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Transcript of The GSI anomaly Alexander Merle Max-Planck-Institute for Nuclear Physics Heidelberg Based on: H....
The GSI anomalyAlexander Merle
Max-Planck-Institute for Nuclear PhysicsHeidelberg
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 GSI2. The Experiment3. Problems & Errors4. Our more formal Treatment5. One question6. 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-ed exponential law in EC-decays of different highly charged ions (Pm-142 & Pr-140)
exponential law
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)
exponential law
periodic modulation
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+mM
2)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+mM
2)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+mM
2)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?
• tritium beta decay: 3H → 3He + e- + ve ˉ
5. One question:Let us assume for a moment that the COHERENT summation is correct.
→ What about the effective mass in the KATRIN-experiment?
• tritium beta decay: 3H → 3He + e- + ve
• the energy spectrum of the electron is given by (Farzan & Smirnov, Phys. Lett. B557, 224 (2003)):
ˉ
5. One question:Let us assume for a moment that the COHERENT summation is correct.
→ What about the effective mass in the KATRIN-experiment?
• tritium beta decay: 3H → 3He + e- + ve
• the energy spectrum of the electron is given by (Farzan & Smirnov, Phys. Lett. B557, 224 (2003)):
ˉ
5. One question:Let us assume for a moment that the COHERENT summation is correct.
→ What about the effective mass in the KATRIN-experiment?
• 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)):
ˉ
5. One question:Let us assume for a moment that the COHERENT summation is correct.
→ What about the effective mass in the KATRIN-experiment?
• 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)):
ˉ
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