1. The GSI oscillation mystery Alexander Merle Max-Planck-Institute for Nuclear Physics Heidelberg, Germany Based on: AM: Why a splitting in the final state cannot explain the GSI-Oscillations, arXiv:0907.3554 H. Kienert, J. Kopp, M. Lindner, AM: The GSI anomaly, J. Phys. Conf. Ser. 136, 022049, 2008, arXiv:0808.2389 Erice, 18th September 2009

2. Contents: 1.The starting point: What has been observed at GSI 2.Basic thoughts: The superposition principle 3.The easiest formulation: Probability Amplitudes 4.Finally: Conclusions

3. 1. The starting point: What has been observed at GSI

4. Litvinov et al: Phys. Lett. B664, 162 (2008)

5. 1. The starting point: What has been observed 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)

6. 1. The starting point: What has been observed 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)

7. 1. The starting point: What has been observed 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)

8. 1. The starting point: What has been observed 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) T~7s

9. 1. The starting point: What has been observed 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)

10. 1. The starting point: What has been observed at GSI Literature on the GSI Anomaly (complete?): Lipkin, arXiv:0801.1465; Litvinov et al., Phys. Lett. B664 (2008) 162–168, arXiv:0801.2079; Ivanov et al., arXiv:0801.2121; Giunti, arXiv:0801.4639; Ivanov et al., arXiv:0804.1311; Faber, arXiv:0801.3262; Walker, Nature 453N7197 (2008) 864–865; Ivanov et al., arXiv:0803.1289; Kleinert & Kienle, arXiv:0803.2938; Ivanov et al., Phys. Rev. Lett. 101 (2008) 182501; Burkhardt et al., arXiv:0804.1099; Peshkin, arXiv:0804.4891; Giunti, Phys. Lett. B665 (2008) 92– 94, arXiv:0805.0431; Lipkin, arXiv:0805.0435; Vetter et al., Phys. Lett. B670 (2008) 196–199, arXiv:0807.0649; Litvinov et al., arXiv:0807.2308; Ivanov et al., arXiv:0807.2750; Faestermann et al., arXiv:0807.3297; Giunti, arXiv:0807.3818; Kienert et al., J. Phys. Conf. Ser. 136 (2008) 022049, arXiv:0808.2389; Gal, arXiv:0809.1213; Pavlichenkov, Europhys. Lett. 85 (2009) 40008, arXiv:0810.2898; Cohen et al., arXiv:0810.4602; Peshkin, arXiv:0811.1765; Lambiase et al., arXiv:0811.2302; Giunti, Nucl. Phys. Proc. Suppl. 188 (2009) 43–45, arXiv:0812.1887; Lipkin, arXiv:0905.1216; Ivanov et al., arXiv:0905.1904; Giunti, arXiv:0905.4620; Faber et al., arXiv:0906.3617; Isakov, arXiv:0906.4219; Winckler et al., arXiv:0907.2277; Merle, arXiv:0907.3554; Ivanov & Kienle, Phys. Rev. Lett. 103 (2009) 062502, arXiv:0908.0877; Flambaum, arXiv:0908.2039; Kienle & Ivanov, arXiv:0909.1285; Kienle & Ivanov, arXiv:0909.1287

11. 2. Basic thoughts: The superposition principle

12. Feynman diagrams:

13. 2. Basic thoughts: The superposition principle Feynman diagrams:Neutrino oscillations

14. 2. Basic thoughts: The superposition principle Feynman diagrams:Neutrino oscillations coherent summation

15. 2. Basic thoughts: The superposition principle Feynman diagrams:Electron capture

16. 2. Basic thoughts: The superposition principle Feynman diagrams:Electron capture incoherent summation

17. 2. Basic thoughts: The superposition principle The superposition principle:

18. 2. Basic thoughts: The superposition principle The superposition principle: 1.If different ways lead to the same final state in one particular process, then one has to add the respective partial amplitudes to obtain the total amplitude. The probability of the process to happen is then proportional to the absolute square of this total amplitude (coherent summation). 2.If a reaction leads to physically distinct final states, then one has to add the probabilities for the different processes (incoherent summation).

19. 2. Basic thoughts: The superposition principle The superposition principle: 1.If different ways lead to the same final state in one particular process, then one has to add the respective partial amplitudes to obtain the total amplitude. The probability of the process to happen is then proportional to the absolute square of this total amplitude (coherent summation). 2.If a reaction leads to physically distinct final states, then one has to add the probabilities for the different processes (incoherent summation). Process: e.g. e + e - → μ + μ - Way: e.g. e + e - → μ + μ - by Z-exchange, but NOT γ or H

20. 2. Basic thoughts: The superposition principle The superposition principle: BUT: Why is the superposition principle true? Can it somehow be derived? Is there an easier (more intuitive) language?

