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Chiral Dynamics

Chiral perturbation theory (CHPT) provides a framework for non-perturbative 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 self-consistent 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, G-parity forbids isospin-violating strong interaction terms $\sim m_{d}-m_{u}$ to leading order in the pion Lagrangian, but allows such leading terms in the pion-nucleon sector. Therefore, precise measurements of elastic pion-nucleon 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 $\pi ^{0}$ production off protons has been already performed. Fig.[*] represents the data for the amplitude of $\pi ^{0}$ photoproduction at threshold compared to the chiral perturbation prediction.
  
Figure: Amplitude of photoproduction of $\pi ^{0}$ at threshold. The data are compared to the prediction of low energy theorems (LET) and chiral perturbation theory (ChPT). 
\begin{figure}\epsfig{file=hadron/fig3.eps, width=\columnwidth}\end{figure}
 

Similarly, the precise pionic atom measurements to determine the S-wave $ \pi N$ 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 md-mu. 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 $\pi^{+}\pi ^{-}$. The inclusion of the strange quark is a challenge since the strange quark mass is much larger than mu,d. Calculations indicate the usefulness of CHPT in the threshold region, but precise data are needed to test the predictions. DA$\Phi $NE will produce large numbers of K-mesons and also $ \eta ,\eta ^{\prime }$ mesons. CELSIUS and the 4$\pi $ WASA detector will provide an $\eta $ 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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