1. DOUBLE BETA DECAY TO THE EXCITED STATES (EXPERIMENTAL REVIEW) A.S. BARABASH ITEP, MOSCOW

2. OUTLINE  Introduction  2 - (2) -decay to the excited ststates - 100 Mo - 150 Nd  2 - (0) –decay to the excite states  ECEC to the excited states  Conclusion

3. I. Introduction

4. 1.1. Historical introduction E. Fiorini (1977, NEUTRINO’77) – first time obtained limit on 0 + -2 + decay in Ge-76 (as by-product for 0 + - 0 + transition) *): T 1/2 (0)> 3·10 21 y (68% C.L.) *) Of course, from geochemical experiments one can extract limits too.

5. 1982 – first special experimental work to investigate 2- decay to the excited states was done: E. Bellotti et al., Lett. Nuov. Cim. 33 (1982) 273. ( 58 Ni, 76 Ge, 92 Mo, 100 Mo, 148 Nd, 150 Nd; Transitions to 2 + 1, O + 1, 2 + 2, … excited states) Limits on the level (1.2-3.2)·10 21 y for 76 Ge and ~ 10 18 -10 19 y for other nuclei were obtained.

6. 1983-1988  Many new results for 76 Ge (0 + -2 + ). And even “evidence” of the decay on 2.5 level (T 1/2  10 22 y) have been obtained.  3 experiments were done by E. Norman ( 50 Cr, 58 Ni, 64 Zn, 92 Mo, 94 Zr, 96 Zr, 96 Ru, 106 Cd, 116 Cd, 124 Sn; natural samples). Limits on the level ~ 10 17 -10 19 y were obtained.

7. 1989-1990  It was demonstrated that 2(2;0+- 0 + 1 )-decay can be detected in 100 Mo, 96 Zr and 150 Nd by existing low-background HPGe detectors and new experiments were proposed (A.S.B. preprint ITEP, 188-89, 1989; JETP Lett. 51 (1990) 207).  ITEP-USC-PNL-UM experiment with 1 kg of 100 Mo was started on 30 May 1990 (in Soudan mine).

8. Measurement was stopped in September’91  First “positive” result was reported at a few International Conferences (Moriond’91, TAUP’91, WEIN’92,…)  Final result was published in 1995 [PL B 345 (1995) 408]: T 1/2 = 6.1 +1.8 -1.1 ·10 20 y

9. 1999 – 2-nd positive result for 100 Mo; 2001 – 3-d positive result for 100 Mo (in ITEP-TUNL experiment); 2004 – 1-st positive result for 150 Nd; 2007 – 4-th positive result for 100 Mo (in NEMO-3 experiment).

11. ITEP-TUNL experiment

12. 1.2. Present motivation  Nuclear spectroscopy  NME problem  Checking of some “creasy” ideas ( “bosonic” neutrino, …)  0-decay: - very nice signature (2 - ); - high sensitivity (ECEC; resonance conditions).

13. II. 2 - (2)-decay to the excited states Table 1. 2 transition to 2 + 1 excited state. Nucle i E 2, keVT 1/2, y Exper. Theory, 2007[1] Theory, 1996- 1997 [2,3] 48 Ca3288.5>1.8·10 20 1.7·10 24 - 150 Nd3033.6>9.1·10 19 - - 96 Zr2572.2>7.9·10 19 2.3·10 25 (3.8-4.8)·10 21 100 Mo2494.5>1.6·10 21 1.2·10 25 3.4·10 22 [4]

14. Table 1. (Continue) 82 Se2218.5>1.4·10 21 -2.8·10 23 - 3.3·10 26 130 Te1992.7>2.8·10 21 6.9·10 26 (2.8-15)·10 23 136 Xe1649.4 -3.9·10 26 2.0·10 24 116 Cd1511.5>2.3·10 21 >3.4·10 26 1.1·10 24 76 Ge1480>1.1·10 21 >5.8·10 28 1.0·10 26 110 Pd1342 ->1.5·10 25 -

