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Higgs boson pair production in gluon fusion at NLO with full top-quark mass dependence

S. Borowka, N. Greiner, G. Heinrich, S. P. Jones, M. Kerner, J. Schlenk, U. Schubert, T. Zirke

TL;DR

This work delivers the first NLO QCD calculation for Higgs boson pair production in gluon fusion with full top-quark mass dependence, using a combination of GoSam, Reduze, and SecDec to handle the virtual two-loop amplitude numerically. By comparing full-mass results to various mt-approximation schemes, the study demonstrates substantial deviations, especially in the high invariant-mass region, and shows that mt effects reduce the total cross section by about 14% relative to Born-improved HEFT. The analysis confirms that accurate mt treatment is essential for reliable predictions across the entire m_hh spectrum and provides a general methodology applicable to other multi-scale, multi-loop amplitudes. These findings have significant implications for precision Higgs self-coupling studies at the LHC and future colliders.

Abstract

We present the calculation of the cross section and invariant mass distribution for Higgs boson pair production in gluon fusion at next-to-leading order (NLO) in QCD. Top-quark masses are fully taken into account throughout the calculation. The virtual two-loop amplitude has been generated using an extension of the program GoSam supplemented with an interface to Reduze for the integral reduction. The occurring integrals have been calculated numerically using the program SecDec. Our results, including the full top-quark mass dependence for the first time, allow us to assess the validity of various approximations proposed in the literature, which we also recalculate. We find substantial deviations between the NLO result and the different approximations, which emphasizes the importance of including the full top-quark mass dependence at NLO.

Higgs boson pair production in gluon fusion at NLO with full top-quark mass dependence

TL;DR

This work delivers the first NLO QCD calculation for Higgs boson pair production in gluon fusion with full top-quark mass dependence, using a combination of GoSam, Reduze, and SecDec to handle the virtual two-loop amplitude numerically. By comparing full-mass results to various mt-approximation schemes, the study demonstrates substantial deviations, especially in the high invariant-mass region, and shows that mt effects reduce the total cross section by about 14% relative to Born-improved HEFT. The analysis confirms that accurate mt treatment is essential for reliable predictions across the entire m_hh spectrum and provides a general methodology applicable to other multi-scale, multi-loop amplitudes. These findings have significant implications for precision Higgs self-coupling studies at the LHC and future colliders.

Abstract

We present the calculation of the cross section and invariant mass distribution for Higgs boson pair production in gluon fusion at next-to-leading order (NLO) in QCD. Top-quark masses are fully taken into account throughout the calculation. The virtual two-loop amplitude has been generated using an extension of the program GoSam supplemented with an interface to Reduze for the integral reduction. The occurring integrals have been calculated numerically using the program SecDec. Our results, including the full top-quark mass dependence for the first time, allow us to assess the validity of various approximations proposed in the literature, which we also recalculate. We find substantial deviations between the NLO result and the different approximations, which emphasizes the importance of including the full top-quark mass dependence at NLO.

Paper Structure

This paper contains 8 sections, 15 equations, 2 figures.

Table of Contents

  1. Introduction
  2. NLO calculation
  3. Amplitude structure
  4. The virtual two-loop amplitude
  5. Real radiation
  6. Checks
  7. Numerical results
  8. Conclusions

Figures (2)

  • Figure 1: Comparison of the full calculation to various approximations for the Higgs pair invariant mass distribution at $\sqrt{s}=13$ TeV. "NLO HEFT" denotes the effective field theory result, i.e approximation (i) above, while "FT$_{approx}$" stands for approximation (ii), where the top-quark mass is taken into account in the real radiation part only. The band results from scale variations by a factor of two around the central scale $\mu=m_{hh}/2$.
  • Figure 2: Comparison of the virtual amplitude with full top-quark mass dependence to various orders in a $1/m_t^{2}$ expansion. $V^\prime_N$ denotes the Born-improved HEFT result to order $N$ in the $1/m_t^{2}$ expansion, i.e. $V^\prime_N=V_N\,B/B_N$.