We compute the two-loop massless QCD corrections to the four-point amplitude g + g → H + H resulting from effective operator insertions that describe the interaction of a Higgs boson with gluons in the infinite top quark mass limit. This amplitude is an essential ingredient to the third-order QCD corrections to Higgs boson pair production. We have implemented our results in a numerical code that can be used for further phenomenological studies.

India

Pulak Banerjee

CERN

Sophia Borowka

Prasanna Dhani

Switzerland

Thomas Gehrmann

V. Ravindran

Two-loop massless QCD corrections to the g + g → H + H four-point amplitude

We present a sensitivity study on the cubic and quartic self couplings in double Higgs production via gluon fusion at hadron colliders. Considering the relevant operators in the Standard Model Effective Field Theory up to dimension eight, we calculate the dominant contributions up to two-loop level, where the first dependence on the quartic interaction appears. Our approach allows to study the independent variations of the two self couplings and to clearly identify the terms necessary to satisfy gauge invariance and to obtain UV-finite results order by order in perturbation theory. We focus on the   <math> <mi>b</mi> <mover> <mi>b</mi> <mo>¯</mo> </mover> <mi>γ</mi> <mi>γ</mi> </math>  $$ b\overline{b}\gamma \gamma $$  signature for simplicity and provide the expected bounds for the cubic and quartic self couplings at the 14 TeV LHC with 3000 fb−1 (HL-LHC) and for a future 100 TeV collider (FCC-100) with 30 ab−1. We find that while the HL-LHC will provide very limited sensitivity on the quartic self coupling, precision measurements of double Higgs production at a FCC-100 will offer the opportunity to set competitive bounds. We show that combining information from double and triple Higgs production leads to significantly improved prospects for the determination of the quartic self coupling.

Belgium

Claude Duhr

Italy

Fabio Maltoni

Germany

Davide Pagani

Ambresh Shivaji

Xiaoran Zhao

Probing the scalar potential via double Higgs boson production at hadron colliders

An algorithm for the systematic analytical approximation of multi-scale Feynman integrals is presented. The algorithm produces algebraic expressions as functions of the kinematical parameters and mass scales appearing in the Feynman integrals, allowing for fast numerical evaluation. The results are valid in all kinematical regions, both above and below thresholds, up to in principle arbitrary orders in the dimensional regulator. The scope of the algorithm is demonstrated by presenting results for selected two-loop threepoint and four-point integrals with an internal mass scale that appear in the two-loop amplitudes for Higgs+jet production.

Daniel Hulme

Systematic approximation of multi-scale Feynman integrals

Higher-order corrections to the MSSM Higgs-boson masses are desirable for accurate predictions currently testable at the LHC. By comparing the prediction with the measured value of the discovered Higgs signal, viable parameter regions can be inferred. For an improved theory accuracy, we compute all two-loop corrections involving the strong coupling for the Higgs-boson mass spectrum of the MSSM with complex parameters. Apart from the dependence on the strong coupling, these contributions depend on the weak coupling and Yukawa couplings, leading to terms of $$\mathcal {O}{\left( \alpha \alpha _s\right) }$$ <math><mrow><mi>O</mi><mfenced><mi>α</mi><msub><mi>α</mi><mi>s</mi></msub></mfenced></mrow></math>  and $$\mathcal {O}{\left( \sqrt{\alpha _{q_1}}\sqrt{\alpha _{q_2}}\alpha _s\right) }$$ <math><mrow><mi>O</mi><mfenced><msqrt><msub><mi>α</mi><msub><mi>q</mi><mn>1</mn></msub></msub></msqrt><msqrt><msub><mi>α</mi><msub><mi>q</mi><mn>2</mn></msub></msub></msqrt><msub><mi>α</mi><mi>s</mi></msub></mfenced></mrow></math> , ($$q_{1,2}=t,b,c,s,u,d$$ <math><mrow><msub><mi>q</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>=</mo><mi>t</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>s</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>d</mi></mrow></math> ). The full dependence on the external momentum and all relevant mass scales is taken into account. The calculation is performed in the Feynman-diagrammatic approach which is flexible in the choice of the employed renormalization scheme. For the phenomenological results presented here, a renormalization scheme consistent with higher-order corrections included in the code FeynHiggs is adopted. For the evaluation of the results, a total of 513 two-loop two-point integrals with up to five different mass scales are computed fully numerically using the program SecDec. A comparison with existing results in the limit of real parameters and/or vanishing external momentum is carried out, and the impact on the lightest Higgs-boson mass is discussed, including the dependence on complex phases. The new results will be included in the public code FeynHiggs.

France

Sebastian Paßehr

Georg Weiglein

Complete two-loop QCD contributions to the lightest Higgs-boson mass in the MSSM with complex parameters