THE EFFECTIVE CHIRAL LAGRANGIAN OF THE MSM AT ONE-LOOP AND 2-LOOP ORDER

The formalism of the matching conditions between transverse connected Green functions is extended to include the two next to leading correct ions, namely the two-loop M(H)(2) and the one-loop 1/M(H)(2) contribut ions to the coefficients of the electroweak chiral lagrangian which ar e relevant to the LEP1 physics: a(0), (a) over cap(1) and (a) over cap (8). We derive general expressions for these three coefficients in ter ms of just bare gauge boson self-energies that can be used to get the leading Higgs mass contribution to these coefficients at each loop ord er. We solve the problems concerning the loss of gauge invariance and the inclusion of only gauge invariant operators by proposing a new for mulation of the matching conditions at two and higher loop orders. As an example of the usefulness of using an electroweak chiral lagrangian to parametrize the MSM, we will give a simple proof of an extra scree ning for the renormalized photon self-energy in the on-shell scheme at all orders. In addition, the automatic cancellation of the unphysical M(H)(4) terms in the other gauge boson self-energies at two loops in this scheme is shown. Finally we will apply the obtained electroweak c hiral lagrangian to compute the different Higgs mass contributions to the bosonic part of Delta rho, Delta r and Delta kappa, carefully anal yzing the hierarchy between corrections.