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The hypothetical world of this analysis is:
- three experiments (, and ) took data in an
collider, at different energies and with different sensitivity
to the particle production (` stands for hypothetical...').
The experiments reported 0 candidates and no background was expected
(this is a minor approximation to simplify the formulae: we have seen
how the background and its uncertainty may be treated).
- The beam energy was 0.09 and 0.1 in arbitrary units
(you may think of TeV)
and the kinematical factor which suppresses the production near
threshold (and eventually takes into account efficiencies, tagging, etc.)
is chosen somehow `arbitrarily' to be factor,
where is the
velocity of the pair produced particles.
- Cross-section and integrated luminosity are summarized into a sensitivity
factor , such that the expected number of events is
- We also have other pieces of information on : two indirect
determinations are characterized by a Gaussian likelihood, and
each of them would allow a Gaussian determination of the mass, if
one considered that this could be uniformly distributed
from to (see Section ).
- The five datasets are considered to be independent.
- The prior of the scientific community about the value of the mass
has changed in recent years, due not only to negative
results, but also to theoretical progress:
- essentially, once
there was uncertainty even in the order of magnitude, i.e.
, yielding
;
as a conservative position,
one could still stick to this position;
- at present, many think that
-;
this state of uncertainty can be modelled
by a uniform distribution over the range
of interest.

** Next:** Analysis of experiment
** Up:** Constraining the mass of
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Giulio D'Agostini
2003-05-15