1. Time-Modulation of Entangled Two-Body Weak Decays with Massive Neutrinos P. Kienle Excellence Cluster “ Universe ” Technische Universit ä t M ü nchen “In order to see something new, one has to do something new.” Georg Christoph Lichtenberg Neutrino Erice 16-24. 09.2009 P. Kienle

2. Studies of Weak 2-Body EC- and ß b -Decays with Mono-Energetic Neutrinos and Anti-Neutrinos  Neutrino Erice 16-24. 09.2009 P. Kienle M.Jung et al. Phys. Rev. Lett. 69 (1992)2164Yu.A.Litvinov et al. Phys.Rev. Lett. 99 (2007) 262501

3. Experimental Storage Ring- ESR constructed 1985-1990 at GSI Darmstadt, C = 108m, B  = 10 Tm, vacuum 10 -11 mb Neutrino Erice 16-24. 09.2009 P. Kienle P. Kienle, Sunshine by Cooling Naturwissenschaften (2001) 88:313-321

4. Neutrino Erice 16-24. 09.2009 P. Kienle Preliminary 122 I Preliminary T=7.06(8)s a=0.18(3) T=7.10(22)s a=0.22(3) T=6.05(3) s A=0.22(2) EC-Modulation Spectra of 140 Pr, 142 Pm, 122 I

5. Neutrino Erice 16-24. 09.2009 P. Kienle Time Spectrum of the ß+ Branch of 142 Pm Preliminary a(ω=0.9 s -1 ) =0.03(3) The ß+ branch of 142Pm, three times stronger than the EC branch and simultaneously observed with a modulation frequency ω = 0.90 s-1 and an amplitude a = 0.18(5), shows a vanishing small modulation amplitude a = 0.03(3) Time following the injection in the ESR t in s Modulation amplitude a(  ) with  in s -1 a(  )

6. The EC decay of H-like ions is ~ 1.5 x faster than for He like ions Neutrino Erice 16-24. 09.2009 P. Kienle

7. The agreement of R EC/ß+ of theory with experiment within 3% excludes neutrino flavour oscillation as reason for the time modulation of the EC decays, which would be reduced relative to the ß + branch and it also excludes F1/2->F3/2 excitations in the ESR with a period of ~7s Neutrino Erice 16-24. 09.2009 P. Kienle

8. Experimental Facts- Summary Decay rate of the two-body EC branch is periodically modulated with λ EC (t) = λ EC (1 + a EC cos(ωt + Φ) The period of modulation T = 2π/ω is about 6s ( 122 I) and 7s ( 140 Pr and 142 Pm) The period T scales with the atomic number A like T  A/20 in s The amplitude of modulation a EC is about equal for all decays with the value a EC ~ 0.21 The phase Φ of the modulation is ~ -π/2, so λ EC (t)~sin(ωt) The ß + branch of 142 Pm shows no modulation with a EC = 0.03(3) The EC/ß+ ratios are within 3% as expected theoretically Neutrino Erice 16-24. 09.2009 P. Kienle

9. Towards Understanding the EC Decay Time Modulation  The 3-body ß + decay branch of 142 Pm shows no modulation (preliminary) in contrast to the two-body EC branch simultaneously measured  This excludes various experimental sources and beats of the mother state (Giunti, Kienert et al.)  It is direct evidence that the modulation originates from transitions to massive neutrinos eigen-states entangled with the observed daughter nuclei  Recoil effects which scale with 1/A are indicated  Modulations are only expected from a two-body final state ( Ivanov et al, PRL 101, 18250 (2008) Neutrino Erice 16-24. 09.2009 P. Kienle

10. Neutrino Quantum Beat Analogy From energy and momentum conservation in both decay channels | 1 >, | 2 >  Neutrino Erice 16-24. 09.2009 P. Kienle 2 decay channels in electron neutrinos | e  is a superposition of mass eigenstates |m 1  and |m 2 

11. Time Differential Observation of the decay Criterion for Neutrino Quantum Beats   12 = 45   decay width  Time differential observation of daughter with time resolution  d introduces an energy uncertainty  E d in the observation of |d>. For  E d  E 2 -E 1, the two decay paths are indistinguishable  interference Asymptotic observation: 2 Lorentz lines Neutrino Erice 16-24. 09.2009 P. Kienle

