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The GSI anomaly Alexander Merle Max-Planck-Institute for Nuclear Physics Heidelberg Based on: H. Kienert, J. Kopp, M. Lindner, AM The GSI anomaly 0808.2389 [hep-ph] Neutrino 2008 Conf. Proc. Trento, 18.11.2008 Contents: 1. The Observation at GSI 2. The Experiment 3. Problems & Errors 4. Our more formal Treatment 5. One question 6. Conclusions 1. The Observation at GSI: Periodic modula- tion of the expect- ed exponential law in EC-decays of different highly charged ions (Pm-142 & Pr- 140) Litvinov et al: Phys. Lett. B664, 162 (2008) 1. The Observation at GSI: Periodic modula- tion of the expect- exponential law ed exponential law in EC-decays of different highly charged ions (Pm-142 & Pr- 140) Litvinov et al: Phys. Lett. B664, 162 (2008) 1. The Observation at GSI: Periodic modula- periodic modulation tion of the expect- exponential law ed exponential law in EC-decays of different highly charged ions (Pm-142 & Pr- 140) Litvinov et al: Phys. Lett. B664, 162 (2008) 1. The Observation at GSI: Periodic modula- tion of the expect- ed exponential law in EC-decays of different highly charged ions (Pm-142 & Pr- 140) Litvinov et al: Phys. Lett. B664, 162 (2008) 2. The Experiment: 2. The Experiment: See previous talk by Yuri Litvinov! 2. The Experiment: See previous talk by Yuri Litvinov! → I will only give a short summary. 2. The Experiment: 2. The Experiment: Injection of a single type of ions 2. The Experiment: Injection of a single type of ions ⇓ Storage in the Experimental Storage Ring (ESR) 2. The Experiment: Injection of a single type of ions ⇓ Storage in the Experimental Storage Ring (ESR) ⇓ Cooling (stochastic & electron) 2. The Experiment: Injection of a single type of ions ⇓ Storage in the Experimental Storage Ring (ESR) ⇓ Cooling (stochastic & electron) ⇓ Frenquency measurement (by Schottky-Pickups) 2. The Experiment: Injection of a single type of ions ⇓ Storage in the Experimental Storage Ring (ESR) ⇓ Cooling (stochastic & electron) ⇓ Frenquency measurement (by Schottky-Pickups) → due to cooling (Δv/v → 0), the fre- quency only depends on the mass over charge ratio M/Q Lifetime determination: Lifetime determination: Lifetime determination: Lifetime determination: • the lifetimes of individual ions are determined Lifetime determination: • the lifetimes of individual ions are determined • their distribution is plotted Lifetime determination: • the lifetimes of individual ions are determined • their distribution is plotted • the result is NOT only an exponential law… 3. Problems & Errors: 3. Problems & Errors: Experimental problems & oddities: 3. Problems & Errors: Experimental problems & oddities: • low statistics: 3. Problems & Errors: Experimental problems & oddities: • low statistics: only 2650 decays of Pr and 2740 of Pm → both fits, with the modified and pure exponential curve, are not so different (e.g. for Pm: χ2/D.O.F.=0.91 vs. 1.68) 3. Problems & Errors: Experimental problems & oddities: • low statistics: only 2650 decays of Pr and 2740 of Pm → both fits, with the modified and pure exponential curve, are not so different (e.g. for Pm: χ2/D.O.F.=0.91 vs. 1.68) • unexplained statistical features (pointed out by us): 3. Problems & Errors: Experimental problems & oddities: • low statistics: only 2650 decays of Pr and 2740 of Pm → both fits, with the modified and pure exponential curve, are not so different (e.g. for Pm: χ2/D.O.F.=0.91 vs. 1.68) • unexplained statistical features (pointed out by us): If we take the data and subtract the best-fit function, the res- ulting errors are significantly SMALLER than the statistical error √N for N events. 3. Problems & Errors: Experimental problems & oddities: • low statistics: only 2650 decays of Pr and 2740 of Pm → both fits, with the modified and pure exponential curve, are not so different (e.g. for Pm: χ2/D.O.F.=0.91 vs. 1.68) • unexplained statistical features (pointed out by us): If we take the data and subtract the best-fit function, the res- ulting errors are significantly SMALLER than the statistical error √N for N events. → “Mann-Whitney-Test”: The probability that the remaining fluctuations are random is about 5% (a truly random list would give about 30% or so). 