15. Table 2. 2-decay to 0 + 1 excited state Nucle i E 2, keVT 1/2, y Exper. Theory [2] Theory [4] 150 Nd2627.1=1.4·10 20 - 96 Zr2202.5>6.8·10 19 2.7·10 21 3.8·10 21 100 Mo1903.7=6.2·10 20 1.6·10 21 [5]2.1·10 21 82 Se1507.5>3.0·10 21 (1.6-3.3)·10 21 - 48 Ca1274.8>1.5·10 20 - -

16. Table 2. (Continue) 124 Sn1131 - - - 116 Cd1048.2>2.0·10 21 1.1·10 22 1.1·10 21 76 Ge916.7>6.2·10 21 7.5·10 21 - 3.1·10 23 4.5·10 21 136 Xe889 -2.5·10 21 6.3·10 21 130 Te735.7>2.3·10 21 5.1·10 22 – 1.4·10 23 -

17. References [1] A.A. Raduta and C.M. Raduta, Phys. Lett. B 647 (2007) 265. [2] M. Aunola and J. Suhonen, Nucl. Phys. A 602 (1996) 133. [3] J. Toivanen and J. Suhonen, Phys. Rev. C 55 (1997) 2314. [4] S. Stoica and I. Mihut, Nucl. Phys. A 602 (1996) 197. [5] J.G. Hirsch et al., Phys. Rev. C 51 (1995) 2252.

18. Table 3. Present “positive” results on 2  (2 ) decay of 100 Mo to the first 0 + excited state of 100 Ru T 1/2, y; x10 20 NS/BYear, method 6.1 +1.8 -1.1 9.3 +2.8 -1.7 ± 1.4 6.0 +1.9 -1.1 ± 0.6 5.7 +1.3 -0.9 ± 0.8 133 153 19.5 37.5 ~ 1/3 8/1 3/1 1995, HPGe [6] 1999, HPGe (many samples) [7] 2001, 2xHPGe (coincidence) [8,9] 2007, NEMO-3, (2e+2  ) [10] Average value: 6.2 +0.9 -0.7 ·10 20 y

19. References [6] A.S. Barabash et al., Phys. Lett. B 345 (1995) 408. [7] A. S. Barabash et al., Phys. At. Nucl. 62 (1999) 2039. [8] L. De Braeckeleer et al., Phys. Rev. Lett. 86 (2001) 3510. [9] M.J. Hornish et al., Phys. Rev. C 74 (2006) 044314. [10] R. Arnold et al., Nucl. Phys. A 781 (2007) 209.

20. NEMO-3 100 Mo: bb decay to exc. states 2  decay to the 0 1 + state: S/B = 3.0 T 1/2 =[ 5.7 +1.3 -0.9 (stat) ± 0.8(syst)]  10 20 y 0  decay to the 0 1 + state: T 1/2 > 8.9  10 22 y @ 90 % C.L. 2  decay to the 2 1 + state: T 1/2 > 1.1  10 21 y @ 90 % C.L. 0  decay to the 2 1 + state: T 1/2 > 1.6  10 23 y @ 90 % C.L. Nucl. Phys. A 781 (2007) 209 2  decay to the 0 1 + state: S/B = 3.0 T 1/2 =[ 5.7 +1.3 -0.9 (stat) ± 0.8(syst)]  10 20 y 0  decay to the 0 1 + state: T 1/2 > 8.9  10 22 y @ 90 % C.L. 2  decay to the 2 1 + state: T 1/2 > 1.1  10 21 y @ 90 % C.L. 0  decay to the 2 1 + state: T 1/2 > 1.6  10 23 y @ 90 % C.L. Nucl. Phys. A 781 (2007) 209 Clear topology: 0 1 + : 2e - + 2  in time & energy and TOF cuts 2 1 + : 2e - + 1  in time & energy and TOF cuts 100 Mo 0+0+ 2 1 + (540 keV) 0 1 + (1130 keV) 4 1 + (1227 keV) 0 + (g.s.) 100 Ru 2 2 + (1362 keV) 3034 keV 11 22 NEMO-3; 334.3 days of data (Phase I)

