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Reconstruction of top-quark mass effects in Higgs pair production and other gluon-fusion processes

Ramona Gröber, Andreas Maier, Thomas Rauh

Abstract

We propose a novel method for the treatment of top-quark mass effects in the production of $H^{(*)}$, $HH$, $HZ$ and $ZZ$ final states in gluon fusion. We show that it is possible to reconstruct the full top-quark mass dependence of the virtual amplitudes from the corresponding large-$m_t$ expansion and the non-analytic part of the amplitude near the top-quark threshold $\hat{s}=4m_t^2$ with a Padé ansatz. The reliability of our method is clearly demonstrated by a comparison with the recent NLO result for Higgs pair production with full top-quark mass dependence.

Reconstruction of top-quark mass effects in Higgs pair production and other gluon-fusion processes

Abstract

We propose a novel method for the treatment of top-quark mass effects in the production of , , and final states in gluon fusion. We show that it is possible to reconstruct the full top-quark mass dependence of the virtual amplitudes from the corresponding large- expansion and the non-analytic part of the amplitude near the top-quark threshold with a Padé ansatz. The reliability of our method is clearly demonstrated by a comparison with the recent NLO result for Higgs pair production with full top-quark mass dependence.

Paper Structure

This paper contains 15 sections, 40 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. The method
  3. Padé approximation for $\mathbf{gg\to H^{(*)}}$
  4. Padé approximation for $\mathbf{gg\to HH}$
  5. The amplitude near threshold
  6. Structure of the amplitude near threshold
  7. Computation of the non-analytic terms
  8. Comparison with the exact result
  9. Numerical setup
  10. Comparison at LO
  11. Comparison at NLO
  12. Conclusions and outlook
  13. Subtractions
  14. Expansion of the P-wave Green function
  15. Results for the $gg\to HH$ form factors near threshold

Figures (11)

  • Figure 1: Invariant Higgs mass distribution for the full LO cross section (dark blue) and the large mass expansion (LME) up to $\mathcal{O}(1/m_t^8)$ as given in Ref. Degrassi:2016vss (red-dashed).
  • Figure 2: The LO diagram for Higgs production in gluon fusion (left) and an example for a NLO diagram that contains a branch cut starting at $\hat{s}=0$ (right).
  • Figure 3: Padé approximants for $F_\triangle$ at LO (top) and NLO (bottom) constructed using only the LME up to the order $1/m_t^8$ as input. Shown are the real/imaginary part of the Padé approximants (blue/orange) and the exact results (black). We constructed in total 20 approximants of the types [1/3], [2/2] and [3/1] for random values of $a_R$ in the range [0.1,10], while approximants with poles in the rectangle $\text{Re}(z)\in[0,8]$ and $\text{Im}(z)\in[-1,1]$ have been excluded since they can cause unphysical resonances in the form factor.
  • Figure 4: We show the same comparison as in Figure \ref{['fig:FboxLME']} but for Padé approximants based on the LME and the threshold expansion. Only [5/2], [4/3], [3/4] and [2/5] approximants were constructed at LO and only [4/2], [3/3] and [2/4] approximants were constructed at NLO.
  • Figure 5: Graphical representation of the terms in the master formula \ref{['eq:Master_eq']}. The diagram on the left (right) corresponds to the 'resonant' ('non-resonant') part of the amplitude. The shaded area indicates that Coulomb exchanges between the top quark pair are resummed.
  • ...and 6 more figures