By Tommaso
Dorigo

A new
paper in the Arxiv attracted
my attention this morning. It is titled "Perturbative QCD
effects and the search for a signal
at the Tevatron".

It is authored by a set of quite distinguished theorists:
C.Anastasiou, G.Dissertori, M.Grazzini, F.Stockli, and B.Webber.

The paper is quite technical and a detailed discussion of its
content does not belong here. However, given the importance of
its results, I wish to provide with a short summary those among
you too lazy to download the paper.

The authors consider the effect of Next-to-Next-to-Leading order
(NNLO) corrections to the process of Higgs boson production by
gluon-gluon fusion at a hadron collider (as in the graphic: a
triangular loop of top quarks "connects" the gluons to the
Higgs), followed by the decay of the Higgs to two W bosons.

That is exactly the process which has been used recently
(together with a dozen of other less constraining ones) by the
CDF and DZERO experiments at the Tevatron to exclude the
existence of the Higgs boson in
the mass region between 160 and 170 GeV, where the Higgs
boson in fact decays preferentially to W boson pairs. For the
distracted among you, below I show the recent Tevatron limits
and an quick-and-dirty explanation of the figure.

*The figure above shows, as a function of the Higgs boson
mass (on the horizontal axis), the 95% CL limit obtained by the
Tevatron experiments, once they combined the results of all
their Higgs searches. The full black line shows the actual
limit, while the dashed one (surrounded by 1- and 2-sigma bands)
shows the expected sensitivity of the experiments. The pink band
on the left shows what mass range of the Higgs boson has been
excluded in the past by the LEP II experiments at CERN, while
the one on the right is the Tevatron exclusion region. The
vertical axis has units of the "times the Standard Model"
limits: an exclusion at, say, 5 times the SM for a mass of 130
GeV implies that a Higgs boson production with a rate five times
higher than what the Standard Model predicts is excluded by the
experiment; an exclusion of 1.0 or less means that Standard
Model Higgs boson is ruled out in the corresponding mass range. *

NNLO corrections may have an impact in the computed acceptance
of selection cuts that the experiments use to pre-select the
sample where they search for the Higgs signal, as well as on the
shape of the kinematical distributions which are used to compute
a global discriminant with Artificial Neural Networks.

These tools are relatively new in data analysis of particle
physics experiments, and many
old dogs show scepticism when
confronted with results obtained with them. One of the most
principled objections that are usually cast is, in fact, the
unknown dependence of the results on shape variations due to
higher-order corrections on signal production.

The paper must be praised for its direct attack of these issues,
and for the effort that the authors have put to bridge the gap
between theoretical calculations and actual distributions and
numbers which are needed as input by experimental measurements.
It is not common to see a theoretical paper getting down to not
just estimating the effect of higher-order terms on a
cross-section, but computing the shape and normalization
differences of a Neural Network output!

Indeed, the CDF and DZERO analyses are kept as a reference
point, and the effect of the QCD corrections is ascertained by
comparing the NNLO calculations to the modeling made by the
experiments, which use a Monte Carlo simulation and rescale the
absolute normalization with the use of so-called "K factors",
mysterious-looking entities which are nothing but multiplicative
factors by which experimentalists rescale their Monte Carlo
predictions.

Surprisingly, **the
results are very good news for CDF and DZERO**, and for
those who root for the Tevatron in the hunt for the Higgs boson.
In fact, it appears that the overall effect of the corrections
is an increased acceptance to Higgs bosons of the data selection
and of the Neural Network analysis. The latter, it must be
stressed, is just an example, since it is very difficult to
reproduce in detail the procedure used by the experiments;
still, it is a very good approximation to the way the data is
analyzed, and it appears that the results obtained by the
theoretical study apply also to the results of the experiments.

Let me quote the paper:

To the best of our knowledge, so far there has been no study of
how the distributions of ANN outputs are modified at higher
orders in perturbation theory. Here we present for the first
time an ANN output distribution, computed at fixed order in
perturbation theory, beyond the leading order.

[...]in Fig. 9 we compare the ANN distribution obtained at NNLO
QCD and with PYTHIA. We see that PYTHIA, even after rescaling
with an inclusive K-factor, yields predictions which are smaller
by 12-20%, depending on the chosen bin. This difference can be
traced back to the difference in efficiency already observed at
the level of the selection cuts placed on the kinematic input
distributions.

Figure 9 is shown below. I cannot describe in detail the input
of the neural network that the authors have used to generate
this output shape; they are kinematical distributions obtained
at generator level (i.e., without any detector effect factored
in). With that in mind, we observe that the NNLO-computed cross
section (in red) is always above the one computed by PYTHIA (in
blue) over all the NN output range. The shape is instead in very
good agreement.

The authors conclude as follows:

[...]we find that the acceptance computed with PYTHIA is between
12% and 21% smaller than the NNLO acceptance, depending on the
choice of the factorization and renormalization scale. This
result is not significantly altered by hadronization and
underlying event and appears instead to be related to the matrix
element and parton shower implementation in PYTHIA itself. Since
the Tevatron analyses are based on PYTHIA, we believe that this
effect could be important and requires a more detailed
investigation within the framework of the full experimental
analysis.

Now, what does this imply for the Tevatron limits on the Higgs
boson ? Of course, if a limit on the existence of the Higgs
boson is computed by NOT observing a certain number of signal
events in the NN distribution, the limit becomes stronger if one
finds out that the Standard Model actually predicts more signal.
So we conclude that the Tevatron results are actually
conservative, and their power of exclusion is slightly stronger.

I believe both CDF and DZERO will use the results of this
theoretical study in their future results of Higgs boson
searches. One simple way to do it is switching from PYTHIA, the
Monte Carlo simulation they have been using, to HERWIG or
MCatNLO, which are shown to be more in line with NNLO
calculations.