Orthopositronium-Lifetime Problem

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Orthopositronium-Lifetime Problem

• By Charles Fang
• Physics 138 Presentation

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Outline

• Introduction/Story
• History
• Experiment Setup
• Analysis
• Conclusion

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Story Time

• Characters
• Eric, the Electron e-
• Patricia, the Positron e
• Physics 138 Class, the Assassins

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How Long Before Eric and Patricia Break-up?

• Once upon a time, there was a guy (Eric) who
  liked to go out to clubs. He was the type of
  person who would always approach girls and one of
  two things would happen.
• First, the girl (Patricia) thinks he is rude, and
  a fight erupts. They annihilate each other and
  produce two or three photons.

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Story (continue)

• The second possibility is that Patricia and Eric
  get married and form a positronium family. Once
  they are married, two more outcomes still could
  occur inside the club.
• First, assassins try to stab Eric. As a result,
  two photons are emitted.
• Another possibility is that Eric and Patricia get
  into a fight and annihilate each other and
  produce 3 photons.
• THE END!

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Introduction

• The orthopositronium(oPs) lifetime problem has
  been a long standing problem.
• It is very interesting to study because the QED
  calculation by theorist is different from
  experimentalists. There has been many
  explanation for the discrepancy such as mirror
  matter.
• Finally in 2003, two groups(Tokyo and Ann Arbor)
  finally got data that are close to the QED
  calculation.

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So What Is Positronium?

• Positron(e) Electron(e-) Positronium
• Two Types of System In Ground State
• Singlet-State - Parapositronium
• Triplet-State - Orthopositronium
• Lifetime of pPs is very small compared to oPs.
  This is significant because when we go measure
  the lifetime of oPs, the pPs will become
  negligible in the experiment.

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Parapositronium(Singlet State)

• Stot 0, L 0
• Spin part of the wave-function is ANTI-SYMMETRIC
• (?e ?p - ?e ?p) / ?2

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Orthopositronium(Triplet State)

• Stot 1, L 0
• Spin part of the wave-function is SYMMETRIC
• ?e ?p (MsTot 1)
• (?e ?p ?e ?p) / ?2 (MsTot 0)
• ?e ?p (MsTot -1)

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Wave-function for Positronium

• ?pos must be have an overall anti-symmetric
  wave-function
• ?pos (spin part) (spatial part)
• ?oPs S A
• ?pPs A S

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So What Are We Trying To Find?

• Solve the orthopositronium-lifetime (the amount
  of time it takes for the oPs to decay into 3
  emitting photons)
• Understand the experiment and analysis (Tokyo
  group which used powder).

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Main Equation

• ?obs(t) ?3? ?pick(t) (Eq. 1)
• ?obs(t) observed oPs decay rate
• ?3? decay rate of oPs in vacuum into 3? (what
  the theorist calculated)
• ?pick(t) pick-off annihilation rate into 2?
• In the experiment, we will calculate the ratio of
  ?pick(t) / ?3? that will help us eventually find
  the theoretical value of?3?

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Outline

• Introduction/Story
• History
• Experiment Setup
• Analysis
• Conclusion

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History of Experimental Data
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Outline

• Introduction/Story
• History
• Experiment Setup
• Analysis
• Conclusion

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Schematic Diagram of Experimental Setup
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Life As An Orthopositronium
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Life As An Orthopositronium (Case 1)
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Life As An Orthopositronium (Case 2)
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Variables In the Experiment

• ?pick(t)
• Density of sand
• Temperature of sand
• ?3?
• Depends only on the e, e-

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Outline

• Introduction/Story
• History
• Experiment Setup
• Analysis
• Conclusion

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Analysis

• Ratio of ?pick(t) / ?3? is determined by the
  energy spectrum measured by the Ge detectors.
• For a time-varing rate ?(t)

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Energy Spectrum of oPs decay
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Pick-off Spectrum
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Ratio of ?pick(t) / ?3? for 2 Runs
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Nobs(t) Graph
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Next

• Plug the ratio ?pick(t) / ?3? into

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Finally!

• Fit the equations and data collected
• Only free fit variables
• Rstop
• C
• ?3? ? What we want to find!!

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Decay Rates as a Function of Fitting Start Time
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Orthopositronium-Lifetime Is

• ?3? 7.0396 0.0012 (stat.) 0.0011(sys.) ?s-1
• Agrees with NRQED prediction corrected up to a
  O(?2) term.
• Agrees with the Ann Arbor group after they
  realized that oPs thermalized.

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Outline

• Introduction/Story
• History
• Experiment Setup
• Analysis
• Conclusion

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Conclusion

• Two groups with two different methods obtained
  results similar to the QED calculation. Problem
  is solved!

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Acknowledgements

• Material from this presentation adapted from
• Asai, S., Jinnouchi, O., Kobayashi, T., Solution
  of Orthopositronium lifetime Puzzle.
• Westbrook, C.I., Gidley, D.W., Conti, R.S., and
  Rich, A., Phys. Rev. Lett. 58 1338 (1987)