Lectures on SMEFT Falkowski, Adam
European physical journal. C, Particles and fields,
07/2023, Volume:
83, Issue:
7
Journal Article
Peer reviewed
Open access
This document contains lectures on SMEFT, which is an effective field theory of the degrees of freedom of the Standard Model. The material is at a basic, introductory level, without assuming any ...prior knowledge of effective field theory techniques. The main focus is on phenomenological applications of SMEFT in collider, flavor, and low-energy physics.
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Which EFT Falkowski, Adam; Rattazzi, Riccardo
The journal of high energy physics,
10/2019, Volume:
2019, Issue:
10
Journal Article
Peer reviewed
Open access
A
bstract
We classify effective field theory (EFT) deformations of the Standard Model (SM) according to the analyticity property of the Lagrangian as a function of the Higgs doublet
H
. Our ...distinction in
analytic
and
non-analytic
corresponds to the more familiar one between linearly and non-linearly realized electroweak symmetry, but offers deeper physical insight. From the UV perspective, non-analyticity occurs when the new states acquire mass from electroweak symmetry breaking, and thus cannot be decoupled to arbitrarily high scales. This is reflected in the IR by the anomalous growth of the interaction strength for processes involving many Higgs bosons and longitudinally polarized massive vectors, with a breakdown of the EFT description below a scale
𝒪
(4
π𝜐
). Conversely, analyticity occurs when new physics can be pushed parametrically above the electroweak scale. We illustrate the physical distinction between these two EFT families by discussing Higgs boson self-interactions. In the analytic case, at the price of some un-naturalness in the Higgs potential, there exists space for
𝒪
(1) deviations of the cubic coupling, compatible with single Higgs and electroweak precision measurements, and with new particles out of the direct LHC reach. Larger deviations are possible, but subject to less robust assumptions about higher-dimensional operators in the Higgs potential. On the other hand, when the cubic coupling is produced by a non-analytic deformation of the SM, we show by an explicit calculation that the theory reaches strong coupling at
𝒪
(4
π𝜐
), quite independently of the magnitude of the cubic enhancement.
A
bstract
We perform an updated fit to LHC Higgs data and LEP electroweak precision tests in the framework of the Standard Model Effective Field Theory (SMEFT). We assume a generic structure of the ...SMEFT operators without imposing any flavour symmetries. The implementation is released as part of the public global SMEFT likelihood. This allows one to fit parameters of a broad class of new physics models to combined Higgs, electroweak, quark flavour, and lepton flavour observables.
A
bstract
We compile information from low-energy observables sensitive to flavor-conserving 4-fermion operators with two or four leptons. Our analysis includes data from
e
+
e
−
colliders, neutrino ...scattering on electron or nucleon targets, atomic parity violation, parity-violating electron scattering, and the decay of pions, neutrons, nuclei and tau leptons. We recast these data as tree-level constraints on 4-fermion operators in the Standard Model Effective Field Theory (SMEFT) where the SM Lagrangian is extended by dimension-6 operators. We allow all independent dimension-6 operators to be simultaneously present with an arbitrary flavor structure. The results are presented as a multi-dimensional likelihood function in the space of dimension-6 Wilson coefficients, which retains information about the correlations. In this form, the results can be readily used to place limits on masses and couplings in a large class of new physics theories.
A
bstract
We discuss the conditions for an effective field theory (EFT) to give an adequate low-energy description of an underlying physics beyond the Standard Model (SM). Starting from the EFT where ...the SM is extended by dimension-6 operators, experimental data can be used without further assumptions to measure (or set limits on) the EFT parameters. The interpretation of these results requires instead a set of broad assumptions (e.g. power counting rules) on the UV dynamics. This allows one to establish, in a bottom-up approach, the validity range of the EFT description, and to assess the error associated with the truncation of the EFT series. We give a practical prescription on how experimental results could be reported, so that they admit a maximally broad range of theoretical interpretations. Namely, the experimental constraints on dimension-6 operators should be reported as functions of the kinematic variables that set the relevant energy scale of the studied process. This is especially important for hadron collider experiments where collisions probe a wide range of energy scales.
A
bstract
We discuss recursion relations for scattering amplitudes with massive particles of any spin. They are derived via a two-parameter shift of momenta, combining a BCFW-type spinor shift with ...the soft limit of a massless particle involved in the process. The technical innovation is that spinors corresponding to
massive
momenta are also shifted. Our recursions lead to a reformulation of the soft theorems. The well-known Weinberg’s soft factors are recovered and, in addition, the subleading factors appear reshaped such that they are directly applicable to massive amplitudes in the modern on-shell language. Moreover, we obtain new results in the context of non-minimal interactions of massive matter with photons and gravitons. These soft theorems are employed for practical calculations of Compton and higher-point scattering. As a by-product, we introduce a convenient representation of the Compton scattering amplitude for any mass and spin.
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