author: Marco Bonvini
Inclusive Higgs cross section in gluon fusion up to N3LO
Developers: Marco Bonvini
This code computes the cross section for the inclusive
Higgs production in gluon fusion at LO, NLO, NNLO and N3LO, optionally with small-x resummation.
All fixed-order results are available in the large-mt effective theory,
rescaled with the exact LO by default.
At LO and NLO the exact result including any number of fermions (top, bottom and charm) running in the loop is available.
At NNLO the top mass dependence can be included as an expansion in mH/mt,
supplemented with the exact small-x behaviour.
At N3LO only the effective theory results is available, and some top mass effects
can be included according to the recipe of arXiv:1603.08000.
Up to version 3.5, the cross sections can also be computed using an approximation based on a combination of
optimized soft-collinear and high-energy behaviours.
Since version 3.3, pseudo-scalar Higgs boson production in the large-mt effective theory
up to NNLO and almost-exact N3LO is also available (arXiv:1606.00837).
Since version 4.0, the exact small-x contributions at NNLO and N3LO are included
according to the procedure described in arXiv:1805.08785.
Since version 4.0, it optionally includes small-x resummation at LLx through HELL-x v3.0 onwards
(since it is based on pretabulated tables, only μF/mH=2,1,1/2,1/4 are available).
Large-x (threshold) resummation can be added a posteriori through the code TROLL
Latest version: ggHiggs v4.1 (recommended)
Warning: In versions v1.x the μF dependence for the soft part is incomplete
when Altarelli-Parisi improvement is done at the exponent (default). Fixed in version 2.0+
- 26-09-2020: ggHiggs v4.1
Compatibility with HELL-x v3.1 and
with some versions of gcc.
- 24-05-2018: ggHiggs v4.0
It now includes the full N3LO of arXiv:1802.00833.
New implementation of small-x contributions at NNLO and N3LO
Small-x resummation through HELL-x v3.0 now available
Removed old soft+high-energy approximation.
- 07-11-2016: ggHiggs v3.5
Fixed another bug appearing with the -e option, introduced in version 3.0, affecting the NLO cross section when mH>2mt
(thanks to Luca Rottoli for guessing the right iε).
- 22-07-2016: ggHiggs v3.4
Fixed a bug appearing with the -e option, introduced in version 3.3.
- 06-05-2016: ggHiggs v3.3
Added pseudo-scalar boson production process (selectable with -o or --CPodd runtime option).
- 12-05-2016: ggHiggs v3.2
Improved numerical stability of exact NLO result at small x. Cleaned up the source code a bit.
- 29-03-2016: ggHiggs v3.1
Fully exact scale dependence at N3LO.
- 07-03-2016: ggHiggs v3.0
It now includes the full N3LO of arXiv:1602.00695 (soft expansion).
Thanks to Claudio Muselli for his help and to Achilleas Lazopoulos for providing the N3LO coefficients in electronic format.
Simplified interface (removed all approximate results from the main example code);
notice that now -f sets only μF/mH and -r sets μR/mH.
Several improvements under the hood: it now compiles faster,
the exact NLO with finite quark masses has been fully rewritten in C++ and it is now incredibly faster and more accurate,
several internal changes towards the direction of a fully object-oriented implementation.
A couple of (very minor) bug fixes.
Usage of MSbar top mass available in the large-mt effective theory.
- 03-12-2015: ggHiggs v2.3
Improved estimate of the uncertainty from the high-energy contribution.
Added LO in the EFT.
- 19-10-2015: ggHiggs v2.2
Added optional ElectroWeak correction factor (thanks to Luca Rottoli).
- 02-03-2015: ggHiggs v2.1
Improved user interface. Introduced a namespace ggHiggs for improved compatibility.
- 06-12-2014: ggHiggs v2.0
Now the μF dependence is done correctly also at order αs3;
several options are possible for the actual dependence: all channels (exact), gg channel (exact), gg channel (approximate)
The code is much faster now for the computation of the approximations.
Now requires Cuba 4.0
- 15-06-2014: ggHiggs v1.9
Important! Fixed a bug on the soft part at order αs3 when Altarelli-Parisi improvement is done at the exponent (default).
