Chiral perturbation theory and dispersive constraints on light meson form factors

Chiral perturbation theory (ChPT) is the modern way of exploiting chiral symmetry at low energies. This symmetry of quantum chromodynamics is spontaneously broken, the resulting Goldstone bosons being identified with the light pseudoscalar mesons. ChPT provides a systematic calculation of the scattering amplitudes and of the electromagnetic and weak form factors of the light mesons as a simultaneous expansion in powers of momenta and meson masses. Calculations were done recently to two loops (i.e. up to O(p6)) for many processes, allowing a better determination of the unknown constants of the ChPT Lagrangian in terms of low energy experimental input. Interesting consequences of ChPT are the so called low-energy theorems, which predict some relations between amplitudes or form factors valid with an accuracy of the order of chiral symmetry breaking. Explicit higher loop calculations give detailed estimates of these symmetry breaking corrections. One example is Sirlin's theorem, which states that a certain linear combination of pion and kaon electromagnetic form factors Fπ+ (t), F K+ (t), FK0(t) and of the weak form factor fKπ(t) should vanish at small momentum transfer t, up to corrections which are quadratic in the symmetry breaking parameter. Dispersive techniques are very useful for improving the predictions of ChPT and providing relations between the parameters of the theory. Up to now techniques exploiting unitarity in coupled channels and Omnes type representations have been applied. In the present paper we resort to a different technique successfully applied recently to the form factors of heavy mesons. The method uses as input perturbative QCD for correlation functions in the Euclidean region, together with dispersion relations and unitarity at the hadronic level, exploited in an optimal way as to provide an integral relation for the form factors of interest along the time-like cut. As a simple application, the expansion of the pion electromagnetic factor is considered. The allowed domain for the derivatives of the pion electromagnetic form factor is obtained. Although the domain is large, some couples of values considered recently in low energy fits are excluded. Other applications, such as bounds on Sirlin function, location of zeros and the optimal treatment of the phase of the form factors are under study. (author)