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