Higgs Boson Cross Section from CTEQ-TEA Global Analysis

TL;DR

This work quantifies the uncertainties in the Higgs boson production cross section through gluon fusion arising from parton distribution functions and the strong coupling $α_s(M_Z)$ within the CT10H NNLO global analysis. It benchmarks two uncertainty-estimation approaches, the Hessian method and the Lagrange multiplier method, finding substantial agreement in the predicted cross sections at $\sqrt{s}=7,8,$ and $14$ TeV and in the combined PDF+$α_s$ uncertainties, thereby validating the common practice of adding PDF and $α_s$ errors in quadrature. The analysis reveals a strong correlation between $σ_H$ and the gluon PDF around $x\sim 0.01$ and highlights the anti-correlation between the gluon-initiated Higgs channel and the vector boson fusion channel. The LM approach provides a complementary cross-check and yields detailed correlations and extreme PDFs that facilitate robust uncertainty propagation for Higgs phenomenology at the LHC, with the CT10H extensions incorporating LHC data to tighten gluon-PDF constraints. Overall, the results support using the Hessian framework for practical Higgs cross-section uncertainty estimates while offering LM-based validation and insight into the underlying correlations.

Abstract

We study the uncertainties of the Higgs boson production cross section through the gluon fusion subprocess at the LHC (with $\sqrt s=7, 8$ and $14$ TeV) arising from the uncertainties of the parton distribution functions (PDFs) and of the value of the strong coupling constant $α_s(M_Z)$. These uncertainties are computed by two complementary approaches, based on the Hessian and the Lagrange Multiplier methods within the CTEQ-TEA global analysis framework. We find that their predictions for the Higgs boson cross section are in good agreement. Furthermore, the result of the Lagrange Multiplier method supports the prescriptions we have previously provided for using the Hessian method to calculate the combined PDF and $α_s$ uncertainties, and to estimate the uncertainties at the $68\%$ confidence level by scaling them from the $90\%$ confidence level.

Figures (9)

• Figure 1: $\chi^{2}$ versus $\sigma_{H}$ with $\alpha_{s}(M_{Z}) = 0.118$. The constrained minimum of $\chi^{2}$ is plotted as a function of the predicted cross section $\sigma_{H}$ for Higgs boson production via gluon fusion channel at the LHC, for $\sqrt{s} = 7, 8~ {\rm and}~ 14\ {\rm TeV}$. The constrained fits without and with the tier-2 penalties are shown as red solid and blue dashed curves, respectively. The red circles and blue boxes indicate the $90\%$ C.L. errors obtained from the Hessian method without and with the tier-2 penalties, respectively.
• Figure 2: Contour plots of $\chi^{2}(\overline{a})$ in the $(\alpha_{s},\sigma_{H})$ plane, for $\sigma_H$ (in pb unit) at the LHC, with 7, 8 and 14 TeV. The thick black outer and inner contours are at $\Delta\chi^2=100$ and $100/(1.645)^2$, respectively, for the $90\%$ C.L. and $68\%$ C.L.. The thin colored contours are at intervals in $\chi^2$ of 10.
• Figure 3: Contour plots of $\chi^{2}+\hbox{tier-2}$ ($T_2$) in the $(\alpha_{s},\sigma_{H})$ plane, for $\sigma_H$ (in pb unit) at the LHC, with 7, 8 and 14 TeV. The thick black outer and inner contours are at $\Delta\chi^2=100$ and $100/(1.645)^2$, respectively, for the $90\%$ C.L. and $68\%$ C.L.. The thin colored contours are at intervals in $\chi^2$ of 10. The fits that give minimum and maximum $\sigma_H$ are indicated by the red square symbols, with $\alpha_s(M_Z)=0.1167$, $0.118$ or $0.1194$. (See the text in Sec. IV.C for its details.)
• Figure 4: Ratio of the prediction of the Higgs boson cross section from each error set to that from the central set. The results for the $gg$ fusion and VBF channels are shown in the upper and lower panels. The dashed, solid, and dotted lines are for the LHC energy at 7, 8, and 14 TeV, respectively.
• Figure 5: Correlation cosine between the $gg \to H$ cross sections and the PDFs at $Q=125\ {\rm GeV}$ as functions of $x$, at the LHC, with 7, 8, and 14 TeV.