How to estimate the experimental acceptance of a particle as a function of its life-time? My lecturer stated that we can calculate the experimental acceptance of the Higgs boson as a function of the life-time and also as a function of the  mass by reading the following article: Davier and Ngoc, “An unambiguous search for a light Higgs boson, Physics Letters B, 1989.

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*What mathematical equations allow us to do that?


*How does one read/interpret the graph in figure 6 (shown below)? Does it help in any way to get the acceptance?

In the article, it is stated that the Higgs' life-time is given $(1)$
$$ \tag{1} \tau^{-1}_H = \frac{1}{2} \alpha_H m_H \left( 1 - \frac{4m^2}{m^2_H} \right)^{3/2} $$
where $\alpha_H = \frac{m^2 G_F \sqrt{2}}{4\pi}$ , $m$ is the electron mass and $m_H$ is the Higgs' mass. I presume this is useful, but I don't know how.

How do I read the following figure? Can this be interpreted into knowing the experimental acceptance based on the life-time?
                            
 A: Compare with the previous figure from the same paper (click to embiggen):

This says that they observed a few hundred, perhaps a thousand, total events in their detector, all with energies well below 1 GeV.  A hypothetical 20 MeV Higgs, interacting as described in the paper and its references, would have produced a few dozen additional events with energies between 1–2 GeV. Since there were no such events (not even background!) that low-mass Higgs is “ruled out.” From your excerpted Figure 4, you can read that the 20 MeV Higgs is only ruled out if its lifetime is in the cross-hatched “excluded range” from $10^{-11}$ to $10^{-9}$ seconds, presumably because a shorter- or longer-lived particle would have decayed mostly before or mostly after the detectors.  A previous experiment ruled out
a teardrop-shaped blob on the lower left.
I think (but it would be useful for you to verify) that your lifetime-versus-mass relation is plotted with the dot-dashed line labeled “SM.” The result of the paper, then, is that nearly all of this curve lies in the excluded region.
Acceptance/exclusion plots are terrifically confusing to read, especially in old papers where they are printed in black-and-white with only one line width available.
(Evidence: I misread this one at least twice.)
Modern exclusion plots show colored regions, which makes them slightly easier to understand, but because they are easier to understand people tend to put dozens of different colored regions on them.
