Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO
R. Arnold, C. Augier, J. Baker, A. S. Barabash, A. Basharina-Freshville, M. Bongrand, V. Brudanin, A. J. Caffrey, S. Cebrián, A. Chapon, E. Chauveau, Th. Dafni, F. F. Deppisch, J. Diaz, D. Durand, V. Egorov, J. J. Evans, R. Flack, K-I. Fushima, I. García Irastorza, X. Garrido, H. Gómez, B. Guillon, A. Holin, K. Holy, J. J. Horkley, Ph. Hubert, C. Hugon, F. J. Iguaz, N. Ishihara, C. M. Jackson, S. Jullian, M. Kauer, O. Kochetov, S. I. Konovalov, V. Kovalenko, T. Lamhamdi, K. Lang, G. Lutter, G. Luzón, F. Mamedov, Ch. Marquet, F. Mauger, F. Monrabal, A. Nachab, I. Nasteva, I. Nemchenok, C. H. Nguyen, M. Nomachi, F. Nova, H. Ohsumi, R. B. Pahlka, F. Perrot, F. Piquemal, P. P. Povinec, B. Richards, J. S. Ricol, C. L. Riddle, A. Rodríguez, R. Saakyan, X. Sarazin, J. K. Sedgbeer, L. Serra, Yu. Shitov, L. Simard, F. Šimkovic, S. Söldner-Rembold, I. Štekl, C. S. Sutton, Y. Tamagawa, J. Thomas, V. Timkin, V. Tretyak, Vl. I. Tretyak, V. I. Umatov, I. A. Vanyushin, R. Vasiliev, V. Vasiliev, V. Vorobel, D. Waters, N. Yahlali, A. Žukauskas
aa r X i v : . [ h e p - e x ] N ov MAN/HEP/2010/2
Probing New Physics Models of Neutrinoless Double Beta Decaywith SuperNEMO
R. Arnold , C. Augier , J. Baker , A.S. Barabash , A. Basharina-Freshville , M. Bongrand , V. Brudanin ,A.J. Caffrey , S. Cebri´an , A. Chapon , E. Chauveau , Th. Dafni , F.F. Deppisch , J. Diaz , D. Durand ,V. Egorov , J.J. Evans , R. Flack , K-I. Fushima , I. Garc´ıa Irastorza , X. Garrido , H. G´omez , B. Guillon ,A. Holin , K. Holy , J.J. Horkley , Ph. Hubert , C. Hugon , F.J. Iguaz , N. Ishihara , C.M. Jackson ,S. Jullian , M. Kauer , O. Kochetov , S.I. Konovalov , V. Kovalenko , T. Lamhamdi , K. Lang , G. Lutter ,G. Luz´on , F. Mamedov , Ch. Marquet , F. Mauger , F. Monrabal , A. Nachab , I. Nasteva , I. Nemchenok ,C.H. Nguyen , M. Nomachi , F. Nova , H. Ohsumi , R.B. Pahlka , F. Perrot , F. Piquemal ,P.P. Povinec , B. Richards , J.S. Ricol , C.L. Riddle , A. Rodr´ıguez , R. Saakyan , X. Sarazin , J.K. Sedgbeer ,L. Serra , Yu. Shitov , L. Simard , F. ˇSimkovic , S. S¨oldner-Rembold , I. ˇStekl , C.S. Sutton , Y. Tamagawa ,J. Thomas , V. Timkin , V. Tretyak , Vl.I. Tretyak , V.I. Umatov , I.A. Vanyushin , R. Vasiliev , V. Vasiliev ,V. Vorobel , D. Waters , N. Yahlali , and A. ˇZukauskas IPHC, Universit´e de Strasbourg, CNRS/IN2P3, F-67037 Strasbourg, France LAL, Universit´e Paris-Sud 11, CNRS/IN2P3, F-91405 Orsay, France INL, Idaho Falls, Idaho 83415, USA Institute of Theoretical and Experimental Physics, 117259 Moscow, Russia University College London, WC1E 6BT London, United Kingdom Joint Institute for Nuclear Research, 141980 Dubna, Russia University of Zaragoza, C/ Pedro Cerbuna 12, 50009 Spain LPC Caen, ENSICAEN, Universit´e de Caen, F-14032 Caen, France Universit´e de Bordeaux, Centre d’Etudes Nucl´eaires de Bordeaux Gradignan, UMR 5797, F-33175 Gradignan, France CNRS/IN2P3, Centre d’Etudes Nucl´eaires de Bordeaux Gradignan, UMR 5797, F-33175 Gradignan, France University of Manchester, M13 9PL Manchester, United Kingdom IFIC, CSIC - Universidad de Valencia, Valencia, Spain Tokushima University, 770-8502, Japan FMFI, Comenius University, SK-842 48 Bratislava, Slovakia KEK,1-1 Oho, Tsukuba, Ibaraki 305-0801 Japan USMBA, Fes, Morocco University of Texas at Austin, Austin, Texas 78712-0264, USA IEAP, Czech Technical University in Prague, CZ-12800 Prague, Czech Republic Osaka University, 1-1 Machikaneyama Toyonaka, Osaka 560-0043, Japan Universitat Aut`onoma de Barcelona, Spain Saga University, Saga 840-8502, Japan Imperial College London, SW7 2AZ, London, United Kingdom MHC, South Hadley, Massachusetts 01075, USA Fukui University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581 Japan INR, MSP 03680 Kyiv, Ukraine Charles 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 isdiscussed. Its ability to study different isotopes and track the outgoing electrons provides the means todiscriminate different underlying mechanisms for the neutrinoless double β decay by measuring the decayhalf-life and the electron angular and energy distributions. Correspondence to : [email protected],[email protected], [email protected]
Oscillation experiments have convincingly shown that atleast two of the three active neutrinos have a finite mass
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. Upperlimits 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 combinedwith cosmological considerations yield an upper bound tobe set on the sum of the three neutrino masses of the or-der of 0.7 eV [4]. However, the most sensitive probe ofthe absolute mass scale of Majorana neutrinos is neutri-noless double β decay (0 νββ ) [5,6,7,8]. In this process,an atomic nucleus with Z protons decays into a nucleuswith Z + 2 protons and the same mass number A underthe emission of two electrons,( A, Z ) → ( A, Z + 2) + 2 e − . (1)This process can be described by the exchange of a lightneutrino connecting two V-A weak interactions, see Fig. 1(a). The process (1) is lepton number violating and, inthe standard picture of light neutrino exchange, it is onlypossible if the neutrino is identical to its own anti-particle,i.e. if neutrinos are Majorana particles. Combined withthe fact that neutrino masses are more than five orders ofmagnitude smaller than the masses of other fermions, sucha possibility suggests that the origin of neutrino masses isdifferent 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-handedneutrinos mix with the left-handed neutrinos and generatelight Majorana masses for the observed active neutrinos.The Majorana character of the active neutrinos can thenbe connected to a breaking of lepton number symmetryclose to the GUT scale and might be related to the baryonasymmetry of the Universe through the baryogenesis vialeptogenesis mechanism [10].Because of its sensitivity to the nature and magnitudeof the neutrino mass, 0 νββ decay is a crucial experimen-tal probe for physics beyond the Standard Model and itsdiscovery will be of the utmost importance. It will provelepton number to be broken, and in most models it willalso provide direct evidence that the light active neutrinosare Majorana particles [12]. However, the measurementof 0 νββ decay in a single isotope is not sufficient to provethat the standard mechanism of light Majorana neutrinoexchange is the dominant source for the decay. There are ahost of other models, such as Left-Right symmetry [5], R-parity violating Supersymmetry (SUSY) [13] or Extra Di-mensions [11], which can provide alternative mechanismsto trigger 0 νββ decay. In some of these models, additionalsources of lepton number violation can supplement lightneutrino exchange. For example, in Left-Right symmet-ric models, there are additional contributions from right-handed currents and the exchange of heavy neutrinos. Inother models, such as R-parity violating SUSY, 0 νββ de-cay can be mediated by other heavy particles that are notdirectly related to neutrinos. See [11] for a counter-example of a model where such aconclusion is not valid.
