Unitarity Constraints On Effective Interaction In Pion N Scattering

From the viewpoint of effective field theory(EFT), new physics effects can be param-eterized as Wilson coefficients(WCs) of higher dimensional effective operators. Usually, these WCs are assumed to be totally free. Of course, concerning the suppression of high energy scale, it is generally believed that these WCs cannot be arbitrarily large, which is also required by the applicability of perturbation methods, for the theory to be of practical use. Were the fundamental theory known, these coefficients should be, at least in principle, uniquely determined as the low energy limit of the underlying one. Naturally one may ask, as there is currently no clear clue about the underlying theory, whether it is still possible to give some constraints-though maybe rather weak in many cases- on the WCs of higher dimensional effective operators. In this thesis, we will study from this angle implications of dispersion relations on effectiveπ-nucleon interactions. Here the underlying theory is supposed to be known (quantum chromodynamics) but difficult to be applied directly, our results will be of help to the analysis of low energy hadronic processes, in addition to illus-trating the general principle of this line reasoning. Using the optical theorem and the isospin crossing symmetry, dispersion relations can be re-interpreted as positivity constraints onπnucleon scattering amplitudes and their even-order derivatives inside the Mandelstam triangle.Fairly interesting constraints are obtained on some of the low energy constants, by a combination of the chiral perturbation theory for heavy baryons and existing fitting results from availableπ-nucleon phase shifts at intermediate energies. If some of the LECs, for example ci and dj, can be obtained from experimental data, fairly non-trivial constraints can be obtained on other LECs e15,16,20,35...