Search for Ericson fluctuations in $pi$$sup +$p scattering at 3.7 and 7.1 GeV/c Page: 3 of 17
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Figs. 3a and 3b show the differential cross section do/dt with the three rgy
bins combined at each momentum. The test for Ericson fluctuations is to ak.e
the corresponding distribution for each c.m. energy bin separately, and compute
the asymmetry parameter, A(t), between pairs of energy bins. A(t) is defined
as follows ('):
A(t) = o(t,higher) - o(t,lower)
t(t,higher) + Q(t,lower)
where o(t,higher) and o(t,lower) are respectively the values of the differential
cross section for the higher and lower energy bins of the pair.
Before looking at the results for A(t), however, let's consider a circumstance
other than Ericson fluctuations that can lead to non-zero values of A(t). That
circumstance is the presence of fixed-u features in the lp differential cross
section. The effect of such features on A(t) is illustrated schematically in
Fig. 4 for two idealized cases. In the case of a fixed-u dip, an oscillation
is induced in A(t), as illustrated in Figs. 4b and 4c. In the case of a fixed-u
slope (i.e. a a ebU), a square-wave shape is induced in A(t), as illustrated
in Figs. 4d and 4e. More generally, a fixed-u surface having both ingredients
may be present, as illustrated in Fig. 41
Do we have evidence for such fixed-u features in our data? Figs. 3c and 3d show
the differential cross section with respect to u for each momentum, and it may
be seen that the shapes are very similar for -u < 3. For greater clarity, a
magnified view of this region is given in Fig. 5. The backward peak and well-
known dip at -u = 0.15 are readily apparent, and there is a smooth fall-off
from a secondary maximum near -u = 0.6 to a minimum near -u = 3. Since this
shape persists from 3.7 to 7.1 GeV/c (an interval of I GeV in c.m. energy) it may be
regarded as an approximately fixed-u shape. A similar shape has also been
observed in CERN experiments at 5 and 10 GeV/c (4). The dip at -u = 0.15 is
too narrow to have an observable effect on A(t) at our statistical level, but
now let's look at the results for A(t) to see if there is any effect from the
fixed-u surface, or any indication of the presence of Ericson fluctuations, and
then make a crude estimate of the expected magnitude of the effect. Fig. 3
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Michael, W. & Gidal, G. Search for Ericson fluctuations in $pi$$sup +$p scattering at 3.7 and 7.1 GeV/c, article, July 1, 1975; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc865321/m1/3/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.