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Top- and bottom-mass effects in hadronic Higgs production at small transverse momenta through lo+nll

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Abstract

The resummed transverse momentum distribution of the Higgs boson in gluon fusion through lo+nll for small transverse momenta is considered, where the Higgs is produced through a top- and bottom-quark loop. We study the mass effects with respect to the infinite top-mass approach. The top-mass effects are small and the heavy-top limit is valid to better than 4.5 % as long as the Higgs’ transverse momentum stays below 150 GeV. When the bottom loop is considered as well, the discrepancy reaches up to about 10 %. We conclude that bottom-mass effects cannot be included in a reasonable manner by a naive reweighting procedure in the heavy-top limit. We compare our results to an earlier, alternative approach based on POWHEG.

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Notes

  1. Throughout this paper we consider the interference terms of the top- and bottom-quark amplitudes as part of the bottom-quark contribution.

  2. The formalism in Ref. [34] is based on the all-order transverse momentum resummation method developed in Refs. [37–45].

  3. Note that we omit the coefficient G introduced in Ref. [47] here and in what follows, since it enters at nlo+nnll which is beyond the accuracy needed in this paper. Furthermore, there is a subtle importance of different arguments of α s in the original formula which is not expressed in this formula, since it is not essential for the purpose of this paper.

  4. Note that only when fixing the resummation scheme the coefficients H, B, and C are unambiguously defined, since they are connected through so-called resummation-scheme transformations. Fixing H (or C) for a single process amounts to fixing the resummation scheme [48].

  5. Since the lo of the process gg→H does not correspond to the lo of the p T distribution of the Higgs, we will refer to σ (0) as the Born factor in the following to avoid confusion.

  6. The N-moments of a function g(z) are defined as \(g_{N}=\int_{0}^{1}\, dz\,z^{N-1}\,g(z)\).

  7. See Ref. [34].

  8. We set μ F =μ R =Q res=m H throughout this section.

  9. We define the finite part of the virtual according to Eq. (38) of Ref. [49].

  10. Those ingredients are known for a long time [22, 56, 57].

  11. See Sect. 2.1.

  12. According to Ref. [61] in the MC@NLO approach [62] the shape of the curve including top- and bottom-mass dependence is much more similar to ours (red, solid curve in Fig. 8).

  13. Please recall that such a scale choice is not suitable for the top contribution in general. Consequently, the purpose of this comparison is just to provide qualitative information about the scale of the bottom contribution.

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Acknowledgements

We would like to thank Robert Harlander and Anurag Tripathi for fruitful discussion and enlightening comments, and the authors of Ref. [16] and Stefano Frixione for helpful communication. This work was supported by bmbf contracts 05H09PXE and 05H12PXE, and the Helmholtz Alliance “Physics at the Terascale”.

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  1. Fachbereich C, Bergische Universität Wuppertal, 42097, Wuppertal, Germany

    Hendrik Mantler & Marius Wiesemann

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Mantler, H., Wiesemann, M. Top- and bottom-mass effects in hadronic Higgs production at small transverse momenta through lo+nll . Eur. Phys. J. C 73, 2467 (2013). https://doi.org/10.1140/epjc/s10052-013-2467-x

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