Equations of motion, symmetry currents and EFT below the electroweak scale

The low-energy effective field theory is constructed by integrating out Standard Model states with masses proximate to the electroweak scale. We report the equations of motion for this theory, including corrections due to higher dimensional operators up to mass dimension six. We construct the corresponding symmetry currents, and discuss how the $\rm SU(2)_L \times U(1)_{\mathsf{y}}$ symmetry, and global symmetries, are manifested when Standard Model states are integrated out. Including contributions from higher dimensional operators to the equations of motion modifies the interpretation of conserved currents. We discuss the corrections to the electromagnetic current as an example, showing how modifications to the equation of motion, and corresponding surface terms, have a direct interpretation in terms of multipole charge distributions that act to source gauge fields.Comment: 13 page

On interference and non-interference in the SMEFT

We discuss interference in the limit $\hat{m}_{W}^2/s \rightarrow 0$ in the Standard Model Effective Field Theory (SMEFT). Dimension six operators that contribute to $\bar{\psi} \psi \rightarrow \bar{\psi'}_1 \psi_2' \bar{\psi'}_3 \psi'_4$ scattering events can experience a suppression of interference effects with the Standard Model in this limit. This occurs for subsets of phase space in some helicity configurations. We show that approximating these scattering events by $2\rightarrow 2$ on-shell scattering results for intermediate unstable gauge bosons, and using the narrow width approximation, can miss interference terms present in the full phase space. Such interference terms can be uncovered using off-shell calculations as we explicitly show and calculate. We also study the commutation relation between the SMEFT expansion and the narrow width approximation, and discuss some phenomenological implications of these results.Comment: 19 pages, 3 figures. Updated to published JHEP versio

Scattering Equations and Factorization of Amplitudes II: Effective Field Theories

We continue the program of extending the scattering equation framework by Cachazo, He and Yuan to a double-cover prescription. We discuss how to apply the double-cover formalism to effective field theories, with a special focus on the non-linear sigma model. A defining characteristic of the double-cover formulation is the emergence of new factorization relations. We present several factorization relations, along with a novel recursion relation. Using the recursion relation and a new prescription for the integrand, any non-linear sigma model amplitude can be expressed in terms of off-shell three-point amplitudes. The resulting expression is purely algebraic, and we do not have to solve any scattering equation. We also discuss soft limits, boundary terms in BCFW recursion, and application of the double-cover prescription to other effective field theories, like the special Galileon theory.Comment: 39+14 page

Gauge fixing the Standard Model Effective Field Theory

We gauge fix the Standard Model Effective Field Theory in a manner invariant under background field gauge transformations using a geometric description of the field connections.Comment: 4 pages. Accepted in PR

Baryon number, lepton number, and operator dimension in the SMEFT with flavor symmetries

For a large set of flavor symmetries, the lowest-dimensional baryon- or lepton-number violating operators in the Standard Model effective field theory (SMEFT) with flavor symmetry are of mass dimension 9. As a consequence, baryon- and lepton-number violating processes are further suppressed with the introduction of flavor symmetries, e.g., the allowed scale associated with proton decay is typically lowered to $10^5$ GeV, which is significantly lower than the GUT scale. To illustrate these features, we discuss Minimal Flavor Violation for the Standard Model augmented by sterile neutrinos.Comment: 6 pages, 2 figure

The double copy for heavy particles

We show how to double-copy Heavy Quark Effective Theory (HQET) to Heavy Black Hole Effective Theory (HBET) for spin $s\leq 1$. In particular, the double copy of spin-$s$ HQET with scalar QCD produces spin-$s$ HBET, while the double copy of spin-1/2 HQET with itself gives spin-1 HBET. Finally, we present novel all-order-in-mass Lagrangians for spin-1 heavy particles.Comment: 6 page

Tidal effects in quantum field theory

We apply the Hilbert series to extend the gravitational action for a scalar field to a complete, non-redundant basis of higher-dimensional operators that is quadratic in the scalars and the Weyl tensor. Such an extension of the action fully describes tidal effects arising from operators involving two powers of the curvature. As an application of this new action, we compute all spinless tidal effects at the leading post-Minkowskian order. This computation is greatly simplified by appealing to the heavy limit, where only a severely constrained set of operators can contribute classically at the one-loop level. Finally, we use this amplitude to derive the $\mathcal{O}(G^{2})$ tidal corrections to the Hamiltonian and the scattering angle.Comment: 13 pages + appendices, 1 figure. v2: corrected typo in EM amplitud

Ward identities for the standard model effective field theory

We derive Ward identities for the Standard Model Effective Field Theory using the background field method. The resulting symmetry constraints on the Standard Model Effective Field Theory are basis independent, and constrain the perturbative and power-counting expansions. A geometric description of the field connections, and real representations for the $\rm SU(2)_L \times U(1)_Y$ generators, underlies the derivation.Comment: 6 page

On-shell heavy particle effective theories

We introduce on-shell variables for Heavy Particle Effective Theories (HPETs) with the goal of extending Heavy Black Hole Effective Theory to higher spins and of facilitating its application to higher post-Minkowskian orders. These variables inherit the separation of spinless and spin-inclusive effects from the HPET fields, resulting in an explicit spin-multipole expansion of the three-point amplitude for any spin. By matching amplitudes expressed using the on-shell HPET variables to those derived from the one-particle effective action, we find that the spin-multipole expansion of a heavy spin-$s$ particle corresponds exactly to the multipole expansion (up to order $2s$) of a Kerr black hole, that is, without needing to take the infinite spin limit. Finally, we show that tree-level radiative processes with same-helicity bosons emitted from a heavy spin-$s$ particle exhibit a spin-multipole universality.Comment: 28 pages + appendice