21. 2. Basic thoughts: The superposition principle The superposition principle: BUT: Why is the superposition principle true? Can it somehow be derived? Is there an easier (more intuitive) language? YES!!! → We can use probability amplitudes.

22. 3. The easiest formulation: Probability Amplitudes

23. First example: Charged pion decay

24. 3. The easiest formulation: Probability Amplitudes First example: Charged pion decay Actually 2 processes: π + →μ + ν μ or π + → e + ν e both decay modes are possible

25. 3. The easiest formulation: Probability Amplitudes First example: Charged pion decay Actually 2 processes: π + →μ + ν μ or π + → e + ν e both decay modes are possible Initial state: 100% charged pion π + → corresponding total amplitude for this state at t=0:

26. 3. The easiest formulation: Probability Amplitudes First example: Charged pion decay Actually 2 processes: π + →μ + ν μ or π + → e + ν e both decay modes are possible Initial state: 100% charged pion π + → corresponding total amplitude for this state at t=0: After some time t>0:

27. 3. The easiest formulation: Probability Amplitudes

28. Important points:

29. 3. The easiest formulation: Probability Amplitudes Important points: normalization:

30. 3. The easiest formulation: Probability Amplitudes Important points: normalization: boundary conditions:

31. 3. The easiest formulation: Probability Amplitudes Important points: normalization: orthogonality: the basis states are clearly distinct → they form an orthogonal basis set for all possible states boundary conditions:

32. 3. The easiest formulation: Probability Amplitudes The process of the measurement:

33. 3. The easiest formulation: Probability Amplitudes The process of the measurement: Every detector does nothing else than projecting the time evolved state onto some state

34. 3. The easiest formulation: Probability Amplitudes The process of the measurement: Every detector does nothing else than projecting the time evolved state onto some state → corresponding probability to measure that state:

35. 3. The easiest formulation: Probability Amplitudes The process of the measurement: Every detector does nothing else than projecting the time evolved state onto some state → corresponding probability to measure that state: → the only question is how looks!

36. 3. The easiest formulation: Probability Amplitudes The process of the measurement: Every detector does nothing else than projecting the time evolved state onto some state → corresponding probability to measure that state: → the only question is how looks! → different cases…

37. 3. The easiest formulation: Probability Amplitudes Trivial case: no measurement at all

38. 3. The easiest formulation: Probability Amplitudes Trivial case: no measurement at all no detection → one has gained no information

39. 3. The easiest formulation: Probability Amplitudes Trivial case: no measurement at all no detection → one has gained no information → the projected state is just the time-evolved state itself:

40. 3. The easiest formulation: Probability Amplitudes Trivial case: no measurement at all no detection → one has gained no information → the projected state is just the time-evolved state itself: Of course, the probability for anything to happen is 100%.

41. 3. The easiest formulation: Probability Amplitudes Next step: the detector can only give us the information that the pion has decayed, but we do not know the exact final state

42. 3. The easiest formulation: Probability Amplitudes Next step: the detector can only give us the information that the pion has decayed, but we do not know the exact final state NOTE: This means that the detector cannot distinguish the two states and !!!!

43. 3. The easiest formulation: Probability Amplitudes Next step: the detector can only give us the information that the pion has decayed, but we do not know the exact final state NOTE: This means that the detector cannot distinguish the two states and !!!! We have only gained the information that the initial state is not present anymore:

44. 3. The easiest formulation: Probability Amplitudes Next step: the detector can only give us the information that the pion has decayed, but we do not know the exact final state NOTE: This means that the detector cannot distinguish the two states and !!!! We have only gained the information that the initial state is not present anymore: → projected state (correctly normalized):

45. 3. The easiest formulation: Probability Amplitudes The corresponding probability is:

46. 3. The easiest formulation: Probability Amplitudes The corresponding probability is: → any phase in will drop out due to the absolute value!

47. 3. The easiest formulation: Probability Amplitudes The corresponding probability is: → any phase in will drop out due to the absolute value! → incoherent summation!!!

48. 3. The easiest formulation: Probability Amplitudes One more case: we detect the pion

49. 3. The easiest formulation: Probability Amplitudes One more case: we detect the pion information gained:

50. 3. The easiest formulation: Probability Amplitudes One more case: we detect the pion information gained: projected state:

51. 3. The easiest formulation: Probability Amplitudes One more case: we detect the pion information gained: projected state: corresponding probability:

52. 3. The easiest formulation: Probability Amplitudes One more case: we detect the pion information gained: projected state: corresponding probability: → no oscillation

53. 3. The easiest formulation: Probability Amplitudes Yet another one: we the particular final state

54. 3. The easiest formulation: Probability Amplitudes information gained: Yet another one: we the particular final state

55. 3. The easiest formulation: Probability Amplitudes information gained: Yet another one: we the particular final state probability:

56. 3. The easiest formulation: Probability Amplitudes information gained: → again no oscillation Yet another one: we the particular final state probability:

57. 3. The easiest formulation: Probability Amplitudes information gained: → again no oscillation Yet another one: we the particular final state probability: Question: When do we get oscillations at all??

