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The GSI anomaly

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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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