On the Size of the Chiral Condensate, Generalized Chiral Perturbation Theory and the DIRAC experiment

In the near future, the DIRAC collaboration will measure pion-pion scattering lengths with great precision. Those measurements are likely to shed some light on the problem of the size of the chiral quark-antiquark condensate. Although it is usually assumed to be as a large as (-225 MeV)^3, in the last years a more general approach, has been developed to accommodate either a large or a small alternative (-100 MeV)^3. Such a low value would also modify the standard temperature estimate at which the chiral phase transition occurs. In this work we briefly review the basic theoretical ideas related to this issue as well as the experiment that could help to establish any of the two scenarios.