Orthopositronium-Lifetime Problem By: Charles Fang Physics 138 Presentation

Outline Introduction/Story History Experiment Setup Analysis Conclusion

Story Time… Characters:  Eric, the Electron e -  Patricia, the Positron e +  Physics 138 Class, the Assassins

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.

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!

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 experimentalist’s. 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.

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.

Parapositronium(Singlet State) S tot = 0, L = 0 Spin part of the wave-function is ANTI- SYMMETRIC:  (  e  p -  e  p ) /  2

Orthopositronium(Triplet State) S tot = 1, L = 0 Spin part of the wave-function is SYMMETRIC:   e  p (Ms Tot = +1)  (  e  p +  e  p ) /  2 (Ms Tot = 0)   e  p (Ms Tot = -1)

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

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).

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 

Outline Introduction/Story History Experiment Setup Analysis Conclusion

History of Experimental Data

Outline Introduction/Story History Experiment Setup Analysis Conclusion

Schematic Diagram of Experimental Setup

Life As An Orthopositronium

Life As An Orthopositronium (Case 1)

Life As An Orthopositronium (Case 2)

Variables In the Experiment pick (t)  Density of sand  Temperature of sand 3   Depends only on the e +, e -

Outline Introduction/Story History Experiment Setup Analysis Conclusion

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

Energy Spectrum of oPs decay

Pick-off Spectrum

Ratio of pick (t) / 3  for 2 Runs

N obs (t) Graph

Next… Plug the ratio pick (t) / 3  into:

Finally! Fit the equations and data collected Only free fit variables  R stop  C  3   What we want to find!!

Decay Rates as a Function of Fitting Start Time

Orthopositronium-Lifetime Is… 3  = (stat.) (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.

Outline Introduction/Story History Experiment Setup Analysis Conclusion

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

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 (1987)