Higgs production cross section

[Safinaz]

Hi all,

I try to find the exact calculated gluon- gluon fusion cross section for the SM- Higgs with mass 125 GeV, for instance at CME = 14 TeV.

I found on twiki page:
" https://twiki.cern.ch/twiki/bin/view/LHCPhysics/CERNYellowReportPageAt1314TeV#s_14_0_TeV "

$\sigma(gg \to h) = 49.47~ pb$

while in reference like "arXiv:hep-ph/0503172 ", table(3.2):

$\sigma(gg \to h) \sim 37 ~ pb$

Both calculations are NLO, but why there is this difference ?

 

[mfb]

The first one is NNLO QCD. For electroweak processes it is just NLO but those should be a small contribution. The NLO calculation discusses some NNLO effects but I don't understand what exactly they do.

 

[Safinaz]

So I wonder can we calculate $\sigma (gg \to h)$ at LO or NLO like in " arXiv:hep-ph/0503172 ",

while take the uncertainties (the standard deviation ) from NNLO calculations ?

The following paper " arXiv:1206.5047 [hep-ph]" made that in Fig. (1). While they use LO formula for the production cross section Equ. (5), they cite the Cern twiki page for $\sigma1~ \mbox{and}~ \sigma2$,

is this consistent to take the uncertainty from NNLO calculation for a cross section calculated at LO?

 

[Vanadium 50]

is this consistent ?

Virtually nothing that is done is consistent. Your choice is a) the latest calculations, or b) a consistent set of calculations. Most people choose a).

For Higgs production, the state of the art is N3LO, Anastasiou et al. PRL 114, 212001 (2015)

 

[Safinaz]

Hi,

I added my last sentence :) , I hope it's clear enough.

 

[mfb]

Here is the NNNLO calculation. They also compare LO, NLO, NNLO and NNNLO in figure 2. The difference between NLO and NNLO is ~10/pb, although both still show significant scale-dependence. NNNLO is significantly better in terms of scale-dependence. Note that the plot is for 13 TeV. Figure 3 includes 14 TeV bands, the same difference is visible there.

I don't understand how you would take a NNLO calculation for a LO uncertainty. Where is the point in having an uncertainty on LO if you have a NNLO calculation?

 

[Safinaz]

I don't understand how you would take a NNLO calculation for a LO uncertainty. Where is the point in having an uncertainty on LO if you have a NNLO calculation?

It's this paper " arXiv:1206.5047 [hep-ph]", as you see for Fig. (1), they take the uncertainty 14.7 % from [10] , which are NNLO. While they use LO formula, ( Equ.5 )for the new physics ( NP) $gg \to h$ cross section.

Even I don't know in Fig. (1), when they normalized $\sigma_{NP}$ by $\sigma_{SM}$ which value for $\sigma_{SM}$ they considered, did they calculate it at LO or they just take [10] value .

 

[mfb]

It's this paper " arXiv:1206.5047 [hep-ph]", as you see for Fig. (1), they take the uncertainty 14.7 % from [10] , which are NNLO. While they use LO formula, ( Equ.5 )for the new physics ( NP) $gg \to h$ cross section.

Those are different things.
As far as I understand it, they compare the cross-section for (LO NP + NNLO SM) with (NNLO SM), and use the NNLO SM uncertainty (which is independent of new physics) as comparison: if the NP prediction is within the uncertainties of the SM calculation, the cross-section alone is not sufficient to see new physics.