Time-Modulation of Entangled Two-Body Weak Decays with Massive Neutrinos P. Kienle Excellence Cluster “ Universe ” Technische Universit ä t M ü nchen “In

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


M.Jung et al. Phys. Rev. Lett. 69 (1992)2164Yu.A.Litvinov et al. Phys.Rev. Lett. 99 (2007) 262501

Experimental Storage Ring- ESR constructed 1985-1990 at GSI Darmstadt, C = 108m, B = 10 Tm, vacuum 10-11 mb


P. Kienle , Sunshine by Cooling Naturwissenschaften (2001) 88:313-321


Preliminary122I

122I

Preliminary

T=7.06(8)sa=0.18(3)

T=7.10(22)sa=0.22(3)

T=6.05(3) sA=0.22(2)

EC-Modulation Spectra of 140Pr, 142Pm, 122I


Time Spectrum of the ß+ Branch of 142Pm

Preliminary

Preliminarya(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()

The EC decay of H-like ions is ~ 1.5 x faster than for He like ions


The agreement of REC/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


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 T scales with the atomic number A like T A/20 in s

The amplitude of modulation aEC is about equal for all decays with the value aEC ~ 0.21

The phase Φ of 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


Towards Understanding the EC Decay Time Modulation

The 3-body ß+ 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 Quantum Beat Analogy

From energy and momentum conservation in both decay channels |1>, |2>


2 decay channels in electron neutrinos

|e is a superposition of mass eigenstates |m1 and |m2

Time Differential Observation of the decayCriterion for Neutrino Quantum Beats

12= 45

decay width

Time differential observation of daughter with time resolution d

introduces an energy uncertainty Ed in the observation of |d>. For Ed E2-E1, the two decay paths are indistinguishable interference

Asymptotic observation: 2 Lorentz lines



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 Uej 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. 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


Transition Rates


Wave Functions of Daughter Ions in the Time Differential Observation


EC Decay Rate


Time Modulated EC Decay Rate in Moving Laboratory Frame ( = 1.43)


Experimental Values of m²


KamLAND Antineutrino Results PRL 100, 221803 (2008)

EC Difference to EC neutrino

m²(KL)=0.759(21)x10-4 eV²

m²(EC)=2.9xm²(KamLAND)

Small amplitude problem ?!?


Vacuum polarisation by lepton-W –boson loops in the Coulomb-field

m1(r)

m2(r)

140Ce, Z=58

Neutrino Mass from Darmstadt OscillationsA.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)


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 proposedPartial restoration of the cancellation of the

interference term due to CP violating phase shifts of the neutrino flavour wave functions?


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]


Interference term cancels due to unitarity of mixing matrix:

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 θ12 and the phase differences φμe;φτeNeutrino Erice 16-24. 09.2009 P. Kienle


Possible Flavour Phase Differences?

• The modulation amplitude vanishes for φμe = φτe = φ and 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 ?

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 m² and new data on 13

Measure B-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)%


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 140Pr, 142Pm and 122I (preliminary) were observed in the ESR storage ring, and no modulation of 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 polarisation are tentatively derived. The time modulation of the recoils reveals the entanglement with massive neutrinos

Conclusion



AcknowledgementI 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.

Thank you !


Transition Probability for the Two-Flavour Approximation K. Yazaki (private communication)

This result shows that adding the transition probabilities using orthogonalneutrino flavor wave functions the interference terms cancel


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 Vacuum Polarisation Neutrino vacuum polarisation of EC decay has opposite 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 Masses from m2(140Pr) and m²(122I)

m1 0.0091 eV/c²

m2 0.0174 eV/c²

(1)

(2)Neutrino Erice 16-24. 09.2009 P. Kienle

Documents

Time-Modulation of Entangled Two-Body Weak Decays with Massive Neutrinos P. Kienle Excellence Cluster “ Universe ” Technische Universit ä t M ü nchen “In