3. Problems & Errors: Experimental problems & oddities: • low statistics: only 2650 decays of Pr and 2740 of Pm → both fits, with the modified and pure exponential curve, are not so different (e.g. for Pm: χ2/D.O.F.=0.91 vs. 1.68) • unexplained statistical features (pointed out by us): If we take the data and subtract the best-fit function, the res- ulting errors are significantly SMALLER than the statistical error √N for N events. → “Mann-Whitney-Test”: The probability that the remaining fluctuations are random is about 5% (a truly random list would give about 30% or so). → the fit function seems to confuse some fluctuations with real data 3. Problems & Errors: 3. Problems & Errors: Physical errors: 3. Problems & Errors: Physical errors: • The process is NOT analogous to neutrino oscillations! 3. Problems & Errors: Physical errors: • The process is NOT analogous to neutrino oscillations! -neutrino oscillations: 3. Problems & Errors: Physical errors: • The process is NOT analogous to neutrino oscillations! -neutrino oscillations: 3. Problems & Errors: Physical errors: • The process is NOT analogous to neutrino oscillations! -neutrino oscillations: the neutrino is produced as FLAVOUR eigenstate (e.g. ve), then propagates as superposition of MASS eigenstates (vi with i=1,2,3, and admixtures Uei), and is then detected as FLAVOUR eigenstate 3. Problems & Errors: Physical errors: • The process is NOT analogous to neutrino oscillations! -neutrino oscillations: the neutrino is produced as FLAVOUR eigenstate (e.g. ve), then propagates as superposition of MASS eigenstates (vi with i=1,2,3, and admixtures Uei), and is then detected as FLAVOUR eigenstate → more than one way to reach THE SAME final state ve 3. Problems & Errors: Physical errors: • The process is NOT analogous to neutrino oscillations! -neutrino oscillations: the neutrino is produced as FLAVOUR eigenstate (e.g. ve), then propagates as superposition of MASS eigenstates (vi with i=1,2,3, and admixtures Uei), and is then detected as FLAVOUR eigenstate → more than one way to reach THE SAME final state ve → amplitude is given by a COHERENT SUM: 3. Problems & Errors: Physical errors: • The process is NOT analogous to neutrino oscillations! -neutrino oscillations: the neutrino is produced as FLAVOUR eigenstate (e.g. ve), then propagates as superposition of MASS eigenstates (vi with i=1,2,3, and admixtures Uei), and is then detected as FLAVOUR eigenstate → more than one way to reach THE SAME final state ve → amplitude is given by a COHERENT SUM: 3. Problems & Errors: Physical errors: • The process is NOT analogous to neutrino oscillations! -GSI experiment: 3. Problems & Errors: Physical errors: • The process is NOT analogous to neutrino oscillations! -GSI experiment: 3. Problems & Errors: Physical errors: • The process is NOT analogous to neutrino oscillations! -GSI experiment: the neutrino is produced as FLAVOUR eigenstate (e.g. ve) and then propagates as superposition of MASS eigenstates (vi with i=1,2,3, and admixtures Uei) 3. Problems & Errors: Physical errors: • The process is NOT analogous to neutrino oscillations! -GSI experiment: the neutrino is produced as FLAVOUR eigenstate (e.g. ve) and then propagates as superposition of MASS eigenstates (vi with i=1,2,3, and admixtures Uei) → BUT: there is no second FLAVOUR measurement 3. Problems & Errors: Physical errors: • The process is NOT analogous to neutrino oscillations! -GSI experiment: the neutrino is produced as FLAVOUR eigenstate (e.g. ve) and then propagates as superposition of MASS eigenstates (vi with i=1,2,3, and admixtures Uei) → BUT: there is no second FLAVOUR measurement → amplitude is given by an INCOHERENT SUM: 3. Problems & Errors: Physical errors: • The process is NOT analogous to neutrino oscillations! -GSI experiment: the neutrino is produced as FLAVOUR eigenstate (e.g. ve) and then propagates as superposition of