We systematically study potential effects of Beyond the Standard Model physics in the $\textit{e}$ $\textit{e}$ → $\textit{ZH}$ process. To this end, we include all relevant dimension-6 Standard Model Effective Field Theory operators and work to next-to-leading order (NLO) accuracy in the electroweak coupling. We consider both polarized and unpolarized electron and positron beams and present results for $$ \sqrt{s} $$ = 240, 365 and 500 GeV, emphasizing contributions where the NLO predictions differ significantly from the leading order results. At NLO, a sensitivity arises to operators that do not contribute at tree level, such as the Higgs tri-linear coupling, CP-violating operators, and dimension-6 operators involving the top quark, among many others. We compare the prospects of future $\textit{e}$ $\textit{e}$ colliders to explore these new physics effects with existing measurements from the LHC, electron EDMs (for CP violating operators), and Z pole measurements.

Germany

Konstantin Asteriadis

United States

Sally Dawson

Spain

Pier Giardino

Robert Szafron

$\textit{e}$

<p>Some of the most precise measurements of Higgs boson couplings are from the Higgs decays to 4 leptons, where deviations from the Standard Model predictions can be quantified in the framework of the Standard Model effective field theory (SMEFT). In this work, we present a complete next-to-leading order (NLO) SMEFT electroweak calculation of the rate for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi><mo stretchy="false">→</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup><mi>Z</mi></math> which we combine with the NLO SMEFT result for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi><mo stretchy="false">→</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> to obtain the NLO rate for the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>H</mi><mo stretchy="false">→</mo><mn>4</mn></mrow></math> lepton process in the narrow width approximation. The NLO calculation provides sensitivity to a wide range of SMEFT operators that do not contribute to the rate at lowest order and demonstrates the importance of including correlations between the effects of different operators when extracting limits on SMEFT parameters. We show that the extraction of the Higgs trilinear coupling from the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi><mo stretchy="false">→</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup><mi>Z</mi><mo>,</mo><mi>Z</mi><mo stretchy="false">→</mo><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> in the narrow width approximation strongly depends on the contributions of other operators that first occur at NLO.</p>

Matthew Forslund

Pier Paolo Giardino

NLO SMEFT electroweak corrections to Higgs boson decays to four leptons in the narrow width approximation

We present results from a complete next-to-leading order (NLO) calculation of <math><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><mi>Z</mi><mi>H</mi></mrow></math> in the standard model effective field theory (SMEFT) framework, including all contributions from dimension-six operators. At NLO, there are novel dependencies on CP violating parameters in the gauge sector, on modifications to the Higgs boson self-couplings, on alterations to the top quark Yukawa couplings, and on four-fermion operators involving the electron and the top quark, among others. We show that including only the logarithms resulting from renormalization group scaling can produce misleading results, and further, we explicitly demonstrate the constraining power of combining measurements from different energy scales.

Impact of Next-to-Leading-Order Weak Standard-Model-Effective-Field-Theory Corrections in <math><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><mi>Z</mi><mi>H</mi></mrow></math>

Heavy neutral gauge bosons arise in many motivated models of beyond the Standard Model Physics. Experimental searches require that such gauge bosons are above the TeV scale in most models which means that the tools of effective field theories, in particular the Standard Model effective field theory (SMEFT), are useful. We match the SMEFT to models with heavy <math><mrow><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></math> bosons, including effects of dimension-8 operators, and consider the restrictions on model parameters from electroweak precision measurements and from Drell Yan invariant mass distributions and forward-backward asymmetry, <math><msub><mi>A</mi><mi>FB</mi></msub></math>, measurements at the LHC. The results demonstrate the model dependence of the resulting limits on SMEFT coefficients and the relatively small impact of including dimension-8 matching. In all cases, the limits from invariant mass distributions are stronger than from <math><msub><mi>A</mi><mi>FB</mi></msub></math> measurements in the <math><msup><mi>Z</mi><mo>′</mo></msup></math> models we consider.

Marvin Schnubel

SMEFT matching to <math><msup><mi>Z</mi><mo>′</mo></msup></math> models at dimension eight

The two-Higgs doublet model (2HDM) is a well understood alternative to the Standard Model of particle physics. If the new particles included in the 2HDM are at an energy scale much greater than the weak scale, the theory can be matched to the Standard Model effective field theory (SMEFT). We compute for the first time the complete one-loop matching at dimension-6. We compare its numerical impact with that of tree-level matching at dimension-8 by performing a global fit to single Higgs and precision electroweak measurements, and we emphasize the importance of comparing one-loop SMEFT results with corresponding one-loop results in the full 2HDM model. In the SMEFT, we consider the relative importance of both one-loop matching and the inclusion of renormalization group evolution. Our results demonstrate the necessity of studying the impact of various expansions to quantify the uncertainties of the SMEFT matching.

