The effective chiral lagrangian of the MSM at one- and two-loop order Original Research Article

The formalism of the matching conditions between transverse connected Green functions is extended to include the two next to leading corrections, namely the two-loop MH2 and the one-loop 1/MH2 contributions to the coefficients of the electroweak chiral lagrangian which are relevant to the LEP1 physics: a0, â8. We derive general expressions for these three coefficients in terms of just bare gauge boson self-energies that can be used to get the leading Higgs mass contribution to these coefficients at each loop order. We solve the problems concerning the loss of gauge invariance and the inclusion of only gauge invariant operators by proposing a new formulation 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 screening for the renormalized photon self-energy in the on-shell scheme at all orders. In addition, the automatic cancellation of the unphysical MH2 terms in the other gauge boson self-energies at two loops in this scheme is shown. Finally we will apply the obtained electroweak chiral lagrangian to compute the different Higgs mass contributions to the bosonic part of Δϱ, Δ, ϱ and Δκ carefully analyzing the hierarchy between corrections.