RECENT RESULTS IN DOUBLE BETA DECAY

Transcription

1 RECENT RESULTS IN DOUBLE BETA DECAY Francesco Iachello Yale University Neutrino Oscillation Workshop Otranto, September 8, 2014

2 CLASSIFICATION OF DOUBLE BETA DECAY (DBD) β - β - modes (i) Two-neutrino double electron decay, 2νβ - β - (A,Z) ö (A,Z+2)+2e - +2ν (ii) Neutrinoless double electron decay, 0νβ - β - (A,Z) ö (A,Z+2)+2e - β + β + modes (iii) Two-neutrino double positron decay, 2νβ + β + (A,Z) ö (A,Z-2)+2e + +2ν (iv) Positron emitting two-neutrino electron capture, 2νβ + EC (A,Z)+e - ö (A,Z-2)+e + +2ν (v) Two-neutrino double electron capture, 2νECEC (A,Z)+2e - ö (A,Z-2)+2ν

3 (vi) Neutrinoless double positron decay, 0νβ + β + (A,Z) ö (A,Z-2)+2e + (vii) Positron emitting neutrinoless electron capture, 0νβ + EC (A,Z)+e - ö (A,Z-2)+e + (viii) Neutrinoless resonant double electron capture, R0νECEC (A,Z)+2e - ö (A,Z-2)

4 For processes allowed by the standard model, the half-life can be, to a good approximation, factorized in the form 2ν 1 2 1/2 G2 ν M2 ν τ = Phase-space factor (Atomic Physics) PSF For processes not allowed by the standard model, the halflife can be factorized as 0ν /2 G0 ν M0 ν f( mi, Uei) τ = HALF-LIVES Matrix elements (Nuclear Physics) NME Phase-space factor (Atomic Physics) PSF Matrix elements (Nuclear Physics) NME Beyond the standard model (Particle Physics)

5 A special case is 0νECEC, which is forbidden by energy and momentum conservation, but can occur under resonance conditions. In this case the inverse half-life is given by 2 0ν ( mc e ) Γ τ 1/2 = G0 ν M0 ν f( mi, Uei) 2 2 Δ + ( Γ /4) Resonance factor Prefactor (Atomic Physics) PF Matrix elements (Nuclear Physics) NME Beyond the SM (Particle Physics) Δ= Q B E Γ=Γ +Γ e 2h e 1 2 Degeneracy parameter (Atomic and Nuclear Physics) Two-hole width (Atomic Physics)

6 NME have been calculated in a variety of models: QRPA, ISM, IBM-2, DFT, Calculations of NME in IBM-2 for all processes have been completed (2014) and are available upon request. A list of references is given in Appendix A. For 0ν processes two scenarios have been considered: (i) Emission and re-absorption of a light (m light á1kev) neutrino. (ii) Emission and re-absorption of a heavy (m heavy à1gev) neutrino. e p 1 e p e p e 2 p ν light ν heavy f m n n n n ν = m νligth á1kev 1 m νheavy à1gev fh = mp mν m e Long range Short range h

7 Most recent (2014) results for 0νβ - β - (light neutrino exchange) IBM-2 * : J. Barea, J. Kotila, and F. Iachello, Phys. Rev. C, to be submitted (2014). QRPA-Tu * : F. Simkovic, V. Rodin, A. Faessler, and P. Vogel, Phys. Rev. C 87, (2013). ISM: J. Menendez, A. Poves, E. Caurier, and F. Nowacki, Nucl. Phys. A 818, 139 (2009). * With isospin restoration and Argonne SRC

8 PHASE SPACE FACTORS (PSF) PSF were calculated in the 1980 s by Doi et al. *. Also, a calculation of phase-space factors is reported in the book of Boehm and Vogel. These calculations use an approximate expression for the electron wave functions at the nucleus. PSF have been recently recalculated ** with exact Dirac electron wave functions and including screening by the electron cloud. These new PSF are available from jenni.kotila@yale.edu and are on the webpage nucleartheory.yale.edu * M. Doi, T. Kotani, N. Nishiura, K. Okuda and E. Takasugi, Prog. Theor. Phys. 66 (1981) F. Bohm and P. Vogel, Physics of massive neutrinos, Cambridge University Press, ** J. Kotila and F. Iachello, Phys. Rev. C 85, (2012).

9 SPECIAL CASE: NEUTRINOLESS DOUBLE ELECTRON CAPTURE This process cannot occur except under resonance conditions

10 These conditions are rarely met and require a delicate calculation of both the prefactors and the NME, especially to states that are excited states in the final nucleus. M.V. Krivoruchenko, F. Šimkovic, D. Frekers and A. Faessler, Nucl. Phys. A859, 140 (2011). J. Kotila, J. Barea and F. Iachello, Phys. Rev. C 89, (2014).

11 Expected half-lives R0νECEC for light-neutrino exchange with <m ν >=1eV and g A =1.269 with IBM-2 NME and KI pre-factors PF J. Kotila, J. Barea and F. Iachello, Phys. Rev. C 89, (2014).

12 RENORMALIZATION OF g A Results in the previous slides are obtained with g A = It is well-known from single β-decay/ec and from 2νββ that g A is renormalized in models of nuclei. Two reasons: (i) Limited model space (ii) Omission of non-nucleonic degrees of freedom (Δ, N *, ) For each model (ISM/QRPA/IBM-2) one can define an effective g A,eff by writing M M 2 eff g Aeff, 2ν = M2 ν g A g = M eff Aeff, β/ EC β/ EC g A The value of g A,eff in each nucleus can then be obtained by comparing the calculated and measured half-lives for β/ec and for 2νββ.