There are several methods proposed in the literatureto disentangle the many possible contributions or at leastto determine the class of models that give rise to the domi-nant mechanism for 0 νββ decay. Results from 0 νββ decaycan be compared with other neutrino experiments and ob-servations such as tritium decay to determine if they areconsistent. At the LHC there could also be signs of newphysics exhibiting lepton number violation that is relatedto 0 νββ (see [14] for such an example in R-parity violat-ing Supersymmetry). Such analyses would compare resultsfor 0 νββ with other experimental searches, but there arealso ways to gain more information within the realm of0 νββ decay and related nuclear processes. Possible tech-niques include the analysis of angular and energy correla-tions between the electrons emitted in the 0 νββ decay [5,15,16,17,18] or a comparison of results for 0 νββ decay intwo or more isotopes [19,20,21,22]. These two approachesare studied in this paper. Other proposed methods are thecomparative analysis of 0 νββ decay to the ground statewith either 0 νβ + β + or electron capture decay [23] and0 νββ decay to excited states [24].Currently, the best limit on 0 νββ decay comes fromthe search for 0 νββ decay of the isotope Ge giving ahalf-life of T / > . · years [25]. This results inan upper bound on the 0 νββ Majorana neutrino mass of h m ν i ≤ −
600 meV. A controversial claim of obser-vation of 0 νββ decay in Ge gives a half-life of T / =(0 . − . · y [26] and a resulting effective Majorananeutrino mass of h m ν i = 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 orexclude the claimed observation. The planned experimentSuperNEMO allows the measurement of 0 νββ decay inseveral isotopes ( Se,
Nd and Ca are currently be-ing considered) to the ground and excited states, and isable to track the trajectories of the emitted electrons anddetermine their individual energies. In this respect, theSuperNEMO experiment has a unique potential to disen-tangle the possible mechanisms for 0 νββ decay.This paper addresses the question of how measure-ments at SuperNEMO can be used to gain informationon the underlying physics mechanism of the 0 νββ decay.The sensitivity of SuperNEMO to new physics parame-ters in two models is determined by performing a detailedsimulation of the SuperNEMO experimental set-up. Byanalysing both the angular and energy distributions inthe standard mass mechanism and in a model incorporat-ing right-handed currents, the prospects of discriminating0 νββ decay mechanisms are examined. The two modelsare specifically chosen to represent all possible mecha-nisms, as they maximally deviate from each other in theirangular and energy distributions.This paper is organised as follows. In Section 2 a shortdescription of the theoretical framework on which the cal-culations of the 0 νββ decay rate and the angular and en-ergy correlations are based is shown. The example physicsmodels are introduced and reviewed. Section 3 gives abrief overview of the SuperNEMO experiment design and . Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO 3(a) (b)
Fig. 1: Diagrams illustrating 0 νββ 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 areshown and the prospects of disentangling 0 νββ mecha-nisms by analysing the angular and energy distributionsand by comparing rates in different isotopes are addressed.Our conclusions are presented in Section 6. Contributions to 0 νββ decay can be categorised as eitherlong-range or short-range interactions. In the first case,the corresponding diagram involves two vertices which areboth point-like at the Fermi scale, and connected by theexchange of a light neutrino. Such long-range interactionsare described by an effective Lagrangian [27,28] L = G F √ j V − A J V − A + L.i. X a,b ǫ lrab j a J b , (2)where G F is the Fermi coupling constant and the leptonicand hadronic Lorentz currents are defined as j a = ¯ e O a ν and J a = ¯ u O a d , respectively. Here, O a denotes the corre-sponding transition operator, with a = V − A, V + A, S − P, S + P, T L , T R [27]. In Equation (2), the contributionfrom V − A currents originating from standard weak cou-plings has been separated off and the summation runs overall Lorentz invariant and non-vanishing combinations ofthe leptonic and hadronic currents, except for the case a = b = V − A . The effective coupling strengths for long-range contributions are denoted as ǫ lrab .For short-ranged contributions, the interactions arerepresented by a single vertex which is point-like at theFermi scale, and they are described by the Lagrangian [28,29] L = G F m − p L.i. X a,b,c ǫ srabc J a J b j ′ c . (3) Here, m p denotes the proton mass and the leptonic andhadronic currents are given by J a = u O a d and j ′ a = e O a e C , respectively. The transition operators O a are de-fined as in the long-range case above, and the summationruns over all Lorentz invariant and non-vanishing combi-nations of the hadronic and leptonic currents. The effec-tive coupling strengths for the short-range contributionsare denoted as ǫ srabc .Described by the first term in Equation (2), the ex-change of light left-handed Majorana neutrinos leads tothe 0 νββ decay rate[ T m ν / ] − = ( h m ν i /m e ) G |M m ν | , (4)where h m ν i is the effective Majorana neutrino mass inwhich the contributions of the individual neutrino masses m i are weighted by the squared neutrino mixing matrixelements, U ei , h m ν i = | P i U ei m i | .Analogously, other new physics (NP) contributions, ofboth long- and short-range nature, can in general be ex-pressed as [ T NP / ] − = ǫ NP G NP |M NP | , (5)where ǫ NP denotes the corresponding effective couplingstrength, i.e. is either given by ǫ lrab for a long-range mech-anism or by ǫ srabc for a short-range mechanism. In Equa-tions (4) and (5), the nuclear matrix elements for the massmechanism and alternative new physics contributions aregiven by M m ν and M NP , respectively, and G , G NP de-note the phase space integrals of the corresponding nuclearprocesses. It is assumed that one mechanism dominatesthe double β decay rate. The focus in this paper is on a subset of the Left-Rightsymmetric model [5], which incorporates left-handed andright-handed currents under the exchange of light andheavy neutrinos. Left-Right symmetric models generallypredict new gauge bosons of the extra right-handed SU(2)gauge symmetry as well as heavy right-handed neutrinos
R. Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMOIsotope C mm [y − ] C λλ [y − ] C mλ [y − ] Ge 1 . × − . × − − . × − Se 4 . × − . × − − . × − Nd 7 . × − . × − − . × − Table 1: Coefficients used in calculating the 0 νββ decayrate [30].which give rise to light observable neutrinos via the seesawmechanism.The 0 νββ decay half-life in the Left-Right symmetricmodel can be written as a function of the effective param-eters µ, η, λ [30],[ T / ] − = C mm µ + C λλ λ + C ηη η + C mλ µλ + C mη µη + C ηλ ηλ, (6)where contributions from the exchange of heavy neutrinosare omitted. The coefficients C mm , C ηη etc. are combina-tions of phase space factors and nuclear matrix elements.The first three terms give the contributions from the fol-lowing processes:1. C mm µ : Fully left-handed current neutrino exchange,see Fig. 1 (a) (mass mechanism);2. C λλ λ : Right-handed leptonic and right-handed had-ronic current neutrino exchange, see Fig. 1 (b);3. C ηη η : Right-handed leptonic and left-handed hadroniccurrent neutrino exchange.The remaining terms in Equation (6) describe interfer-ence effects between these three processes. The effectiveparameters µ, η, λ in (6) are given in terms of the under-lying physics parameters as µ = m − e X i =1 (cid:0) U ei (cid:1) m ν i = h m ν i m e , (7) η = tan ζ X i =1 U ei U ei , (8) λ = (cid:18) M W L M W R (cid:19) X i =1 U ei U ei , (9)with the electron mass m e , the left- and right-handed Wboson masses M W L and M W R , respectively, and the mix-ing angle ζ between the W bosons. The 3 × U and U connect the weak eigenstates ( ν e , ν µ , ν τ ) ofthe light neutrinos with the mass eigenstates of the lightneutrinos ( ν , ν , ν ), and heavy neutrinos, ( N , N , N ),respectively. We assume that the neutrino sector consistsof three light neutrino states, m ν i ≪ m e , and three heavyneutrino states, M N i ≫ m p , i = 1 , ,
3. Consequently, thesummations in (7, 8, 9) are only over the light neutrinostates. For a simple estimate of the sensitivity of 0 νββ de-cay to the model parameters, we neglect the flavour struc-ture in U and U ; using the assumption that the ele-ments in U are of order unity (almost unitary mixing),and those in U are of order m D /M R ∼ p m ν /M R , withthe effective magnitude m D of the neutrino Dirac mass matrix, and the light and heavy neutrino mass scales, m ν and M R , leads to the approximate relations: µ ≈ m ν m e , (10) η ≈ tan ζ r m ν M R , (11) λ ≈ (cid:18) M W L M W R (cid:19) r m ν M R . (12)In the following analysis a simplified model incorporatingonly an admixture of mass mechanism (MM) due to a neu-trino mass term µ = h m ν i /m e and right-handed currentdue to the λ term (RHC λ ) is considered:[ T / ] − = C mm µ + C λλ λ + C mλ µλ. (13)As we will see in Section 2.4, these two mechanisms exhibitmaximally different angular and energy distributions, andwith an admixture between them, to a good approxima-tion any possible angular and energy distribution can beproduced. In our numerical calculation we use the valuesas given in Table 1 for the coefficients C mm , C λλ and C mλ in Equation (13). Furthermore, we assume that the pa-rameter µ is real-valued positive and λ is real-valued. As demonstrated in Equations (4) and (5), a calculation ofthe nuclear matrix elements (NMEs) is required to convertthe measured half-life rates or limits into new physics pa-rameters. Exact solutions for the NMEs do not exist, andapproximations have to be used. Calculations using thenuclear shell model exist for lighter nuclei such as Geand Se, though the only reliable results are for Ca.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( Se and
Nd) and the isotope that gives the currentbest limit ( Ge) is made. Consistent calculations of theNMEs for these three isotopes in both the MM and RHCare rare (only [30] and [31]). All the results are shownusing NMEs from [30], displayed in Table 1.Recent work on the calculation of NMEs for the heavyisotope
Nd suggests that nuclear deformation must beincluded, 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 anapproximation arising from the BCS overlap factor [32], M ( Nd)/2.7. This gives a suppression C mm,λλ,mλ / (2 . in Table 1. The Se nuclei are assumed to be sphericaland no correction is added in this paper.The NMEs are a significant source of uncertainty indouble β decay physics and quantitative results in thispaper could change with different calculations (particu-larly for Nd). For example, more recent studies [33]suggest the NMEs from
Nd for the MM are an addi-tional factor 1.3-1.7 smaller. In our analysis we assume a . Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO 5 theoretical uncertainty of 30% in the NMEs of all isotopesand mechanisms considered throughout. Even though thechoice of NME changes quantitative results for the ex-tracted physics parameters, the conclusions about the ad-vantages of using different kinematic variables will not beaffected.
