Summary of HE/HL-LHC cross section estimations

We report here results for cross-sections and theoretical uncertainties at the 13, 14 and 27 TeV LHC. If not specified, the same setup of YR4 has been used.

These results will be properly documented and commented in the following note: hlhehiggs.pdf [PRELIMINARY!]

ggF

For the 13 TeV and 14 TeV, the small difference with respect to the YR4 numbers is because here the exact result (as opposed to the threshold expansion) was used for the N3LO contribution. This was unknown at the time of YR4. ggF theoretical predictions are already quite sophisticated, hence improving substantially on any of the current sources of uncertainty represents a major theoretical challenge.

The major source of theoretical uncertainties were already outlined in the YR4. Their contribution to the total uncertainty does not change significantly at 27 TeV, as illustrated in the following figure.

VBF

The small difference w.r.t. YR4 is because the more precise LUXqed_plus_PDF4LHC_nnlo_100 PDFs set was used in these predictions (compared to the NNPDF23_nlo_as_0118_qed set used for the YR4). Otherwise the setup is the same of YR4.

VBF Higgs production is currently know at a very high theoretical accuracy. In the VBF approximation the cross section has been computed fully inclusively at N3LO -QCD. Fiducial calculations in the same approximation exist at NNLO-QCD. The only contribution which is currently unknown is the contribution from two-loop diagrams with gluon exchange between the two VBF quark lines. The conceptual difficulty is that it is a 2->3 process and that currently there are no methods available for evaluating two-loop diagrams with more than four external legs. It is realistic that such methods will become available before the HE-LHC is in operation.

Outside of the VBF approximation the full NLO corrections in both the strong and electroweak coupling have been computed. The electroweak contributions are of the same order as, or in certain phase space regions even larger than, the NNLO-QCD corrections. Taking all of this into account it has been estimated that the VBF cross section under typical VBF cuts has an accuracy at the 1% level. In order to connect these calculations to experimental measurements one would ideally need merged 2- and 3-jet samples at the NLOPS level or even better a full NNLOPS generator for VBF. It is realistic that this will become available within the next few years and certainly before the HL-/HE-LHC phases.

VH

The results show here have been obtained combining NNLO QCD and NLO EW corrections by means of a multiplicative scheme, as described in the YR4 studies. For ZH production, the loop-induced gg->HZ channel has been added linearly.

At the time of writing, the numbers shown above are the best estimates available for the $gg\rightarrow HZ$ contribution. Due to the progress made in the last couple of years for the computation loop amplitudes, it is foreseable that, in the forthcoming years (definitely in the timescale of HL/HE LHC), an exact NLO result (including finite-m_t effects) will be available also for gg->rightarrow HZ. If one assumes that a pattern similar to what was found for di-higgs production also holds for gg->HZ, one can expect that the total NLO/LO K-factor will be slightly smaller than in the HEFT limit and the final scale uncertainty for the gg->rightarrow HZ cross section will go from 18-25% to about 15%.

The matching of fixed-order correction to parton showers is available for the pp->rightarrow VH signal processes, at NLO as well as at NNLO. For the signal itself, the uncertainty due to PS effects is not a major issue, as it amounts to about 2-3% level for a stable Higgs. Furthermore, when the exact gg->HZ computation at NLO will be computed, a NLO matching to parton-shower will be straightforward to achieve.

Recently there has been also the completion of the NLO EW corrections matched to the parton shower showing once again the relevance of the EW corrections for the distributions for both the fixed order and the matched predictions.

The above results have been obtained for a stable Higgs boson. For the Higgs decay to bottom quarks, it is known that higher-order corrections to the m_{bb} lineshape are relevant. Although explicit studies are not available, one can expect that effects similar to those observed at 13-14 TeV in the region m_{bb}<m_H will persist also at higher energies. A solid prediction of the $H\to b\bar{b}$ decay, also matched to parton-showers, can definitely be expected in the timescale of HL/HE LHC.

ttH/tH

The cross sections for $t\bar t H$ and $tH$ production are known at NLO QCD and, in the case of $t \bar t H$, NLO EW corrections have also been calculated. The corresponding theoretical uncertainty is of the order of 10-15% and is mainly induced by the residual scale dependence and, to a lesser extent, by PDF uncertainties. A drastic improvement can only come from the calculation of the NNLO QCD corrections. Given the ongoing rapid progress in NNLO calculation, it is foreseeable that NNLO QCD corrections to $t\bar t H$ and $tH$ will become available in the next decade. In this scenario it is reasonable to expect a factor-two improvement of the theoretical accuracy.

On the other hand, the extraction of the $t \bar t H$ signal is at the moment mainly limited by the theoretical uncertainties in the modelling of the background, mainly $t\bar t b \bar b$ and $t \bar t W+$jets, via Monte Carlo generators. The reliable assessment of the related uncertainties and their further reduction are the main goals of an ongoing campaign of theoretical studies within the HXSWG. On a time scale of 5-10 years such background uncertainties may be reduced by a factor two to three.

Offshell

-- RobertoCovarelli - 2018-07-26