Abstract
We use the amplitude soft bootstrap method to explore the space of effective field theories (EFT) of massless vectors and scalars. It is known that demanding vanishing soft limits fixes uniquely a special class of EFTs: non-linear sigma model, scalar Galileon and Born-Infeld theories. Based on the amplitudes analysis, we conjecture no-go theorems for higher-derivative vector theories and theories with coupled vectors and scalars. We then allow for more general soft theorems where the non-trivial part of the soft limit of the (n+1)-pt amplitude is equal to a linear combination of n-pt amplitudes. We derive the form of these soft theorems for general power-counting and spins of particles and use it as an input into the soft bootstrap method in the case of Galileon power-counting and coupled scalar-vector theories. We show that this unifies the description of existing Galileon theories and leads us to the discovery of a new exceptional theory: Special scalar-vector Galileon.
Highlights
Structures and symmetries in the perturbative S-matrix which are completely invisible in the standard Feynman diagrams approach
In the extension of tree-level unitarity and BCFW recursion relations, the scattering amplitudes in non-linear sigma model, DiracBorn-Infeld theory, Volkov-Akulov, and Galileons were uniquely specified by special soft limit behavior [28,29,30,31,32,33] and further lead to the discovery of Special Galileon theory [31, 34]
We focus on the case of scalar-vector theories with fixed power-counting and demonstrate that there is a unique theory fixed by these soft theorems which we call Special scalar-vector Galileon as the scalar part of this theory corresponds to the Special Galileon
Summary
The low-energy effective field theories are defined by the Lagrangian which can have in principle an infinite tower of terms with undefined coupling constants. We start with the space of all tree-level S-matrices which have only physical poles and factorize properly Such S-matrix ansatz has a certain number of unfixed parameters which are in one-to-one correspondence (up to field redefinitions) to free coupling constants in Lagrangian (when redundant terms are eliminated by equations of motion and total derivatives). The soft bootstrap approach is following: generate an ansatz for the tree-level amplitudes where each independent kinematical invariant is multiplied by a free parameter. These parameters are in one-to-one correspondence with the independent parameters in the Lagrangian (2.3) after the off-shell redundancies are removed. In analogy with BCFW we can reconstruct the amplitude recursively from the sum of residua over the factorization channels
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