MASS eigenstates (vi with i=1,2,3, and admixtures Uei) → BUT: there is no second FLAVOUR measurement → amplitude is given by an INCOHERENT SUM: 3. Problems & Errors: Physical errors: • This has been done differently in: 3. Problems & Errors: Physical errors: • This has been done differently in: - Ivanov, Reda, Kienle: 0801.2121 [nucl-th] - Ivanov, Kryshen, Pitschmann, Kienle: 0804.1311 [nucl-th] - Ivanov, Kryshen, Pitschmann, Kienle: Phys. Rev. Lett. 101, 182501 (2008) - Faber: 0801.3262 [nucl-th] - Lipkin: 0801.1465 [hep-ph] - Lipkin: 0805.0435 [hep-ph] - Walker: Nature 453, 864 (2008) 3. Problems & Errors: Physical errors: • This has been done differently in: - Ivanov, Reda, Kienle: 0801.2121 [nucl-th] - Ivanov, Kryshen, Pitschmann, Kienle: 0804.1311 [nucl-th] - Ivanov, Kryshen, Pitschmann, Kienle: Phys. Rev. Lett. 101, 182501 (2008) - Faber: 0801.3262 [nucl-th] - Lipkin: 0801.1465 [hep-ph] - Lipkin: 0805.0435 [hep-ph] - Walker: Nature 453, 864 (2008) • Works that agree with us: 3. Problems & Errors: Physical errors: • This has been done differently in: - Ivanov, Reda, Kienle: 0801.2121 [nucl-th] - Ivanov, Kryshen, Pitschmann, Kienle: 0804.1311 [nucl-th] - Ivanov, Kryshen, Pitschmann, Kienle: Phys. Rev. Lett. 101, 182501 (2008) - Faber: 0801.3262 [nucl-th] - Lipkin: 0801.1465 [hep-ph] - Lipkin: 0805.0435 [hep-ph] - Walker: Nature 453, 864 (2008) • Works that agree with us: - Giunti: 0801.4639 [hep-ph] - Giunti: Phys. Lett. B665, 92 (2008) - Burkhardt et al.: 0804.1099 [hep-ph] - Peshkin: 0804.4891 [hep-ph] - Peshkin: 0811.1765 [hep-ph] - Gal: 0809.1213 [nucl-th] - Cohen, Glashow, Ligeti: 0810.4602 [hep-ph] 3. Problems & Errors: Further points: 3. Problems & Errors: Further points: • wrong Δm2~10-4 eV2 → neither solar nor atmospheric Δm2 3. Problems & Errors: Further points: • wrong Δm2~10-4 eV2 → neither solar nor atmospheric Δm2 • necessary energy splitting ΔE~10-15 eV → not (yet) explained, coherence over the experiment time doubtful 3. Problems & Errors: Further points: • wrong Δm2~10-4 eV2 → neither solar nor atmospheric Δm2 • necessary energy splitting ΔE~10-15 eV → not (yet) explained, coherence over the experiment time doubtful • other (but different!) experiments have not found the oscila- tory behavior: Vetter et al.: 0807.0649 [nucl-ex] Faestermann et al.: 0807.3297 [nucl-ex] 3. Problems & Errors: Further points: • wrong Δm2~10-4 eV2 → neither solar nor atmospheric Δm2 • necessary energy splitting ΔE~10-15 eV → not (yet) explained, coherence over the experiment time doubtful • other (but different!) experiments have not found the oscila- tory behavior: Vetter et al.: 0807.0649 [nucl-ex] Faestermann et al.: 0807.3297 [nucl-ex] • wrong statement: ve and vμ are called „mass eigenstates“ by Walker, Nature 453, 864 (2008) → OBVIOUSLY WRONG!!! 4. Our more formal treatment: 4. Our more formal treatment: Several works have tried to relate the GSI-oscillations to neutrino mixing. 4. Our more formal treatment: Several works have tried to relate the GSI-oscillations to neutrino mixing. We have shown, that, even when using wave packets, this is not the case and neutrino mixing is not related to any oscilla- tions in the decay rate. 4. Our more formal treatment: Several works have tried to relate the GSI-oscillations to neutrino mixing. We have shown, that, even when using wave packets, this is not the case and neutrino mixing is not related to any oscilla- tions in the decay rate. Our formalism: 4. Our more formal treatment: Several works have tried to relate the GSI-oscillations to neutrino mixing. We have shown, that, even when using wave packets, this is not the case and neutrino mixing is not related to any oscilla- tions in the decay rate. Our formalism: • We describe both, mother (A=M) and daughter (D=M) nuclear state by Gaussian wave packets with central momentum pA0 and spread σA: 4. Our more formal treatment: Several works have tried to relate the GSI-oscillations to neutrino mixing. We have shown, that, even when using wave packets, this is not the case and neutrino mixing is not related to any