12. The transition amplitude of the EC decay m  d + e is given by the sum of the amplitudes A (m  d + j ) (t), with the coefficient U ej taking into account that the electron in the mother ion m couples to electron neutrino e only. Assuming  13 ~ 0 with only two neutrino mass eigen-states. U e1 = cos  12, and U e2 = sin  12 In time dependent perturbation theory the partial amplitude A (m  d + j) (t), is defined in the rest frame of the mother ion m by

13. Neutrino Erice 16-24. 09.2009 P. Kienle

14. Transition Rates Neutrino Erice 16-24. 09.2009 P. Kienle

15. Wave Functions of Daughter Ions in the Time Differential Observation Neutrino Erice 16-24. 09.2009 P. Kienle

16. EC Decay Rate Neutrino Erice 16-24. 09.2009 P. Kienle

17. Time Modulated EC Decay Rate in Moving Laboratory Frame (  = 1.43) Neutrino Erice 16-24. 09.2009 P. Kienle

18. Experimental Values of  m² Neutrino Erice 16-24. 09.2009 P. Kienle

19. KamLAND Antineutrino Results PRL 100, 221803 (2008)  EC Difference to EC neutrino  m²(KL)=0.759(21)x10-4 eV²  m²(EC)=2.9x  m²(KamLAND) Small amplitude problem ?!? Neutrino Erice 16-24. 09.2009 P. Kienle

20. Vacuum polarisation by lepton-W – boson loops in the Coulomb-field  m 1 (r)  m 2 (r) 140 Ce, Z=58 Neutrino Mass from Darmstadt Oscillations A.N. Ivanov, E.L. Kryshen, M. Pitschmann and P.Kienle Similar mass corrections expected for antineutrinos from fission products but opposite sign (mass increase) arXiv: 0804 1311 (nucl-th) Neutrino Erice 16-24. 09.2009 P. Kienle

21. Origin of Small Modulation Amplitudes? The observed modulation amplitudes are a = 018  0.03( 140 Pr); a = 0.22  0.03( 142 Pm), a = 0.22  0.02( 122 I) and thus equal within errors. = 0.21  0.02 which results in a small mixing angle  = 6 o compared with  ~ 34 o from sun neutrinos Reduction of the modulation amplitude? Loss of phase relation by F=3/2->1/2 transition? Measurement of He-like systems proposed Partial restoration of the cancellation of the interference term due to CP violating phase shifts of the neutrino flavour wave functions? Neutrino Erice 16-24. 09.2009 P. Kienle

22. In case that the neutrinos are not observed all flavours α= e, μ,τ contribute to the decay amplitude Cancellation of the Interference Terms in using Orthogonal Neutrino Flavour Wave Functions (A. Gal, arXiv:0809.1213v2 [nucl-th] Neutrino Erice 16-24. 09.2009 P. Kienle Interference term cancels due to unitarity of mixing matrix:

23. Arbitrary Phases φ α Restore InterferenceTerm partially Transition amplitude summed over flavors α = e,μ,τ with arbitrary phases φ α Transition probability with interference term Interference term with time modulation ~ sin(ω 21 t). θ 13 =0; θ 23 = π/4 Amplitude of the modulation depends on the mixing angle θ 12 and the phase differences φ μe; φ τe Neutrino Erice 16-24. 09.2009 P. Kienle

24. Possible Flavour Phase Differences? The modulation amplitude vanishes for φ μe = φ τe = φ and the special case φ = 0 as expected For θ 12 = 34° and a EC = 0.21 one gets for the phase differences the following preliminary values: φ μe  1.75 rad and φ τe  o.73 rad The origin of these CP violating phases is so far unknown Charged lepton Coulomb field-final state interaction ?

