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


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


Periodic modula-tion of the expect-ed exponential law in EC-decays of different highly charged ions (Pm-142 & Pr-140)




exponential law




exponential law

periodic modulation




exponential law

periodic modulation


T~7s


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


Feynman diagrams:


Feynman diagrams: Neutrino oscillations


Feynman diagrams: Neutrino oscillations

coherent summation


Feynman diagrams: Electron capture


Feynman diagrams: Electron capture

incoherent summation


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).



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



BUT:Why is the superposition principle true?Can it somehow be derived?Is there an easier (more intuitive) language?



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.


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:





Initial state: 100% charged pion π+

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

After some time t>0:


Important points:


Important points:

normalization:


Important points:

normalization:

boundary conditions:


Important points:

normalization:

orthogonality: the basis states are clearly distinct → they form an orthogonal basis set for all possible states

boundary conditions:


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!





→ the only question is how looks!

→ different cases…


Trivial case: no measurement at all



no detection → one has gained no information




→ the projected state is just the time-evolved state itself:




→ the projected state is just the time-evolved state itself:

Of course, the probability for anything to happen is 100%.


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:




We have only gained the information that the initial state is not present anymore:

→ projected state (correctly normalized):


The corresponding probability is:



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



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

→ incoherent summation!!!


One more case: we detect the pion



information gained:



information gained:

projected state:



information gained:

projected state:

corresponding probability:



information gained:

projected state:


→ no oscillation


Yet another one: we the particular final state


information gained:



information gained:


probability:


information gained:

→ again no oscillation


probability:


information gained:



probability:

Question:When do we get oscillations at all??


information gained:



probability:

Question:When do we get oscillations at all??Answer:

If the detector does more than only killing some partial amplitudes.


Hypothetical example: measurement of a new quantum number, under which neither e+ nor μ+ is an eigenstate, but some superposition of them


possible measured state (example):




this term can oscillate!




Second example: Neutrinos


Consideration: neutrino that is produced (together with a daughter ion D) in an electron capture decay of the mother ion M





time-evolved amplitude (Uei factored out):




time-evolved amplitude (Uei factored out):

with:


Again as start: the mother is seen



information:



projection:

information:


→ NO oscillation…


projection:

information:


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


only information: the mother is not there anymore



normalized state:

only information: the mother is not there anymore



projection:


projection:

→ NO OSCILLATION!!!


projection:

→ NO OSCILLATION!!!

BUT: Why do some authors obtain oscillations?


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):


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?


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!




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!


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

oscillate?



oscillate?

The obvious answer: Of course!



oscillate?


BUT: This can also be shown explicitely!



oscillate?


BUT: This can also be shown explicitely!

State after detection of the mother:

(for simplicity ; does not change anything here)


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



Time-evolution:



Time-evolution:

with:


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!



• 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!


Density matrix of the time-evolved state:

with:


Density matrix of the time-evolved state:

with:

Ion not measured → trace over the corresponding states:


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



Corresponding projection operator:




Probability to detect the νμ:





Explicit:





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: [email protected]

THANK YOU!!!!

The GSI oscillation mystery Alexander Merle Max-Planck-Institute for Nuclear Physics Heidelberg,...

Documents

Transcript of The GSI oscillation mystery Alexander Merle Max-Planck-Institute for Nuclear Physics Heidelberg,...