oscilla- tions in the decay rate. Our formalism: • We describe both, mother (A=M) and daughter (D=M) nuclear state by Gaussian wave packets with central momentum pA0 and spread σA: 4. Our more formal treatment: Several works have tried to relate the GSI-oscillations to neutrino mixing. We have shown, that, even when using wave packets, this is not the case and neutrino mixing is not related to any oscilla- tions in the decay rate. Our formalism: • We describe both, mother (A=M) and daughter (D=M) nuclear state by Gaussian wave packets with central momentum pA0 and spread σA: • The neutrino mass eigenstate νj is described by a plane wave: 4. Our more formal treatment: Several works have tried to relate the GSI-oscillations to neutrino mixing. We have shown, that, even when using wave packets, this is not the case and neutrino mixing is not related to any oscilla- tions in the decay rate. Our formalism: • We describe both, mother (A=M) and daughter (D=M) nuclear state by Gaussian wave packets with central momentum pA0 and spread σA: • The neutrino mass eigenstate νj is described by a plane wave: 4. Our more formal treatment: • There is one initial state: 4. Our more formal treatment: • There is one initial state: 4. Our more formal treatment: • There is one initial state: • There are three distinct final states (the different neutrino mass eigenstates vj are orthogonal vectors in Hilbert space) with j=1,2,3: 4. Our more formal treatment: • There is one initial state: • There are three distinct final states (the different neutrino mass eigenstates vj are orthogonal vectors in Hilbert space) with j=1,2,3: 4. Our more formal treatment: • There is one initial state: • There are three distinct final states (the different neutrino mass eigenstates vj are orthogonal vectors in Hilbert space) with j=1,2,3: • Then, the Feynman rules in coordinate space tell us unambi- guously how to write down the decay amplitude: 4. Our more formal treatment: • There is one initial state: • There are three distinct final states (the different neutrino mass eigenstates vj are orthogonal vectors in Hilbert space) with j=1,2,3: • Then, the Feynman rules in coordinate space tell us unambi- guously how to write down the decay amplitude: 4. Our more formal treatment: • We adopt the following approximations: 4. Our more formal treatment: • We adopt the following approximations: - we expand EM=(pM2+mM2)1/2 to first order in (pM-pM0) → this approximation neglects the wave packet spreading 4. Our more formal treatment: • We adopt the following approximations: - we expand EM=(pM2+mM2)1/2 to first order in (pM-pM0) → this approximation neglects the wave packet spreading - we neglect the energy dependence of the pre-factors for mother and daughter (1/√EA → 1/√E0A) → this is okay, because these factors varies much more slowly than the Gaussian exponentials 4. Our more formal treatment: • We adopt the following approximations: - we expand EM=(pM2+mM2)1/2 to first order in (pM-pM0) → this approximation neglects the wave packet spreading - we neglect the energy dependence of the pre-factors for mother and daughter (1/√EA → 1/√E0A) → this is okay, because these factors varies much more slowly than the Gaussian exponentials - we also neglect the energy dependence of the matrix element (also because of slow variation) 4. Our more formal treatment: • one then has to evaluate Gaussian integrals like the following (with the group velocity v0M=p0M/E0M of the wave packet): 4. Our more formal treatment: • one then has to evaluate Gaussian integrals like the following (with the group velocity v0M=p0M/E0M of the wave packet): 4. Our more formal treatment: • one then has to evaluate Gaussian integrals like the following (with the group velocity v0M=p0M/E0M of the wave packet): • the result is: 4. Our more formal treatment: • one then has to evaluate Gaussian integrals like the following (with the group velocity v0M=p0M/E0M of the wave packet): • the result is: 4. Our more formal treatment: • one then has to evaluate Gaussian integrals like the following (with the group velocity v0M=p0M/E0M of the wave packet): • the result is: • the same can be done for the daughter and one finally gets, after solving the time-integrals, too, an easy solution: 4. Our more formal treatment: • one then has to evaluate Gaussian integrals like the following (with the group velocity v0M=p0M/E0M of the wave packet): • the result is: • the same can be done for the daughter and one finally gets, after solving the time-integrals, too, an easy solution: 4. Our more formal treatment: • here, we have used some abbreviations: 4. Our more formal treatment: • here, we have used some abbreviations: 4. Our more formal treatment: • but let„s go back to the point of the result: 4. Our more formal treatment: • but let„s go back to the point of the result: • and look more closely: 4. Our more formal treatment: • but let„s go back to the point of the result: • and look more closely: 4. Our more formal treatment: • but let„s go back to the point of the result: • and look more closely: 4. Our more formal treatment: • but let„s go back to the point of the result: • and look more closely: dependences on the neutrino mass eigenstates j=1,2,3 4. Our more formal treatment: • but let„s go back to the point of the result: • and look more closely: dependences on the neutrino mass eigenstates j=1,2,3 → will be summed incoherently (because the three mass eigenstates v1, v2, and v3 are distinct!): 4. Our more formal treatment: • but let„s go back to the point of the result: • and look more closely: dependences on the neutrino mass eigenstates j=1,2,3 → will be summed incoherently (because the three mass eigenstates v1, v2, and v3 are distinct!): 4. Our more formal treatment: • of course, the phases cancel out due to the absolute value: 4. Our more formal treatment: • of course, the phases cancel out due to the absolute value: 4. Our more formal treatment: • of course, the phases cancel out due to the absolute value: 4. Our more formal treatment: • of course, the phases cancel out due to the absolute value: This seems to be easy, but has inspite of that caused a lot of confusion in the community… 4. Our more formal treatment: • the only possibility for oscillations: if the initial state is a superposition of several states n of different energies 4. Our more formal treatment: • the only possibility for oscillations: if the initial state is a superposition of several states n of different energies 4. Our more formal treatment: • the only possibility for oscillations: if the initial state is a superposition of several states n of different energies • then, also the phases Φ get a dependence on n: 4. Our more formal treatment: • the only possibility for oscillations: if the initial state is a superposition of several states n of different energies • then, also the phases Φ get a dependence on n: 4. Our more formal treatment: • the only possibility for oscillations: if the initial state is a superposition of several states n of different energies • then, also the phases Φ get a dependence on n: • then, the absolute squares show indeed oscillatory behavior: 4. Our more formal treatment: • the only possibility for oscillations: if the initial state is a superposition of several states n of different energies • then, also the phases Φ get a dependence on n: • then, the absolute squares show indeed oscillatory behavior: 4. Our more formal treatment: • the only possibility for oscillations: if the initial state is a superposition of several states n of different energies • then, also the phases Φ get a dependence on n: • then, the absolute squares show indeed oscillatory behavior: 4. Our more formal treatment: HOWEVER: 4. Our more formal treatment: HOWEVER: • duration of the GSI-oscillations: 4. Our more formal treatment: HOWEVER: • duration of the GSI-oscillations: 4. Our more formal treatment: HOWEVER: • duration of the GSI-oscillations: • this would require an energy splitting of: 4. Our more formal treatment: HOWEVER: • duration of the GSI-oscillations: • this would require an energy splitting of: 4. Our more