For our event simulation, the three-dimensional distribu-tion of the 0 νββ decay rate in terms of the kinetic energies t , of the two emitted electrons and the cosine of the anglebetween the electrons cos θ is used: ρ ( t , t , cos θ ) = dΓdt dt d cos θ . (14)The distributions for the MM and for the RHC λ mecha-nism are given by ρ MM ( t , t , cos θ ) = c × ( t + 1) p ( t + 1) p F ( t , Z ) F ( t , Z ) × δ ( Q − t − t ) (1 − β β cos θ ) , (15) ρ RHC ( t , t , cos θ ) = c × ( t + 1) p ( t + 1) p F ( t , Z ) F ( t , Z )( t − t ) × δ ( Q − t − t ) (1 + β β cos θ ) , (16)with the electron momenta p i = p t i ( t i + 2) and velocities β i = p i / ( t i + 1), and the mass difference Q between themother and daughter nucleus. All energies and momentaare expressed in units of the electron mass and c and c are normalisation constants. The Fermi function F isgiven by F ( t, Z ) = c × p s − e πu | Γ ( s + iu ) | , (17)where s = p − ( αZ ) , u = αZ ( t + 1) /p , α = 1 / . Γ is the Gamma function and c is a normalisation con-stant. Here, Z is the atomic number of the daughter nu-cleus. The normalisation of the distributions is irrelevantwhen discussing energy and angular correlations.Using Equations (15) and (16), the differential decaywidths with respect to the cosine of the angle θ , dΓd cos θ = Z Q dt ρ ( t , Q − t , cos θ ) , (18)and the energy difference ∆t = t − t , dΓd ( ∆t ) = Z − d cos θ ρ (cid:18) Q + ∆t , Q − ∆t , cos θ (cid:19) , (19)may be determined.The differential width in Equation (18) can be writtenas [5,18] dΓd cos θ = Γ − k θ cos θ ) , (20) with the total decay width Γ . The distribution shape islinear in cos θ , with the slope determined by the param-eter k θ which can range between − ≤ k θ ≤
1, dependingon the underlying decay mechanism. Assuming the domi-nance of one scenario, the shape does not depend on theprecise values of new physic parameters (mass scales, cou-pling constants) but is a model specific signature of themechanism. For the MM and RHC λ mechanisms, the the-oretically predicted k θ is found from Equation (18) and isgiven by k Se θ MM = +0 . , k Nd θ MM = +0 . , (21) k Seθ
RHC = − . , k Ndθ
RHC = − . . (22)The correlation coefficient k θ is modified when taking intoaccount nuclear physics effects and exhibits only a smalldependence on the type of nucleus. The MM and theRHC λ mechanisms give the maximally and minimally pos-sible values for the angular correlation coefficient k θ in agiven isotope, respectively.Experimentally, k θ can be determined via the forward-backward asymmetry of the decay distribution, A θ ≡ (cid:18)Z − dΓd cos θ d cos θ − Z dΓd cos θ d cos θ (cid:19) /Γ = N + − N − N + + N − = k θ . (23)Here, N + ( N − ) counts the number of signal events withthe angle θ larger (smaller) than 90 ◦ .Analogously, the MM and RHC λ mechanism also differin the shape of the electron energy difference distribution,Equation (19). For the isotopes Se and
Nd, these dis-tributions are shown in Fig. 2. Again, the shape is largelyindependent of the isotope under inspection. The followingasymmetry in the electron energy-difference distributionis determined, A E ≡ Z Q/ dΓd ( ∆t ) d ( ∆t ) − Z QQ/ dΓd ( ∆t ) d ( ∆t ) ! /Γ = N + − N − N + + N − = k E , (24)thereby defining an energy correlation coefficient k E , 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 andRHC λ mechanism, the theoretical k E parameter may befound from Equation (19) and is given by k Se E MM = +0 . , k Nd E MM = +0 . , (25) k Se E RHC = − . , k Nd E RHC = − . , (26)in the isotopes Se and
Nd. As can be seen in Fig. 2,the MM and RHC λ mechanisms correspond to differentshapes of the energy difference distribution. Analogous to R. Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO È D t È (cid:144) Q G - d G (cid:144) d H È D t È (cid:144) Q L MM RHC Λ Fig. 2: Normalised 0 νββ decay distribution with respect tothe electron energy difference in the MM (red) and RHC λ mechanism (blue) for the isotopes Se (solid curves) and
Nd (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 limitsin a given isotope.
SuperNEMO is a next generation experiment building ontechnology 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 emittingisotope in the form of a thin foil (with a surface densityof 40 mg/cm ). Isotopes under consideration for Super-NEMO are Se,
Nd and Ca.The foil is surrounded by a tracking chamber compris-ing nine planes of drift cells (44 mm diameter) on eachside operating in Geiger mode in a magnetic field of 25Gauss. The tracking chamber has overall dimensions of 4m height (parallel to the drift cells), 5 m length and 1 mwidth (perpendicular to the foil); the foil is centred in thisvolume 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 angularcorrelations.Calorimetry consisting of 25 ×
25 cm square blocks of 5cm thickness scintillating material connected to low activ-ity photomultiplier tubes (PMTs) surrounds the detectoron four sides. An energy resolution of 7% (FWHM) and time resolution of 250 ps (Gaussian σ ) at 1 MeV for theblocks 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 detectoron all sides. The modules are contained in shared back-ground shielding and will be housed in an undergroundlaboratory to reduce the cosmic ray flux. A diagram of theplanned SuperNEMO module design is shown in Fig. 3. A full simulation of the SuperNEMO detector was per-formed including realistic digitisation, tracking and eventselection. Signals for two mechanisms of 0 νββ decay (massmechanism MM and right-handed current via the λ pa-rameter RHC λ ) and the principal internal backgroundswere generated using DECAY0 [41]. This models the fullevent kinematics, including angular and energy distribu-tions.A GEANT-4 Monte Carlo simulation of the detectorwas constructed. Digitisation of the hits in cells was ob-tained by assuming a Geiger hit model validated withNEMO-III with a transverse resolution of 0.6 mm and alongitudinal resolution of 0.3 cm. The calorimeter responsewas simulated assuming a Gaussian energy resolution of7%/ √ E (FWHM) and timing resolution of 250 ps (Gaus-sian σ at 1 MeV). Inactive material in front of the γ -vetowas partially simulated.Full tracking was developed consisting of pattern recog-nition and helical track fitting. The pattern recognitionuses a cellular automaton to select adjacent hits in thetracking layers. Helical tracks are fitted to the particles.Tracks are extrapolated into the foil to find an appropriateevent origin and into the calorimeter where they may beassociated with calorimeter energy deposits. The realisticevent selection (validated using NEMO-III) was optimisedfor double β decay electrons (two electrons with a commonvertex 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 tracksmust have a common vertex of <
10 standard devia-tions between intersection points in the plane of thesource foil; – the time of flight of the electrons in the detector mustbe consistent with the hypothesis of the electrons orig-inating in the source foil; – the number of Geiger drift cell hits unassociated witha track must be less than 3; – the energy deposited in individual calorimeter blocksmust be >
