We calculate the gauge terms of one-loop anomalous dimension matrix for dimension-six operators Standard Model effective field theory (SM EFT). Combining these results with our previous λ and Yukawa coupling completes calculation operators. There are 1350 CP -even 1149 -odd parameters in Lagrangian 3 generations, give entire 2499 × matrix. discuss how renormalization operators, additional d ≤ 4 SM due to lays groundwork future precision studies EFT aimed at constraining effects new physics...

We calculate the complete order y^2 and y^4 terms of 59 x one-loop anomalous dimension matrix for dimension-six operators Standard Model effective field theory, where y is a generic Yukawa coupling. These terms, together with lambda, lambda^2 lambda depending on Higgs self-coupling which were calculated in previous work, yield limit vanishing gauge couplings. The contributions result non-trivial flavor mixing various operator sectors theory.

We calculate the order \lambda, \lambda^2 and \lambda y^2 terms of 59 x one-loop anomalous dimension matrix dimension-six operators, where y are Standard Model Higgs self-coupling a generic Yukawa coupling, respectively. The operators modify running parameters themselves, we compute complete result for this. discuss how there is mixing between which no direct one-particle-irreducible diagram exists, due to operator replacements by equations motion.

A systematic expansion in $\frac{1}{{N}_{c}}$ is constructed for baryons QCD. Predictions of the at leading and subleading order baryon axial vector current coupling constant ratios such as $\frac{F}{D}$, masses, magnetic moments are derived. The sector QCD has a light quark spin-flavor symmetry $\frac{1}{{N}_{c}}$. formalism induced representations contracted Lie algebras introduced to explain consequences this symmetry. Relations first derived case two flavors. generalization large...

The spin-flavor structure of large ${\mathit{N}}_{\mathit{c}}$ baryons is described in the 1/${\mathit{N}}_{\mathit{c}}$ expansion QCD using quark operators. complete set operator identities obtained, and used to derive an reduction rule which simplifies expansion. applied axial vector currents, masses, magnetic moments, hyperon nonleptonic decay amplitudes SU(3) limit, first order breaking, without assuming symmetry. connection between Skyrme representations discussed. An explicit formula...

We calculate the one-loop anomalous dimension matrix for dimension-six baryon number violating operators of Standard Model effective field theory, including right-handed neutrino fields. discuss flavor structure renormalization group evolution in contexts minimal violation and unification.

A bstract We compute the renormalization of dimension six Higgs-gauge boson operators that can modify h → γγ rate at tree-level. Operator mixing is shown to lead an important modification new physics effects which has been neglected in past calculations. also find usual formula for S oblique parameter contribution these needs additional terms be consistent with group evolution. study implications our results Higgs phenomenology and models attempt explain a deviation rate. derive relation...

The gauge-invariant operators up to dimension six in the low-energy effective field theory below electroweak scale are classified. There 70 Hermitian dimension-five and 3631 dimension-six that conserve baryon lepton number, as well $\Delta B= \pm \Delta L = 1$, L=\pm 2$, 4$ operators. matching onto these from Standard Model Effective Field Theory (SMEFT) order $1/\Lambda^2$ is computed at tree level. SMEFT imposes constraints on coefficients of theory, which can be checked experimentally...

A bstract We compute the one-loop anomalous dimensions of low-energy effective Lagrangian below electroweak scale, up to terms dimension six. The theory has 70 dimension-five and 3631 dimension-six Hermitian operators that preserve baryon lepton number, as well additional violate number number. renormalization group equations for quark masses QCD QED gauge couplings are modified by operator contributions. from one insertion operators, two insertions all less than or equal use motion...

A geometric formulation of Higgs Effective Field Theory (HEFT) is presented. Experimental observables are given in terms invariants the scalar sigma model sector such as curvature field manifold $\mathcal M$. We show how can be measured experimentally via cross-sections, $W_L$ scattering, and $S$ parameter. The one-loop action HEFT distinction between Standard Model (SM) whether M$ flat or curved, not scalars transform linearly non-linearly under electroweak group.

The S-matrix of a quantum field theory is unchanged by redefinitions, and so it only depends on geometric quantities such as the curvature space. Whether Higgs multiplet transforms linearly or non-linearly under electroweak symmetry subtle question since one can make coordinate change to convert that into non-linearly. Renormalizability Standard Model (SM) does not depend choice scalar fields whether transform gauge group, but requirement manifold $$ \mathrm{\mathcal{M}} flat. Effective...

A bstract We perform a model-independent analysis of the magnetic and electric dipole moments muon electron. give expressions for in terms operator coefficients low-energy effective field theory (LEFT) Standard Model (SMEFT). use one-loop renormalization group improved perturbation theory, including matching from SMEFT onto LEFT, lepton matrix elements effective-theory operators. Semileptonic four-fermion operators involving light quarks sizable non-perturbative contributions to moments,...

A bstract S -matrix elements are invariant under field redefinitions of the Lagrangian. They determined by geometric quantities such as curvature field-space manifold scalar and gauge fields. We present a formalism where fields treated together, with metric on combined space both types Scalar scattering amplitudes given Riemann R ijkl this space, indices i , j k l chosen to be or depending type external particle. One-loop divergences can also computed in terms invariants which greatly...

A bstract We derive a general formula for two-loop counterterms in Effective Field Theories (EFTs) using geometric approach. This allows the results of our previous paper to be applied wide range theories. The hold loop graphs EFTs where interaction vertices contain operators arbitrarily high dimension, but at most two derivatives. also extend one-loop result include with an arbitrary number derivatives, as long there is one derivative acting on each field. final written terms quantities...

Dark energy models which alter the relative scaling behavior of dark and matter could provide a natural solution to cosmic coincidence problem-why densities are comparable today. A generalized class is introduced allows noncanonical ratio with Robertson-Walker scale factor a(t). We show that determining whether there problem, extent coincidence, can be addressed by several forthcoming experiments.

The anomalous dimensions of dimension-six operators in the Standard Model Effective Field Theory (SMEFT) respect holomorphy to a large extent. conditions are reminiscent supersymmetry, even though SMEFT is not supersymmetric theory.

We derive the general counting rules for a quantum effective field theory (EFT) in $$\mathsf {d}$$ dimensions. The are valid strongly and weakly coupled theories, they predict that all kinetic energy terms canonically normalized. They determine dependence of scattering cross sections range validity EFT expansion. show size is controlled by $$\Lambda $$ power EFT, not chiral counting, even perturbation ( $$\chi PT). relation between f generalized to naive dimensional analysis $$4\pi related...