initial commit of likelihood fit for muons

This commit contains code to fit for the energy, position, and direction of
muons in the SNO detector. Currently, we read events from SNOMAN zebra files
and fill an event struct containing the PMT hits and fit it with the Nelder
Mead simplex algorithm from GSL.

I've also added code to read in ZEBRA title bank files to read in the DQXX
files for a specific run. Any problems with channels in the DQCH and DQCR banks
are flagged in the event struct by masking in a bit in the flags variable and
these PMT hits are not included in the likelihood calculation.

The likelihood for an event is calculated by integrating along the particle
track for each PMT and computing the expected number of PE. The charge
likelihood is then calculated by looping over all possible number of PE and
computing:

    P(q|n)*P(n|mu)

where q is the calibrated QHS charge, n is the number of PE, and mu is the
expected number of photoelectrons. The latter is calculated assuming the
distribution of PE at a given PMT follows a Poisson distribution (which I think
should be correct given the track, but is probably not perfect for tracks which
scatter a lot).

The time part of the likelihood is calculated by integrating over the track for
each PMT and calculating the average time at which the PMT is hit. We then
assume the PDF for the photons to arrive is approximately a delta function and
compute the first order statistic for a given time to compute the probability
that the first photon arrived at a given time. So far I've only tested this
with single tracks but the method was designed to be easy to use when you are
fitting for multiple particles.

1 files changed, 23 insertions, 0 deletions

diff --git a/pdg.c b/pdg.c
new file mode 100644
index 0000000..d6a2161
--- /dev/null
+++ b/pdg.c
@@ -0,0 +1,23 @@
+#include "pdg.h"
+#include "math.h"
+
+double get_scattering_rms(double x, double p, double beta, double z, double rho)
+{
+    /* Returns the RMS width of the scattering angle for a particle deflected
+     * by many small-angle scatters after a distance `x`. `p` is the momentum
+     * of the particle in MeV, `beta` is the speed of the particle in units of
+     * the speed of light, `z` is the charge of the particle in units of the
+     * electron charge, and `rho` is the density of the water in units of
+     * g/cm^3.
+     *
+     * `x` should be in cm.
+     *
+     * Note: I'm not sure if this will work for particles other than electrons
+     * since the radiation length is only discussed in terms of an
+     * electromagnetic shower induced by electrons (see Section 33.4.2).
+     *
+     * See Equation 33.15 in
+     * http://pdg.lbl.gov/2018/reviews/rpp2018-rev-passage-particles-matter.pdf. */
+    if (x == 0.0) return 0.0;
+    return (13.6/(beta*p))*z*sqrt(x*rho/RADIATION_LENGTH)*(1+0.038*log((x*z*z)/(RADIATION_LENGTH*beta*beta/rho)));
+}