Positivity constraints on interacting spin-2 fields

Self Cite

We consider the effective field theory of multiple interacting massive spin-2 fields. We focus on the case where the interactions are chosen so that the cutoff is the highest possible, and highlight two distinct classes of theories. In the first class, the mass eigenstates only interact through potential operators that carry no derivatives in unitary gauge at leading order. In the second class, a specific kinetic mixing between the mass eigenstates is included non-linearly. Performing a decoupling and ADM analysis, we point out the existence of a ghost present at a low scale for the first class of interactions. For the second class of interactions where kinetic mixing is included, we derive the full Λ 3decoupling limit and confirm the absence of any ghosts. Nevertheless both formulations can be used to consistently describe an EFT of interacting massive spin-2 fields which, for a suitable technically natural tuning of the EFT, have the same strong coupling scale Λ 3. We identify the generic form of EFT corrections in each case. By using Galileon Duality transformations for the specific case of two massive spin-2 fields with suitable couplings, the decoupling limit theory is shown to be a bi-Galileon.

Section: Discussionmentioning

confidence: 99%

Section: Jhep01(2020)131mentioning

confidence: 99%

EFT of interacting spin-2 fields

Alberte

Rham

Momeni

et al. 2020

Self Cite

“…Whether or not any single or multiple interacting massive spin-2 fields could have a standard UV completion remains as yet unclear [26]. By assuming the UV completion to be Lorentz invariant, causal and unitary it is possible to derive particular bounds on the scattering amplitudes of the low energy EFTs, so called positivity bounds, which restrict the allowed parameter space of the EFT [27][28][29][30][31][32][33][34][35][36]. We stress that a failure to satisfy these bounds does not imply the EFT is inconsistent but only that it could not have a standard UV completion, but this does not preclude a non-standard UV completion [33].…”

Section: Jhep07(2020)121mentioning

confidence: 99%

“…In a recent work [36] we applied the positivity bounds to EFTs of interacting multiple spin-2 fields described in [41], which were extensions of ghost-free massive gravity. In this paper we apply these bounds to effective field theories of one or more interacting pseudolinear massive spin-2 fields.…”

Section: Jhep07(2020)121mentioning

confidence: 99%

“…In this paper we apply these bounds to effective field theories of one or more interacting pseudolinear massive spin-2 fields. The particular case of a single pseudo-linear spin-2 field was considered already in [31] where it was shown that for the leading 'ghost-free' interactions some of the definite helicity positivity bounds have to be marginal, unlike its close cousin 'ghost-free massive gravity' [30,33,35,36]. Another interesting example where positivity bounds are marginal is in the case of massless Galileons [42].…”

Section: Jhep07(2020)121mentioning

confidence: 99%

See 1 more Smart Citation

Positivity constraints on interacting pseudo-linear spin-2 fields

Alberte

Rham

Momeni

et al. 2020

Self Cite

We explore the effective field theory for single and multiple interacting pseudolinear spin-2 fields. By applying forward limit positivity bounds, we show that among the parameters contributing to elastic tree level scattering amplitude, there is no region of compatibility of the leading interactions with a standard local UV completion. Our result generalizes to any number of interacting pseudo-linear spin-2 fields. These results have significant implications for the organization of the effective field theory expansion for pseudo-linear fields.

Elastic positivity vs extremal positivity bounds in SMEFT: a case study in transversal electroweak gauge-boson scatterings

Yamashita

Zhang

Zhou

2021

The positivity bounds, derived from the axiomatic principles of quantum field theory (QFT), constrain the signs of Wilson coefficients and their linear combinations in the Standard Model Effective Field Theory (SMEFT). The precise determination of these bounds, however, can become increasingly difficult as more and more SM modes and oper- ators are taken into account. We study two approaches that aim at obtaining the full set of bounds for a given set of SM fields: 1) the traditional elastic positivity approach, which exploits the elastic scattering amplitudes of states with arbitrarily superposed helicities as well as other quantum numbers, and 2) the newly proposed extremal positivity approach, which constructs the allowed coefficient space directly by using the extremal representation of convex cones. Considering the electroweak gauge-bosons as an example, we demonstrate how the best analytical and numerical positivity bounds can be obtained in several ways. We further compare the constraining power and the efficiency of various approaches, as well as their applicability to more complex problems. While the new extremal approach is more constraining by construction, we also find that it is analytically easier to use, nu- merically much faster than the elastic approach, and much more applicable when more SM particle states and operators are taken into account. As a byproduct, we provide the best positivity bounds on the transversal quartic-gauge-boson couplings, required by the axiomatic principles of QFT, and show that they exclude ≈ 99.3% of the parameter space currently being searched at the LHC.