We develop Standard Model Effective Field Theory (SMEFT) predictions of σ(  <math> <mi>GG</mi> </math>  $$ \mathcal{GG} $$  → h), Γ(h →   <math> <mi>GG</mi> </math>  $$ \mathcal{GG} $$ ), Γ(h →   <math> <mi>AA</mi> </math>  $$ \mathcal{AA} $$ ) to incorporate full two loop Standard Model results at the amplitude level, in conjunction with dimension eight SMEFT corrections. We simultaneously report consistent Γ(h →   <math> <mover> <mi>Ψ</mi> <mo>¯</mo> </mover> <mi>Ψ</mi> </math>  $$ \overline{\Psi}\Psi $$ ) results including leading QCD corrections and dimension eight SMEFT corrections. This extends the predictions of the former processes Γ, σ to a full set of corrections at   <math> <mi>O</mi> <mfenced> <mrow> <msubsup> <mover> <mi>v</mi> <mo>¯</mo> </mover> <mi>T</mi> <mn>2</mn> </msubsup> <mo>/</mo> <msup> <mi>Λ</mi> <mn>2</mn> </msup> <msup> <mfenced> <mrow> <mn>16</mn> <msup> <mi>π</mi> <mn>2</mn> </msup> </mrow> </mfenced> <mn>2</mn> </msup> </mrow> </mfenced> </math>  $$ \mathcal{O}\left({\overline{v}}_T^2/{\varLambda}^2{\left(16{\pi}^2\right)}^2\right) $$  and   <math> <mi>O</mi> <mfenced> <mrow> <msubsup> <mover> <mi>v</mi> <mo>¯</mo> </mover> <mi>T</mi> <mn>4</mn> </msubsup> <mo>/</mo> <msup> <mi>Λ</mi> <mn>4</mn> </msup> </mrow> </mfenced> </math>  $$ \mathcal{O}\left({\overline{v}}_T^4/{\Lambda}^4\right) $$ , where   <math> <msub> <mover> <mi>v</mi> <mo>¯</mo> </mover> <mi>T</mi> </msub> </math>  $$ {\overline{v}}_T $$  is the electroweak scale vacuum expectation value and Λ is the cut off scale of the SMEFT. Throughout, cross consistency between the operator and loop expansions is maintained by the use of the geometric SMEFT formalism. For Γ(h →   <math> <mover> <mi>Ψ</mi> <mo>¯</mo> </mover> <mi>Ψ</mi> </math>  $$ \overline{\Psi}\Psi $$ ), we include results at   <math> <mi>O</mi> <mfenced> <mrow> <msubsup> <mover> <mi>v</mi> <mo>¯</mo> </mover> <mi>T</mi> <mn>2</mn> </msubsup> <mo>/</mo> <msup> <mi>Λ</mi> <mn>2</mn> </msup> <mfenced> <mrow> <mn>16</mn> <msup> <mi>π</mi> <mn>2</mn> </msup> </mrow> </mfenced> </mrow> </mfenced> </math>  $$ \mathcal{O}\left({\overline{v}}_T^2/{\Lambda}^2\left(16{\pi}^2\right)\right) $$  in the limit where subleading m Ψ → 0 corrections are neglected. We clarify how gauge invariant SMEFT renormalization counterterms combine with the Standard Model counter terms in higher order SMEFT calculations when the Background Field Method is used. We also update the prediction of the total Higgs width in the SMEFT to consistently include some of these higher order perturbative effects.

United States

Adam Martin

Canada

Michael Trott

More accurate   <math> <mi>σ</mi> <mfenced> <mrow> <mi>GG</mi> <mo>→</mo> <mi>h</mi> </mrow> </mfenced> <mo>,</mo> <mi>Γ</mi> <mfenced> <mrow> <mi>h</mi> <mo>→</mo> <mi>GG</mi> </mrow> <mi>AA</mi> <mrow> <mover> <mi>Ψ</mi> <mo>¯</mo> </mover> <mi>Ψ</mi> </mrow> </mfenced> </math>  $$ \sigma \left(\mathcal{GG}\to h\right),\Gamma \left(h\to \mathcal{GG},\mathcal{AA},\overline{\Psi}\Psi \right) $$  and Higgs width results via the geoSMEFT

We examine how subleading results in the operator and loop expansion for <math><mi>σ</mi><mo>(</mo><mi>G</mi><mi>G</mi><mo>→</mo><mi>h</mi><mo>)</mo></math> in the Standard Model effective field theory (SMEFT) inform theoretical error estimates when studying this production channel in global SMEFT studies. We also discuss the relationship between geometric SMEFT results and the <math><mi>κ</mi></math> formalism.

