S-matrix bootstrap for effective field theories: massless pions

Bootstrap equations in effective theories

Presently, there are known two different approaches to the problem of constructing of a relativistic quantum theory suitable to describe the scattering processes. According to the first – canonical – approach one has to fix a finite set of (fundamental) fields and the Lagrangian that satisfies certain conditions (locality, hermiticity, symmetry, renormalizability, etc.). To obtain the quantum v...

Pions in the Pionless Effective Field Theory

We show that processes involving pions that remain very near their massshell can be reliably computed in the pionless effective field theory, with the pion integrated in as a heavy field. As an application, we compute the πdeuteron scattering amplitude near threshold to next-to-leading order in the momentum expansion. This amplitude is formally dominated by an infrared logarithm of the form log...

Are Pions Perturbative in Effective Field Theory?

It is shown that pions can be included perturbatively into effective field theory only for the external momenta, well below the pion mass. But for such low energies it is not necessary to include pions explicitly. 03.65.Nk, 11.10.Gh, 12.39.Fe, 13.75.Cs. Typeset using REVTEX

Nucleon-Nucleon Effective Field Theory Without Pions

Nuclear processes involving momenta much below the mass of the pion may be described by an effective field theory in which the pions do not appear as explicit degrees of freedom. The effects of the pion and all other virtual hadrons are reproduced by the coefficients of gauge-invariant local operators involving the nucleon field. Nucleon-nucleon scattering phase shift data constrains many of th...

Effective Field Theories for Inflation