50 keV; – there are zero calorimeter hits not associated with atrack; – tracks must have hits in at least one of the first threeand one of the last three planes of Geiger drift cells; . Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO 7 Fig. 3: A SuperNEMO module. The source foil (not shown) sits in the centre of a tracking volume consisting of driftcells 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 from Bi-
Po events must be zero; – there are no hits in the γ -veto detectors with energy >
50 keV.Using these experimental selection criteria the signalefficiency was found to be 28.2% for the MM and 17.0%for the RHC λ in Se and 29.1% for the MM and 17.3%for the RHC λ in Nd. This is higher than the efficiencyfor MM detection in
Mo decays in NEMO-III of 17.4%(in the electron energy sum range 2-3.2 MeV) [40].The variables reconstructed from the simulation arethe energy sum, where a peak is expected at the energyrelease, Q , of the 0 νββ decay, the energy difference andthe cosine of the opening angle of the two electrons. Sim-ulations of the angular and energy difference distributionsof the two electrons in a signal sample are shown in Fig. 4for the isotope Se (similar results hold for
Nd). Thereconstructed distributions, normalised to the theoreticaldistributions, 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 sothe shape of the distribution is changed (on average a30 ◦ deviation from the generated distribution). The recon-struction efficiency is also low for small angular separationbetween the electrons when they travel through the samedrift cells.The backgrounds were processed by the same detectorsimulation and reconstruction programs as the signal. Thedominant two neutrino double β decay (2 νββ ) backgroundand the background due to foil contamination were nor-malised assuming a detector exposure of 500 kg y. Due tothe high decay energy Q for 0 νββ in Nd, the
Bi back-ground may be neglected. The activities were assumed tobe 2 µ Bq/kg for
Tl and 10 µ Bq/kg for
Bi. Theseare the target radioactive background levels in the base-line SuperNEMO design. Reconstructed distributions of the experimental variables including background eventsfor the MM at an example signal half-life of 10 y areshown in Figure 5. To determine the longest half-life that can be probed withSuperNEMO, 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( CL s ) [42] method. This method uses a log-likelihood ra-tio (LLR) of the signal-plus-background hypothesis andthe background-only hypothesis, where the signal is dueto the 0 νββ process. The effect of varying the Bi back-ground activities on the expected limit to the MM is shownin Fig. 6. The expected limit is given by the median ofthe distribution of the LLR and the widths of the bandsshown represent one and two standard deviations of theLLR distributions for a given
Bi activity. For com-parison, the NEMO-III internal
Bi background is < µ Bq/kg in
Mo and 530 ± µ Bq/kg in Se. TheNEMO-III internal
Tl background is 110 ± µ Bq/kgin
Mo, 340 ± µ Bq/kg in Se and 9320 ± µ Bq/kgin
Nd [39]. The γ -veto used reduces the number of ra-dioactive background events by 30% for Bi in the elec-tron energy sum window > . µ Bq/kg of
Bi in the foil is equivalentto 280 µ Bq/m of Bi in the gas volume and 2 µ Bq/kgof
Tl in the foil is equivalent to 26 µ Bq/m of Tl inthe gas volume. Figure 6 shows that this level of externalbackground would lead to a ∼
15% reduction in the half-life limit. The dominant 2 νββ background is measured bySuperNEMO and statistical uncertainties on its half-life
R. Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO
Cosine of angle between electrons-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 E ve n t s E ve n t s Mass MechanismTheoretical distributionReconstructed distribution (a)
Cosine of angle between electrons-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 E ve n t s E ve n t s Right Handed CurrentTheoretical distributionReconstructed distribution (b)
Difference in energy of electrons (MeV)0 0.5 1 1.5 2 2.5 3 E ve n t s E ve n t s Mass MechanismTheoretical distributionReconstructed distribution (c)
Difference in energy of electrons (MeV)0 0.5 1 1.5 2 2.5 3 E ve n t s E ve n t s Right Handed CurrentTheoretical distributionReconstructed distribution (d)
Fig. 4: Theoretical and experimental electron angular distributions for (a) MM and (b) RHC λ . Theoretical andexperimental electron energy difference distributions for (c) MM and (d) RHC λ . All distributions are shown for theisotope Se and the reconstructed distributions are normalised to the theoretical distribution to show signal efficiency.are expected to be negligible. Inclusion of an estimated7% correlated systematic uncertainty on the signal andbackground distributions [35] leads to a ∼
5% reduction inthe MM half-life limit. The effects of external backgroundand of systematic uncertainties on the 2 νββ backgroundare not included in the results of this paper.Expected exclusion limits at 90% confidence level onthe half-life are shown in Fig. 7. Results are displayed as afunction of RHC λ admixture, where the signal distributionis produced by combining weighted combinations per binof the MM and RHC λ contributions at the event level. Anadmixture of 0% corresponds to a pure MM contribution,and an admixture of 100% to pure RHC λ . Interferenceterms are assumed to be small and are neglected in theexperimental simulation. The lower efficiency in the caseof RHC λ results in a lower limit for larger admixtures.The half-life limit is approximately twice as sensitive in measurements of Se due to the lower mass number andhigher 2 νββ decay half-life, though this is compensatedin
Nd by more favourable phase space when convert-ing into physics parameter space. In the case where onemechanism dominates SuperNEMO is expected to be ableto exclude 0 νββ half-lives up to 1 . · y (MM) and6 . · y (RHC λ ) for Se, and 5 . · y (MM) and2 . · y (RHC λ ) for Nd.
A 0 νββ signal rate with significant excess over the back-ground expectation, as for example shown in Fig. 5, wouldlead to an observation. The expected experimental sta-tistical uncertainties on the decay half-life are calculatedfrom the Gaussian uncertainties on the observed number . Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO 9
Electron energy sum (MeV)2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 E ve n t s E ve n t s Mass Mechanism (500 kg y) y) (10 ββν ββν Tl (a) Difference in energy of electrons (MeV)0 0.5 1 1.5 2 2.5 3 E ve n t s E ve n t s Mass Mechanism (500 kg y) y) (10 ββν ββν Tl (b) Cosine of angle between electrons-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 E ve n t s E ve n t s Mass Mechanism (500 kg y) y) (10 ββν ββν Tl (c) Fig. 5: Expected number of MM signal (half-life of 10 y) and background events in Se after 500 kg y exposureshown for (a) electron energy sum, (b) electron energy difference and (c) cosine of angle between electrons.
