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Time-Modulation of Entangled Two-Body Weak Decays with Massive Neutrinos

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## Time-Modulation of Entangled Two-Body Weak Decays with Massive Neutrinos

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**Time-Modulation of Entangled Two-Body Weak Decays with**Massive Neutrinos P. Kienle Excellence Cluster “Universe” Technische Universität München “In order to see something new, one has to do something new.” Georg Christoph Lichtenberg Neutrino Erice 16-24. 09.2009 P. Kienle**Studies of Weak 2-Body EC- and ßb-Decayswith Mono-Energetic**Neutrinos and Anti-Neutrinos Yu.A.Litvinov et al. Phys.Rev. Lett. 99 (2007) 262501 M.Jung et al. Phys. Rev. Lett. 69 (1992)2164 Neutrino Erice 16-24. 09.2009 P. Kienle**Experimental Storage Ring- ESRconstructed 1985-1990 at GSI**Darmstadt, C = 108m, B = 10 Tm, vacuum 10-11mb P. Kienle , Sunshine by CoolingNaturwissenschaften (2001) 88:313-321 Neutrino Erice 16-24. 09.2009 P. Kienle**EC-Modulation Spectra of 140Pr, 142Pm, 122I**T=7.10(22)s a=0.22(3) T=7.06(8)s a=0.18(3) T=6.05(3) s A=0.22(2) Preliminary Preliminary 122I 122I Neutrino Erice 16-24. 09.2009 P. Kienle**Time Spectrum of the ß+ Branch of 142Pm**a() a(ω=0.9 s-1) =0.03(3) Preliminary Preliminary Time following the injection in the ESR t in s Modulation amplitude a() with in s-1 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) Neutrino Erice 16-24. 09.2009 P. Kienle**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**The agreement of REC/ß+ of theory with experiment within 3%**excludesneutrino flavour oscillationas reason for the time modulation of the EC decays, which would be reduced relative to the ß+ branch and it also excludesF1/2->F3/2 excitationsin the ESR with a period of ~7s Neutrino Erice 16-24. 09.2009 P. Kienle**Experimental Facts- Summary**• Decay rate of the two-body EC branch is periodically modulated with λEC(t) = λEC (1 + aEC cos(ωt + Φ) • The period of modulation T = 2π/ω is about 6s (122I) and 7s(140Pr and 142Pm) • The period Tscales with the atomic number Alike T A/20 in s • The amplitude of modulation aEC is about equal for all decays with the value aEC ~ 0.21 • The phase Φof the modulation is ~ -π/2, so λEC(t)~sin(ωt) • The ß+ branch of 142Pm shows no modulation with aEC = 0.03(3) • The EC/ß+ ratios are within 3% as expected theoretically Neutrino Erice 16-24. 09.2009 P. Kienle**Towards Understanding the EC Decay Time Modulation**The 3-bodyß+ decay branch of 142Pm 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**Neutrino Quantum Beat Analogy**2 decay channels in electron neutrinos |e is a superposition of mass eigenstates |m1 and |m2 From energy and momentum conservation in both decay channels |1>, |2> Neutrino Erice 16-24. 09.2009 P. Kienle**Time Differential Observation of the decayCriterion for**Neutrino Quantum Beats Asymptotic observation: 2 Lorentz lines 12= 45 Time differential observation of daughter with time resolution dintroduces an energy uncertainty Edin the observation of |d>. For Ed E2-E1, the two decay paths are indistinguishable interference decay width Neutrino Erice 16-24. 09.2009 P. Kienle**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 Uejtaking 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. Ue1 = cos12, and Ue2 = sin12 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 Neutrino Erice 16-24. 09.2009 P. Kienle**Transition Rates**Neutrino Erice 16-24. 09.2009 P. Kienle**Wave Functions of Daughter Ions in the Time Differential**Observation Neutrino Erice 16-24. 09.2009 P. Kienle**EC Decay Rate**Neutrino Erice 16-24. 09.2009 P. Kienle**Time Modulated EC Decay Rate in Moving Laboratory Frame (**= 1.43) Neutrino Erice 16-24. 09.2009 P. Kienle**Experimental Values of m²**Neutrino Erice 16-24. 09.2009 P. Kienle**KamLAND Antineutrino ResultsPRL 100, 221803 (2008)** EC Difference to EC neutrino m²(KL)=0.759(21)x10-4 eV² m²(EC)=2.9xm²(KamLAND) Small amplitude problem ?!? Neutrino Erice 16-24. 09.2009 P. Kienle**Neutrino Mass from Darmstadt Oscillations**A.N. Ivanov, E.L. Kryshen, M. Pitschmann and P.Kienle arXiv: 0804 1311 (nucl-th) Vacuum polarisation by lepton-W –boson loops in the Coulomb-field 140Ce, Z=58 m2(r) m1(r) Similar mass corrections expected for antineutrinos from fission products but opposite sign (mass increase) Neutrino Erice 16-24. 