Supratim Das Bakshi

Duarte Fontes

Samuel Homiller

Relevance of one-loop SMEFT matching in the 2HDM

Physics beyond the Standard Model (BSM) can be described in a consistent and general way through the Higgs effective field theory (HEFT). Measurements of model-independent HEFT coefficients allow one to constrain the parameter space of BSM models via a matching procedure. In this work, we show that this procedure is not unique and depends on the scalings of the parameters of the Lagrangian. As examples, we consider three BSM models: the real singlet extension of the SM with a <math><msub><mi>Z</mi><mn>2</mn></msub></math> symmetry, the complex singlet extension of the SM and the two Higgs doublet model. We discuss several physical observables, and show that different scalings of the model parameters with the UV scale in the matching to the HEFT can yield quite different results. This complicates the interpretation of HEFT measurements in terms of parameters of BSM models. Additionally, as a byproduct, we report the first matching of the complex singlet extension to the HEFT.

Carlos Quezada-Calonge

Juan José Sanz-Cillero

Is the HEFT matching unique?

We consider the 2 Higgs doublet model (2HDM) and compare two effective field theory (EFT) approaches to it, according to whether the heavy degrees of freedom are integrated out before [standard model EFT (SMEFT)] or after [Higgs EFT (HEFT)] spontaneous symmetry breaking. By requiring decoupling and perturbativity in the 2HDM, we define a consistent EFT expansion in inverse powers of the heavy masses which is applied to both the SMEFT and the HEFT tree-level matchings to the 2HDM. We organize this expansion with a dimensionless parameter <math><mrow><mi>ξ</mi></mrow></math>, and investigate the tree-level scatterings <math><mi>h</mi><mi>h</mi><mo>→</mo><mi>h</mi><mi>h</mi></math> and <math><mi>W</mi><mi>W</mi><mo>→</mo><mi>h</mi><mi>h</mi></math> up to <math><mi>O</mi><mo>(</mo><msup><mi>ξ</mi><mn>2</mn></msup><mo>)</mo></math>. We find no differences between the HEFT and the SMEFT approaches at this order. We show scenarios where even including dimension-8 operators of the SMEFT is insufficient to obtain an accurate matching to the 2HDM.

Matching the 2HDM to the HEFT and the SMEFT: Decoupling and perturbativity

Effective field theory tools are essential for exploring non-Standard Model physics at the LHC in the absence of the discovery of new light particles. Predictions for observables are typically made at the lowest order in the QCD and electroweak expansions in the Standard Model effective field theory (SMEFT) and often ignore the effects of flavor. Here, we present results for electroweak precision observables (EWPOs) at the next-to-leading order QCD and electroweak expansions (NLO) of the SMEFT with an arbitrary flavor structure for the fermion operators. Numerical NLO SMEFT fits to EWPOs have a strong dependence on the assumed flavor structures and we demonstrate this using various popular assumptions for flavor symmetries.

Luigi Bellafronte

The importance of flavor in SMEFT Electroweak Precision Fits

Deviations from the Standard Model (SM) can be parametrized in terms of the SM effective field theory (SMEFT), which is typically truncated at dimension-6. Including higher dimension operators—as well as considering simultaneous insertions of multiple dimension-6 operators—may be necessary in some processes, in order to correctly capture the properties of the underlying UV theory. As a step toward clarifying this in the Higgs boson production in gluon fusion process, we study double insertions of dimension-6 operators in the 1-loop virtual amplitude. We present needed Feynman rules up to <math><mi>O</mi><mrow><mo>(</mo><mrow><mn>1</mn><mo>/</mo><msup><mi>Λ</mi><mn>4</mn></msup></mrow><mo>)</mo></mrow></math> and we numerically study the impact of various approximations to the <math><mi>O</mi><mrow><mo>(</mo><mrow><mn>1</mn><mo>/</mo><msup><mi>Λ</mi><mn>4</mn></msup></mrow><mo>)</mo></mrow></math> expansion.

Double insertions of SMEFT operators in gluon fusion Higgs boson production

The Standard Model effective field theory (SMEFT) is the tool of choice for studying deviations of Higgs couplings from the Standard Model predictions. The SMEFT is an expansion in an infinite tower of higher dimension operators, which is typically truncated at dimension-six. We consider the effective theory including dimension-eight operators and examine the matching to the 2 Higgs doublet model (2HDM) that is assumed to be valid at some high scale. Both the limits from the direct production of single Higgs bosons and the indirect limits on the Higgs trilinear coupling are considered in the context of the SMEFT matched to the 2HDM, and the importance of the assumptions about the expansions in powers of the high scale are examined numerically.