We present a complete list of the dimension-eight operator basis in standard model effective field theory using group theoretic techniques systematic and automated way. adopt new form operators terms irreducible representations Lorentz identify structures as states $SU(N)$ group. In this way, redundancy from equations motion is absent that integration by part treated fact independent forms an invariant subspace also decompose into ones with definite permutation symmetries among flavor...

We present a complete and independent list of the dimension-nine operator basis in Standard Model effective field theory by an automatic algorithm based on amplitude-operator correspondence. A ($Y$-basis) is first constructed enumerating Young tableau auxiliary $SU(N)$ group gauge groups, with equation-of-motion integration-by-part redundancies all removed. In presence repeated fields, another ($P$-basis) explicit flavor symmetries among them derived from $Y$-basis, which further induces...

We obtain the complete and independent bases of effective operators at mass dimension 5, 6, 7, 8, 9 in both standard model field theory with light sterile right-handed neutrinos ($\nu$SMEFT) low energy ($\nu$LEFT). These theories provide systematical parametrizations on all possible Lorentz-invariant physical effects involving Majorana/Dirac neutrinos, with/without lepton number violations. In $\nu$SMEFT, we find that there are 2 (18), 29 (1614), 80 (4206), 323 (20400), 1358 (243944)...

We derive the generalized partial wave expansion for $N\ensuremath{\rightarrow}M$ scattering amplitude in terms of spinor helicity variables. The basis amplitudes with definite angular momentum $j$ consist Poincar\'e Clebsch-Gordan coefficients. Moreover, we obtain a series selection rules that restrict anomalous dimension matrix effective operators and how contribute to some $2\ensuremath{\rightarrow}N$ at loop level.

We establish a systematic construction of the on-shell amplitude/operator basis for Chiral Perturbation Theory (ChPT) in $D=4$ spacetime dimensions and with an arbitrary number flavors $N_f$. For kinematic factors, we employ spinor-helicity variables to construct soft blocks, which are local amplitudes satisfying Adler's zero condition, as well take into account reduction due Gram determinant, arises at $O(p^{10})$ when multiplicity $N$ amplitude becomes large: $N>D$. flavor include...

A bstract We construct the on-shell amplitude basis and corresponding effective operators for generic modified gravity theory, such as pure with higher derivatives, scalar-tensor gravity, Einstein-Yang-Mills, etc. Taking Weyl tensor building block, we utilize Young technique to obtain independent operators, without equation of motion total derivative redundancies. update our algorithm vastly increase speed finding monomial (m-basis) expressed in terms tensors Lorentz indices, familiar form...

A bstract We obtain the complete operator bases at mass dimensions 5, 6, 7, 8, 9 for low energy effective field theory (LEFT), which parametrize various physics effects between QCD scale and electroweak scale. The independence of basis regarding equation motion, integration by parts flavor relations, is guaranteed our algorithm [1, 2], whose validity LEFT with massive fermions involved proved a generalization amplitude-operator correspondence. At dimension 8 9, we list 35058 (756) 704584...

We construct the general partial wave amplitude basis for $N\ensuremath{\rightarrow}M$ scattering, which consists of Poincar\'e Clebsch-Gordan coefficients, in a Lorentz invariant form given terms spinor-helicity variables. The inner product coefficients is defined, converts on-shell phase space integration into an algebraic problem. also develop technique expansions arbitrary amplitudes, including those with infrared divergence. These are applied to computation anomalous dimension matrix...

We construct the on-shell amplitude basis and corresponding effective operators for generic modified gravity theory, such as pure with higher derivatives, scalar-tensor gravity, Einstein-Yang-Mills, etc. Taking Weyl tensor building block, we utilize Young technique to obtain independent operators, without equation of motion total derivative redundancies. update our algorithm vastly increase speed finding monomial (m-basis) expressed in terms tensors Lorentz indices, familiar form General...