Quenching of gA and its impact in double beta decay

This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail. Author(s): Title: Year: Version: Please cite the original version: All material supplied via JYX is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user. Quenching of gA and its impact in double beta decay Iachello, Francesco; Kotila, Jenni-Mari; Barea, Jose Iachello, F., Kotila, J.-M., & Barea, J. (2015). Quenching of gA and its impact in double beta decay. In NEUTEL 2015 : XVI International Workshop on Neutrino Telescopes. Sissa. PoS : Proceedings of Science, NEUTEL2015. http://pos.sissa.it/archive/conferences/244/047/NEUTEL2015_047.pdf 2015 PoS(NEUTEL2015)047 Quenching of gAand its impact in double beta decay F. Iachello∗ Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520-8120, USA E-mail: [email protected] J. Barea Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción 4070386, Chile E-mail: [email protected] J. Kotila Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520-8120, USA Department of Physics, University of Jyväskylä, B.O. Box 35, FIN-40014, Jyväskylä, Finland E-mail: [email protected] The theory of double beta decay is briefly reviewed. The most recent (2015) results for 0 νβ − β − nuclear matrix elements in the interacting boson model (IBM-2) with light and heavy neutrino exchange are given for all nuclei of interest from 48Ca to 238U. The question of quenching of the axial vector coupling constant gAin nuclei is discussed. Possible additional scenarios, such as Majoron emission, and mechanisms, such as sterile neutrino exchanges, are also discussed. XVI International Workshop on Neutrino Telescopes, 2-6 March 2015 Palazzo Franchetti - Istituto Veneto, Venice, Italy ∗Speaker. c Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it/ PoS(NEUTEL2015)047 Quenching of gAand its impact in double beta decay F. Iachello 1. Introduction Double beta decay is a process in which a nucleus Xdecays into a nucleus Ywith emission of two electrons (or positrons) and usually, other light particles A ZXN→A Z±2YN∓2+2e∓+anything.(1.1) The half-life for processes not allowed by the standard model, 0 νββ , can be written as [ τ 0 ν 1/2]−1=G0 ν |M0 ν |2|f(mi,Uei)|2,(1.2) where G0 ν is a phase space factor (PSF), M0 ν the nuclear matrix element (NME) and f(mi,Uei) contains physics beyond the standard model through the masses miand mixing matrix elements Uei of neutrino species. For processes allowed by the standard model, the half-life can be, to a good approximation, factorized in the form [1, 2, 3] h τ 2 ν 1/2i−1=G2 ν |M2 ν |2,(1.3) where G2 ν is a PSF and M2 ν the NME. 2. Nuclear matrix elements, NME The nuclear matrix elements, NME, for neutrinoless double beta decay can be written as M0 ν =g2 AM(0 ν ),M(0 ν )≡M(0 ν ) GT −gV gA2 M(0 ν ) F+M(0 ν ) T.(2.1) In the calculation of NME, two scenarios have been mostly considered, (1) emission and reabsorption of light (m ν light ≪1keV)and (2) emission and re-absorption of heavy (m ν heavy ≫1GeV) neutrinos. In scenario 1, light neutrino exchange, the function fand the neutrino “potential” are given by f=hm ν i me ,hm ν i=∑ k=light (Uek)2mk,v(p) = 2 π 1 p(p+˜ A)(2.2) with ˜ A=closure energy=1.12A1/2(MeV). In the last few years atmospheric, solar, reactor, and accelerator neutrino oscillation experiments have provided information on light neutrino mass differences and their mixings. The average light neutrino mass can be written as [4] hm ν i=c2 13c2 12m1+c2 13s2 12m2ei ϕ 2+s2 13m3ei ϕ 3, ci j =cos ϑ i j,si j =sin ϑ i j, ϕ 2,3= [0,2 π ], m2 1,m2 2,m2 3=m2 1+m2 2 2+− δ m2 2,+ δ m2 2,±∆m2. (2.3) The