Some more curve-fitting.
The trailing edge of the proton current follows the exp(exp()) form, as expected, though the fit is slightly less impressive than on the leading edge.
OPERA did not attempt to fit a pulse to the neutrino events. Instead if you think of the neutrino events as occurring at times t1, t2, t3, etc. (less than 1 per nanosecond on the average from the 10,000 nanoseconds of pulse), and the shape of the proton pulse to be W(t), then OPERA computed
W(t1+δt)*W(t2+δt)*W(t3+δt)*...
and found the δt that maximizes the product.
This requires both the leading and trailing edges to line up.
The value of having an analytical expression is only that one can more easily do a simulation. Of course, I'll be missing the features in the plateau of the pulse, but then, I think they are mostly irrelevant.
I might add diagrams later to make all of the above points clear.
The trailing edge of the proton current follows the exp(exp()) form, as expected, though the fit is slightly less impressive than on the leading edge.
OPERA did not attempt to fit a pulse to the neutrino events. Instead if you think of the neutrino events as occurring at times t1, t2, t3, etc. (less than 1 per nanosecond on the average from the 10,000 nanoseconds of pulse), and the shape of the proton pulse to be W(t), then OPERA computed
W(t1+δt)*W(t2+δt)*W(t3+δt)*...
and found the δt that maximizes the product.
This requires both the leading and trailing edges to line up.
The value of having an analytical expression is only that one can more easily do a simulation. Of course, I'll be missing the features in the plateau of the pulse, but then, I think they are mostly irrelevant.
I might add diagrams later to make all of the above points clear.
