the gsi oscillation mystery alexander merle max-planck-institute for nuclear physics heidelberg,...

The GSI oscillation mystery

Alexander MerleMax-Planck-Institute for Nuclear Physics

Heidelberg, Germany

Based on:AM: Why a splitting in the final state cannot explain the GSI-Oscillations, arXiv:0907.3554H. Kienert, J. Kopp, M. Lindner, AM: The GSI anomaly, J. Phys. Conf. Ser. 136, 022049, 2008, arXiv:0808.2389

Erice, 18th September 2009

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

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

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

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

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)

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)

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)

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

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)

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

2. Basic thoughts: The superposition principle

2. Basic thoughts: The superposition principle

Feynman diagrams:

2. Basic thoughts: The superposition principle

Feynman diagrams: Neutrino oscillations

2. Basic thoughts: The superposition principle

Feynman diagrams: Neutrino oscillations

coherent summation

2. Basic thoughts: The superposition principle

Feynman diagrams: Electron capture

2. Basic thoughts: The superposition principle

Feynman diagrams: Electron capture

incoherent summation

2. Basic thoughts: The superposition principle

The superposition principle:

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).

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

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?

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.

3. The easiest formulation: Probability Amplitudes

3. The easiest formulation: Probability Amplitudes

First example: Charged pion decay

3. The easiest formulation: Probability Amplitudes

First example: Charged pion decay

• Actually 2 processes: π+→μ+νμ or π+ → e+νe

• both decay modes are possible

3. The easiest formulation: Probability Amplitudes

First example: Charged pion decay

• Actually 2 processes: π+→μ+νμ or π+ → e+νe

• both decay modes are possible

Initial state: 100% charged pion π+

→ corresponding total amplitude for this state at t=0:

3. The easiest formulation: Probability Amplitudes

First example: Charged pion decay

• Actually 2 processes: π+→μ+νμ or π+ → e+νe

• 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:

3. The easiest formulation: Probability Amplitudes

3. The easiest formulation: Probability Amplitudes

Important points:

3. The easiest formulation: Probability Amplitudes

Important points:

normalization:

3. The easiest formulation: Probability Amplitudes

Important points:

normalization:

boundary conditions:

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:

3. The easiest formulation: Probability Amplitudes

The process of the measurement:

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

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:

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!

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…

3. The easiest formulation: Probability Amplitudes

Trivial case: no measurement at all

3. The easiest formulation: Probability Amplitudes

Trivial case: no measurement at all

no detection → one has gained no information

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:

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%.

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

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 !!!!

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:

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):

3. The easiest formulation: Probability Amplitudes

The corresponding probability is:

3. The easiest formulation: Probability Amplitudes

The corresponding probability is:

→ any phase in will drop out due to the absolute value!

3. The easiest formulation: Probability Amplitudes

The corresponding probability is:

→ any phase in will drop out due to the absolute value!

→ incoherent summation!!!

3. The easiest formulation: Probability Amplitudes

One more case: we detect the pion

3. The easiest formulation: Probability Amplitudes

One more case: we detect the pion

information gained:

3. The easiest formulation: Probability Amplitudes

One more case: we detect the pion

information gained:

projected state:

3. The easiest formulation: Probability Amplitudes

One more case: we detect the pion

information gained:

projected state:

corresponding probability:

3. The easiest formulation: Probability Amplitudes

One more case: we detect the pion

information gained:

projected state:

corresponding probability:

→ no oscillation

3. The easiest formulation: Probability Amplitudes

Yet another one: we the particular final state

3. The easiest formulation: Probability Amplitudes

information gained:

Yet another one: we the particular final state

3. The easiest formulation: Probability Amplitudes

information gained:

Yet another one: we the particular final state

probability:

3. The easiest formulation: Probability Amplitudes

information gained:

→ again no oscillation

Yet another one: we the particular final state

probability:

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??

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.

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

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

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:

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:

3. The easiest formulation: Probability Amplitudes

Second example: Neutrinos

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

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 (Uei factored out):

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 (Uei factored out):

with:

3. The easiest formulation: Probability Amplitudes

Again as start: the mother is seen

3. The easiest formulation: Probability Amplitudes

Again as start: the mother is seen

information:

3. The easiest formulation: Probability Amplitudes

Again as start: the mother is seen

projection:

information:

3. The easiest formulation: Probability Amplitudes

→ NO oscillation…

Again as start: the mother is seen

projection:

information:

3. The easiest formulation: Probability Amplitudes

The GSI-case: we detect the daughter ion, but cannot distinguish the states and

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

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

3. The easiest formulation: Probability Amplitudes

projection:

3. The easiest formulation: Probability Amplitudes

projection:

→ NO OSCILLATION!!!

3. The easiest formulation: Probability Amplitudes

projection:

→ NO OSCILLATION!!!

BUT: Why do some authors obtain oscillations?

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):

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?

3. The easiest formulation: Probability Amplitudes

corresponding projection:

3. The easiest formulation: Probability Amplitudes

corresponding projection:

→ The last term does oscillate!

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!

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!

3. The easiest formulation: Probability Amplitudes

The remaining question:Does the neutrino that is emitted in the GSI-experiment

oscillate?

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!

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!

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)

3. The easiest formulation: Probability Amplitudes

Re-phasing this state and measuring the time from t on → new initial state:

3. The easiest formulation: Probability Amplitudes

Re-phasing this state and measuring the time from t on → new initial state:

Time-evolution:

3. The easiest formulation: Probability Amplitudes

Re-phasing this state and measuring the time from t on → new initial state:

Time-evolution:

with:

3. The easiest formulation: Probability Amplitudes

Further complication:Entanglement of the neutrino and the daughter ion.

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!

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!

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!

3. The easiest formulation: Probability Amplitudes

Density matrix of the time-evolved state:

with:

3. The easiest formulation: Probability Amplitudes

Density matrix of the time-evolved state:

with:

Ion not measured → trace over the corresponding states:

3. The easiest formulation: Probability Amplitudes

This can, e.g., be projected onto a μ-neutrino:

3. The easiest formulation: Probability Amplitudes

This can, e.g., be projected onto a μ-neutrino:

Corresponding projection operator:

3. The easiest formulation: Probability Amplitudes

This can, e.g., be projected onto a μ-neutrino:

Corresponding projection operator:

Probability to detect the νμ:

3. The easiest formulation: Probability Amplitudes

This can, e.g., be projected onto a μ-neutrino:

Corresponding projection operator:

Probability to detect the νμ:

Explicit:

3. The easiest formulation: Probability Amplitudes

This can, e.g., be projected onto a μ-neutrino:

Corresponding projection operator:

Probability to detect the νμ:

Explicit:

… oscillates!!!

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: +49/6221/516-817E-Mail: Alexander.Merle@mpi-hd.mpg.de

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: +49/6221/516-817E-Mail: Alexander.Merle@mpi-hd.mpg.de

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: +49/6221/516-817E-Mail: Alexander.Merle@mpi-hd.mpg.de

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: +49/6221/516-817E-Mail: Alexander.Merle@mpi-hd.mpg.de

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: +49/6221/516-817E-Mail: Alexander.Merle@mpi-hd.mpg.de

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: +49/6221/516-817E-Mail: Alexander.Merle@mpi-hd.mpg.de

THANK YOU!!!!