13 Effective axial vector coupling constant in nuclei from 2νββ One obtains g A,eff IBM-2 ~ The extracted values can be parametrized as A similar analysis can be done for the ISM for which g A,eff ISM ~ g IBM Aeff, = 1.269A g, = ISM Aeff J. Barea, J. Kotila and F. Iachello, Phys. Rev. C 87, (2013) A

14 g A,eff, has been extracted also from β/ec in QRPA, recently by Suhonen (QRPA-Jy), g A,eff QRPA ~ , and a few years ago by Faessler et al. (QRPA-Tü) ~ 0.7 *. The axial vector coupling constant, g A, appears to the second power in the NME M = 2 (2 ) 2 gam ν ν M 0ν = g M 2 (0 ν ) A M = M g M + M and hence to the fourth power in the half-life! (0 ν ) (0 ν) V (0 ν) (0 ν) GT F T g A Therefore, the results of the previous slides should be multiplied by 4-16 to have realistic estimates of expected half-lives. [See also, H. Robertson, and S. Dell Oro, S. Marcocci, F. Vissani # (following talk).] J. Suhonen and O. Civitarese, Phys. Lett. B 725, 153 (2013). * A Faessler, G.L. Fogli, E. Lisi, V. Rodin, A.M. Rotunno, and F. Šimkovic, J. Phys. G: Nucl. Part. Phys. 35, (2008). R.G.H. Robertson, Modern Phys. Lett. A 28, (2013). # S. Dell Oro, S. Marcocci, and F. Vissani, Phys. Rev. D90, (2014). 2

15 The question of whether or not g A in 0νββ is renormalized as much as in 2νββ is of much debate. In 2νββ only the 1 + (GT) multipole contributes. In 0νββ all multipoles 1 +, 0 +, 2 -, 1 - contribute. Some of these could be unquenched. However, even in 0νββ, 1 + intermediate states dominate. Hence, our current understanding is that g A is renormalized in 0νββ as much as in 2νββ. This problem is currently being addressed from various sides. Experimentally by measuring the matrix elements to and from the intermediate odd-odd nucleus in 2νββ decay. Theoretically, by using effective field theory (EFT) to estimate the effect of nonnucleonic degrees of freedom (two-body currents). P. Puppe et al., Phys. Rev. C 86, (2012). J. Menendez, D. Gazit, and A. Schwenk, Phys. Rev. Lett. 107, (2011).

16 Another question is whether or not the vector coupling constant, g V, is renormalized in nuclei. Because of CVC, the mechanism (ii) omission of nonnucleonic degrees of freedom cannot contribute. However, the mechanism (i), limited model space, can contribute, and, if so, the ratio g V /g A may remain the same as the non-renormalized ratio 1/ No experimental information is available, but is could be obtained by measuring with ( 3 He,t) and (d, 2 He) reactions the F matrix elements to and from the intermediate odd-odd nucleus. Also some novel experimental information could be obtained by double charge exchange reactions with heavy ions, ( 18 O, 18 Ne) and ( 20 Ne, 20 O), F. Cappuzzello, C. Agodi (following talk).

17 CONCLUSIONS Major progress has been made in the last two years to narrow down predictions of 0νββ decay to realistic values in all nuclei of interest. Current limits on the neutrino mass from 0νβ - β - (light neutrino exchange) with g A =1.269, IBM-2 NME, and KI PSF x H.V. Klapdor- Kleingrothaus et al., Phys. Lett. B586, 198 (2004).

18 With current estimates and g A =1.269: For light neutrino exchange, only the degenerate region can be tested in the immediate future. The current best limit (with g A =1.269) is from EXO, m ν <0.18 ev. Exploration of the inverted region >1 ton Exploration of the normal region >>1 ton For heavy neutrino exchange, the limit is model dependent. In the model of Tello et al., the current best limit from EXO is m νh >14.6 GeV(3.5/M WR ) 4. (For M WR =1TeV, m νh >2.19TeV). V. Tello, M. Nemevšek, F. Nesti, O. Senjanovic, and F. Vissani, Phys. Rev. Lett. 106, (2011).

19 If g A is renormalized to ~ , all estimates should be increased by factors of 4-16, making it impossible to reach in the foreseeable future even the inverted region. Possibilities to escape this negative conclusion are: (1)The neutrino masses are degenerate and large. (Cosmology?) (2) Both processes light and heavy contribute simultaneously, are of the same order, and interfere constructively. m [ T (0 0 )] = G M + M 0νββ + + ν 1/2 0ν 0 ν, light 0 ν, heavy me (3) Other scenarios (Majoron emission, ) and/or new mechanisms (sterile neutrinos, ) must be considered. m m ν p h 2 e p M 3 e p n n

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21 APPENDIX A: REFERENCES PSF 2νβ - β - /0νβ - β - J. Kotila and F. Iachello, Phys. Rev. C 85, (2012). 2νβ + β + /0νβ + β + J. Kotila and F. Iachello, Phys. Rev. C 87, (2013). NME 2νβ - β - /0νβ - β - J. Barea and F. Iachello, Phys. Rev. C 79, (2009). J. Barea, J. Kotila and F. Iachello, Phys. Rev. C 87, (2013). J. Barea, J. Kotila and F. Iachello, in preparation (2014). 2νβ + β + /0νβ + β + J. Barea, J. Kotila and F. Iachello, Phys. Rev. C87, (2013). R0νECEC J. Kotila, J. Barea, and F. Iachello, Phys. Rev. C 89, (2014).

22 APPENDIX B: RECENT IBM-2 RESULTS WITH ERROR FOR 0νββ (2013)

23 APPENDIX C: SUMMARY OF RESULTS β - β - (2013)

24 SUMMARY OF RESULTS β + β + (2013)