Bq/kg) µ Bi (
Background Activity 1 10 y ) H a l f- li f e li m i t ( Se (500 kg y) Expected half-life limit for 90% CL limit1 sigma2 sigma Se (500 kg y) Expected half-life limit for 90% CL limit1 sigma2 sigma
Bq/kg) µ Bi (
Background Activity 1 10 y ) H a l f- li f e li m i t ( Fig. 6: Expected limit on the 0 νββ 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
Bi in Se (a
Tl activity of 2 µ Bq/kg is assumed).of signal and background events in the simulation. Fig-ure 8 shows the results for Se and
Nd as a functionof the admixture of RHC λ . Acceptance effects cause theuncertainty to increase with admixture of RHC λ . The sta- tistical uncertainty increases significantly for large admix-tures of RHC λ at T / = 10 y which go beyond theexclusion limit of SuperNEMO. Admixture of right-handed current (%)0 20 40 60 80 100 y r s ) H a l f- li f e li m i t ( Se (500 kg y) Expected half-life limit for 90% CL limit1 sigma2 sigma (a)
Admixture of right-handed current (%)0 20 40 60 80 100 y r s ) H a l f- li f e li m i t ( Expected half-life limit for 90% CL limit1 sigma2 sigma (b)
Fig. 7: Expected limit on the 0 νββ half-life for SuperNEMO under the background-only hypothesis. The expectedlimit with the one and two standard deviation bands is shown as a function of admixture of the RHC λ mechanism for(a) Se and (b)
Nd.
Admixture of right-handed current (%)0 20 40 60 80 100 O b se r ve d h a l f- li f e ( y )
10 Admixture of right-handed current (%)0 20 40 60 80 100 O b se r ve d h a l f- li f e ( y ) Se Experimental statistical uncertainty yr = 10 T yr = 10 T yr = 10 T (a) Admixture of right-handed current (%)0 20 40 60 80 100 O b se r ve d h a l f- li f e ( y )
10 Admixture of right-handed current (%)0 20 40 60 80 100 O b se r ve d h a l f- li f e ( y ) Nd Experimental statistical uncertainty yr = 10 T yr = 10 T (b) Fig. 8: One standard deviation statistical uncertainties in the measurement of double β decay half-lives at SuperNEMOas a function of admixture of the RHC λ mechanism represented as band thickness for (a) Se and (b)
Nd.The angular asymmetry parameter k θ in Equation (23)is experimentally accessible by defining N + as the numberof events with measured angle cos θ < − as thenumber of events with cos θ >
0. Similarly, an energy dif-ference asymmetry k E can be obtained where N + is thenumber of events with energy difference < Q/ νββ decay) and N − is the number of eventswith energy difference > Q/
2. The electron energy sum isrequired to be greater than 2.7 MeV for Se and 3.1 MeVfor
Nd to maximise signal to background ratio. This re-sults in signal efficiencies of 23.2% for the MM and 13.2%for the RHC λ in Se and 19.1% for the MM and 10.4%for the RHC λ in Nd.Experimentally, the distributions are only available asa sum of signal plus background so the measured valuesdiffer from the theoretically expected values due to thebackground distributions. This generally results in recon-structed correlation factors that are biased towards pos-itive values. The measured values of k θ,E are shown inFig. 9 for a number of half-lives in the two isotopes. Sta-tistical uncertainties are shown as the width of the bands. All reconstructed k θ,E values are displayed as a function ofthe corresponding theoretical k Tθ,E parameter, to allow fora model independent generalisation. It can be seen thatthe energy difference distribution allows stronger modeldiscrimination than the angular distribution.
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 theSuperNEMO experiment to new physics parameters of thecombined MM and RHC λ model of 0 νββ decay.Using Equation (13) for the 0 νββ decay half-life to-gether with the coefficients listed in Table 1, the expected90% CL limit on T / shown in Fig. 7 can be translatedinto a constraint on the model parameters m ν and λ . As-suming all other contributions are negligible this is shown . 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 -0.2 0 0.2 0.4 0.6 0.8 1 θ R ec on s t r u c t e d k Se parameter for θ k yr = 10 T yr = 10 T yr = 10 T (a) T θ Theoretical k-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 θ R ec on s t r u c t e d k Nd parameter for θ k yr = 10 T yr = 10 T (b) TE Theoretical k-1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 E R ec on s t r u c t e d k -1-0.500.511.5 Se parameter for E k yr = 10 T yr = 10 T yr = 10 T (c) TE Theoretical k-1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 E R ec on s t r u c t e d k -1-0.500.511.5 Nd parameter for E k yr = 10 T yr = 10 T (d) Fig. 9: Simulation of the correlation coefficients k θ and k E as a function of theoretical k Tθ,E . The bands represent theone standard deviation statistical uncertainties. Shown are the angular correlation factor k θ for Se (a) and
Nd(b) and the energy difference correlation factor k E for Se (c) and
Nd (d).in Fig. 10 (a), as a contour in the m ν − λ parameter plane.In the case SuperNEMO does not see a signal these pa-rameters would be constrained to be located within thecoloured contour. The odd shape of the coloured contouris a direct consequence of the SuperNEMO 90% CL exclu-sion limit as a function of the specific admixture betweenthe MM and the RHC λ shown in Fig. 7. The small in-terference term, though not included in the experimentalsimulation, is taken into account through Equation (13) inthis figure and results in the asymmetry of the distributionwith respect to the sign of the parameter λ .As shown in Section 4, SuperNEMO is expected tobe more sensitive to the 0 νββ half-life when using theisotope Se, but this is compensated by the larger phasespace of
Nd. As a result, the constraint on the modelparameters is slightly stronger for
Nd. Due to the largeuncertainty in the NMEs, this might be different for otherNME calculations. To demonstrate the improvement overexisting experimental bounds, the parameter constraintsare shown in Fig. 10 (b) on a logarithmic scale (for positivevalues of λ ), comparing the expected SuperNEMO reach with the current constraints from the 0 νββ experimentsNEMO-III [40,38] and Heidelberg Moscow [25].Figure 10 shows that SuperNEMO is expected to con-strain model parameters at 90% CL down to h m ν i =70-73meV and λ =(1-1.3) · − . This would be an improvementby 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. As a more intriguing scenario it is now assumed thatSuperNEMO actually observes a 0 νββ decay signal in Seor
Nd. Because of the tracking abilities described inSection 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, thiscan be crucial in distinguishing between different 0 νββ decay mechanisms. In the analysis a reconstruction of theangular and energy correlation coefficients k θ and k E isused to determine the theoretical coefficients, and thereby - - Λ @ - D X m Ν \ @ m e V D Se Nd (a) - - - - Λ X m Ν \ @ m e V D Nd exp82 Se exp76 Ge exp82 Se Nd (b) Fig. 10: (a) Expected SuperNEMO constraints on the model parameters ( m ν , λ ) for the isotopes Se (light bluecontour) and
Nd (dark blue contour). (b) Comparison with current bounds on 0 νββ half-lives of the isotopes Se(NEMO-III [40]),
