<p>We study Drell-Yan production in universal theories consistently including effects beyond dimension six in the Standard Model effective field theory (SMEFT). Within universal SMEFT and with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>P</mi></math> conservation we find that 11 dimension-eight operators contribute in addition to the six contributing at dimension six. We first work in an operator basis in which operators with higher derivatives of the bosonic fields have been rotated by equations of motion in favor of combinations of operators involving SM fermion currents. We derive the general form of the amplitudes consistently in the expansion to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mi mathvariant="normal">Λ</mi><mrow><mo>−</mo><mn>4</mn></mrow></msup><mo stretchy="false">)</mo></math> and identify eight combinations of the 17 Wilson coefficients which are physically distinguishable by studying the invariant mass distribution of the lepton pairs produced. We then introduce an extension of the parametrization of universal effects in terms of oblique parameters obtained by linearly expanding the self-energies of the electroweak gauge bosons to <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mi>q</mi><mn>6</mn></msup><mo stretchy="false">)</mo></math>. It contains 11 oblique parameters of which only eight are generated within SMEFT at dimension eight: <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>S</mi><mo stretchy="false">^</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>T</mi><mo stretchy="false">^</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Y</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>U</mi><mo stretchy="false">^</mo></mover></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>X</mi></math>, plus two additional which we label <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>W</mi><mo>′</mo></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>Y</mi><mo>′</mo></msup></math> and show how they match at linear order with the eight identified combinations of operator coefficients. We then perform a combined analysis of a variety of LHC data on the neutral- and charged-current Drell-Yan processes with the aim of constraining the eight combinations. We compare and combine the LHC bounds with those from electroweak precision <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>Z</mi></math> pole observables which can only provide constraints in four directions of the eight-parameter space. We present the results in terms of limits on the eight effective Wilson coefficients as well as on the eight oblique parameters. In each case, we study the dependence of the derived constraints on the order of the expansion considered.</p>

Austria

Tyler Corbett

United States

Jay Desai

Brazil

O.J.P. Éboli

Spain

M.C. Gonzalez-Garcia

France

Matheus Martines

Peter Reimitz

Drell-Yan production in universal theories beyond dimension-six SMEFT

We present the basis of dimension-eight operators associated with universal theories. We first derive a complete list of independent dimension-eight operators formed with the Standard Model bosonic fields characteristic of such universal new physics scenarios. Without imposing C or P symmetries the basis contains 175 operators—that is, the assumption of universality reduces the number of independent Standard Model effective field theory (SMEFT) coefficients at dimension eight from 44807 to 175. 89 of the 175 universal operators are included in the general dimension-eight operator basis in the literature. The 86 additional operators involve higher derivatives of the Standard Model bosonic fields and can be rotated in favor of operators involving fermions using the Standard Model equations of motion for the bosonic fields. By doing so we obtain the allowed fermionic operators generated in this class of models which we map into the corresponding 86 independent combinations of operators in the dimension-eight basis of [C. W. Murphy, Dimension-8 operators in the standard model effective field theory, J. High Energy Phys. 10 (2020) 174.].

O. J. P. Éboli

M. C. Gonzalez-Garcia

Dimension-eight operator basis for universal standard model effective field theory

We perform a complete study of the electroweak precision observables and electroweak gauge boson pair production in terms of the Standard Model effective field theory up to <math><mi>O</mi><mo>(</mo><mn>1</mn><mo>/</mo><msup><mi>Λ</mi><mn>4</mn></msup><mo>)</mo></math> under the assumption of universal <math><mi>C</mi></math> and <math><mi>P</mi></math> conserving new physics. We show that the analysis of data from those two sectors allows us to obtain closed constraints in the relevant parameter space in this scenario. In particular, we find that the Large Hadron Collider data can independently constrain the Wilson coefficients of the dimension-six and -eight operators directly contributing to the triple gauge boson vertices. Our results show that the impact of dimension-eight operators in the study of triple gauge couplings is small.

