<p>We formalize energy-scaling arguments in the standard model effective field theory (SMEFT) to estimate the effects of operators up to dimension ten. Our approach relies on weakly coupled UV completions with no presumed large hierarchies between the Wilson coefficients. We introduce a classification based on the number of external legs and an energy-counting parameter. We establish a dual expansion in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>v</mi><mo>/</mo><mi mathvariant="normal">Λ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>E</mi><mo>/</mo><mi mathvariant="normal">Λ</mi></math>. Extending to four-, five-, and six-particle vertices, our framework highlights energy-enhanced operators that dominate high-energy processes at the High Luminosity-Large Hadron Collider. This organization streamlines experimental analyses to only include operators with energetic impact in their analyses and enhances the discoverability of new physics within the SMEFT framework.</p>

United States

Benoît Assi

Adam Martin

Energy-enhanced expansion of the standard model effective field theory

We investigate the impact of dimension-8 operators on $\textit{W}$ $\textit{W}$ production at the LHC for the incoming gluon-gluon channel. To this end, we have identified all dimension-8 CP-even operators contributing to the process in question, and computed the corresponding tree-level helicity amplitudes for fully-leptonic decays of the $\textit{W}$ bosons. These are implemented in the program MCFM-RE, which automatically incorporates the effect of a jet-veto to reduce the otherwise overwhelming $$ t\overline{t} $$ background. We find that, unless we break the hierarchy of the effective field theory (EFT), the interference of the dimension-8 operators with the Standard Model is negligible across the considered distributions. This justifies including the square of dimension-6 operators when performing EFT fits with this channel. We then present new constraints on CP-even and CP-odd dimension-6 operators within the EFT regime. Lastly, we postulate a scenario in which the hierarchy of the EFT is broken, justified by the strong constraints on dimension-6 operators from existing on-shell Higgs data. In this scenario, we discuss the constraints that can be reasonably set on CP-even dimension-8 operators with current and future data. We remark that the effect of the jet-veto on the ability to constrain new physics in the $\textit{W}$ $\textit{W}$ channel is quite dramatic and must be properly taken into account.

United Kingdom

Daniel Gillies

Andrea Banfi

Matthew Lim

Dimension-8 operators in $\textit{W}$

<p>We present analytical expressions for the transverse momentum dependent (unintegrated) gluon and quark densities in a proton derived at leading order of QCD running coupling and valid at both small and large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>. The calculations are performed using the Kimber-Martin-Ryskin/Watt-Martin-Ryskin prescription (in both differential and integral formulations) with different treatment of kinematical constraint, which reflects the angular and strong ordering conditions for parton emissions. As an input, the analytical solution of QCD evolution equations for conventional (collinear) parton distributions is applied, where the valence and nonsinglet quark parts obey the Gross-Llewellyn-Smith and Gottfried sum rules, and momentum conservation for the singlet quark and gluon densities is taken into account. Several phenomenological parameters are extracted from the combined fit to precision data on the proton structure function <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> collected by the BCDMS, H1, and ZEUS Collaborations, comprising a total of 933 points from 5 datasets. Comparison with the numerical results obtained by other groups is presented, and the phenomenological application to the inclusive <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-jet production at the LHC is given.</p>

JINR

A.V. Kotikov

Russia

A.V. Lipatov

Updating TMD parton densities in a proton within the Kimber-Martin-Ryskin approach

Romania

Victor E. Ambrus

France

Maxim N. Chernodub

Corrigendum to “Acceleration as a circular motion along an imaginary circle: Kubo-Martin-Schwinger condition for accelerating field theories in imaginary-time formalism” [Physics Letters B 855 (2024) 138757/PLB 138795]

We study Higgs boson production via vector boson fusion at the LHC, focusing on the process → + and capturing the leading energy-enhanced contributions within the Standard Model Effective Field Theory (SMEFT) up to order 1 Λ . Employing energy-scaling arguments, we predict the magnitude of each higher-dimensional operator’s contribution. Utilizing the geometric formulation of SMEFT, our analysis incorporates dimension-eight operators not previously considered. We find that the kinematics of vector boson fusion — characterized by two highly forward jets — tend to suppress contributions from higher-dimensional operators, requiring a lower scale Λ for SMEFT effects to become observable. This suggests that the SMEFT remains valid for lower Λ than expected. Combined with the fact that LEP constrains the dimension-six operators with the most considerable impact on vector boson fusion, a regime exists where dimension-eight operators can have significant effects. In many cases, these dimension-eight operators also influence associated production processes like → ( ), though differences in analysis cuts and kinematics mean this is not always the case. Our findings provide insights that could refine the search for SMEFT signals in collider experiments.