58. 3. The easiest formulation: Probability Amplitudes information gained: → again no oscillation Yet another one: we the particular final state probability: Question: When do we get oscillations at all?? Answer: If the detector does more than only killing some partial amplitudes.

59. 3. The easiest formulation: Probability Amplitudes Hypothetical example: measurement of a new quantum number, under which neither e + nor μ + is an eigenstate, but some superposition of them

60. 3. The easiest formulation: Probability Amplitudes possible measured state (example): Hypothetical example: measurement of a new quantum number, under which neither e + nor μ + is an eigenstate, but some superposition of them

61. 3. The easiest formulation: Probability Amplitudes possible measured state (example): Hypothetical example: measurement of a new quantum number, under which neither e + nor μ + is an eigenstate, but some superposition of them corresponding probability:

62. 3. The easiest formulation: Probability Amplitudes possible measured state (example): this term can oscillate! Hypothetical example: measurement of a new quantum number, under which neither e + nor μ + is an eigenstate, but some superposition of them corresponding probability:

63. 3. The easiest formulation: Probability Amplitudes Second example: Neutrinos

64. 3. The easiest formulation: Probability Amplitudes Consideration: neutrino that is produced (together with a daughter ion D) in an electron capture decay of the mother ion M Second example: Neutrinos

65. 3. The easiest formulation: Probability Amplitudes Consideration: neutrino that is produced (together with a daughter ion D) in an electron capture decay of the mother ion M Second example: Neutrinos time-evolved amplitude (U ei factored out):

66. 3. The easiest formulation: Probability Amplitudes Consideration: neutrino that is produced (together with a daughter ion D) in an electron capture decay of the mother ion M Second example: Neutrinos time-evolved amplitude (U ei factored out): with:

67. 3. The easiest formulation: Probability Amplitudes Again as start: the mother is seen

68. 3. The easiest formulation: Probability Amplitudes Again as start: the mother is seen information:

69. 3. The easiest formulation: Probability Amplitudes Again as start: the mother is seen projection: information:

70. 3. The easiest formulation: Probability Amplitudes → NO oscillation… Again as start: the mother is seen projection: information:

71. 3. The easiest formulation: Probability Amplitudes The GSI-case: we detect the daughter ion, but cannot distinguish the states and

72. 3. The easiest formulation: Probability Amplitudes only information: the mother is not there anymore The GSI-case: we detect the daughter ion, but cannot distinguish the states and

73. 3. The easiest formulation: Probability Amplitudes normalized state: only information: the mother is not there anymore The GSI-case: we detect the daughter ion, but cannot distinguish the states and

74. 3. The easiest formulation: Probability Amplitudes projection:

75. 3. The easiest formulation: Probability Amplitudes projection: → NO OSCILLATION!!!

76. 3. The easiest formulation: Probability Amplitudes projection: → NO OSCILLATION!!! BUT: Why do some authors obtain oscillations?

77. 3. The easiest formulation: Probability Amplitudes The reason is the following: Instead of correctly projecting on the evolved state they project, e.g., onto an electron neutrino state which is different from the time-evolved one (it is simply not the same state as the one which they claim to be present):

78. 3. The easiest formulation: Probability Amplitudes The reason is the following: Instead of correctly projecting on the evolved state they project, e.g., onto an electron neutrino state which is different from the time-evolved one (it is simply not the same state as the one which they claim to be present): → What does this change?

79. 3. The easiest formulation: Probability Amplitudes corresponding projection:

80. 3. The easiest formulation: Probability Amplitudes corresponding projection: → The last term does oscillate!

81. 3. The easiest formulation: Probability Amplitudes corresponding projection: → The last term does oscillate! BUT: One has not used the complete information that has been obtained in the experiment! The time that has passed since the production of the mother ion has been neglected!

82. 3. The easiest formulation: Probability Amplitudes corresponding projection: → The last term does oscillate! BUT: One has not used the complete information that has been obtained in the experiment! The time that has passed since the production of the mother ion has been neglected! → This treatment is not complete!

83. 3. The easiest formulation: Probability Amplitudes The remaining question: Does the neutrino that is emitted in the GSI-experiment oscillate?

84. 3. The easiest formulation: Probability Amplitudes The remaining question: Does the neutrino that is emitted in the GSI-experiment oscillate? The obvious answer: Of course!

85. 3. The easiest formulation: Probability Amplitudes The remaining question: Does the neutrino that is emitted in the GSI-experiment oscillate? The obvious answer: Of course! BUT: This can also be shown explicitely!