21. TOP VIEWSIDE VIEW 11 22 11 22 e1e1 e2e2 e1e1 e2e2 100 Mo (NEMO-3) Reconstructed event-candidate

22. 100 Mo (NEMO-3) The main characteristics of selected events

23. 150 Nd Decay scheme 150 Nd 0+0+ 2 1 + (333.9keV) 0 1 + (740.4 keV) 4 1 + (773.3 keV) 0 + (g.s.) 150 Sm 2 2 + (1046.1 keV) 3367 keV 11 22 E  1 = 333.9 keV E  2 = 406.5 keV

24. SCHEME OF EXPERIMENT E = 1.9 keV (for 1332 keV) T = 11320.5 h Experiment is done in Modane Underground Laboratory, 4800 m w.e.

25. Energy spectrum in the range 333.9 keV

26. Energy spectrum in the range 406.5 keV

27. Analysis of events in the range of peaks under study Peak, keV333.9 ± 1.12406.5 ± 1.12 Number of events 779603 Continuous background 656.6484.5 Isotopes E, keV 214 Bi 227 Th 228 Ac 333.1, 334.78; 334.37; 332.37 214 Bi 211 Pb 405.74 404.85 Contributio n from background 8.8 22.6 5.49.7 8.7 Excess of events 86 ± 28100 ± 25

28. 150 Nd. Transition to the 0 + excited state T 1/2 = [1.4 +0.4 -0.2 (stat) ± 0.3(syst)]·10 20 y [JETP. Lett. 79 (2004) 10]

29. Comparison of NME for transition to the 0 + ground and 0 + 1 excited states (for 100 Mo and 150 Nd)  Conclusion is NME(g.s.)  NME(0 + 1 )  But, in fact, it looks like: NME(g.s.)  (1.2-1.3)xNME(0 + 1 )

30. III. 2(0)-decay to excited states Very nice signature: 2e - and two (one) gamma with fixed energy  Possibility to have “zero” background  Possibility to have high sensitivity (if registration efficiency and energy resolution are high enough)

31. 3.1. 2(0)-decay to 2 + 1 excited state Many years people thought that this decay is sensitive only to right-handed currents. T. Tomoda demonstrated that this is not through: “…relative sensitivity of 0 + -2 + decays to the neutrino mass and the right-handed currents are comparable to those of 0 + -0 + decays.” [T. Tomoda, Phys. Lett. B 474 (2000) 245] The decay is suppressed in ~ two order of magnitude in comparison to transition to 0 + g.s.

32. Table 4. Best present limits on 2  (0 )- decay to 2 + 1 excited state NucleiE 2, keVT 1/2, y (90%CL) 76 Ge1480> 8.2·10 23 (G-M) 100 Mo2494.5> 1.6·10 23 (NEMO-3) 130 Te1992.7> 1.4·10 23 (MiBeta) 116 Cd1511.5> 2.9·10 22 (Solotvino) 136 Xe1649.4> 6.5·10 21 (Milan) 82 Se2218.5> 2.8·10 21 (HPGe)

33. Table 5. Best present limits on 2(0)-decay to the 0 + 1 excited state NucleiE 2 , keVT 1/2, y (90%CL) Theory [11- 14] Theory [15] 150 Nd2627.1>1.0·10 20 - - 96 Zr2202.5>6.8·10 19 2.6·10 24 *) - 100 Mo1903.7>8.9·10 22 2.6·10 26 *) 1.5·10 25 *) 82 Se1507.5>3.0·10 21 9.5·10 26 *) 4.5·10 25 *) 48 Ca1274.8>1.5·10 20 - -

