Scalar Higgs boson production in a fusion of two off-shell gluons

TL;DR

This work computes the exact off-shell gg*→H amplitude with finite top-quark mass in the triangle loop, uncovering a new term relative to the effective Lagrangian approach. By decomposing the amplitude into two form factors G1 and G2 and projecting with symmetric/antisymmetric tensors, the authors quantify how off-shell gluon virtualities affect both form factors and the Higgs production cross section within kt-factorization. They find that inclusive cross sections shift by at most about 1%, while the angular distribution near φ=π/2 is more sensitive, with potential ~45% local enhancements in M^2 due to G2 at large gluon transverse momenta; however, the observable asymmetry remains tiny (order 10^-3) in realistic scenarios. Overall, the finite-mass, off-shell effects are important for precision and in specific angular regions but are unlikely to be observable in current inclusive Higgs production measurements at the LHC.

Abstract

The amplitude for scalar Higgs boson production in a fusion of two off-shell gluons is calculated including finite (not infinite) masses of quarks in the triangle loop. In comparison to the effective Lagrangian approach, we have found a new term in the amplitude. The matrix element found can be used in the kt-factorization approach to the Higgs boson production. The results are compared with the calculations for on-shell gluons. Small deviations from the cos(phi)^2-dependence are predicted. The off-shell effects found are practically negligible.

Figures (5)

• Figure 1: Gluon coupling to the Higgs boson via $t$-quark triangle loop.
• Figure 2: Off-shell form factors $G_{1}$ (left) and $G_{2}$ (right) normalized to their on-shell values, as functions of $\xi=-{\bf k}_{1\perp}^{2}/4m_{top}^2$ and $\eta=-{\bf k}_{2\perp}^{2}/4m_{top}^2.$
• Figure 3: Averaged square of off-shell matrix element $\langle M^2 \rangle_{\phi}$ normalized to its on-shell value $\langle M_0^2 \rangle_{\phi}$ as a function of $\xi=-{\bf k}_{1\perp}^{2}/4m_{top}^2$ and $\eta=-{\bf k}_{2\perp}^{2}/4m_{top}^2.$
• Figure 4: Azimuthal angle distribution of the cross section. In this calculation the BFKL UGDF was used and $- 2 < y_H < 2$. The solid line represents the calculation with the full amplitude, whereas the dashed line is the modulus of the interference term.
• Figure 5: The asymmetry term normalized to the symmetric terms as a function of $\phi$. In this calculation the BFKL UGDF was used and $-2 < y_H < 2$. The solid curve corresponds to the inclusive case while the dash-dotted curve is for the extra cut $|{\bf p}_{\perp}| >$ 50 GeV.