Impact of dimension-eight SMEFT operators in the electroweak precision observables and triple gauge couplings analysis in universal SMEFT

We examine current Large Hadron Collider constraints on some simple  $$Z^\prime $$  <math> <msup> <mi>Z</mi> <mo>′</mo> </msup> </math>   models that significantly improve on Standard Model fits to  $$b\rightarrow s \mu ^+\mu ^-$$  <math> <mrow> <mi>b</mi> <mo>→</mo> <mi>s</mi> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> </mrow> </math>   transition data. The models that we consider are the ‘third family baryon number minus second family lepton number’ ( $${B_3-L_2}$$  <math> <mrow> <msub> <mi>B</mi> <mn>3</mn> </msub> <mo>-</mo> <msub> <mi>L</mi> <mn>2</mn> </msub> </mrow> </math>  ) model and the ‘third family hypercharge’ model and variants. The constraints are applied on parameter regions of each model that fit the  $$b\rightarrow s \mu ^+\mu ^-$$  <math> <mrow> <mi>b</mi> <mo>→</mo> <mi>s</mi> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> </mrow> </math>   transition data and come from high-mass Drell–Yan di-muons and measurements of Standard Model processes. This latter set of observables place particularly strong bounds upon the parameter space of the  $${B_3-L_2}$$  <math> <mrow> <msub> <mi>B</mi> <mn>3</mn> </msub> <mo>-</mo> <msub> <mi>L</mi> <mn>2</mn> </msub> </mrow> </math>   model when the mass of the  $$Z^\prime $$  <math> <msup> <mi>Z</mi> <mo>′</mo> </msup> </math>   boson is less than 300 GeV.

United Kingdom

B. Allanach

J. Butterworth

Denmark

Large hadron collider constraints on some simple  $$Z^\prime $$  <math> <msup> <mi>Z</mi> <mo>′</mo> </msup> </math>   models for  $$b\rightarrow s \mu ^+\mu ^-$$  <math> <mrow> <mi>b</mi> <mo>→</mo> <mi>s</mi> <msup> <mi>μ</mi> <mo>+</mo> </msup> <msup> <mi>μ</mi> <mo>-</mo> </msup> </mrow> </math>   anomalies

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.

Adam Martin

Michael Trott

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

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 present a package for FeynRules which derives the Feynman rules for the Standard Model Effective Field Theory up to dimension-six using the background field method for gauge fixing. The package includes operators which shift the kinetic and mass terms of the Lagrangian up to dimension-eight and including dimension-six squared effects consistently. To the best of the author’s knowledge this is the first publicly available package to include dimension-six squared effects consistently. The package is validated in a partner publication by analyzing the Ward Identities at dimension-six and one-loop order. We also extend the partner work in this article by including the dimension-six squared effects further demonstrating the consistency of their implementation. In doing so we find that failure to consistently include field shifts to dimension-six squared causes a breakdown in the Ward identities implying concerns about many calculations in the literature which do not properly incorporate these effects.

The Feynman rules for the SMEFT in the background field gauge

We estimate the future sensitivity of the high luminosity (HL-) and high energy (HE-) modes of the Large Hadron Collider (LHC) and of a 100 TeV future circular collider (FCC-hh) to leptoquark (LQ) pair production in the muon-plus-jet decay mode of each LQ. Such LQs are motivated by the fact that they provide an explanation for the neutral current B-anomalies. For each future collider, Standard Model (SM) backgrounds and detector effects are simulated. From these, sensitivities of each collider are found. Our measures of sensitivity are based upon a Run II ATLAS search, which we also use for validation. We illustrate with a narrow scalar (‘$$S_3$$ <math><msub><mi>S</mi><mn>3</mn></msub></math> ’) LQ and find that, in our channel, the HL-LHC has exclusion sensitivity to LQ masses up to 1.8 TeV, the HE-LHC up to 4.8 TeV and the FCC-hh up to 13.5 TeV.

Maeve Madigan

Sensitivity of future hadron colliders to leptoquark pair production in the di-muon di-jets channel

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.

Ward identities for the standard model effective field theory

We examine current collider constraints on some simple Z ′ models that fit neutral current B-anomalies, including constraints coming from measurements of Standard Model (SM) signatures at the LHC. The ‘MDM’ simplified model is not constrained by the SM measurements but is strongly constrained by a 139 fb−1 13 TeV ATLAS di-muon search. Constraints upon the ‘MUM’ simplified model are much weaker. A combination of the current B  s  mixing constraint and ATLAS’ Z ′ search implies   <math> <msub> <mi>M</mi> <msup> <mi>Z</mi> <mo>′</mo> </msup> </msub> <mo>&gt;</mo> <mn>1.2</mn> </math>  $$ {M}_{Z^{\prime }}&gt;1.2 $$  TeV in the Third Family Hypercharge Model example case. LHC SM measurements rule out a portion of the parameter space of the model for   <math> <msub> <mi>M</mi> <msup> <mi>Z</mi> <mo>′</mo> </msup> </msub> <mo>&gt;</mo> <mn>1.5</mn> </math>  $$ {M}_{Z^{\prime }}&gt;1.5 $$  TeV.