Eur. Phys. J. C 9, 643-671 (1999)
https://doi.org/10.1007/PL00021673

Baryon chiral perturbation theory in manifestly Lorentz invariant form

Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland

Received: 11 February 1999
Published online: 18 June 1999

Abstract

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 converges in only 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_π². In the language of heavy baryon chiral perturbation theory, the proper behaviour in the threshold region results only 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 p⁴