The RAPID experiment
PION RADIATIVE DECAY
Pion --> Muon
In the 50's Fry (Phys. Rev. 90 (1953), 130) first, and Castagnoli and
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.
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
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
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
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.
BR(E_gamma>=1 MeV) = 2.0*10^-4 +- 12% (stat) +- 4% (syst)
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:
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