Nd (NEMO-III [38]) and Ge (Heidelberg Moscow [25]). The contours show the 90% CL exclusionregion.the admixture between the left- and right-handed currentsin the combined MM and RHC λ model.For the isotope Se, this is shown in Fig. 11 for dif-ferent RHC λ admixtures. The two blue elliptical contourscorrespond to the allowed one standard deviation ( m ν − λ )parameter space at SuperNEMO when observing a signalat T / = 10 y and T / = 10 y, respectively. Thistakes into account a nominal theoretical uncertainty onthe NME of 30% and a one standard deviation statisticaluncertainty on the measurement determined from the sim-ulation (Fig. 8). The blue elliptical error bands thereforegive the allowed parameter region when only consideringthe total 0 νββ rate, which does not allow to distinguishbetween the MM and RHC λ contributions.When taking into account the information providedby the angular and energy difference distribution shape,the parameter space can be constrained significantly. Thisis shown using the green contours in Fig. 11 for (a) apure MM model, (b) a RHC λ admixture of 30%, corre-sponding to an angular correlation of k θ ≈ . λ model. This fixes two specific directionsin the m ν − λ plane (one for positive and one for neg-ative λ ). The widths of the contours are determined bythe uncertainty in determining the theoretical correlationand admixture from the apparent distribution shape, seeFig. 9. The outer (light green) contours in Fig. 11 givethe one standard deviation uncertainty on the parame-ters from reconstructing the angular distribution, whilethe inner (darker green) contour gives the one standard deviation uncertainty when using the distributions of theelectron energy difference. As was outlined in Section 4,the energy difference distribution is expected to be easierto reconstruct and therefore gives a better determinationof the RHC λ admixture and a better constraint. While in-terference between MM and RHC λ is neglected in the sim-ulation, it is taken into account in Equation (13) throughthe term C mλ µλ resulting in the slightly tilted ellipticalcontours and the asymmetry for λ ↔ − λ . Finally, the redcontours in Fig. 11 show the constraints on the modelparameters when combining both the determination ofthe 0 νββ decay rate and the decay energy distribution.This demonstrates that such a successful combination canmake it possible to determine the mechanism (i.e. the de-gree of MM and RHC λ admixture in this case), and pro-vide a better constraint on the model parameters. FromFig. 11 (a), the Majorana mass term can be determined at h m ν i = 245 +56 − meV while the λ parameter is constrainedto be − . · − < λ < . · − in the case of a mea-sured 0 νββ decay half-life of Se of T / = 10 y. For a Se half-life of T / = 10 y, the uncertainty on the decayrate increases as SuperNEMO reaches its exclusion limitfor RHC λ admixtures. It is therefore only possible to ex-tract upper limits on the model parameters from Fig. 11for T / = 10 y. However, the shape information pro-vides additional constraints on the parameter space. InFig. 12 we show the analogous plots for the isotope Ndassuming a decay half-life of T / = 10 y. . Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO 13 - - Λ @ - D X m Ν \ @ m e V D (a) - - Λ @ - D X m Ν \ @ m e V D (b) - - Λ @ - D X m Ν \ @ m e V D (c) Fig. 11: Constraints at one standard deviation on the model parameters m ν and λ for Se from: (1) an observationof 0 νββ decay half-life at T / = 10 y (outer blue elliptical contour) and 10 y (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). Theadmixture of the MM and RHC λ contributions is assumed to be: (a) pure MM contribution; (b) 30% RHC λ admixture;and (c) pure RHC λ contribution. NME uncertainties are assumed to be 30% and experimental statistical uncertaintiesare determined from the simulation. - - Λ @ - D X m Ν \ @ m e V D (a) - - Λ @ - D X m Ν \ @ m e V D (b) - - Λ @ - D X m Ν \ @ m e V D (c) Fig. 12: As Fig. 11 but for the isotope
Nd with a decay half-life of T / = 10 y. Nd and Se While reconstruction of the decay distribution can be anideal way to distinguish between different mechanisms, itmight be of little help if 0 νββ decay is observed close tothe exclusion limit of SuperNEMO, or not at all. This isdemonstrated in Fig. 11 where, for a half-life of T / =10 y, 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 0 νββ rate in different isotopes. This method,which could provide crucial information close to the ex-clusion limit, is especially relevant for SuperNEMO whichcould potentially measure 0 νββ 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 statisticalsignificance [22].The possibility of sharing the two isotopes equally inSuperNEMO, each with a total exposure of 250 kg y, isnow considered. In the cases where the MM or the RHC λ contributions dominate, the following half-life ratios canbe found:MM : T Se1 / T Nd1 / = C Nd mm (2 . · C Se mm = 2 . , (27) RHC λ : T Se1 / T Nd1 / = C Nd λλ (2 . · C Se λλ = 3 . . (28)These ratios and their uncertainties are determined by the0 νββ decay NMEs and phase spaces. The factor 2.7 is thecorrection added to the Nd NMEs as described in Sec-tion 2.3. It has recently been suggested that uncertaintiesin NME calculations are highly correlated [43] so mea-surements made with two or more isotopes could reducethe uncertainty on the physics parameters significantly.Additionally, most experimental systematic uncertaintieswould cancel if different isotopes are studied in a singleexperiment such as SuperNEMO. This would not be pos-sible when comparing results with other experiments. Thestatistical uncertainties are naturally greater than in thesingle-isotope case, due to the exposure being halved foreach isotope.The results of the combined NME and statistical un-certainties analysis, including a possible correlation of theNMEs, are illustrated in Fig. 13. It shows the 0 νββ half-life of
Nd as a function of the half-life in Se assuminga pure MM model, with the coloured contours giving thedeviation from the hypothesis that the mass mechanismis the single source of 0 νββ decay in both isotopes at the1, 2 and 5 standard deviation level. The statistical uncer-tainties used in Fig. 13 are derived from our experimentalsimulation and the standard 30% NME uncertainties areapplied. The effect of a possible correlation of the NMEsis shown by assuming the covariance coefficient betweenthe NME uncertainties of Se and
Nd to be (a) zero(no correlation), (b) 0.7 and (c) 1.0 (full correlation). Theexperimental uncertainties and expected sensitivity (90%CL exclusion) limits are calculated for 250 kg y of ex-posure of each isotope and assume a 50% Se and 50%
Nd option for SuperNEMO. The red line shows the re-lationship for the half-life ratio in the pure RHC λ model(Equation (28)). It can be seen that an exclusion at twostandard deviations is possible if the NME errors are per-fectly correlated and at the one standard deviation level ifthe 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 thatit provides a possibility to falsify the mass mechanism asthe sole source for 0 νββ . A measurement within the bluecontour would indicate that the pure MM model can beexcluded at the 5 standard deviation level and new physicsis required to explain the measured half-lives. Ndand Se In the most favourable case, signal event rates in two iso-topes could be high enough (0 νββ decay half-lives smallenough) 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%
Nd - 50% Se two-isotopeoption (red contours) is compared to the single-isotope op-tions 100% Se (green contours) and 100%
Nd (bluecontours). The 0 νββ decay half-life of Se is assumedto be 10 y, and the half-life of Nd is determinedby the respective MM-RHC λ admixture, i.e. (a) T Nd / =10 / .
