84 research outputs found
On-Shell Recursion Relations for Effective Field Theories
We derive the first ever on-shell recursion relations for amplitudes in
effective field theories. Based solely on factorization and the soft behavior
of amplitudes, these recursion relations employ a new rescaling momentum shift
to construct all tree-level scattering amplitudes in theories like the non-
linear sigma model, Dirac-Born-Infeld theory, and the Galileon. Our results
prove that all theories with enhanced soft behavior are on-shell constructible.Comment: 5 page
Effective Field Theories from Soft Limits of Scattering Amplitudes
We derive scalar effective field theories—Lagrangians, symmetries, and all—from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galilean internal shift symmetries. Moreover, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist
Goldstone bosons on celestial sphere and conformal soft theorems
In this paper, we study celestial amplitudes of Goldstone bosons and
conformal soft theorems. Motivated by the success of soft bootstrap in momentum
space and the important role of the soft limit behavior of tree-level
amplitudes, our goal is to extend some of the methods to the celestial sphere.
The crucial ingredient of the calculation is the Mellin transformation which
transforms four-dimensional scattering amplitudes to correlation functions of
primary operators in the celestial CFT. The soft behavior of the amplitude is
then translated to the singularities of the correlator. Only for amplitudes in
"UV completed theories" (with sufficiently good high energy behavior) the
Mellin integration can be properly performed, in all other cases, the celestial
amplitude is only defined in a distributional sense with delta functions. We
provide many examples of celestial amplitudes in UV-completed models including
linear sigma models and Z-theory, which is a certain completion of the SU(N)
non-linear sigma model. We also comment on the BCFW-like and soft recursion
relations for celestial amplitudes and the extension of soft bootstrap ideas.
45 pages of main text + 6 appendicess and 6 figuresComment: 45 pages of the main text, 6 appendices and 6 figure
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