Pion-pion scattering at low energies is analysed in terms of scattering
lengths. At present pion-pion scattering is still an unresolved problem in
the framework of QCD. However the approach based on an effective lagrangian
and Chiral Perturbation Theory (CHPT) allows to predict S-wave 
scattering lengths within 5%. These predictions have not yet been tested at
such a level of accuracy (the best precision is 20%).
To obtain the pion scattering lengths in a model-independent way, a
measurement of the lifetime of exotic atoms formed by 
and 
mesons ( 
or dimesoatom) in their ground state is suggested. There
exists a precise relationship between this lifetime 
and the
difference of the isoscalar 
and isotensor 
S-wave scattering
lengths: 
. To determine 
down to 5%,
corresponding to the theoretical uncertainty, the lifetime has to be
measured with 10% accuracy. This is the goal of the proposed experiment.
The value of predicted by CHPT is 
s.
This measurement will submit the modern concept of chiral symmetry breaking to a crucial test. Any significant discrepancy between the theory and the experiment would demonstrate a basic problem in our understanding of the QCD vacuum structure.
Atoms will be produced in
proton-nucleus (e.g. Ti) interactions at 24 GeV/c (CERN
Proton Synchrotron). After production in the target, these
relativistic atoms ( 
) may either decay into
or get excited
or break up (be ionized) in the target material. In the case of breakup,
characteristic charged pion pairs, called ``atomic pairs'', will emerge.
These pairs have a low relative momentum q in their centre of mass system
(q< 3 MeV/c) and so a small opening angle ( 
mrad) and
nearly identical energies ( 
at the 0.3% level) in the lab
system. The proposed experimental setup consists of a magnetic
double arm spectrometer with a resolution on relative
pair momenta of 
MeV/c. By these
means, it is possible to determine the number of ``atomic pairs'' above the
background of pion pairs produced in a free state. The total
number of produced is related by an exact expression to the
number of ``free'' pion pairs with a low relative momentum. For a given
target material and thickness, the ratio of the number of observed ``atomic
pairs'' to the total number of produced depends on the lifetime
in a unique way. For the optimum target the observation of
``atomic pairs'' allows to measure with the
desired accuracy of 10%. Considering the experiment at CERN PS, the
necessary amount of data should be collected in a running time of
about 7 weeks, including a reasonable safety factor.
The experimental setup consists of a scintillating fibre detector and a
scintillation hodoscope near the target, a spectrometer magnet (bending
power of 2 Tm) and two telescope arms, each equipped with drift chambers,
scintillation hodoscopes, gas Cherenkov counters and muon identifiers. The
relative momentum resolution required for identification of ``atomic pairs''
is provided by the high coordinate resolution of the fibre detector and of
the drift chambers. In addition, thin targets and thin windows in the vacuum
system must keep the effect of multiple scattering small. With a primary
intensity of 
protons per spill, a first level trigger rate of
events per spill, due to free and accidental pairs, is
expected. This high LHC-like trigger rate will be reduced by a factor
30 with the trigger system. Special purpose processors
will reject events with an opening angle of more than 3 mrad as well as
events with a relative momentum larger than 30 MeV/c.
Among other physics subjects accessible to the proposed setup, only three topics are mentioned here:
states helps to study the
feasibility of a Lamb shift measurement in . This energy shift is
related to the pion scattering length combination 
and hence its
measurement, coupled with the lifetime measurement, would provide a
determination of and , separately.
atoms and measurement of their
lifetime would allow to extract model-independent values for 
scattering lengths. A comparison of these lengths with CHPT predictions
would give the possibility to test the chiral symmetry breaking in processes
with strange quarks.
correlations in the range of very small
relative momenta with high momentum resolution using high statistics
.