The RAPID experiment
PION RADIATIVE DECAY
Pion --> Muon Neutrino Gamma

In the 50's Fry (Phys. Rev. 90 (1953), 130) first, and Castagnoli and Muchnik (Phys. Rev. 112 (1958), 1779) later, measured the branching ratio of the process

2. Theory

The gamma-ray can be emitted either from the charged lines involved in the decay process -  pion and  muon - (this term is called Internal Bremsstrahlung IB) or directly from the decay vertex (Structure Dependent term SD). When squaring the decay matrix to get the decay probability, an Interference Term (INT) appears, which is proportional to SD*IB.
The IB term is a pure QED term, well described and calculable within the frame of this theory.
The SD term takes into account the fact that the pion is not an elementary particle but is constitued by quarks.
In the pion-to-muon radiative decay, however, both the SD term and the INT term are heavily suppressed compared to the IB term. With a very good approximation, the gamma-rays emitted from this decay can be thought as a pure QED process.
QED calculations show that for a pion decay at rest the gamma spectrum has approximately a 1/E_gamma shape (E_gamma is the gamma-ray energy) up to the maximum energy, 30 MeV. So the gamma spectrum "diverges" at low energies.

For more details on the theory, read S.G.Brown and S.A.Bludmann, Phys.Rev.136 (1964), 1160 and D.E.Neville, Phys.Rev.124(1961),2037. The most relevant formulae can be also found in G. Bressi et al., Nucl. Phys.B 513 (1998), 555.

3. Back to the experiment

Castagnoli and Muchnik measured the muon range spectrum (related to the gamma spectrum) with the highest statistic so far. Both their branching ratio and spectrum DO NOT AGREE with QED expectations in the low-energy region, i.e., for E_gamma below a few MeV. It seems that there is an excess of low-energy gammas.
This is why we want to measure study again this decay. We want to detect directly the gamma-ray and measure its energy and simultaneously measure the muon energy (the pion decays at rest). We can therefore draw the Dalitz plot of the process.

4. Experimental apparatus

Here we quickly describe the experimental set-up. More details can be found in our papers.

• Beam. 50 MeV/c pi+ beam at the Paul Scherrer Institute
• Beam counter. The pions are first detected by a fast CF4 gas scintillating detector (for fast timing).
• Electrostatic separator. Actually, the pion beam contains a lot of muons and positrons (positrons are about a factor 1000 more than pions). To increase the relative pion content in the beam an electrostatic deflector is used to bend away muons and positrons.
• Active target. The pions are brought to rest by 10 Silicon detectors, 5x5 cm^2, 0.5 mm thickness each. The pion plus muon kinetic energy is measured. Then the pion energy is subtracted (it's known from the beam momentum) to yield the muon kinetic energy.
  The 10 Silicon diodes are inside a box made by 0.5 cm thick plastic scintillators, which veto positrons from muon decays.
• Gamma-ray detector. The gamma-rays are detected by a Liquid Xenon (LXe) ionization chamber. The scintillation light is exploited for the trigger, whereas the ionization charge is used to measure the gamma-ray energy. The sensitive volume of the chamber is about 60 liters. 12 UltraViolet PMT's detect the LXe scintillation light. So far this is the largest LXe chamber ever built and the first one to put on floor for a physics experiment.
  A description of the chamber is in G.Carugno et al., NIMA 376 (1996), 149-154.
  The performance and the calibration of the detector is described in G.Bressi et al., NIMA 396 (1997), 67.

5. Results

Although the detection threshold for the gamma-rays was about 200 keV, the huge low-energy gamma-ray background prevented us to measure the spectrum at energy below 1 MeV.
However we measured the branching ratio for E_gamma >= 1 MeV:

Our result appears now on the