The GSI anomaly

1
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

2
Contents

1. The Observation at GSI
2. The Experiment
3. Problems Errors
4. Our more formal Treatment
5. One question
6. Conclusions

3
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)
4
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)
5
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)
periodic modulation
exponential law
Litvinov et al Phys. Lett. B664, 162 (2008)
6
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)
7
2. The Experiment
8
2. The Experiment
See previous talk by Yuri Litvinov!
9
2. The Experiment
See previous talk by Yuri Litvinov! ? I will only
give a short summary.
10
2. The Experiment
11
2. The Experiment
Injection of a single type of ions

12
2. The Experiment
Injection of a single type of ions
? Storage in the Experimental Storage Ring
(ESR)
13
2. The Experiment
Injection of a single type of ions
? Storage in the Experimental Storage Ring
(ESR) ? Cooling (stochastic
electron)
14
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)
15
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 (?v/v ? 0), the fre-quency only depends
on the mass over charge ratio M/Q
16
Lifetime determination
17
Lifetime determination
18
Lifetime determination
19
Lifetime determination

• the lifetimes of individual ions are determined

20
Lifetime determination

• the lifetimes of individual ions are determined
• their distribution is plotted

21
Lifetime determination

• the lifetimes of individual ions are determined
• their distribution is plotted
• the result is NOT only an exponential law

22
3. Problems Errors
23
3. Problems Errors
Experimental problems oddities
24
3. Problems Errors

• Experimental problems oddities
• low statistics

25
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 ?2/D.O.F.0.91 vs. 1.68)

26
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 ?2/D.O.F.0.91 vs. 1.68)
• unexplained statistical features (pointed out by
  us)

27
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 ?2/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 vN for N
  events.
  

28
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 ?2/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 vN 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).
  

29
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 ?2/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 vN 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

30
3. Problems Errors
31
3. Problems Errors
Physical errors
32
3. Problems Errors

• Physical errors
• The process is NOT analogous to neutrino
  oscillations!

33
3. Problems Errors

• Physical errors
• The process is NOT analogous to neutrino
  oscillations!
• neutrino oscillations

34
3. Problems Errors

• Physical errors
• The process is NOT analogous to neutrino
  oscillations!
• neutrino oscillations

35
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 i1,2,3, and admixtures
  Uei), and is then detected as FLAVOUR eigenstate

36
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 i1,2,3, and admixtures
  Uei), and is then detected as FLAVOUR eigenstate
  ? more than one way to reach THE SAME final state
  ve

37
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 i1,2,3, 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

38
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 i1,2,3, 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

39
3. Problems Errors

• Physical errors
• The process is NOT analogous to neutrino
  oscillations!
• GSI experiment

40
3. Problems Errors

• Physical errors
• The process is NOT analogous to neutrino
  oscillations!
• GSI experiment

41
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 i1,2,3, and admixtures
  Uei)
  

42
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 i1,2,3, and admixtures
  Uei)
  ? BUT there is no second FLAVOUR
  measurement

43
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 i1,2,3, and admixtures
  Uei)
  ? BUT there is no second FLAVOUR
  measurement ? amplitude is given by
  an INCOHERENT SUM

44
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 i1,2,3, and admixtures
  Uei)
  ? BUT there is no second FLAVOUR
  measurement ? amplitude is given by
  an INCOHERENT SUM

45
3. Problems Errors

• Physical errors
• This has been done differently in
  

46
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)

47
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
  

48
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
  

49
3. Problems Errors
Further points
50
3. Problems Errors

• Further points
• wrong ?m210-4 eV2 ? neither solar nor
  atmospheric ?m2

51
3. Problems Errors

• Further points
• wrong ?m210-4 eV2 ? neither solar nor
  atmospheric ?m2
• necessary energy splitting ?E10-15 eV ? not
  (yet) explained, coherence over the experiment
  time doubtful

52
3. Problems Errors

• Further points
• wrong ?m210-4 eV2 ? neither solar nor
  atmospheric ?m2
• necessary energy splitting ?E10-15 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

53
3. Problems Errors

• Further points
• wrong ?m210-4 eV2 ? neither solar nor
  atmospheric ?m2
• necessary energy splitting ?E10-15 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!!!

54
4. Our more formal treatment
55
4. Our more formal treatment
Several works have tried to relate the
GSI-oscillations to neutrino mixing.
56
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.
57
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
58
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 (AM) and daughter
  (DM) nuclear state by Gaussian wave packets with
  central momentum pA0 and spread sA

59
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 (AM) and daughter
  (DM) nuclear state by Gaussian wave packets with
  central momentum pA0 and spread sA

60
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 (AM) and daughter
  (DM) nuclear state by Gaussian wave packets with
  central momentum pA0 and spread sA
• The neutrino mass eigenstate ?j is described by
  a plane wave

61
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 (AM) and daughter
  (DM) nuclear state by Gaussian wave packets with
  central momentum pA0 and spread sA
• The neutrino mass eigenstate ?j is described by
  a plane wave

62
4. Our more formal treatment

• There is one initial state

63
4. Our more formal treatment

• There is one initial state

64
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
  j1,2,3

65
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
  j1,2,3

66
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
  j1,2,3
• Then, the Feynman rules in coordinate space tell
  us unambi-guously how to write down the decay
  amplitude

67
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
  j1,2,3
• Then, the Feynman rules in coordinate space tell
  us unambi-guously how to write down the decay
  amplitude

68
4. Our more formal treatment

• We adopt the following approximations

69
4. Our more formal treatment

• We adopt the following approximations
• we expand EM(pM2mM2)1/2 to first order in
  (pM-pM0) ? this approximation
  neglects the wave packet spreading
  
  