formal treatment: HOWEVER: • duration of the GSI-oscillations: • this would require an energy splitting of: ⇓ 4. Our more formal treatment: HOWEVER: • duration of the GSI-oscillations: • this would require an energy splitting of: ⇓ → no know mechanism that could produce such a tiny splitting 4. Our more formal treatment: HOWEVER: • duration of the GSI-oscillations: • this would require an energy splitting of: ⇓ → no know mechanism that could produce such a tiny splitting → no reason for production of a superposition of such states 4. Our more formal treatment: FURTHERMORE: 4. Our more formal treatment: FURTHERMORE: • it was objected in 0811.0922 [nucl-th] (Faber et al.) and in the talk by Andrei Ivanov at the EXA08-Meeting, Vienna, Sept- ember 2008 that this level splitting would also lead to slow oscillations in β+-decays 4. Our more formal treatment: FURTHERMORE: • it was objected in 0811.0922 [nucl-th] (Faber et al.) and in the talk by Andrei Ivanov at the EXA08-Meeting, Vienna, Sept- ember 2008 that this level splitting would also lead to slow oscillations in β+-decays • this does not happen in the β+-decays of the same ions as used for the EC-measurements (Faber et al.) 4. Our more formal treatment: FURTHERMORE: • it was objected in 0811.0922 [nucl-th] (Faber et al.) and in the talk by Andrei Ivanov at the EXA08-Meeting, Vienna, Sept- ember 2008 that this level splitting would also lead to slow oscillations in β+-decays • this does not happen in the β+-decays of the same ions as used for the EC-measurements (Faber et al.) • we were not aware of this data when we wrote our paper 4. Our more formal treatment: FURTHERMORE: • it was objected in 0811.0922 [nucl-th] (Faber et al.) and in the talk by Andrei Ivanov at the EXA08-Meeting, Vienna, Sept- ember 2008 that this level splitting would also lead to slow oscillations in β+-decays • this does not happen in the β+-decays of the same ions as used for the EC-measurements (Faber et al.) • we were not aware of this data when we wrote our paper • BUT: we also did not claim to be able to explain the GSI- oscillations 4. Our more formal treatment: FURTHERMORE: • it was objected in 0811.0922 [nucl-th] (Faber et al.) and in the talk by Andrei Ivanov at the EXA08-Meeting, Vienna, Sept- ember 2008 that this level splitting would also lead to slow oscillations in β+-decays • this does not happen in the β+-decays of the same ions as used for the EC-measurements (Faber et al.) • we were not aware of this data when we wrote our paper • BUT: we also did not claim to be able to explain the GSI- oscillations • at the moment, we have no objection against the above argument 5. One question: 5. One question: Let us assume for a moment that the COHERENT summation is correct. 5. One question: Let us assume for a moment that the COHERENT summation is correct. → What about the effective mass in the KATRIN-experiment? 5. One question: Let us assume for a moment that the COHERENT summation is correct. → What about the effective mass in the KATRIN-experiment? ˉ • tritium beta decay: 3H → 3He + e- + ve 5. One question: Let us assume for a moment that the COHERENT summation is correct. → What about the effective mass in the KATRIN-experiment? ˉ • tritium beta decay: 3H → 3He + e- + ve • the energy spectrum of the electron is given by (Farzan & Smirnov, Phys. Lett. B557, 224 (2003)): 5. One question: Let us assume for a moment that the COHERENT summation is correct. → What about the effective mass in the KATRIN-experiment? ˉ • tritium beta decay: 3H → 3He + e- + ve • the energy spectrum of the electron is given by (Farzan & Smirnov, Phys. Lett. B557, 224 (2003)): 5. One question: Let us assume for a moment that the COHERENT summation is correct. → What about the effective mass in the KATRIN-experiment? ˉ • tritium beta decay: 3H → 3He + e- + ve • the energy spectrum of the electron is given by (Farzan & Smirnov, Phys. Lett. B557, 224 (2003)): → this is an INCOHERENT sum over the contributions from the different mass eigenstates (Vissani, Nucl. Phys. Proc. Suppl.100, 273 (2001)): 