The RAPID experiment
Pion --> Muon Neutrino Gamma

1. Introduction

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

pi+  -->  mu+   nu   gamma
stopping pions in photografic emulsions. The process is quite rare since the branching ratio is of the order of 10^-4. They inferred the muon momentum from the length of its track (range) in the emulsion. Since the pion decays at rest, if the muon is monoenergetic (as expected from a two body decay) the range spectrum would be a line (although broadened by the range fluctuations). Instead, they measured a continuum spectrum, extended from 0 (i.e., muons at rest) to the maximum range (two body decay). From this fact they deduced that a neutral particle is emitted besides the neutrino. The gamma-ray is the most natural candidate.

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.

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:

BR(E_gamma>=1 MeV) = 2.0*10^-4 +- 12% (stat) +- 4% (syst)

to be compared with the theoretical QED expectation 2.283*10^-4.
For other details read our final paper G.Bressi et al, Nucl.Phys.B 513 (1998), 555.

Our result appears now on the