45 y, (b) 10 / .
73 y and (c) 10 / .
64 y. The NMEuncertainties are assumed to be 30% with a 0.7 covariancebetween the uncertainties of the NMEs of Se and
Nd.As can be seen in Fig. 14, the two-isotope option can im-prove the constraints on the parameter space along theradial direction, e.g. it allows a more accurate determina-tion of the MM neutrino mass m ν in Fig. 14 (a). On theother hand, the accuracy in the lateral direction (the pa-rameter λ in Fig. 14 (a)) becomes worse compared to thebest single-isotope option due to the reduced statistics fora given isotope. The 0 νββ decay is a crucial process for physics beyond theStandard Model, and the next generation SuperNEMO ex-periment is designed to be a sensitive probe of this leptonnumber violating observable. In addition to being able tomeasure the 0 νββ half-life of one or more isotopes, it alsoallows the determination of the angular and energy differ-ence distributions of the outgoing electrons.In this paper we have focussed on the sensitivity ofSuperNEMO to new physics and its ability to discriminatebetween different 0 νββ mechanisms. This was achieved bya detailed analysis of two important models, namely thestandard mass mechanism via light left-handed Majorananeutrino exchange and a contribution from right-handedcurrent via the effective λ parameter stemming from Left-Right symmetry. The study included a full simulation ofthe process and the SuperNEMO detector at the eventlevel, allowing a realistic estimation of the experimental90% CL exclusion limit and statistical uncertainties.SuperNEMO is expected to exclude 0 νββ half-lives upto 1 . · y (MM) and 6 . · y (RHC λ ) for Se and5 . · y (MM) and 2 . · y (RHC λ ) for Nd at 90%CL with a detector exposure of 500 kg y. This correspondsto a Majorana neutrino mass of m ν ≈
70 meV and a λ parameter of λ ≈ − , giving an improvement of morethan one order of magnitude compared to the NEMO-IIIexperiment.It has been shown that the angular and electron en-ergy difference distributions can be used to discriminatenew 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 bedetermined. For a half-life of T / = 10 y 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% whilethe λ parameter can be constrained at the same time tobe smaller than | λ | < . · − . Such a decay distributionanalysis could be easily extended further to include othernew physics scenarios with distinct distributions and the . Arnold et al.: Probing New Physics Models of Neutrinoless Double Beta Decay with SuperNEMO 15 T (cid:144) @ y D T (cid:144) N d @ y D Σ Σ Σ Sensitivity limit S e n s iti v it y li m it (a) T (cid:144) @ y D T (cid:144) N d @ y D Σ Σ Σ Sensitivity limit S e n s iti v it y li m it (b) T (cid:144) @ y D T (cid:144) N d @ y D Σ Σ Σ Sensitivity limit S e n s iti v it y li m it (c) Fig. 13: The 0 νββ half-life of
Nd as a function of measured half-life in Se for the hypothesis that the MMis the single 0 νββ decay source. The contours show the 1, 2 and 5 standard deviation levels assuming statisticaluncertainties 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 calculatedfor 250 kg y of exposure (assuming a 50% Se and 50%
Nd option). The red line shows the relationship for theRHC λ . The blue contour shows the 5 σ exclusion of the MM. - - Λ @ - D X m Ν \ @ m e V D (a) - - Λ @ - D X m Ν \ @ m e V D (b) - - Λ @ - D X m Ν \ @ m e V D (c) Fig. 14: Constraints at one standard deviation on the model parameters m ν and λ from: (1) an observation of 0 νββ decay half-life of Se at T / = 10 y with 500 kg y exposure and reconstruction of the energy difference distribution(outer green contour); (2) an observation of 0 νββ decay half-life of Nd at a half-life corresponding to T / = 10 yin Se 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 in Se and
Nd (red contour). The admixtureof the MM and RHC λ contributions is assumed to be: (a) pure MM contribution; (b) 30% RHC λ admixture; and (c)pure RHC λ contribution. NME uncertainties are assumed to be 30% with a correlation of the uncertainties of 0.7, andexperimental statistical uncertainties are determined from the simulation.results are quoted in terms of a generalised distributionasymmetry parameter to allow new physics scenarios tobe compared. As the two example mechanisms consideredexhibit 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 theright-handed current λ contribution by looking at boththe angular and energy difference decay distribution. Thiswould allow a determination of all three model parameters m ν , λ and η by looking at the total rate and the angularand energy difference distribution shapes.Further insight into the mechanism of 0 νββ can begained by using multiple isotopes within the SuperNEMO setup. This possibility was explored by studying the op-tion of having 50% Nd and 50% Se, each with anexposure 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 twoisotopes can be used as additional information on the un-derlying physics mechanism responsible for 0 νββ decay.As was shown for the isotopes Se and
Nd at Super-NEMO, this could be a powerful method to falsify themass mechanism as the dominant 0 νββ 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 sucha correlation could also be found between the systematicuncertainties in the measurements of different isotopes.SuperNEMO also has a number of other possibilitiesto disentangle the underlying physics. The detection tech-nology is not dependent on one particular isotope and anydouble β emitting source could be studied in the detector.In this paper Se and
Nd have been considered butother isotopes such as Ca or
Mo are feasible. Theanalysis can be extended to cover more than two isotopesthereby achieving a higher significance and a comparisonwith other experimental results will provide additional in-formation. SuperNEMO is also able to measure a 0 νββ decay to an excited state, by measuring two electrons andan accompanying photon. This again could be used to aidthe analysis to discriminate between new physics mecha-nisms.A combination of the above methods makes Super-NEMO an exciting test of new physics. These methodswould prove invaluable in excluding or confirming domi-nating mechanisms of lepton number violation in the reachof the next generation 0 νββ 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 supportfrom the staff of the Modane Underground Laboratory (LSM).
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