Takeshi K. Komatsubara
last update 2002-Apr-18

Motivation of the  study in E949-2002

1. Definition:
• region (``above  ''):  > 215MeV/c
• region (``below  ''): 100 <  < 180MeV/c
2. Results from E787: 1991 data, PRL 79(1997)4079
• B( ) <  at 90%C.L.
• assuming the phase-space distribution
• = ,  triggers
• B( ) = 
• 31 signal events
• = ,  triggers
3. Predicted kinematic spectrum:

Chiral Perturbation Theory (ChPT) predicts a peculiar  momentum spectrum to the  decay, and is supported by the E787's  spectrum.
• Phase Space (phsp)
• E787- does not reproduce this spectrum.

B( ) is large.
• ChPT with Unitarity Correction,  = 1.8 (wpigg)
• This spectrum is favored by E787- .

B( ) is small but finite.
• ChPT without Unitarity Correction,  = 1.6 (wpigg_nouc)
• This spectrum is still consistent with E787- .

B( ) is much smaller because it goes to zero at the endpoint (227MeV/c).

 
        top left                            spectrum

top right invariant mass of  and 

2nd left 

2nd right  vs. 

3rd left 

3rd right  vs. 

bottom left 

bottom right  vs. 

4. Predicted Branching ratio of  :

Based on B( ) =  and the spectra above, the follownig branching ratioes are calculated. The kinematic spectrum of the decay to the  region is linked.
• Phase Space: 
• ChPT with Unitarity Correction,  = 1.8: 
• The  and  spectra are different from those in the Phase Space.
• ChPT without Unitarity Correction,  = 1.6: 
• The  spectrum is different from those in the Phase Space.

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