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The paper was initially rejected by the editor, on the basis
of the referee report.
The referee report, together with the reply of the authors,
is almost worth a publication in an interdisciplary journal dealing
with physics, statistics and sociology of science .....
The reader can draw his/her own conclusions.
Later, after the editor consulted another referee and another
editor, the paper was finally accepted as it was originally submitted.
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Reply to the referee's report on the paper:
"Constraints on the Higgs boson mass..."
by G. D'Agostini and G. Degrassi.
In the following we reply to the objections raised by the referee.
The lines starting with > are original statements of the referee.
> This paper presents an attempt to combine the existing informations on
> the Higgs mass with the goal to construct a probability density
> distribution which can in turn be used to determine confidence level
> intervals.
- This paper has a two-fold purpose:
1. combine in the a consistent logical way the most important
experimental information concerning the Higgs mass;
2. try to convince the experimental groups to publish results
in the form of likelihood, so that they can be easily
interpreted and combined.
> Indirect determinations from sin(theta)^2_W and M_W measurements, which
> are regularly updated by the SLC-LEP EW Working Group, are reproduced
> here with a method using a parameterization. This procedure gives no
> perceptible improvement in the fit, but is simpler than the usual
> less transparent global fit.
- The parameterization is well suited for the purpose, valid
in the range of M_H of interest and allows to trace the contributions
to the global uncertainty of the individual ingredients.
> The available limits from the direct search
> at LEP2 are reviewed, discussed and turned into probabilities. The last
> step is a questionable procedure.
- This statement of the referee is not correct.
We do not turn "available limits" into probabilities. In fact, at the
beginning of sect. 6 we review and discuss the LEP2 Higgs mass CL
limits and we explicitly say that, because of the way the Lep Higgs
working group computes them, the reported CL cannot be interpreted
as likelihoods. Instead, we use the values of the cross section
e+ e- -> Z H plus the detailed information contained in the published
papers (efficiency, background and number of observed candidates)
to calculate the likelihoods.
> The real difficulty comes when the two pieces of information are put
> together using a Bayesian approach. While such a procedure is
> mathematically simple, its physical interpretation is obscure and the
> derived confidence level intervals are to my opinion meaningless.
- These are just personal prejudices of the referee. Bayesian approach
is rather natural and it has become to be used now in particle
physics. Just to make one example. Always in the contest of the
Higgs mass limit, a 95% CL including the direct search information
through a Bayesian approach (however quite different from ours)
has been derived by J.Erler and P. Langacker (see hep-ph/9809352,
page 14 and Review of Particle Physics, EPJ C 3, 1998 page 96).
> Indeed, for a Higgs mass far above the presently ruled out region, the
> direct searches have of course nothing to say and therefore the upper
> 95% CL limit derived in the indirect determination should be unchanged.
> Opposite conclusions are drawn in the paper.
- This statement of the referee is wrong.
As we have explicitly written in sect.3, subsection "Including the
constraint from direct search", far above the presently ruled out
region what is unchanged is the relative probability between two
intervals not the absolute one.
To make one example. Let us consider a situation in
which an integer is extracted uniformly between 1 and 100, and that
somebody has the chance to look at it, and this person tells us that
the number is greater than 50. In this case according to the referee way
of thinking the probability that the number is greater than 90 would be
10% while we think everyone agrees that is 20%. Therefore a ruled out
region affects the CL because one has to renormalize the probability
integral.
> One could imagine a situation where the most probable value from the
> radiative corrections is inconsistent within errors with the direct
> limit. A 'normal' approach would conclude that the Standard Model is
> ruled out at some CL. In the proposed method instead, the 95% CL upper
> limit would simply be pushed far above the direct limit.
- Our analysis does not imply the conclusion of the referee. In fact we
have repeated several time in the paper that the analysis is performed
under the assumption that the Standard Model is true. In the situation
envisaged by the referee the validity of this assumption would be very
questionable and therefore our analysis would not be applicable.
However, the present experimental situation does not support the scenario
suggested by the referee, while the validity of the SM is a very
reasonable assumption. Therefore our analysis is perfectly justified.
> It can be added that the CL limits in this method are not independent on
> the choice of the variable: M_H, ln(M_H), anything else...
- This is not true. We could have done the analysis till the very
end in ln(M_H), getting EXACTLY the same numerical results for
the probability intervals. In case the analysis is performed
in terms of ln(M_H) one has simple to express the likelihoods
as functions of ln(M_H). The reason to switch from ln(M_H) to
M_H is that the physical quantity of interest (what LEP, CDF or LHC
will hopefully measure one day) is M_H, and then we find more
natural to present the result (the p.d.f) in terms of M_H.
> This is a
> recurrent problem raised against the Bayesian approach.
- This sentence shows clearly that the referee has based his
judgment on some prejudice about the Bayesian-frequentist
querelle, rather than on a careful reading of the paper
and of cited works.
> My conclusion is that the analysis presented in this paper is
> controversial, does not add information to the subject and that the
> results are misleading. In my view this paper is not suitable
> for publication in EPJ C.
- All the objections raised by the referee turned out to be either
wrong or generic statements about the Bayesian approach that do
not have any connection with the present paper.
We would like to add that our analysis is absolutely logical and
consistent and that the referee was not able to disprove this
statement. The result represents, in our views, the best way to
combine the available information and it is valid under some clearly
stated conditions which are commonly shared in our community.
May 21, 1999