5. One question: Let us assume for a moment that the COHERENT summation is correct. → What about the effective mass in the KATRIN-experiment? ˉ • tritium beta decay: 3H → 3He + e- + ve • the energy spectrum of the electron is given by (Farzan & Smirnov, Phys. Lett. B557, 224 (2003)): → this is an INCOHERENT sum over the contributions from the different mass eigenstates (Vissani, Nucl. Phys. Proc. Suppl.100, 273 (2001)): 5. One question: • for (E0-E)>>mj, this can be parametrized by a single para- meter, the „effective mass“ of the electron-neutrino, which is: 5. One question: • for (E0-E)>>mj, this can be parametrized by a single para- meter, the „effective mass“ of the electron-neutrino, which is: → this is the expression mostly used 5. One question: • for (E0-E)>>mj, this can be parametrized by a single para- meter, the „effective mass“ of the electron-neutrino, which is: → this is the expression mostly used • my questions: 5. One question: • for (E0-E)>>mj, this can be parametrized by a single para- meter, the „effective mass“ of the electron-neutrino, which is: → this is the expression mostly used • my questions: Should the definition of the „effective electron neutrino mass“ then be modified??? 5. One question: • for (E0-E)>>mj, this can be parametrized by a single para- meter, the „effective mass“ of the electron-neutrino, which is: → this is the expression mostly used • my questions: Should the definition of the „effective electron neutrino mass“ then be modified??? Would the planned KATRIN-analysis be in- correct??? 5. One question: • for (E0-E)>>mj, this can be parametrized by a single para- meter, the „effective mass“ of the electron-neutrino, which is: → this is the expression mostly used • my questions: Should the definition of the „effective electron neutrino mass“ then be modified??? Would the planned KATRIN-analysis be in- correct??? What about MAINZ & TROITSK??? 5. One question: I don‘t think so!!! 6. Conclusions: 6. Conclusions: • the oscillations at GSI are NOT YET EXPLAINED 6. Conclusions: • the oscillations at GSI are NOT YET EXPLAINED • they are definitely NOT related to neutrino mixing 6. Conclusions: • the oscillations at GSI are NOT YET EXPLAINED • they are definitely NOT related to neutrino mixing • of course, people (including us) had a careful look at all sorts of systematics 6. Conclusions: • the oscillations at GSI are NOT YET EXPLAINED • they are definitely NOT related to neutrino mixing • of course, people (including us) had a careful look at all sorts of systematics • HOWEVER: there are some unexplained strange statistical properties of the data 6. Conclusions: • the oscillations at GSI are NOT YET EXPLAINED • they are definitely NOT related to neutrino mixing • of course, people (including us) had a careful look at all sorts of systematics • HOWEVER: there are some unexplained strange statistical properties of the data • that all has caused some confusion in the community 6. Conclusions: • the oscillations at GSI are NOT YET EXPLAINED • they are definitely NOT related to neutrino mixing • of course, people (including us) had a careful look at all sorts of systematics • HOWEVER: there are some unexplained strange statistical properties of the data • that all has caused some confusion in the community • the new run using I-122 will hopefully clarify some issues THANKS TO MY COLLABORATORS!!!! THANKS TO MY COLLABORATORS!!!! … AND, OF COURSE, TO YOU ALL FOR YOUR ATTENTION! References: "The GSI-Anomaly": Talk by Manfred Lindner, Neutrino 2008 Conference, Christchurch/New Zealand, 30th May 2008 & Proceedings "Observation of Non-Exponential Orbital Electron Capture Decays of Hydrogen-Like $^{140}$Pr and $^{142}$Pm Ions": Yu.A. Litvinov et al.; Phys.Lett.B664:162-168,2008; e-Print: arXiv:0801.2079 [nucl-ex] "Observation of non-exponential two-body beta decays of highly-charged, stored ions": Talks by Fritz Bosch & Yuri Litvinov, Transregio 27 "Neutrinos and Beyond"-Meeting, Heidelberg, 30th January 2008; Milos, 21st May 2008

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