[Paper Review] NNLO event generation for $\boldsymbol{pp o Zh o \ell^+\ell^- b \bar b}$ production in the SM effective field theory

Ulrich Haisch, Darren J. Scott+3 more|arXiv (Cornell University)|Apr 1, 2022

Particle physics theoretical and experimental studies5 citations

TL;DR

This paper presents a next-to-next-to-leading order (NNLO) + parton shower (PS) Monte Carlo event generator for $pp \to Zh \to \ell^+\ell^- b\bar{b}$ production in the Standard Model effective field theory (SMEFT), incorporating QCD corrections from six dimension-six operators, including effective Yukawa and chromomagnetic dipole interactions. The key result is that higher-order QCD effects from SMEFT operators have a sub-percent impact on the total cross section under current experimental constraints, with the invariant mass $m_{b\bar{b}}$ and three-jet mass $m_{b\bar{b}j}$ emerging as sensitive observables for probing SMEFT effects due to shape modifications dependent on jet definition.

ABSTRACT

We consider associated $Zh$ production with $Z o \ell^+ \ell^-$ and $h o b \bar b$ decays in hadronic collisions. In the framework of the Standard Model effective field theory (SMEFT) we calculate the QCD corrections to this process and achieve next-to-next-to-leading order plus parton shower (NNLO$+$PS) accuracy using the MiNNLO$_{ m PS}$ method. This precision is obtained for a subset of six SMEFT operators, including the corrections from effective Yukawa- and chromomagnetic dipole-type interactions. Missing higher-order QCD effects associated with the considered dimension-six operators are estimated to have a relative numerical impact of less than a percent on the total rate once existing experimental limits on the relevant Wilson coefficients are taken into account. We provide a dedicated Monte Carlo (MC) code that evaluates the NNLO SMEFT corrections on-the-fly in the event generation. This MC generator is used to study the numerical impact of NNLO$+$PS corrections on the kinematic distributions in $pp o Zh o \ell^+ \ell^- b \bar b$ production employing simple SMEFT benchmark scenarios. We identify the invariant mass $m_{b \bar b}$ of the two $b$-tagged jets as well as the three-invariant jet mass $m_{b \bar b j}$ as particularly interesting observables to study SMEFT effects. These distributions receive contributions that change both their normalisation and shape with the latter modifications depending on the exact jet definition. To our knowledge SMEFT effects of this type have so far not been discussed in the literature. The presented MC generator can also serve as a starting point to obtain NNLO$+$PS accuracy for a suitable enlarged set of effective operators in the future.

Motivation & Objective

• To achieve NNLO + parton shower accuracy in the SMEFT for $pp \to Zh \to \ell^+\ell^- b\bar{b}$ production, including QCD corrections from relevant dimension-six operators.
• To assess the numerical impact of higher-order QCD corrections from SMEFT operators on differential distributions, particularly focusing on kinematic observables sensitive to new physics.
• To develop a dedicated Monte Carlo generator that evaluates NNLO SMEFT corrections on-the-fly during event generation for precision phenomenology.
• To identify and analyze observables that are sensitive to SMEFT effects through both normalization and shape modifications, especially those dependent on jet definition.

Proposed method

• The MiNNLO PS method is employed to achieve NNLO + PS accuracy in QCD corrections for $pp \to Zh \to \ell^+\ell^- b\bar{b}$ within SMEFT.
• The calculation includes QCD corrections from six dimension-six SMEFT operators, specifically those contributing to effective Yukawa and chromomagnetic dipole-type interactions.
• The SMEFT corrections are implemented in a Monte Carlo generator that computes NNLO corrections on-the-fly during event generation, enabling fully differential predictions.
• The generator is used to study the impact of NNLO + PS corrections on kinematic distributions using benchmark SMEFT scenarios.
• Theoretical estimates of missing higher-order QCD effects are performed using existing experimental limits on Wilson coefficients to bound the relative numerical impact.
• The analysis focuses on the invariant mass $m_{b\bar{b}}$ of $b$-tagged jets and the three-jet invariant mass $m_{b\bar{b}j}$ as key observables for SMEFT sensitivity.

Experimental results

Research questions

• RQ1 What is the numerical impact of NNLO QCD corrections from SMEFT operators on the total cross section and differential distributions in $pp \to Zh \to \ell^+\ell^- b\bar{b}$ production?
• RQ2 How do SMEFT effects modify the shape of the $m_{b\bar{b}}$ and $m_{b\bar{b}j}$ invariant mass distributions, and how does this depend on the jet definition?
• RQ3 To what extent can higher-order QCD corrections from SMEFT operators be neglected in precision SMEFT analyses, given current experimental constraints on Wilson coefficients?
• RQ4 Can the $m_{b\bar{b}}$ and $m_{b\bar{b}j}$ distributions serve as sensitive probes for new physics beyond the SM in the context of SMEFT?
• RQ5 What is the role of effective Yukawa and chromomagnetic dipole-type interactions in shaping the differential distributions at NNLO + PS accuracy?

Key findings

• The relative numerical impact of missing higher-order QCD corrections from the considered SMEFT operators on the total cross section is less than 1% when existing experimental limits on Wilson coefficients are applied.
• The invariant mass $m_{b\bar{b}}$ of the two $b$-tagged jets is identified as a particularly sensitive observable due to both normalization and shape modifications induced by SMEFT effects.
• The three-jet invariant mass $m_{b\bar{b}j}$ also exhibits shape modifications that depend on the specific jet definition, a feature not previously discussed in the SMEFT literature.
• The $m_{b\bar{b}}$ and $m_{b\bar{b}j}$ distributions receive both normalization and shape corrections from SMEFT, with the latter being sensitive to jet reconstruction details.
• The N³LO corrections from the $Q_{3G}$ operator contribute less than a permille to the $h \to b\bar{b}$ decay width, justifying their neglect in the analysis.
• The N³LO corrections from the $Q_{HG}$ operator contribute less than 0.3% to the inclusive $pp \to Zh$ cross section at 95% CL, confirming their negligible impact.