solution with +∆m2denotes the normal hierarchy, while that with −∆m2denotes the inverted hierarchy. A fit to the oscillation experiments gives sin2 ϑ 12 =0.312,sin2 ϑ 13 =0.016,sin2 ϑ 23 =0.466 δ m2=7.67 ×10−5eV2,∆m2=2.39 ×10−3eV2(2.4) PoS(NEUTEL2015)047 Quenching of gAand its impact in double beta decay F. Iachello A recent result from Daya Bay, gives sin2 ϑ 13 =0.024 ±0.005, which slightly modifies the fit. Variation of the phases ϕ 2and ϕ 3from 0 to 2 π gives the values of hm ν iconsistent with oscillation experiments (constraints on the neutrino masses), in the so-called Vissani-plot. In scenario 2, heavy neutrino exchange, the function f and the neutrino “potential” are given by f=mpm−1 ν h,hm−1 ν hi=∑ k=heavy (Uekh)21 mkh ,v(p) = 2 π 1 mpme .(2.5) Constraints on the average inverse heavy neutrino mass are model dependent. Tello et al. [5] have recently worked out constraints from lepton flavor violating processes and LHC experiments. In this model f≡ η =M4 W M4 WR ∑ k=heavy (Vekh)2mp mkh ≡M4 W M4 WR mp hm ν hi,(2.6) where MWis the mass of the W-boson, MW= (80.41 ±0.10)GeV , MWR is the mass of an hypothetical Wright boson, MWR =1.75TeV. The value of η is called lepton violating parameter. Constraints on η can be then converted into constraints on the average heavy neutrino mass as hm ν hi=mpMW MWR 41 η .(2.7) 2.1 Results Several methods have been used to evaluate M0 ν , including the quasiparticle random phase approximation, QRPA, in the two versions QRPA-Tü [6] and QRPA-Jy [7], the shell model, ISM, [8], and the density functional theory, DFT, [9], and others. The most recent results for IBM-2, QRPA-Tü, and ISM are shown in Fig. 1 for light neutrino exchange and in Fig. 2 for heavy neutrino exchange, and for gA=1.269. The IBM-2 results are given in Table I, together with the estimated error. æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ à à à à à à à à à à à ì ì ì ì ì ì ì æ à ì IBM-2 QRPA-Tü ISM Ca Ge Se Zr Mo Pd Cd Sn Te Te Xe Nd Nd Sm Gd Pt Th U 20 40 60 80 100 120 140 0 1 2 3 4 5 6 7 Neutron number MH0ΝL Figure 1: Most recent IBM-2 results [3] for 0 νβ − β −decay compared with QRPA-Tü [6] and the ISM [8]. PoS(NEUTEL2015)047 Quenching of gAand its impact in double beta decay F. Iachello æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ æ à à à à à à à à à à à ì ì ì æ à ì IBM-2 QRPA-Tü ISM Ca Ge Se Zr Mo Pd Cd Sn Te Te Xe Xe Nd Nd Sm Gd Pt Th U 20 40 60 80 100 120 140 0 100 200 300 400 Neutron number Mh H0ΝL Figure 2: Most recent IBM-2 results [3] for 0 ν h β − β −decay compared with QRPA-Tü [6] and the ISM [8, 10]. 3. Phase space factors, PSF PSF for 0 νββ and 2 νββ decays have been recently recalculated [11] with exact Dirac electron wave functions and including screening by the electron cloud. These new PSF are available from jenni.kot[email protected]du and are on the webpage nucleartheory.yale.edu. 4. Half-lives and limits on neutrino masses By combining the nuclear matrix elements and phase space factors one can calculate the expected half-lives and, from those, set some limits on the neutrino masses. These are given in Table II for light neutrino exchange and in Table III for heavy neutrino exchange. The limits hm ν iare also shown in the Vissani plot of Fig. 3. The current best limits on the neutrino mass from 0 νβ − β −with gA=1.269, IBM-2 NME, and KI PSF are, for light neutrino exchange, m ν <0.20eV (EXO/KamLAND-Zen), and for heavy neutrino exchange, in the model of Tello et al.,m ν h>257GeV(1.75/MW R)4(EXO/KamLANDZen). It is clear from Fig. 3 that even with gA=1.269, exploration of the inverted region requires >1ton experiments, and exploration of the normal region ≫1ton experiments. 