50.5111.51.5222.5 2.533

Events

00

0.20.2

0.4 0.4

0.6 0.6

0.80.8

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 2.82.9 2.9333.1 3.13.23.23.33.33.43.4

Events

00

55

10 10

1515

2020

25 25

3030

3535

4040

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)

000.5 0.511 1.51.5222.5 2.533

Events

00

22

44

66

88

10 10

1212

14 14

1616

1818

Events

Mass Mechanism (500 kg y)

y)

25

(10

ββν

0

ββν

2

Bi

214

Tl

208

(b)

Cosine of angle between electrons Cosine of angle between electrons

-1-1 -0.8-0.8 -0.6-0.6 -0.4-0.4 -0.2-0.200 0.20.2 0.40.40.6 0.60.8 0.811

Events

00

22

44

66

88

10 10

1212

1414

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

11 1010

22

1010

y)

25

Half-life limit (10

00

55

10 10

1515

2020

2525

3030

Se (500 kg y)Se (500 kg y)

8282

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 (%)

020 406080 100

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 406080100

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 (%)

002020 404060 6080 80100100

Observed half-life (y)

2323

10 10

24 24

1010

25 25

1010

26 26

10 10

2727

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 (%)

0020 2040 406060 8080100100

Observed half-life (y)

2323

1010

2424

1010

25 25

10 10

2626

1010

2727

10 10

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 0.20.40.6 0.81

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

-1.2-1-0.8-0.6-0.4-0.20 0.20.40.60.8

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 -0.6-0.4-0.200.20.40.60.8

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 SuperNEMO 15

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