Energy-enhanced dimension eight SMEFT effects in VBF Higgs production

In this paper we develop a semi-standard Young tableau (SSYT) approach to construct a basis of non-factorizable superamplitudes in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 massless supersymmetry. This amplitude basis can be directly translated to a basis for higher dimensional supersymmetric operators, yielding both the number of independent operators and their form. We deal with distinguishable (massless) chiral/vector superfields at first, then generalize the result to the indistinguishable case. Finally, we discuss the advantages and disadvantages of this method compared to the previously studied Hilbert series approach.

Antonio Delgado

Runqing Wang

Basis for non-factorizable superamplitudes in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 supersymmetry

In this paper, we address the reduced beauty cross section [<math><msubsup><mi>σ</mi><mi>red</mi><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math>] and the beauty structure function [<math><msubsup><mi>F</mi><mn>2</mn><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math>], to study the beauty content of a proton. We calculate <math><msubsup><mi>σ</mi><mi>red</mi><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup></math> and <math><msubsup><mi>F</mi><mn>2</mn><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup></math> in the <math><msub><mi>k</mi><mi>t</mi></msub></math>-factorization formalism by using the integral form of the Kimber-Martin-Ryskin and Martin-Ryskin-Watt unintegrated parton distribution function (KMR and MRW-UPDF) with the angular ordering constraint (AOC) and the <math><mi>M</mi><mi>M</mi><mi>H</mi><mi>T</mi><mn>2014</mn></math> <math><mi>P</mi><mi>D</mi><mi>F</mi></math> set as the input. Recently Guiot and van Hameren demonstrated that the upper limit, <math><msub><mi>k</mi><mi>max</mi></msub></math>, of the transverse-momentum integration performed in the <math><msub><mi>k</mi><mi>t</mi></msub></math>-factorization formalism should be almost equal to <math><mi>Q</mi></math>, where <math><mi>Q</mi></math> is the hard scale, otherwise it leads to an overestimation of the proton structure function [<math><msub><mi>F</mi><mn>2</mn></msub><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math>]. In the present work, we show that <math><msub><mi>k</mi><mi>max</mi></msub></math> cannot be equal to <math><mi>Q</mi></math> at low and moderate energy region, and also by considering the gluon and quark contributions to the same perturbative order and a physical gauge for the gluon, i.e., <math><msup><mi>A</mi><mi>μ</mi></msup><msubsup><mi>q</mi><mi>μ</mi><mo>′</mo></msubsup><mo>=</mo><mn>0</mn></math> in the calculation of <math><msubsup><mi>F</mi><mn>2</mn><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup></math> in the <math><msub><mi>k</mi><mi>t</mi></msub></math>-factorization formalism, we do not encounter any overestimation of the theoretical predictions due to different choices of <math><msub><mi>k</mi><mi>max</mi></msub><mo>&gt;</mo><mi>Q</mi></math>. Finally, the resulted <math><msubsup><mi>σ</mi><mi>red</mi><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup></math> and <math><msubsup><mi>F</mi><mn>2</mn><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup></math> are compared to the experimental data and the theoretical predictions. In general, the extracted <math><msubsup><mi>σ</mi><mi>red</mi><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup></math> and <math><msubsup><mi>F</mi><mn>2</mn><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup></math> based on the KMR and MRW approaches are in perfect agreement with the experimental data and theoretical predictions at high energies, but at low and moderate energies, the one developed from the KMR approach has better consistency than that of the MRW approach.

Iran

N. Olanj

Phenomenological investigation of the beauty content of a proton in the framework of <math><msub><mi>k</mi><mi>t</mi></msub></math>-factorization using Kimber-Martin-Ryskin and Martin-Ryskin-Watt unintegrated parton distributions

We discuss the imaginary-time formalism for field theories in thermal equilibrium in uniformly accelerating frames. We show that under a Wick rotation of Minkowski spacetime, the Rindler event horizon shrinks to a point in a two-dimensional subspace tangential to the acceleration direction and the imaginary time. We demonstrate that the accelerated version of the Kubo-Martin-Schwinger (KMS) condition implies an identification of all spacetime points related by integer-multiple rotations in the tangential subspace about this Euclidean Rindler event-horizon point, with the rotational quanta defined by the thermal acceleration, <math><mi>α</mi><mo>=</mo><mi>a</mi><mo>/</mo><mi>T</mi></math>. In the Wick-rotated Rindler hyperbolic coordinates, the KMS relations reduce to standard (anti-)periodic boundary conditions in terms of the imaginary proper time (rapidity) coordinate. Our findings pave the way to study, using first-principle lattice simulations, the Hawking-Unruh radiation in geometries with event horizons, phase transitions in accelerating Early Universe and early stages of quark-gluon plasma created in relativistic heavy-ion collisions.