5. Quenching of gA Results in Sect. 2.1 have been obtained with gA=1.269. It is well-known from single β −decay/EC [12, 13] and from 2 νββ -decay that gAis renormalized in models of nuclei. There are two reasons for the renormalization: (i) The omission of non-nucleonic degrees of freedom (∆,N∗,...)and (ii) the limitation of the space in which calculation is done. The first of these reasons gives rise to a quenching of gAwhich is independent of mass number, A. The second gives rise to a quenching of gAthat depends on Aand is model dependent. The larger A, the larger the quenching. PoS(NEUTEL2015)047 Quenching of gAand its impact in double beta decay F. Iachello Decay Light neutrino exchange Heavy neutrino exchange 48Ca 1.75(28) 47(13) 76Ge 4.68(75) 104(29) 82Se 3.73(60) 83(23) 96Zr 2.83(45) 99(28) 100Mo 4.22(68) 164(46) 110Pd 4.05(65) 154(43) 116Cd 3.10(50) 110(31) 124Sn 3.19(51) 79(22) 128Te 4.10(66) 101(28) 130Te 3.70(59) 92(26) 134Xe 4.05(65) 91(26) 136Xe 3.05(59) 73(20) 148Nd 2.31(37) 103(29) 150Nd 2.67(43) 116(32) 154Sm 2.82(45) 113(32) 160Gd 4.08(65) 155(43) 198Pt 2.19(35) 104(29) 232Th 4.04(65) 159(45) 238U 4.81(77) 189(53) Table 1: Most recent IBM-2 matrix elements M(0 ν )with error estimate [3]. For each model (ISM/QRPA/IBM-2) one can define effective gA,e f f by writing Me f f β /EC =gA,e f f gAM β /EC Me f f 2 ν =gA,e f f gA2 M2 ν (5.1) The value of gA,e f f in each nucleus can be obtained by comparing the calculated and measured half-lives for β /EC and for 2 νββ . By comparing the values of Me f f 2 ν compiled in [11] with those of |M2 ν |given in Table XII of [3], one can extract the values of gA,e f f for IBM-2 shown in Fig. 4. In this figure, the values of gA,e f f for the ISM are also shown. They are obtained by comparing the experimental values Me f f 2 ν with the calculated values [10]. Both results show a massive renormalization to gA,e f f ∼0.6−0.5 for IBM-2 and to gA,e f f ∼0.8−0.7 for ISM. The overall trend can be parametrized to gIBM−2 A,e f f =1.269A−0.18,gISM A,e f f =1.269A−0.12. Values of gA,e f f have been extracted from single β /EC in QRPA-Jy very recently [14] with results gA,e f f ∼ 0.8−0.4, and in QRPA-Tü a few years ago [15] with result ∼0.7. The axial vector coupling constant, gA, appears to the second power in the NME M2 ν =g2 AM(2 ν ), M0 ν =g2 AM(0 ν ),M(0 ν )=M(0 ν ) GT −gV gA2 M(0 ν ) F+MT(0 ν )(5.2) PoS(NEUTEL2015)047 Quenching of gAand its impact in double beta decay F. Iachello Decay τ 0 ν 1/2(1024yr) τ 0 ν 1/2,exp(yr) hm ν i(eV) 48Ca→48Ti 1.33 >5.8×1022 <4.8 76Ge→76Se 1.95 >1.9×1025 <0.32 1.2×1025 0.40 >1.6×1025 <0.35 >2.1×1025 <0.30 82Se→82Kr 0.71 >3.6×1023 <1.4 96Zr→96Mo 0.61 >9.2×1021 <8.1 100Mo→100Ru 0.36 >1.1×1024 <0.57 110Pd→110Cd 1.27 116Cd→116Sn 0.63 >1.7×1023 <1.9 124Sn→124Te 1.09 128Te→128Xe 10.19 >1.5×1024 <2.6 130Te→130Xe 0.52 >2.8×1024 <0.43 134Xe→124Ba 10.23 136Xe→136Ba 0.74 >1.9×1025 <0.20 >1.1×1025 <0.22 148Nd→148Sm 1.87 150Nd→150Sm 0.22 >1.8×1022 <3.5 154Sm→154Gd 4.19 160Gd→160Dy 0.63 198Pt→198Hg 2.77 232Th→232U 0.44 238U→238Pu 0.13 Table 2: Left: Calculated half-lives in IBM-2 Argonne SRC for neutrinoless doubleβ decay for hm ν i= 1 eV and gA=1.269 [3]. Right: Upper limit on neutrino mass from current experimental limit from a compilation of Barabash [16]. The value reported by Klapdor-Kleingrothaus et al. [17], IGEX collaboration [18], and the recent limits from KamLAND-Zen [19], EXO [20], and GERDA [21] are also included. and hence to the fourth power in the half-life. Therefore if gAis renormalized in 0 νββ as much as in 2 νββ the results of Sect. 