The Standard Model as an Effective Field Theory

Projecting measurements of the interactions of the known Standard Model (SM) states into an effective field theory (EFT) framework is an important goal of the LHC physics program. The interpretation of measurements of the properties of the Higgs-like boson in an EFT allows one to consistently study the properties of this state, while the SM is allowed to eventually break down at higher energies. In this review, basic concepts relevant to the construction of such EFTs are reviewed pedagogically. Electroweak precision data is discussed as a historical example of some importance to illustrate critical consistency issues in interpreting experimental data in EFTs. A future precision Higgs phenomenology program can benefit from the projection of raw experimental results into consistent field theories such as the SM, the SM supplemented with higher dimensional operators (the SMEFT) or an Electroweak chiral Lagrangian with a dominantly $J^P = 0^+$ scalar (the HEFT). We discuss the developing SMEFT and HEFT approaches, that are consistent versions of such EFTs, systematically improvable with higher order corrections, and comment on the pseudo-observable approach. We review the challenges that have been overcome in developing EFT methods for LHC studies, and the challenges that remain.Comment: Version accepted by Physics Reports. Sections on the EFT landscape and the method of regions added. Typos fixe

Scheming in the SMEFT... and a reparameterization invariance!

We explain a reparameterization invariance in the Standard Model Effective Field Theory present when considering $\bar{\psi} \psi \rightarrow \bar{\psi} \psi$ scatterings (with $\psi$ a fermion) and how this leads to unconstrained combinations of Wilson coefficients in global data analyses restricted to these measurements. We develop a $\{\hat{m}_W, \hat{m}_Z,\hat{G}_F\}$ input parameter scheme and compare results to the case when an input parameter set $\{\hat{\alpha}, \hat{m}_Z,\hat{G}_F\}$ is used to constrain this effective theory from the global data set, confirming the input parameter independence of the unconstrained combinations of Wilson coefficients, and supporting the reparameterization invariance explanation. We discuss some conceptual issues related to these degeneracies that are relevant for LHC data reporting and analysis.Comment: 41 pages, 8 tables, 8 figures. addendum in appendix - results obtained allowing two independent flavor contractions for the operator Q_ll in the U(3)^5 flavor symmetric limi

The Neutrino Option

The minimal seesaw scenario can radiatively generate the Higgs potential to induce electroweak symmetry breaking while supplying an origin of the Higgs vacuum expectation value from an underlying Majorana scale. If the Higgs potential and (derived) electroweak scale have this origin, the heavy $\rm SU(3) \times SU(2) \times U(1)_Y$ singlet states are expected to reside at $m_N \sim 10-500 \, {\rm PeV}$ for couplings $|\omega| \sim 10^{-4.5}-10^{-6}$ between the Majorana sector and the Standard Model. In this framework, the challenge of the electroweak scale hierarchy problem is replaced with a need to generate or accommodate PeV Majorana mass scales in ultraviolet models; the usual hierarchy problem is absent as the electroweak scale is not a fundamental scale.Comment: 5 pages, 5 figures, one radiative potential. Updated version consistent with the one accepted for publication in PRL (title changed in the journal

Scheming in the SMEFT

We discuss the constraints on the Standard Model Effective Field Theory inferred from global fits to electroweak data. Special attention is paid to two unconstrained combinations of Wilson coefficients that are present when the analysis is restricted to measurements of $\bar\psi\psi\to\bar\psi\psi$ scatterings. We illustrate how these unconstrained directions arise due to a reparameterization invariance that characterizes $\bar\psi\psi\to\bar\psi\psi$ processes but is not respected in $\bar\psi\psi\to\bar\psi\psi\bar\psi\psi$ scatterings. This invariance is independent of the operator basis adopted and of the choice of the input parameters. This is verified comparing the results obtained in the {$\hat \alpha_{em}, \hat m_Z, \hat G_F$} input scheme with those of a {$\hat m_W, \hat m_Z, \hat G_F$} scheme.Comment: 5 + 1 pages, 2 figures. Contribution to the proceedings of EPS-HEP 2017, European Physical Society conference on High Energy Physics, 5-12 July 2017, Venice, Ital

Signatures of dynamical scalars

Effective Lagrangians represent an important, model independent tool for studying physics beyond the Standard Model, via its impact on electroweak scale observables. In particular, two different effective descriptions may be appropriate, depending on how the electroweak symmetry breaking is realized at high energies: a linear effective Lagrangian is best suited in presence of linear dynamics, while a non-linear -chiral- one is more pertinent for scenarios featuring a non-linear realization. In this talk I will present a few examples of low-energy signals that differentiate the phenomenology of the two descriptions, thus providing a powerful insight into the nature of the Higgs boson.Comment: 4 pages; contribution to the Proceedings of the 50th Rencontres de Moriond, Electroweak Session. arXiv admin note: substantial text overlap with arXiv:1505.0063

Probing the Charm Yukawa Coupling in Higgs + Charm Production

We propose a new method to determine the coupling of the Higgs boson to charm quarks, via Higgs production in association with a charm-tagged jet: $pp\to hc$. As a first estimate, we find that at the LHC with 3000 fb$^{-1}$ it should be possible to derive a constraint of order one, relative to the SM value of the charm Yukawa coupling. As a byproduct of this analysis, we present an estimate of the exclusive $pp \to hD^{(*)}$ electroweak cross section. Within the SM, the latter turns out to be not accessible at the LHC even in the high-luminosity phase.Comment: 5 pages, 3 figure

Higgs physics beyond the SM: the non-linear EFT approach

Depending on whether electroweak physics beyond the Standard Model is based on a linear or on a non-linear implementation of the electroweak symmetry breaking, a linear or a chiral Effective Lagrangian is more appropriate. In this talk, the main low-energy signals that allow to recognize whether the observed Higgs scalar is a dynamical (composite) particle or rather an elementary one are presented, in a model-independent way. The patterns of effective couplings produced upon the assumption of specific composite Higgs models are also discussed.Comment: 8 pages, 1 figure. Proceedings of the talk given at the XXIXth Rencontres de Physique de la Vall\'ee d'Aoste, La Thuile (Italy), March 201