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Chiral Dynamics
Chiral perturbation theory (CHPT) provides a framework for nonperturbative
calculations in the long wave length limit of QCD. Within this framework
one would like to understand the mechanism of the spontaneous violation
of the approximate chiral symmetry of QCD in the light quark sector at
low energies. While it is believed that this mechanism is similar to that
in ferromagnets below the Curie temperature, no ab initio QCD calculation
has hitherto been done, which would show the quark pair condensation in
the vacuum. CHPT leads to selfconsistent relations between various physical
processes which have to be fulfilled, if the spontaneous chiral symmetry
breaking occurs as believed. Combined with precise measurements, one will
be able to pin down the value of the pertinent order parameter B.
Another major goal of theory is to understand the explicit chiral symmetry
breaking due to the small but finite light quark masses. CHPT offers an
important tool for the determination of the ratios of these fundamental
parameters of the standard model. While these ratios can be inferred from
the meson sector (e.g. from the ratios of the Goldstone boson masses),
the nucleon (baryon) sector can give important additional bounds. Furthermore,
as stressed by Weinberg already in 1979, for the two flavour sector of
the light u and d quarks, Gparity forbids isospinviolating
strong interaction terms
to leading order in the pion Lagrangian, but allows such leading terms
in the pionnucleon sector. Therefore, precise measurements of elastic
pionnucleon scattering and single pion photoproduction (in the corresponding
threshold regions) would sharpen the understanding of the fundamental question
of isospin violation in the strong interactions. An extensive programm
of high precision measurements is in progress at MAMI. The measurement
of
production off protons has been already performed. Fig.
represents the data for the amplitude of
photoproduction at threshold compared to the chiral perturbation prediction.
Figure: Amplitude of photoproduction of
at threshold. The data are compared to the prediction of low energy theorems
(LET) and chiral perturbation theory (ChPT).

Similarly, the precise pionic atom measurements to determine the Swave
scattering lengths at PSI clearly show the relevance of chiral pion loops
and when supplemented with a full scale calculation of virtual photons
can lead to bounds on m_{d}m_{u}.
Such precision measurements at low energies are truly quantitative tests
of QCD. Such studies also include pion electroproduction as performed and
planned at NIKHEF and MAMI, which allow to pin down the nucleon axial radius
and lead to detailed tests of CHPT predictions. For that, L/T separations
and polarisation observables are a must. The DIRAC experiment at CERN also
aims at this goal by measuring the lifetime of the pionic atom .
The inclusion of the strange quark is a challenge since the strange quark
mass is much larger than m_{u}_{,d}. Calculations
indicate the usefulness of CHPT in the threshold region, but precise data
are needed to test the predictions. DANE
will produce large numbers of Kmesons and also
mesons. CELSIUS and the 4
WASA detector will provide an
factory. Chiral symmetry makes detailed predictions for decays of these
mesons. Precise data in hadronic processes like threshold single and double
meson production in pp collisions close to threshold will be available
from COSY and CELSIUS.
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