The effective field theory for single Higgs and double Higgs production beyond leading order

Authors

Long-Bin Chen

• Guangzhou University
• chenlb_AT_gzhu_dot_edu_dot_cn

Hai Tao Li

• LANL
• haitaoli_AT_lanl_dot_gov

Hua-Sheng Shao

• LPTHE
• huasheng_dot_shao_AT_lpthe_dot_jussieu_dot_fr

Jian Wang

• Shandong University
• j_dot_wang_AT_sdu_dot_edu_dot_cn

References

• L.-B. Chen, H. T. Li, H.-S. Shao and J. Wang, ​arXiv:1909.06808, ​arXiv:1912.13001.

Description of the model

In the infinite top-quark mass limit, the interaction between the Higgs field and the gluon field can be effectively described by

$\mathcal{L}_{\rm eff}=-\frac{1}{4}(C_h \frac{h}{v}-C_{hh}\frac{h^2}{2v^2})G^a_{\mu\nu}G^{a~\mu\nu}$

where

$G^a_{\mu\nu}$

is the gluon field strength tensor.

The NLO UFO model based on

$\mathcal{L}_{\rm eff}+\mathcal{L}_{\rm SM}$

can be downloaded from here.

The analytical expressions for

$R_2$

Feynman rules can be found in appendix B of ​arXiv:1912.13001.

An example in MadGraph5_aMC@NLO

In order to handle mixed-order senarios, one has to use the version 3.0.1+ of MadGraph5_aMC@NLO.

In version 3.0.X, the NLO QCD correction to di-Higgs+jet at

$\mathcal{O}(\alpha_s^3)$

is generated by

> import model HEFT_DH_UFO
> generate p p > h h j / t t~ QCD=3 QED=2 NP=2 [QCD] QCD^2<=6 QED^2<=4 NP^2<=4

In versions 3.1.0+, the generation syntax has been changed ​here. It is generated by two processes, i.e.,

> import model HEFT_DH_UFO
> generate p p > h h j / t t~ QCD=3 QED=2 NP=2 [QCD] QCD^2<=6 QED^2<=4 NP^2<=4

and

> import model HEFT_DH_UFO
> generate p p > h h j / t t~ QCD^2==8 QED^2<=4 NP^2<=4

The second part is the pure interference term at tree level but contributing to

$\mathcal{O}(\alpha_s^4)$

.