We present the automation of one-loop computations in the standard-model effective field theory at dimension six. Our general implementation, dubbed SMEFT@NLO, covers all types of operators: bosonic, two- and four-fermion ones. Included ultraviolet a
nd rational counterterms presently allow for fully differential predictions, possibly matched to parton shower, up to the one-loop level in the strong coupling or in four-quark operator coefficients. Exact flavor symmetries are imposed among light quark generations and an initial focus is set on top-quark interactions in the fermionic sector. We illustrate the potential of this implementation with novel loop-induced and next-to-leading-order computations relevant for top-quark, electroweak, and Higgs-boson phenomenology at the LHC and future colliders.
The purely on-shell approach to effective field theories requires the construction of independent contact terms. Employing the little-group-covariant massive-spinor formalism, we present the first systematic derivation of independent four-point conta
ct terms involving massive scalars, spin-1/2 fermions, and vectors. Independent three-point amplitudes are also listed for massive particles up to spin-3. We make extensive use of the simple relations between massless and massive amplitudes in this formalism. Our general results are specialized to the (broken-phase) particle content of the electroweak sector of the standard model. The (anti)symmetrization among identical particles is then accounted for. This work opens the way for the on-shell computation of massive four-point amplitudes.
We establish a simple formula for the minimal dimension of operators leading to any helicity amplitude. It eases the systematic enumeration of independent operators from the construction of massless non-factorizable on-shell amplitudes. Little-group
constraints can then be solved algorithmically for each helicity configuration to extract a complete set of spinor structures with lowest dimension. Occasionally, further reduction using momentum conservation, on-shell conditions and Schouten identities is required. A systematic procedure to account for the latter is presented. Dressing spinor structures with dot products of momenta finally yields the independent Lorentz structures for each helicity amplitude. We apply these procedures to amplitudes involving particles of spins 0,1/2,1,2. Spin statistics and elementary selection rules due to gauge symmetry lead to an enumeration of operators involving gravitons and standard-model particles, in the effective field theory denoted GRSMEFT. We also list the independent spinor structures generated by operators involving standard-model particles only. In both cases, we cover operators of dimension up to eight.
We apply on-shell methods to the bottom-up construction of electroweak amplitudes, allowing for both renormalizable and non-renormalizable interactions. We use the little-group covariant massive-spinor formalism, and flesh out some of its details alo
ng the way. Thanks to the compact form of the resulting amplitudes, many of their properties, and in particular the constraints of perturbative unitarity, are easily seen in this formalism. Our approach is purely bottom-up, assuming just the standard-model electroweak spectrum as well as the conservation of electric charge and fermion number. The most general massive three-point amplitudes consistent with these symmetries are derived and studied in detail, as the primary building blocks for the construction of scattering amplitudes. We employ a simple argument, based on tree-level unitarity of four-point amplitudes, to identify the three-point amplitudes that are non-renormalizable at tree level. This bottom-up analysis remarkably reproduces many low-energy relations implied by electroweak symmetry through the standard-model Higgs mechanism and beyond it. We then discuss four-point amplitudes. The gluing of three-point amplitudes into four-point amplitudes in the massive spinor helicity formalism is clarified. As an example, we work out the $psi^c psi Zh$ amplitude, including also the non-factorizable part. The latter is an all-order expression in the effective-field-theory expansion. Further constraints on the couplings are obtained by requiring perturbative unitarity. In the $psi^c psi Zh$ example, one for instance obtains the renormalizable-level relations between vector and fermion masses and gauge and Yukawa couplings. We supplement our bottom-up derivations with a matching of three- and four-point amplitude coefficients onto the standard-model effective field theory (SMEFT) in the broken electroweak phase.
We propose a procedure to cross-validate Monte Carlo implementations of the standard model effective field theory. It is based on the numerical comparison of squared amplitudes computed at specific phase-space and parameter points in pairs of impleme
ntations. Interactions are fully linearised in the effective field theory expansion. The squares of linear effective field theory amplitudes and their interference with standard-model contributions are compared separately. Such pairwise comparisons are primarily performed at tree level and a possible extension to the one-loop level is also briefly considered. We list the current standard model effective field theory implementations and the comparisons performed to date.