4 should be multiplied by a factor of 6-34 to have realistic estimates of the expected half-lives, as discussed also in Refs. [22, 23]. In conclusion, three possible scenarios for gAare: gA=1.269 (free value) gA=1 (quark value) gA=1.269A−0.18 (maximal quenching) (5.3) Correspondingly, there will be three possible limits on neutrino masses [23], as shown in Fig. 5 for EXO in 136Xe decay. In the worst case scenario, gA∼0.5 it would be impossible to reach, in the foreseeable future, even the inverted region. PoS(NEUTEL2015)047 Quenching of gAand its impact in double beta decay F. Iachello Decay τ 0 ν h 1/2(1024yr) τ 0 ν h 1/2,exp(yr) | η |(10−6)hm ν hi(GeV) 48Ca→48Ti 0.72 >5.8×1022 <0.36 >11.9 76Ge→76Se 1.51 >1.9×1025 <0.028 >148 1.2×1025 0.035 118 >1.6×1025 <0.031 >136 >2.1×1025 <0.027 156 82Se→82Kr 0.55 >3.6×1023 <0.12 >34 96Zr→96Mo 0.19 >9.2×1021 <0.46 >9.15 100Mo→100Ru 0.09 >1.1×1024 <0.028 >146 110Pd→110Cd 0.33 116Cd→116Sn 0.19 >1.7×1023 <0.11 >39.5 124Sn→124Te 0.67 128Te→128Xe 6.43 >1.5×1024 <0.21 >20.2 130Te→130Xe 0.32 >2.8×1024 <0.034 >123 134Xe→134Ba 8.57 136Xe→136Ba 0.50 >1.9×1025 <0.016 >257 >1.1×1025 <0.018 >236 148Nd→148Sm 0.36 150Nd→150Sm 0.05 >1.8×1022 <0.16 >26.3 154Sm→154Gd 1.00 160Gd→160Dy 0.17 198Pt→198Hg 0.48 232Th→232U 0.11 238U→238Pu 0.03 Table 3: Left: Calculated half-lives for neutrinoless doubleβ decay with exchange of heavy neutrinos for η =1×10−7and gA=1.269 [3]. Right: Upper limits of | η |and lower limits of heavy neutrino mass (see text for details) from current experimental limit from a compilation of Barabash [16]. The value reported by Klapdor-Kleingrothaus et al. [17], IGEX collaboration [18], and the recent limit from KamLAND-Zen [19], EXO [20], and GERDA [21] are also included. 6. Other scenarios: Sterile neutrino exchange Possibilities to escape the negative conclusion of Sect. 5 are: (1) Neutrino masses are degenerate and large. This possibility will be in tension with the cosmological bound on the sum of the neutrino masses [24] ∑ i mi≤0.230eV (6.1) (2) Both mechanism, light and heavy exchange, contribute simultaneously, are of the same order of magnitude, and interfere constructively [ τ 0 ν 1/2]−1=G0 ν  M0 ν hm ν i me +M0 ν h mp hm ν hi 2 .(6.2) PoS(NEUTEL2015)047 Quenching of gAand its impact in double beta decay F. Iachello NORMAL INVERTED CUORICINO IGEX NEMO-3 KamLAND-Zen GERDA EXO X 10-4 0.001 0.01 0.1 1 10-4 0.001 0.01 0.1 1 lightest neutrino mass in eV ÈXmΝ\È in eV Figure 3: Current limits to hm ν ifrom CUORICINO [25], IGEX [18], NEMO-3 [26], KamLAND-Zen [19], EXO [20], and GERDA [21], and most recent IBM-2 Argonne SRC nuclear matrix elements and gA=1.269 [3]. The value of Ref. [17] is shown by X. The figure is in logarithmic scale. à à àò ò ò ò ò à à à ò ò á á á á á æ æ æ æ æ æ æ æ æ æ ç ç ç ç ç áfrom experimental Τ12HISML çgA,eff ISM =1.269A-0.12 àòfrom experimental Τ12HIBM-2 CASSDL ægA,eff IBM-2=1.269A-0.18 Ca Ge Se Zr Mo Cd Te Xe Nd 40 60 80 100 120 140 160 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Mass number gA, eff Figure 4: Value of gA,e f f extracted from experiment for IBM-2 and ISM. This possibility requires a fine tuning which is quite unlikely. (3) Other scenarios (Majoron emission, ...) and new mechanisms (sterile neutrino exchange,...) must be considered [27]. For the scenario 3, Majoron emission, 0 νββφ decay suggested in [28], the inverse half-life is given by h τ 0 νββφ 1/2i−1=G0 νφ |M0 ν |2|hgi|2,(6.3) where gis the effective Majoron coupling constant. The NME for this scenario are the same as for 1 and 2. The PSF have been recalculated recently [29]. The best limit with IBM-2, KBI PSF, and