Eur. Phys. J. C (2025) 85: 84
https://doi.org/10.1140/epjc/s10052-025-13823-9

Regular Article - Experimental Physics

QCD predictions for simultaneously produced Higgs and vector bosons at $\sqrt{s}$ = 13, 14, 27 and 100 TeV with a comprehensive study of systematic uncertainty and charge asymmetry

¹ Department of Physics, Faculty of Art and Science, Bingol University, 12000, Bingol, Turkey
² Department of Physics and Astronomy, The University of Iowa, 52241, Iowa City, IA, USA
³ Department of Physics, Faculty of Science, Erciyes University, 38030, Kayseri, Turkey
⁴ Department of Nuclear Engineering, Faculty of Engineering and Architecture, Sinop University, 57000, Sinop, Turkey

^a kdilsiz@bingol.edu.tr

Received: 30 June 2024
Accepted: 16 January 2025
Published online: 26 January 2025

Abstract

A comprehensive study of high-order QCD cross-section for the Higgs boson that is simultaneously produced with a vector boson is presented at $\sqrt{s}=13,14,27$ and 100 TeV in this manuscript. The simultaneous Higgs production with a vector boson facilitates the investigation of the Higgs signal. In the calculations, three different branching states of the Higgs (${\tau }^{-}{\tau }^{+}$, $b\overline{b}$, $\gamma \gamma$) and vector bosons [$W^{\pm }(e^{\pm }\nu (\overline{\nu })),Z(e^{-}{e}^{+}$)] were taken into account. Here, leading order (LO), next-to-leading order (NLO), and next-to-NLO (NNLO) QCD cross-sections were calculated for these branching states. A simulation framework was built for the calculations at the TRUBA high-performance grid computing center. Then, the threshold values (selection cuts) close to the values used by the CMS and ATLAS Collaborations were selected and used on several parameters such as invariant mass, transverse momentum ($p_T$), pseudorapidity ($\eta$), etc. In addition, NNPDF3.1 parton distribution functions (PDF) were used during the calculation. The results showed that the numerical value of the QCD prediction increases at NLO and NNLO as compared to the LO predictions. In addition to the higher-orders, the cross-section value increases as the center-of-mass energy increases. In addition to the QCD predictions, PDF, scale, and ${\alpha }_S$ uncertainties of the QCD predictions were also calculated to test the reliability of the high-order QCDs. The results showed that total and scale uncertainties decrease as the QCD order increases. In addition, it was found that LO total and scale uncertainties increase significantly as the center-of-mass energy increases, while NLO and NNLO scale and total uncertainties remain almost constant or show a negligible increase as the center-of-mass energy increases. This indicates that high-order QCDs not only provide more accurate results by the addition of extra partonic diagrams but also provide lower uncertainties in the relevant production channels. Furthermore, the required data that provides the exact statistics for physics measurements of simultaneously produced Higgs and vector bosons as the data at 13 TeV were predicted at $\sqrt{s}$ = 14, 27, and 100 TeV. As a result, we found that the same statistics for accurate physics measurements can be obtained at $\sqrt{s}$ = 14, 27, and 100 TeV with approximately 1.1, 2.0, and 6.5 times less data than the amount of data at $\sqrt{s}$ = 13 TeV, respectively. In the last section of this study, W boson charge asymmetry was computed at NNLO QCD. The lowest charge asymmetry between $W^{+}$ and $W^{-}$ was obtained at the WH(${\tau }^{-}{\tau }^{+}$) decay channel and the highest charge asymmetry results were obtained at the WH($b\overline{b}$) decay channel.