Victor E. Ambruş

Acceleration as a circular motion along an imaginary circle: Kubo-Martin-Schwinger condition for accelerating field theories in imaginary-time formalism

In this paper we explore pp → W  ± (ℓ  ±  ν)γ to   <math> <mi>O</mi> <mfenced> <mrow> <mn>1</mn> <mo>/</mo> <msup> <mi>Λ</mi> <mn>4</mn> </msup> </mrow> </mfenced> </math>  $$ \mathcal{O}\left(1/{\Lambda}^4\right) $$  in the SMEFT expansion. Calculations to this order are necessary to properly capture SMEFT contributions that grow with energy, as the interference between energy-enhanced SMEFT effects at   <math> <mi>O</mi> <mfenced> <mrow> <mn>1</mn> <mo>/</mo> <msup> <mi>Λ</mi> <mn>2</mn> </msup> </mrow> </mfenced> </math>  $$ \mathcal{O}\left(1/{\Lambda}^2\right) $$  and the Standard Model is suppressed. We find that there are several dimension eight operators that interfere with the Standard Model and lead to the same energy growth, ~   <math> <mi>O</mi> <mfenced> <mrow> <msup> <mi>E</mi> <mn>4</mn> </msup> <mo>/</mo> <msup> <mi>Λ</mi> <mn>4</mn> </msup> </mrow> </mfenced> </math>  $$ \mathcal{O}\left({E}^4/{\Lambda}^4\right) $$ , as dimension six squared. While energy-enhanced SMEFT contributions are a main focus, our calculation includes the complete set of   <math> <mi>O</mi> <mfenced> <mrow> <mn>1</mn> <mo>/</mo> <msup> <mi>Λ</mi> <mn>4</mn> </msup> </mrow> </mfenced> </math>  $$ \mathcal{O}\left(1/{\Lambda}^4\right) $$  SMEFT effects consistent with U(3)5 flavor symmetry. Additionally, we include the decay of the W  ±  → ℓ  ±  ν, making the calculation actually   <math> <mover> <mi>q</mi> <mo>¯</mo> </mover> <msup> <mi>q</mi> <mo>′</mo> </msup> <mo>→</mo> <msup> <mi>ℓ</mi> <mo>±</mo> </msup> <mi>νγ</mi> </math>  $$ \overline{q}{q}^{\prime}\to {\ell}^{\pm}\nu \gamma $$ . As such, we are able to study the impact of non-resonant SMEFT operators, such as   <math> <mfenced> <mrow> <msup> <mi>L</mi> <mo>†</mo> </msup> <msup> <mover> <mi>σ</mi> <mo>¯</mo> </mover> <mi>μ</mi> </msup> <msup> <mi>τ</mi> <mi>I</mi> </msup> <mi>L</mi> </mrow> </mfenced> <mfenced> <mrow> <msup> <mi>Q</mi> <mo>†</mo> </msup> <msup> <mover> <mi>σ</mi> <mo>¯</mo> </mover> <mi>ν</mi> </msup> <msup> <mi>τ</mi> <mi>I</mi> </msup> <mi>Q</mi> </mrow> </mfenced> </math>  $$ \left({L}^{\dagger }{\overline{\sigma}}^{\mu }{\tau}^IL\right)\left({Q}^{\dagger }{\overline{\sigma}}^{\nu }{\tau}^IQ\right) $$  B  μν , which contribute to   <math> <mover> <mi>q</mi> <mo>¯</mo> </mover> <msup> <mi>q</mi> <mo>′</mo> </msup> <mo>→</mo> <msup> <mi>ℓ</mi> <mo>±</mo> </msup> <mi>νγ</mi> </math>  $$ \overline{q}{q}^{\prime}\to {\ell}^{\pm}\nu \gamma $$  directly and not to   <math> <mover> <mi>q</mi> <mo>¯</mo> </mover> <msup> <mi>q</mi> <mo>′</mo> </msup> <mo>→</mo> <msup> <mi>W</mi> <mo>±</mo> </msup> <mi>γ</mi> </math>  $$ \overline{q}{q}^{\prime}\to {W}^{\pm}\gamma $$ . We show several distributions to illustrate the shape differences of the different contributions.

A case study of SMEFT   <math> <mi>O</mi> <mfenced> <mrow> <mn>1</mn> <mo>/</mo> <msup> <mi>Λ</mi> <mn>4</mn> </msup> </mrow> </mfenced> </math>  $$ \mathcal{O}\left(1/{\Lambda}^4\right) $$  effects in diboson processes: pp → W ±(ℓ ± ν)γ

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.

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