38 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
Renormalization and additional degrees of freedom within the chiral effective theory for spin-1 resonances
We study in detail various aspects of the renormalization of the spin-1
resonance propagator in the effective field theory framework. First, we briefly
review the formalisms for the description of spin-1 resonances in the path
integral formulation with the stress on the issue of propagating degrees of
freedom. Then we calculate the one-loop 1-- meson self-energy within the
Resonance chiral theory in the chiral limit using different methods for the
description of spin-one particles, namely the Proca field, antisymmetric tensor
field and the first order formalisms. We discuss in detail technical aspects of
the renormalization procedure which are inherent to the power-counting
non-renormalizable theory and give a formal prescription for the organization
of both the counterterms and one-particle irreducible graphs. We also construct
the corresponding propagators and investigate their properties. We show that
the additional poles corresponding to the additional one-particle states are
generated by loop corrections, some of which are negative norm ghosts or
tachyons. We count the number of such additional poles and briefly discuss
their physical meaning.Comment: 65 pages, 12 figure