Denmark

<math><mi>g</mi><mi>g</mi><mi>h</mi></math> variations

We report consistent results for Γ(h → γγ),   <math> <mi>σ</mi> <mfenced> <mrow> <mi>GG</mi> <mo>→</mo> <mi>h</mi> </mrow> </mfenced> </math>  $$ \sigma \left(\mathcal{GG}\to h\right) $$  and   <math> <mi>Γ</mi> <mfenced> <mrow> <mi>h</mi> <mo>→</mo> <mi>GG</mi> </mrow> </mfenced> </math>  $$ \Gamma \left(h\to \mathcal{GG}\right) $$  in the Standard Model Effective Field Theory (SMEFT) perturbing the SM by corrections   <math> <mi>O</mi> <mfenced> <mrow> <msubsup> <mover> <mi>υ</mi> <mo>¯</mo> </mover> <mi>T</mi> <mn>2</mn> </msubsup> <mo>/</mo> <mn>16</mn> <msup> <mi>π</mi> <mn>2</mn> </msup> <msup> <mi>Λ</mi> <mn>2</mn> </msup> </mrow> </mfenced> </math>  $$ \mathcal{O}\left({\overline{\upsilon}}_T^2/16{\pi}^2{\Lambda}^2\right) $$  in the Background Field Method (BFM) approach to gauge fixing, and to   <math> <mi>O</mi> <mfenced> <mrow> <msubsup> <mover> <mi>υ</mi> <mo>¯</mo> </mover> <mi>T</mi> <mn>4</mn> </msubsup> <mo>/</mo> <msup> <mi>Λ</mi> <mn>4</mn> </msup> </mrow> </mfenced> </math>  $$ \mathcal{O}\left({\overline{\upsilon}}_T^4/{\Lambda}^4\right) $$  using the geometric formulation of the SMEFT. We combine and modify recent results in the literature into a complete set of consistent results, uniforming conventions, and simultaneously complete the one loop results for these processes in the BFM. We emphasize calculational scheme dependence present across these processes, and how the operator and loop expansions are not independent beyond leading order. We illustrate several cross checks of consistency in the results.

Tyler Corbett

Consistent higher order   <math> <mi>σ</mi> <mfenced> <mrow> <mi>GG</mi> <mo>→</mo> <mi>h</mi> </mrow> </mfenced> </math>  $$ \sigma \left(\mathcal{GG}\to h\right) $$ ,   <math> <mi>Γ</mi> <mfenced> <mrow> <mi>h</mi> <mo>→</mo> <mi>GG</mi> </mrow> </mfenced> </math>  $$ \Gamma \left(h\to \mathcal{GG}\right) $$  and Γ(h → γγ) in geoSMEFT

A process specific methodology is defined to systematically assign theoretical uncertainties in the Standard Model effective field theory when performing leading-order global fits. The method outlined also minimizes the computational and theoretical burden to systematically advance such analyses to dimension eight.

Methodology for theory uncertainties in the standard model effective field theory

We report a set of exact formulae for computing Dirac masses, mixings, and CP-violation parameter(s) from 3×3 Yukawa matrices Y valid when YY † → U † YY † U under global   <math> <mi>U</mi> <msub> <mfenced> <mn>3</mn> </mfenced> <msub> <mi>Q</mi> <mi>L</mi> </msub> </msub> </math>  $$ \mathrm{U}{(3)}_{Q_L} $$  flavour symmetry transformations U. The results apply to the Standard Model Effective Field Theory (SMEFT) and its ‘geometric’ realization (geoSMEFT). We thereby complete, in the Dirac flavour sector, the catalogue of geoSMEFT parameters derived at all orders in the   <math> <msqrt> <mrow> <mn>2</mn> <mfenced> <mrow> <msup> <mi>H</mi> <mo>†</mo> </msup> <mi>H</mi> </mrow> </mfenced> </mrow> </msqrt> </math>  $$ \sqrt{2\left\langle {H}^{\dagger }H\right\rangle } $$  /Λ expansion. The formalism is basis-independent, and can be applied to models with decoupled ultraviolet flavour dynamics, as well as to models whose infrared dynamics are not minimally flavour violating. We highlight these points with explicit examples and, as a further demonstration of the formalism’s utility, we derive expressions for the renormalization group flow of quark masses, mixings, and CP-violation at all mass dimension and perturbative loop orders in the (geo)SM(EFT) and beyond.