86. 3. The easiest formulation: Probability Amplitudes The remaining question: Does the neutrino that is emitted in the GSI-experiment oscillate? The obvious answer: Of course! BUT: This can also be shown explicitely! State after detection of the mother: (for simplicity ; does not change anything here)

87. 3. The easiest formulation: Probability Amplitudes Re-phasing this state and measuring the time from t on → new initial state:

88. 3. The easiest formulation: Probability Amplitudes Re-phasing this state and measuring the time from t on → new initial state: Time-evolution:

89. 3. The easiest formulation: Probability Amplitudes Re-phasing this state and measuring the time from t on → new initial state: Time-evolution: with:

90. 3. The easiest formulation: Probability Amplitudes Further complication: Entanglement of the neutrino and the daughter ion.

91. 3. The easiest formulation: Probability Amplitudes Further complication: Entanglement of the neutrino and the daughter ion. the daughter ion is localized → has to be described by a wave packet the daughter ion is detected, but not with sufficient kinematical precision to distinguish the different neutrino mass eigenstates → the same like a non-measurement!

92. 3. The easiest formulation: Probability Amplitudes Further complication: Entanglement of the neutrino and the daughter ion. the daughter ion is localized → has to be described by a wave packet the daughter ion is detected, but not with sufficient kinematical precision to distinguish the different neutrino mass eigenstates → the same like a non-measurement!

93. 3. The easiest formulation: Probability Amplitudes Further complication: Entanglement of the neutrino and the daughter ion. the daughter ion is localized → has to be described by a wave packet the daughter ion is detected, but not with sufficient kinematical precision to distinguish the different neutrino mass eigenstates → the same like a non-measurement! → This is done most easily in the density matrix formalism!

94. 3. The easiest formulation: Probability Amplitudes Density matrix of the time-evolved state: with:

95. 3. The easiest formulation: Probability Amplitudes Density matrix of the time-evolved state: with: Ion not measured → trace over the corresponding states:

96. 3. The easiest formulation: Probability Amplitudes This can, e.g., be projected onto a μ-neutrino:

97. 3. The easiest formulation: Probability Amplitudes This can, e.g., be projected onto a μ-neutrino: Corresponding projection operator:

98. 3. The easiest formulation: Probability Amplitudes This can, e.g., be projected onto a μ-neutrino: Corresponding projection operator: Probability to detect the ν μ :

99. 3. The easiest formulation: Probability Amplitudes This can, e.g., be projected onto a μ-neutrino: Corresponding projection operator: Probability to detect the ν μ : Explicit:

100. 3. The easiest formulation: Probability Amplitudes This can, e.g., be projected onto a μ-neutrino: Corresponding projection operator: Probability to detect the ν μ : Explicit: … oscillates!!!

101. 4. Finally: Conclusions the modification of the exponential decay not in the GSI-experiment cannot be explained by neutrino oscillations this can be seen most easily in the formulation with probability amplitudes unfortunately, a satisfying explanation is still missing… … if you have any idea: Phone: +49/6221/516-817 E-Mail: Alexander.Merle@mpi-hd.mpg.de

102. 4. Finally: Conclusions the modification of the exponential decay not in the GSI-experiment cannot be explained by neutrino oscillations this can be seen most easily in the formulation with probability amplitudes unfortunately, a satisfying explanation is still missing… … if you have any idea: Phone: +49/6221/516-817 E-Mail: Alexander.Merle@mpi-hd.mpg.de

103. 4. Finally: Conclusions the modification of the exponential decay not in the GSI-experiment cannot be explained by neutrino oscillations this can be seen most easily in the formulation with probability amplitudes unfortunately, a satisfying explanation is still missing… … if you have any idea: Phone: +49/6221/516-817 E-Mail: Alexander.Merle@mpi-hd.mpg.de

104. 4. Finally: Conclusions the modification of the exponential decay not in the GSI-experiment cannot be explained by neutrino oscillations this can be seen most easily in the formulation with probability amplitudes unfortunately, a satisfying explanation is still missing… … if you have any idea: Phone: +49/6221/516-817 E-Mail: Alexander.Merle@mpi-hd.mpg.de

105. 4. Finally: Conclusions the modification of the exponential decay not in the GSI-experiment cannot be explained by neutrino oscillations this can be seen most easily in the formulation with probability amplitudes unfortunately, a satisfying explanation is still missing… … if you have any idea: Phone: +49/6221/516-817 E-Mail: Alexander.Merle@mpi-hd.mpg.de

106. 4. Finally: Conclusions the modification of the exponential decay not in the GSI-experiment cannot be explained by neutrino oscillations this can be seen most easily in the formulation with probability amplitudes unfortunately, a satisfying explanation is still missing… … if you have any idea: Phone: +49/6221/516-817 E-Mail: Alexander.Merle@mpi-hd.mpg.de

107. THANK YOU!!!!