HNNLO: a MC program for Higgs boson production at hadron colliders\address
INFN, Sezione di Firenze, Via Sansone 1, I-50019 Sesto Fiorentino, Florence, Italy
We consider Higgs boson production through gluon–gluon fusion in hadron collisions. We present a numerical program that computes the cross section up to NNLO in QCD perturbation theory. The program allows the user to apply arbitrary cuts on the momenta of the partons and of the photons or leptons that are produced in the final state. We present selected numerical results at the Tevatron and the LHC.
The Higgs boson is a fundamental ingredient in the Standard Model (SM) but it has not been observed yet. Its search is currently being carried out at the Tevatron, and will be continued at the LHC. Once the Higgs boson is found, the LHC will be able to study its properties like couplings and decay widths.
At hadron colliders, the SM Higgs boson is mainly produced by gluon-gluon fusion through a heavy-quark loop. For such an important process, it is essential to have reliable theoretical predictions for the cross section and the associated distributions. At leading order (LO) in QCD perturbation theory, the cross section is proportional to , being the QCD coupling. The QCD radiative corrections to the total cross section are known at the next-to-leading order (NLO)  and at the next-to-next-to-leading order (NNLO) . The effects of a jet veto on the total cross section has been studied up to NNLO . We recall that all the results at NNLO have been obtained by using the large- approximation, being the mass of the top quark.
These NNLO calculations can be supplemented with soft-gluon resummed calculations at next-to-next-to-leading logarithmic (NNLL) accuracy either to improve the quantitative accuracy of the perturbative predictions (as in the case of the total cross section [4, 5]) or to provide reliable predictions in phase-space regions where fixed-order calculations are known to fail .
These fixed order and resummed calculations share a common feature: they are fully inclusive over the produced final state (in particular, over final-state QCD radiation). Therefore they refer to situations where the experimental cuts are either ignored (as in the case of the total cross section) or taken into account only in simplified cases (as in the case of the jet vetoed cross section). The impact of higher-order corrections may be strongly dependent on the details of the applied cuts and also the shape of various distributions is typically affected by these details.
The first NNLO calculation that fully takes into account experimental cuts was reported in Ref. , considering the decay mode . In Ref.  the calculation is extended to the decay mode (see also ).
In Ref.  we have proposed a method to perform NNLO calculations and we have applied it to perform an independent computation of the Higgs production cross section. The calculation is implemented in a fully-exclusive parton level event generator. This feature makes it particularly suitable for practical applications to the computation of distributions in the form of bin histograms. Our numerical program can be downloaded from . The decay modes that are currently implemented are , and leptons .
In the following we present a brief selection of results that can be obtained by our program. We use the MRST2004 parton distributions , with parton densities and evaluated at each corresponding order (i.e., we use -loop at NLO, with ). Unless stated otherwise, the renormalization and factorization scales are fixed to the value , where is the mass of the Higgs boson.
2 Results at the LHC
We consider the production of a Higgs boson with mass GeV at the LHC ( collisions at TeV) in the decay mode . The NLO and NNLO inclusive -factors are and , respectively. We apply a set of selection cuts taken from the study of Ref. . The charged leptons (with ) are classified according to their maximum () and minimum () transverse momentum. Then should be larger than 25 GeV, and should be between 35 and 50 GeV. The missing of the event is required to be larger than GeV and the invariant mass of the charged leptons must be smaller than GeV. The azimuthal separation of the charged leptons in the transverse plane () is smaller than . Finally, there should be no jet with larger than GeV.
The corresponding cross sections are reported in Table 1.
The cuts are quite hard, the efficiency being at NLO and at NNLO. The scale dependence of the result is strongly reduced at NNLO, being of the order of the error from the numerical integration. The impact of higher order corrections is also drastically changed. The -factor is now 1.19 at NLO and 1.11 at NNLO. As expected, the jet veto tends to stabilize the perturbative expansion, and the NNLO cross section turns out to be smaller than the NLO one. The study of Ref.  shows that the efficiencies obtained at NNLO are in good agreement with those predicted by the MC@NLO event generator .
We now consider the production of a Higgs boson with mass GeV . In this mass region the dominant decay mode is leptons, providing a clean four lepton signature. In the following we consider the decay of the Higgs boson in two identical lepton pairs. When no cuts are applied, the NLO -factor is whereas at NNLO we have .
We consider the following cuts . The transverse momenta of the leptons, ordered from the largest () to the smallest () are required to fulfil , , and . The leptons should be central () and isolated: the total transverse energy in a cone of radius 0.2 around each lepton should fulfil . For each possible pair, the closest () and next-to-closest () to are found. Then and are required to be GeV GeV and GeV GeV. The corresponding cross sections are reported in Table 2.
Contrary to what happens in the decay mode, the cuts are quite mild, the efficiency being at NLO and at NNLO. The NLO and NNLO -factors are and , respectively. Comparing with the inclusive case, we conclude that these cuts do not change significantly the impact of QCD radiative corrections.
In Fig. 1 we report the spectra of the charged leptons. We note that at LO, without cuts, the and are kinematically bounded by , whereas and . As is well known, in the presence of a kinematical boundary, fixed order predictions may develop perturbative instabilities  at higher orders. In the present case, the distributions smoothly reach the kinematical boundary and no perturbative instability is observed beyond LO.
3 Results at the Tevatron
We now consider the production of a Higgs boson of mass GeV at the Tevatron ( collisions at TeV). We consider the decay mode with and use the cuts from . The inclusive -factors at NLO and NNLO are and , respectively. The trigger requires either a central electron with and GeV, or a forward electron with with GeV and GeV, or a central muon with and GeV. The leptons should be isolated: the energy in a cone of radius around each lepton should fulfill . The selection cuts require , and GeV. If GeV the azimuthal separation should be larger than for each lepton or jet. The invariant mass of the charged leptons should be between 16 and 75 GeV. The scalar sum of the of the leptons and of should be smaller than . Finally, jets with GeV and are counted. We require either no such jet, or one of such jets with smaller than 55 GeV, or two of such jets with smaller than 40 GeV. Since the small region is the most important, we further require .
With these cuts the LO, NLO and NNLO cross sections are , , fb. The corresponding -factors are and , and exibit a strong reduction with respect to the inclusive case. As for the LHC, the selection cuts drastically change the impact of radiative corrections. Also the efficiencies are reduced: comparing the accepted and inclusive cross sections we obtain: , and . These results suggest the existence of large theoretical uncertainties that need to be further investigated.
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