70
4. Our more formal treatment

• We adopt the following approximations
• we expand EM(pM2mM2)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/vEA ? 1/vE0A)
  ? this is okay, because
  these factors varies much more slowly than the
  Gaussian exponentials
  

71
4. Our more formal treatment

• We adopt the following approximations
• we expand EM(pM2mM2)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/vEA ? 1/vE0A)
  ? 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)

72
4. Our more formal treatment

• one then has to evaluate Gaussian integrals like
  the following (with the group velocity
  v0Mp0M/E0M of the wave packet)

73
4. Our more formal treatment

• one then has to evaluate Gaussian integrals like
  the following (with the group velocity
  v0Mp0M/E0M of the wave packet)

74
4. Our more formal treatment

• one then has to evaluate Gaussian integrals like
  the following (with the group velocity
  v0Mp0M/E0M of the wave packet)
• the result is

75
4. Our more formal treatment

• one then has to evaluate Gaussian integrals like
  the following (with the group velocity
  v0Mp0M/E0M of the wave packet)
• the result is

76
4. Our more formal treatment

• one then has to evaluate Gaussian integrals like
  the following (with the group velocity
  v0Mp0M/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

77
4. Our more formal treatment

• one then has to evaluate Gaussian integrals like
  the following (with the group velocity
  v0Mp0M/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

78
4. Our more formal treatment

• here, we have used some abbreviations

79
4. Our more formal treatment

• here, we have used some abbreviations

80
4. Our more formal treatment

• but lets go back to the point of the result

81
4. Our more formal treatment

• but lets go back to the point of the result
• and look more closely

82
4. Our more formal treatment

• but lets go back to the point of the result
• and look more closely

83
4. Our more formal treatment

• but lets go back to the point of the result
• and look more closely

84
4. Our more formal treatment

• but lets go back to the point of the result
• and look more closely

dependences on the neutrino mass eigenstates
j1,2,3
85
4. Our more formal treatment

• but lets go back to the point of the result
• and look more closely

dependences on the neutrino mass eigenstates
j1,2,3 ? will be summed incoherently (because
the three mass eigenstates v1, v2, and v3 are
distinct!)
86
4. Our more formal treatment

• but lets go back to the point of the result
• and look more closely

dependences on the neutrino mass eigenstates
j1,2,3 ? will be summed incoherently (because
the three mass eigenstates v1, v2, and v3 are
distinct!)
87
4. Our more formal treatment

• of course, the phases cancel out due to the
  absolute value

88
4. Our more formal treatment

• of course, the phases cancel out due to the
  absolute value

89
4. Our more formal treatment

• of course, the phases cancel out due to the
  absolute value

90
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
91
4. Our more formal treatment

• the only possibility for oscillations if the
  initial state is a superposition of several
  states n of different energies

92
4. Our more formal treatment

• the only possibility for oscillations if the
  initial state is a superposition of several
  states n of different energies

93
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 F get a dependence on n

94
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 F get a dependence on n

95
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 F get a dependence on n
• then, the absolute squares show indeed
  oscillatory behavior

96
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 F get a dependence on n
• then, the absolute squares show indeed
  oscillatory behavior

97
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 F get a dependence on n
• then, the absolute squares show indeed
  oscillatory behavior

98
4. Our more formal treatment
HOWEVER
99
4. Our more formal treatment

• HOWEVER
• duration of the GSI-oscillations

100
4. Our more formal treatment

• HOWEVER
• duration of the GSI-oscillations

101
4. Our more formal treatment

• HOWEVER
• duration of the GSI-oscillations
• this would require an energy splitting of

102
4. Our more formal treatment

• HOWEVER
• duration of the GSI-oscillations
• this would require an energy splitting of

103
4. Our more formal treatment

• HOWEVER
• duration of the GSI-oscillations
• this would require an energy splitting of
• ?

104
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

105
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

106
4. Our more formal treatment
FURTHERMORE
107
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 ß-decays

108
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 ß-decays
• this does not happen in the ß-decays of the
  same ions as used for the EC-measurements (Faber
  et al.)

109
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 ß-decays
• this does not happen in the ß-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

110
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 ß-decays
• this does not happen in the ß-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

111
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 ß-decays
• this does not happen in the ß-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

112
5. One question
113
5. One question
Let us assume for a moment that the COHERENT
summation is correct.
114
5. One question
Let us assume for a moment that the COHERENT
summation is correct. ? What about the effective
mass in the KATRIN-experiment?
115
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

116
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))

117
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))

118
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))

119
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))

120
5. One question

• for (E0-E)gtgtmj, this can be parametrized by a
  single para-meter, the effective mass of the
  electron-neutrino, which is

121
5. One question

• for (E0-E)gtgtmj, this can be parametrized by a
  single para-meter, the effective mass of the
  electron-neutrino, which is
• ? this is the expression mostly used

122
5. One question

• for (E0-E)gtgtmj, 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

123
5. One question

• for (E0-E)gtgtmj, 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???

124
5. One question

• for (E0-E)gtgtmj, 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???

125
5. One question

• for (E0-E)gtgtmj, 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???

126
5. One question
I dont think so!!!
127
6. Conclusions
128
6. Conclusions

• the oscillations at GSI are NOT YET EXPLAINED

129
6. Conclusions

• the oscillations at GSI are NOT YET EXPLAINED
• they are definitely NOT related to neutrino
  mixing

130
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

131
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

132
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

133
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

134

• THANKS TO MY
• COLLABORATORS!!!!

135

• THANKS TO MY
• COLLABORATORS!!!!
• AND, OF COURSE, TO YOU ALL FOR YOUR ATTENTION!

136
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
140Pr and 142Pm Ions" Yu.A. Litvinov
et al. Phys.Lett.B664162-168,2008 e-Print
arXiv0801.2079 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