Jim Talbert

Dirac masses and mixings in the (geo)SM(EFT) and beyond

We calculate the   <math> <mi>O</mi> <mfenced> <mrow> <msup> <mfenced> <mrow> <msup> <mi>H</mi> <mo>†</mo> </msup> <mi>H</mi> </mrow> </mfenced> <mn>2</mn> </msup> <mo>/</mo> <msup> <mi>Λ</mi> <mn>4</mn> </msup> </mrow> </mfenced> </math>  $$ \mathcal{O}\left({\left\langle {H}^{\dagger }H\right\rangle}^2/{\Lambda}^4\right) $$  corrections to LEP electroweak precision data using the geometric formulation of the Standard Model Effective Field Theory (SMEFT). We report our results in simple-to-use interpolation tables that allow the interpretation of this data set to dimension eight for the first time. We demonstrate the impact of these previously unknown terms in the case of a general analysis in the SMEFT, and also in the cases of two distinct models matched to dimension eight. Neglecting such dimension-eight corrections to LEP observables introduces a theoretical error in SMEFT studies. We report some preliminary studies defining such a theory error, explicitly demonstrating the effect of previously unknown dimension-eight SMEFT corrections on LEP observables.

Andreas Helset

EWPD in the SMEFT to dimension eight

We discuss the possible origin of the Majorana mass scale(s) required for the “neutrino option” where the electroweak scale is generated simultaneously with light neutrino masses in a type-I seesaw model by common dimension four interactions. We establish no-go constraints on the perturbative generation of the Majorana masses required due to global symmetries of the seesaw Lagrangian.

Germany

Ilaria Brivio

CERN

No-go limitations on UV completions of the neutrino option

The Standard Model Effective Field Theory (SMEFT) theoretical framework is increasingly used to interpret particle physics measurements and constrain physics beyond the Standard Model. We investigate the truncation of the effective-operator expansion using the geometric formulation of the SMEFT, which allows exact solutions, up to mass-dimension eight. Using this construction, we compare the exact solution to the expansion at   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (v 2 /Λ2), partial   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (v 4 /Λ4) using a subset of terms with dimension-6 operators, and full   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (v 4 /Λ4), where v is the vacuum expectation value and Λ is the scale of new physics. This comparison is performed for general values of the coefficients, and for the specific model of a heavy U(1) gauge field kinetically mixed with the Standard Model. We additionally determine the input-parameter scheme dependence at all orders in v/Λ, and show that this dependence increases at higher orders in v/Λ.

United Kingdom

Chris Hays

Exact SMEFT formulation and expansion to   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (v 4/Λ4)

We develop the geometric formulation of the Standard Model Effective Field Theory (SMEFT). Using this approach we derive all-orders results in the   <math> <msqrt> <mrow> <mn>2</mn> <mfenced> <mrow> <msup> <mi>H</mi> <mo>†</mo> </msup> <mi>H</mi> </mrow> </mfenced> </mrow> </msqrt> <mo>/</mo> <mi>Λ</mi> </math>  $$ \sqrt{2\left\langle {H}^{\dagger }H\right\rangle }/\Lambda $$  expansion relevant for studies of Electroweak Precision and Higgs data.

The geometric Standard Model Effective Field Theory

We derive Ward identities for the standard model effective field theory using the background-field method. The resulting symmetry constraints on the standard model effective field theory are basis independent, and constrain the perturbative and power-counting expansions. A geometric description of the field connections, and real representations for the <math><mrow><mi>SU</mi><mo>(</mo><mn>2</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>L</mi></mrow></msub><mo>×</mo><mi>U</mi><mo>(</mo><mn>1</mn><msub><mrow><mo>)</mo></mrow><mrow><mi>Y</mi></mrow></msub></mrow></math> generators, underlies the derivation.