The following table gives our current estimations on resolutions in energy, position and timing for the detection of the mu -> e gamma process and its backgrounds. Based on these number, the reachable branching ratio sensitivity is calculated. The numbers in the last column can be changed interactively to see their effect on the sensitivity.

It should be noted that the accidental background rate contains a (conservative) quadratic dependency of the muon stopping rate. So by changing the muon stopping rate and the measurement time, one can optimize the sensitivity vs. background rate.

Single event sensitivity
Item Unit Proposal Revised MC Measured Value
Muon stopping rate s-1 0.3 * 108 0.25 * 108 1 * 108 5)
Measurement time PSI beam weeks
(= 4*105s)
65 100 -
Solid angle sr/4Pi 0.09 - -
Positron detection efficiency 1 0.90 0.65 -
Gamma detection efficiency 1 0.6 0.6 0.46)
Event selection efficiency 1 0.7 0.7 -
Single event sensitivity *10^

Accidental background rate
Resolution Unit Proposal Revised MC Measured Value
Photon Detector
Energy % (FWHM) @ 52.8 MeV/c2 4.0 4.3 56)
Timing ps (FWHM) 100 100 1506)
Position mm (FWHM) 9 10 96)
Positron Detector
Energy % (FWHM) @ 52.8 MeV/c2 0.8 0.8 -
Timing ps (FWHM) 100 100 1001)
Angle mrad (FWHM) 9 10.5 -
Muon decay position mm (FWHM) 2.1 - -
Reference values
Photon yield/muon (y > y min) Pure number 5 * 10-7 5 * 10-7 -
Minimum y value Pure number 0.965 0.965 -
Combined values
Relative Timing ps (FWHM)
Gamma Angle 2) mrad (FWHM)
Relative Angle mrad (FWHM)
Accidental Background Rate 3) *10^
Number of expected Background Events
90% C.L. sensitivity 4) *10^


  1. This is a result from a measurement at a muon energy deposit of ~2MeV which resulted in a resolution of 140ps (FWHM). Since the resolution is dominated by photoelectron statistics, it is expected to reach 100ps or better in the final experiment, where a threshold of 5MeV can be applied.
  2. The uncertainty of the gamma angle is roughly estimated by dphi_gamma = sqrt((dx_gamma/lxe_radius)2 + (dx_muon/lxe_radius)2) where dx_gamma is the uncertainty in the position determination of the gamma in the calorimeter, dx_muon is the uncertainty in the position of the muon decay point in the target and lxe_radius = 678.5 mm is the inner rate of the LXe calorimeter. A more precise value comes from the MC, which takes into account all geometrical effects, but is within 10% of this rough estimation.
  3. The accidental background rate is computed using the Kuno-Okada-Maki formula (MEG Technical Note, 1, (1999)) and the accidental photon rate in the calorimeter is obtained by the MC simulation. The accidental photon rate is proportional to the square of the size of the gamma (normalized) energy window. In addition, a conservative quadratic dependency of the background rate from the muon stopping rate is taken into account.
  4. The 90% C.L. sensitivity is calculated according to the paper of Feldman and Cousins in presence of an expected background with no true signal using an approximation of their table 12.
  5. Measured in 2004 in front of the beam transport solenoid with a 4cm target E.
  6. Preliminary values from PSI beam times 2003 and 2004. To be improved with refined analysis methods.

MEG Home Page
For the calculator: S. Ritt, July 2nd, 2001
For the numbers: MEG Collaboration, Feb. 11th, 2005