09.2009 P. Kienle**Origin of Small Modulation Amplitudes?**• The observed modulation amplitudes are a = 0180.03(140Pr); a = 0.220.03(142Pm), a = 0.220.02(122I) and thus equal within errors. • <a>= 0.210.02 which results in a small mixing angle = 6o compared with ~ 34o 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**Cancellation of the Interference Terms in using Orthogonal**Neutrino Flavour Wave Functions (A. Gal, arXiv:0809.1213v2 [nucl-th] In case that the neutrinos are not observed allflavours α= e, μ ,τ contribute to the decay amplitude Interference term cancels due to unitarity of mixing matrix: Neutrino Erice 16-24. 09.2009 P. Kienle**Arbitrary Phases φα Restore InterferenceTerm partially**Transition amplitude summed over flavors α = e,μ,τ with arbitrary phases φα Transition probability with interference term Interference term with time modulation ~ sin(ω21t). θ13 =0; θ23 = π/4 Amplitude of the modulation depends on the mixing angle θ12and the phase differences φμe;φτe Neutrino Erice 16-24. 09.2009 P. Kienle**Possible Flavour Phase Differences?**• The modulation amplitude vanishes for φμe= φτe= φand the special case φ = 0 as expected • For θ12= 34° and aEC = 0.21 one gets for the phase differences the following preliminary values: φμe 1.75 rad and φτe o.73 rad • The origin of these CP violating phases is so far unknown • Charged lepton Coulomb field-final state interaction ? Neutrino Erice 16-24. 09.2009 P. Kienle**Experiments for Solving the Problems**• Measure the decay of He-like 142Pm for testing the influence of the F=3/2 hyperfine state • Measure the ß+ decay of completely ionized 142Pm61+ and determine an accurate limit of the modulation amplitude a. • In case the 142Pm59+ modulation increases we gain precise data on m²andnewdataon13 • MeasureB-field dependence of the modulation period for μ neutrino search (Gal). Preliminary data of 122I taken at 3% different B-field show no change of ,only A-dependence. • Compare EC- and ßb- modulation of 108Ag (,). Both decay channels have a branching ratio of ~ (2-3)% Neutrino Erice 16-24. 09.2009 P. Kienle**We have developed an efficient,**new methodfor the study of neutrino properties by making use of quantum entanglement in two bodyweak decays, thus avoiding the inefficient direct detection of the neutrinos. The recoil ionsshow the neutrino mass difference. Time modulationof EC decays of H- like ions of 140Pr,142Pm and 122I (preliminary) were observed in the ESR storage ring, and no modulationof the ß+ branch of 142Pm (preliminary). Using time dependent perturbation theory with wave functions of massive neutrinos, their properties, such as mass, mixing, and vacuum polarisationare tentatively derived. The time modulationof the recoils reveals the entanglement with massive neutrinos Conclusion Neutrino Erice 16-24. 09.2009 P. Kienle**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. Neutrino Erice 16-24. 09.2009 P. Kienle**Thank you !**Neutrino Erice 16-24. 09.2009 P. Kienle**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**The Phase Problem**• In the analysis the time of the appearance of the daughter, ta is determined, where ta= td + tc with the decay time td and the cooling time tc which depends on the recoil of the daughter ion. • tc is only poorly determined and shows a large variation: tc(Ce)~(0.9 ±0.3)s and tc(Nd)~(1.4±0.4)s. It introduces phase shifts of Φc~(0.8±0.3) and (1.2±0.4) radian. • Observed:Φa(Pr)=(+0.4±0.4) and Φa(Pm)=(-1.6±0.5) radian which give different values for Φd=-Φa-Φc • ΦdPr)=(-1.2±0.5) and Φd(Pm)=(+0.4±0.6) radian with an average of Φd=(-0.8±0.8) radian which is inconsistent and criticized from various sides. • Conclusion: we have to measure td, 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**Neutrino Vacuum Polarisation**• Neutrino vacuum polarisation of EC decay hasopposite value of mass correction as for anti-neutrinos of KamLAND • From precise determinations of m²EC for nuclei with different M and Z one can in principle determine the neutrino masses m1 and m2 • m²EC = (m2 + m2)² - (m1 + m1)² • m² (122I) - m² (140Pr) = 2m2m2 – 2m1m1(1) • m² (122I)+ m² (140Pr)= 2(m²2-m²1)+m2{m2(122)+ m2(140)}+ m1{m1(122)+m1(140)} (2) • Eq. (1) and (2) allows to determine m1 and m2 Neutrino Erice 16-24. 09.2009 P. Kienle**Neutrino Masses from m2(140Pr) and m²(122I)** (1) m1 0.0091 eV/c² m2 0.0174 eV/c² (2) Neutrino Erice 16-24. 09.2009 P. Kienle