34. Table 5. (Continue) 116 Cd 1048.2>1.4·10 22 1.25·10 27 *) - 76 Ge 916.7>1.3·10 22 5.6·10 26 *) 2.4·10 26 *) 130 Te 735.3>3.1·10 22 7.5·10 25 - *) For = 1 eV [11] J. Suhonen, Phys. Lett. B 477 (2000) 99. [12] J. Suhonen, Phys. Rev. C 62 (2001) 042501. [13] J. Suhonen, Nucl. Phys. A 700 (2002) 649. [14] J. Suhonen and M. Aunola, Nucl. Phys. A 723 (2003) 271. [15] F. Simkovic et al., Phys. Rev. C 64 (2001) 035501.

35. 2(0)-decay to 0 + 1 excited state  Future possibilities: - MAJORANA and GERDA with 76 Ge  ~ 10 27 y; - CUORE with 130 Te  ~ 10 26 y; - SuperNEMO with 82 Se (or 150 Nd)  ~ 10 24 -10 25 y;

36. IV. ECEC to the excited states  1994 (A.S.B. JETP Lett. 59 (1994) 677). Main assumption: NME(2 ; 0 + g.s. )  NME(2 ; 0 + 1 ): then T 1/2 (0 + 1 ) ~ 10 21 -10 22 y for 96 Ru, 106 Cd, 124 Xe, 136 Ce; ~ 10 23 y for 78 Kr and 130 Ba Very nice signature: in addition to two X-rays we have here two gamma with strictly fixed energy (E ~ 300-1300 keV)  New experiments were proposed

37. Table 6. Best present limits on ECEC(2) to the 0 + 1 excited state NucleiE ECEC, keVT 1/2, y (90%CL) Theory 130 Ba1236>1.5·10 21 *) ~ 10 22 -10 24 106 Cd1580>7.3·10 19 ~ 10 21 -10 23 78 Kr1343>1.2·10 21 **) ~ 10 23 -10 27 92 Mo230>8.1·10 20 ~ 10 29 96 Ru1519>4.5·10 16 ~ 10 23 -10 27 *) Extracted from geochemical experiment **) Extracted from result for 0 + -0 + g.s. transition

38. IV.2. ECEC(0); resonance conditions Transition to the ground state. For the best candidates ( = 1 eV):  +  + (0) ~ 10 28 -10 30 y  + EC(0) ~ 10 26 -10 27 y ECEC(0) ~ 10 28 -10 31 y (One can compare these values with ~ 10 24 -10 25 y for 2 - -decay)

39. ECEC(0) to the ground state  2e b + (A,Z)  (A,Z-2) + 2X +  brem + 2 + e + e - + e - int E ,.. = M -  e1 - e2 Suppression factor is ~ 10 4 (in comparison with EC + (0)) – M. Doi and T. Kotani, Prog. Theor. Phys. 89 (1993)139.

40. Resonance conditions  In 1955 (R.Winter, Phys. Rev. 100 (1955) 142) it was mentioned that if there is excited level with “right” energy then decay rate can be very high. (Q’-E has to be close to zero. Q’-energy of decay, E- energy of excited state)  In 1982 the same idea for transition to ground and excited states was discussed (M. Voloshin, G. Mizelmacher, R. Eramzhan, JETP Lett. 35 (1982)).  In 1983 (J. Bernabeu, A. De Rujula, C. Jarlskog, Nucl. Phys. B 223 (1983) 15) this idea was discussed for 112 Sn (transition to 0 + excited state). It was shown that enhancement factor can be on the level ~ 10 6 !

