Baryon Chiral Perturbation Theory in Manifestly Lorentz Invariant Form
We show that in the presence of massive particles such as nucleons, the standard low energy expansion in powers of meson momenta and light quark masses in general only converges in part of the low energy region. The expansion of the scalar form factor $σ(t)$, for instance, breaks down in the vicinity of $t=4M_π^2$. In the language of heavy baryon chiral perturbation theory, the proper behaviour in the threshold region only results if the multiple internal line insertions generated by relativistic kinematics are summed up to all orders. We propose a method that yields a coherent representation throughout the low energy region while keeping Lorentz and chiral invariance explicit at all stages. The method is illustrated with a calculation of the nucleon mass and of the scalar form factor to order $p^4$.