Authors: Karol Kampf Jirí Novotný Jaroslav Trnka
Publish Date: 2013/05/07
Volume: 2013, Issue: 5, Pages: 32-
Abstract
We study in detail the general structure and further properties of the treelevel amplitudes in the SUN nonlinear sigma model We construct the flavorordered Feynman rules for various parameterizations of the SUN fields U x write down the BerendsGiele relations for the semionshell currents and discuss their efficiency for the amplitude calculation in comparison with those of renormalizable theories We also present an explicit form of the partial amplitudes up to ten external particles It is well known that the standard BCFW recursive relations cannot be used for reconstruction of the the onshell amplitudes of effective theories like the SUN nonlinear sigma model because of the inappropriate behavior of the deformed onshell amplitudes at infinity We discuss possible generalization of the BCFW approach introducing “BCFW formula with subtractions” and with help of BerendsGiele relations we prove particular scaling properties of the semionshell amplitudes of the SUN nonlinear sigma model under specific shifts of the external momenta These results allow us to define alternative deformation of the semionshell amplitudes and derive BCFWlike recursion relations These provide a systematic and effective tool for calculation of Goldstone bosons scattering amplitudes and it also shows the possible applicability of onshell methods to effective field theories We also use these BCFWlike relations for the investigation of the Adler zeroes and double soft limit of the semionshell amplitudes
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