25. Experiments for Solving the Problems Measure the decay of He-like 142 Pm for testing the influence of the F=3/2 hyperfine state Measure the ß + decay of completely ionized 142 Pm 61+ and determine an accurate limit of the modulation amplitude a. In case the 142 Pm 59+ modulation increases we gain precise data on  m ² and new data on  13 Measure B-field dependence of the modulation period for μ neutrino search (Gal). Preliminary data of 122 I taken at 3% different B-field show no change of , only A-dependence. Compare EC- and ß b - modulation of 108 Ag (, ). Both decay channels have a branching ratio of ~ (2-3)% Neutrino Erice 16-24. 09.2009 P. Kienle

26. We have developed an efficient, new method for the study of neutrino properties by making use of quantum entanglement in two body weak decays, thus avoiding the inefficient direct detection of the neutrinos. The recoil ions show the neutrino mass difference. Time modulation of EC decays of H- like ions of 140 Pr, 142 Pm and 122 I (preliminary) were observed in the ESR storage ring, and no modulation of the ß + branch of 142 Pm (preliminary). Using time dependent perturbation theory with wave functions of massive neutrinos, their properties, such as mass, mixing, and vacuum polarisation are tentatively derived. The time modulation of the recoils reveals the entanglement with massive neutrinos Conclusion Neutrino Erice 16-24. 09.2009 P. Kienle

27. Acknowledgement I acknowledge numerous contributions of members of the GO collaboration, in particular from Fritz Bosch, Thomas Faestermann, Yuri Litvinov, and Ludwig Maier for making available preliminary data and their analyses. I appreciate especially the very close collaboration in the interpretation of our results with Manfried Faber, Andrei Ivanov, Hagen Kleinert and Ranja Reda. A. Gal and K. Yazaki contributed with critical issues with respect to the neutrino flavor structure. Murray Gell-Mann reassured me concerning the interference of massive neutrinos in time dependent observations of two body decays. R. Hayano and T. Yamazaki introduced us into their  ²(  ) method of analyzing periodically modulated decays. I appreciate the continuing discussion with Harry Lipkin on his original view of the origin of the observed modulations. Discussions with A. Suzuki on the difference with the KamLAND antineutrino oscillation results are gratefully acknowledged.

28. Thank you ! Neutrino Erice 16-24. 09.2009 P. Kienle

29. Transition Probability for the Two-Flavour Approximation K. Yazaki (private communication) This result shows that adding the transition probabilities using orthogonal neutrino flavor wave functions the interference terms cancel Neutrino Erice 16-24. 09.2009 P. Kienle

30. The Phase Problem In the analysis the time of the appearance of the daughter, t a is determined, where t a = t d + t c with the decay time t d and the cooling time t c which depends on the recoil of the daughter ion. t c is only poorly determined and shows a large variation: t c (Ce)~(0.9 ±0.3)s and t c (Nd)~(1.4±0.4)s. It introduces phase shifts of Φ c ~(0.8±0.3) and (1.2±0.4) radian. Observed:Φ a (Pr)=(+0.4±0.4) and Φ a (Pm)=(-1.6±0.5) radian which give different values for Φ d =-Φ a -Φ c Φ d Pr)=(-1.2±0.5) and Φ d (Pm)=(+0.4±0.6) radian with an average of Φ d =(-0.8±0.8) radian which is inconsistent and criticized from various sides. Conclusion: we have to measure t d, by observation of the disappearance of the mother ion when we want to determine a meaningful value for the decay phase. Neutrino Erice 16-24. 09.2009 P. Kienle

31. Neutrino Vacuum Polarisation  Neutrino vacuum polarisation of EC decay has opposite value of mass correction as for anti- neutrinos of KamLAND  From precise determinations of  m² EC for nuclei with different M and Z one can in principle determine the neutrino masses m 1 and m 2   m² EC = (m 2 +  m 2 )² - (m 1 +  m 1 )²   m² ( 122 I) -  m² ( 140 Pr) = 2m 2  m 2 – 2m 1  m 1 (1)   m² ( 122 I)+  m² ( 140 Pr)= 2(m² 2 -m² 1 )+m 2 {  m 2 (122)+  m 2 (140)}+ m 1 {  m 1 (122)+  m 1 (140)} (2)  Eq. (1) and (2) allows to determine m 1 and m 2 Neutrino Erice 16-24. 09.2009 P. Kienle

32. Neutrino Masses from  m 2 ( 140 Pr) and  m ² ( 122 I)     m 1  0.0091 eV/c² m 2  0.0174 eV/c² (1) (2) Neutrino Erice 16-24. 09.2009 P. Kienle