The N3LO cross section at central scales becomes about 1% smaller.
Extended the range of validity of the high-energy approximation for mH up to 5 TeV (as requested by Ayan Paul and Ennio Salvioni).
- 04-06-2014: ggHiggs v1.8
Now compatible with LHAPDF 6.1.x (and still back-compatible with LHAPDF 5)
- 23-05-2014: ggHiggs v1.7
Fixed a compatibility issue with some compilers related to the definition of a class of name "complex".
Extended the range of validity of the high-energy approximation for mH up to 2 TeV.
- 15-05-2014: ggHiggs v1.6
Compatiblility with ResHiggs.
- 10-04-2014: ggHiggs v1.5
Updated coefficient of the δ(1-z) term (see arXiv:1404.3204).
- 28-02-2014: ggHiggs v1.4
The code has been made slightly faster using improved access to PDFs (thanks to Luca Rottoli).
- 11-02-2014: ggHiggs v1.3
Finally added full mass dependence of small-x coefficients.
- 10-02-2014: ggHiggs v1.2
Fixed a memory leak issue that can appear with some compiler versions (thanks to Gherardo Vita).
- 09-06-2013: ggHiggs v1.1
- 23-05-2013: ggHiggs v1.0
New: all channels have been included, now it computes directly the cross section.
Limitation: the small-x behaviour is currently correct only for a 125 GeV Higgs (will be fixed soon).
- 27-03-2013: ggHiggs v0.3
Only gluon-gluon channel, computes only the K-factors.
Limitation: the small-x behaviour is currently correct only for a 125 GeV Higgs.
ggHiggs depends on the following libraries:
- LHAPDF - Les Houches Accord PDF interface, either version 5 or version 6 (the latter from ggHiggs v1.8 onwards)
- GSL - Gnu Scientific Libraries
- Cuba 4.x (ggHiggs v1.x requires Cuba 3.0)
- HELL-x (v3.0 onwards), needed for accessing small-x resummation (you need to tell to the makefile where HELL-x has been installed)
The results and implementation are described in the papers:
- R.D. Ball, M. Bonvini, S. Forte, S. Marzani and G. Ridolfi,
- M. Bonvini, R.D. Ball, S. Forte, S. Marzani and G. Ridolfi,
- M. Bonvini, S. Marzani, C. Muselli and L. Rottoli,
Bonvini:2016frm (version 3.x onwards)
- T. Ahmed, M. Bonvini, M.C. Kumar, P. Mathews, N. Rana, V. Ravindran and L. Rottoli,
Ahmed:2016otz (for pseudo-scalar Higgs production, version 3.3+)
- M. Bonvini, S. Marzani,
Bonvini:2018ixe (version 4.0 onwards)
- M. Bonvini,
Bonvini:2018iwt (version 4.0 onwards)
Please cite them if you use the code.
The original results are included in ggHiggs according to the following list (which you should also cite when using these parts of the code):
- NLO with finite top mass has been extracted from a private code by Bonciani, Degrassi, Vicini
(thanks to Alessandro Vicini for providing the code). From version 3.0 this has been independently rewritten in C++.
- NNLO in the large top mass approximation has been extracted from
by Harlander, Kilgore (hep-ph/0201206).
- NNLO with finite top mass has been implemented using the full result
by Harlander, Ozeren
and Harlander, Mantler, Marzani, Ozeren
(thanks to Robert Harlander for providing the analytic result).
- N3LO has been implemented from the results of
Anastasiou, Duhr, Dulat, Furlan, Gehrmann, Herzog, Mistlberger
and Anastasiou, Duhr, Dulat, Furlan, Gehrmann, Herzog, Lazopoulos, Mistlberger
(thanks to Achilleas Lazopoulos for providing the coefficients in electronic format).
From version 4.0 the exact EFT result of Mistlberger (arXiv:1802.00833) is available.
Soft-gluon resummed Higgs cross section in gluon fusion up to N3LL'
Developers: Marco Bonvini, Luca Rottoli
This code evolved into a new code called TROLL:
visit TROLL webpage
For any problem, request or suggestion, contact me at
- marco.bonvini [at] ge.infn.it