In composite Higgs (CH) models, large mixings between the top quark and the new strongly interacting sector are required to generate its sizeable Yukawa coupling. Precise measurements involving top as well as left-handed bottom quarks therefore offer
an interesting opportunity to probe such new physics scenarios. We study the impact of third-generation-quark pair production at future lepton colliders, translating prospective effective-field-theory sensitivities into the CH parameter space. Our results show that one can probe a significant fraction of the natural CH parameter space through the top portal, especially at TeV centre-of-mass energies.
We study the sensitivity to physics beyond the standard model of precise top-quark pair production measurements at future lepton colliders. A global effective-field-theory approach is employed, including all dimension-six operators of the Warsaw basi
s which involve a top-quark and give rise to tree-level amplitudes that interfere with standard-model $e^+e^-to t,bar tto bW^+bar bW^-$ ones in the limit of vanishing $b$-quark mass. Four-fermion and CP-violating contributions are taken into account. Circular-collider-, ILC- and CLIC-like benchmark run scenarios are examined. We compare the constraining power of various observables to a set of statistically optimal ones which maximally exploit the information contained in the fully differential $bW^+bar bW^-$ distribution. The enhanced sensitivity gained on the linear contributions of dimension-six operators leads to bounds that are insensitive to quadratic ones. Even with statistically optimal observables, two centre-of-mass energies are required for constraining simultaneously two- and four-fermion operators. The impact of the centre-of-mass energy lever arm is discussed, that of beam polarization as well. A realistic estimate of the precision that can be achieved in ILC- and CLIC-like operating scenarios yields individual limits on the electroweak couplings of the top quark that are one to three orders of magnitude better than constraints set with Tevatron and LHC run I data, and three to two hundred times better than the most optimistic projections made for the high-luminosity phase of the LHC. Clean global constraints can moreover be obtained at lepton colliders, robustly covering the multidimensional effective-field-theory space with minimal model dependence.
We examine the constraints that future lepton colliders would impose on the effective field theory describing modifications of top-quark interactions beyond the standard model, through measurements of the $e^+e^-to bW^+:bar bW^-$ process. Statistical
ly optimal observables are exploited to constrain simultaneously and efficiently all relevant operators. Their constraining power is sufficient for quadratic effective-field-theory contributions to have negligible impact on limits which are therefore basis independent. This is contrasted with the measurements of cross sections and forward-backward asymmetries. An overall measure of constraints strength, the global determinant parameter, is used to determine which run parameters impose the strongest restriction on the multidimensional effective-field-theory parameter space.
Beauty baryons are being observed in large numbers in the LHCb detector. The rich kinematic distributions of their multibody decays are therefore becoming accessible and provide us with new opportunities to search for CP violation. We analyse the ang
ular distributions of some three- and four-body decays of spin-$1/2$ baryons using the Jacob-Wick helicity formalism. The asymmetries that provide access to small differences of CP-odd phases between decay amplitudes of identical CP-even phases are notably discussed. The understanding gained on processes featuring specific resonant intermediate states allows us to establish which asymmetries are relevant for what purpose. It is for instance shown that some CP-odd angular asymmetries measured by the LHCb collaboration in the $Lambda_b to Lambda,varphi to p,pi, K^+ K^-$ decay are expected to vanish identically.
We revisit the topic of triple-product asymmetries which probe CP violation through differential distributions. We construct distributions with well-defined discrete symmetry properties and characterize the asymmetries formed upon them. It is stresse
d that the simplest asymmetries may not be optimal. We explore systematic generalizations having limited reliance on the process dynamics and phase-space parametrization. They exploit larger fractions of the information contained in differential distributions and may lead to increased sensitivities to CP violation. Our detailed treatment of the case of spinless four-body decays paves the way for further experimental studies.
