Effective Field Theory for Higgs Plus Jet Production

TL;DR

This work develops an effective field theory for Higgs production in association with a jet by including gluon-Higgs interactions up to dimension-7, enabling a model-independent study of finite top mass effects and beyond-the-Standard-Model modifications. The authors derive the complete renormalization structure for the dimension-7 operators, formulate RG running to resum large logs, and compute NLO QCD corrections to Higgs+jet within this EFT, including both virtual and real emission pieces. They show that, at NLO, the dimension-7 operator $O_3$ remains largely suppressed in the gluon channel but acquires nonzero interference with $O_1$ at one loop, while $O_5$ becomes significant in quark-initiated channels and can dominate at high $p_T$, highlighting where BSM effects are most visible. The results provide phase-space slicing-based, IR-finite predictions and $p_T$-dependent K-factors that can be reweighted for arbitrary BSM coefficients, offering a practical framework for disentangling heavy-mass effects and new physics in Higgs-gluon interactions across LHC observables.

Abstract

We use an effective field theory (EFT) which includes all possible gluon-Higgs dimension-5 and dimension-7 operators to study Higgs boson plus jet production in next-to-leading order QCD. The EFT sheds light on the effect of a finite top quark mass as well as any Beyond-the-Standard Model (BSM) modifications of Higgs-gluon effective couplings. In the gluon channel, the accuracy of the heavy-top approximation for differential distributions arises from the non-interference between the helicity amplitudes of the G^3 h and G^2 h operators in the m_h < p_T limit at lowest order. One dimension-7 operator involving quark bilinears, however, contributes significantly at high p_T, and potentially offers a channel for seeing BSM effects. One-loop renormalization of these operators is determined, allowing resummation of large logarithms via renormalization group running. NLO numerical results at the LHC are presented, which include O(1/m_t^2) contributions in the SM limit.

Figures (12)

• Figure 1: An example diagram showing the $\mathcal{O}(1/m_t^2)$ gluon self-interaction vertex from integrating out the top quark. The Higgs is produced through the $O_1$ operator in the $m_t \to \infty$ limit, but the overall power of this Feynman diagram is still of $\mathcal{O}(1/m_t^2)$ and should be considered on the same footing as diagrams producing the Higgs through $1/m_t^2$-suppressed dimension-7 operators.
• Figure 2: Leading order Higgs transverse momentum distributions from the dimension-5 and dimension-7 EFT operators for Higgs plus jet production at LO using CJ12 NLO PDFs with $\mu_R=\mu_F=m_h$. The curves use the ${\cal O}(\alpha_s)$ SM values of the $C_i$ and include terms to ${\cal O}\left( 1/m_t^2 \right)$.
• Figure 3: Leading order Higgs transverse momentum distributions from the dimension-5 and dimension-7 EFT operators for Higgs plus jet production at LO using CJ12 NLO PDFs with $\mu_R=\mu_F=m_h$. The curves use the ${\cal O}(\alpha_s)$ SM values of the $C_i$ and include terms to ${\cal O}\left( 1/m_t^2 \right)$. Contributions from $gg$, $qg$, and $qq$ partonic channels are shown separately.
• Figure 4: Deviations of the EFT predictions including all dimension-5 and dimension-7 operators (solid curve) from the exact result for Higgs plus jet production at LO using CJ12 NLO PDFs with $\mu_R=\mu_F=m_h$. The curves use the ${\cal O}(\alpha_s)$ SM values of the $C_i$ and include terms to ${\cal O}\left( 1/m_t^2 \right)$. The dotted curve includes only the contribution from $O_1$.
• Figure 5: Deviations of the EFT predictions from the exact results (dotted curves) , broken up into partonic channels, for Higgs plus jet production at LO using CJ12 NLO PDFs with $\mu_R=\mu_F=m_h$. The curves use the ${\cal O}(\alpha_s)$ SM values of the $C_i$ and include terms to ${\cal O}\left( 1/m_t^2 \right)$. The solid curves includes only the contribution from $O_1$. The red dashed and red solid curves are indistinguishable.