41. J. Bernabeu, A. De Rujula, C. Jarlskog, Nucl. Phys. B 223 (1983) 15 112 Sn  112 Cd [0 + (1871)] M = 1919.5±4.8 keV Q’(KK;0 + ) = M – E*(0 + ) – 2E K = = (-4.9 ± 4.8) keV T 1/2  3·10 24 y (for m = 1 eV) (if Q’ ~ 10 eV)

42. Resonance conditions  In 2004 the same conclusion was done by Z. Sujkowski and S. Wycech (Phys. Rev. C 70 (2004) 052501).  Resonance condition (using EC(2) arguments): E brems = Q’ res = E(1S,Z-2)-E(2P,Z-2) (i.e. when the photon energy becomes comparable to the 2P-1S level difference in the final atom) Q’-Q’res < 1 keV

43. Decay-scheme of 74 Se Here Q = M = 1209.7 keV Q’ = M - 2E b Q’(E*) = Q’ – 1204.2

44. 74 Se. (Nucl. Phys. A 785 (2007) 371)  400 cm 3 HPGe detector (Modane Underground Laboratory; 4800 m w.e.)  563 g of natural Se (4.69 g of 74 Se)  Measurement time is 436.56 h

45. 74 Se

46. 74 Se (Nucl. Phys. 785 (2007) 371.)

47. 74 Se. (Nucl. Phys. A 785 (2007) 371) Transition to 2 + 2 (1204.2 keV) state (595.8 keV and 608.4 keV lines were investigated): T 1/2 (0;L 1 L 2 ) > 0.55·10 19 y

48. 74 Se. Possible improvements  1 kg of 74 Se  ~ 3·10 21 y  200 kg of 74 Se (using an installation such as GERDA or MAJORANA)  ~ 10 26 y

49. Other isotope-candidates NucleiA,% M,keV E*,keVEKEK E L2 74 Se0.891209.7±2.31204.2(2 + )11.11.23 78 Kr0.352846.4±2.02838.9(2 + )12.61.47 96 Ru5.522718.5±8.22700(?)202.86 106 Cd1.252770±7.22741.0(1,2 + )24.33.33 112 Sn0.971919.5±4.81871.0(0 + )26.73.73 130 Ba0.112617.1±2.02608.4(?)34.55.10 136 Ce0.202418.9±132399.9(1 +,2 + 2392.1(1 +,2 + 37.45.62 162 Er0.141843.8±5.61745.7(1 + )53.88.58

50. Table 7. Best present limits on ECEC(0) to the excited state (for isotope-candidates with possible resonance conditions) NucleiE*(J  f )T 1/2, y 106 Cd2741 (1,2 + )> 3·10 19 [16] > 5·10 19 *) [17] 74 Se1204.2(2 + )> 0.55·10 19 [18] 130 Ba2608.4(?)> 1.5·10 21 [19,20] (geochemical) 78 Kr2838.9(2 + )> 1.2·10 21 *) [21] *) Extracted from result for 2(0 + -0 + g.s. ) transition

51. References [16] P. Belli et al., Astr. Phys. 10 (1999) 115. [17] N.I. Rukhadze et al., Phys. At. Nucl. 69 (2006) 2117. [18] A.S. Barabash et al., Nucl. Phys. A 785 (2007) 371. [19] A. P. Meshik et al., Phys. Rev. 64 (2001) 035205. [20] A.S. Barabash and R.R. Saakyan, Phys. At. Nucl. 59 (1996) 179. [21] Ju.M. Gavriljuk et al., Phys. At. Nucl. 69 (2006) 2124.

52. g.s.-g.s. transitions 152 Gd (0.2%), 164 Er (1.56%), 180 W(0.13%) (There are only X-rays in this case)

53. Problems  There is no good theoretical description  Accuracy of M (and Q as a result) is not very good (~ 2-10 keV) [It is possible to improve the accuracy of M to ~ 200 eV]

54. CONCLUSION  2(2)-decay to 0 + excited state was detected for 100 Mo and 150 Nd  There are good prospects to search for 2(2) and 2(0)-decay to 0 + excited states in future (large) experiments  ECEC(0) is a “new-old” possibility to search for neutrino mass (in case of resonance conditions)