move everything to src directory

1 files changed, 318 insertions, 0 deletions

diff --git a/src/calculate_limits.c b/src/calculate_limits.c
new file mode 100644
index 0000000..6dd37f0
--- /dev/null
+++ b/src/calculate_limits.c
@@ -0,0 +1,318 @@
+#include <stdio.h>
+#include <gsl/gsl_integration.h>
+#include <math.h> /* For M_PI */
+
+/* Mass of dark matter particle (MeV). */
+double mass = 1000.0;
+
+/* Decay length of mediator V (in mm). */
+double decay_length = 1000e9;
+
+/* Cross section for dark matter interaction (in mm^2). */
+double dm_cross_section = 1e-30;
+
+/* Approximate dark matter density in MeV/mm^3. From Tom Caldwell's thesis. */
+double dm_density = 400e3;
+
+/* Approximate dark matter velocity in mm/s. The true distribution is expected
+ * to be a Maxwell Boltzmann distribution which is modulated annually by the
+ * earth's rotation around the sun, but we just assume a single constant
+ * velocity here. From Tom Caldwell's thesis page 26. */
+double dm_velocity = 244e6;
+
+/* Number density of scatterers in the Earth.
+ *
+ * FIXME: Currently just set to the number density of atoms in water. Need to
+ * update this for rock, and in fact this will change near the detector since
+ * there is water outside the AV. */
+double number_density = 30e18; /* In 1/mm^3 */
+
+/* From Google maps. Probably not very accurate, but should be good enough for
+ * this calculation. */
+double latitude = 46.471857;
+double longitude = -81.186755;
+
+/* Radius of the earth in mm. */
+double radius_earth = 6.371e9;
+
+/* Depth of the SNO detector in mm. Don't be fooled by all the digits. I just
+ * converted 6800 feet -> mm. */
+double sno_depth = 2072640;
+
+/* Fiducial volume in mm. */
+double radius_fiducial = 5000;
+
+/* Cartesian coordinates of SNO in earth frame. They need to be global since
+ * they are used in some functions. */
+double x_sno[3];
+
+double epsabs = 1e-1;
+double epsrel = 1e-1;
+
+double deg2rad(double deg)
+{
+    return deg*M_PI/180.0;
+}
+
+double rad2deg(double rad)
+{
+    return rad*180.0/M_PI;
+}
+
+/* Convert spherical coordinates to cartesian coordinates.
+ *
+ * See https://en.wikipedia.org/wiki/Spherical_coordinate_system. */
+void sphere2cartesian(double r, double theta, double phi, double *x, double *y, double *z)
+{
+    *x = r*sin(theta)*cos(phi);
+    *y = r*sin(theta)*sin(phi);
+    *z = r*cos(theta);
+}
+
+/* Convert cartesian coordinates to spherical coordinates.
+ *
+ * See https://en.wikipedia.org/wiki/Spherical_coordinate_system. */
+void cartesian2sphere(double x, double y, double z, double *r, double *theta, double *phi)
+{
+    *r = sqrt(x*x + y*y + z*z);
+    *theta = acos(z/(*r));
+    *phi = atan2(y,x);
+}
+
+void cross(double *a, double *b, double *c)
+{
+    c[0] = a[1]*b[2] - a[2]*b[1];
+    c[1] = a[2]*b[0] - a[0]*b[2];
+    c[2] = a[0]*b[1] - a[1]*b[0];
+}
+
+double dot(double *a, double *b)
+{
+    return a[0]*b[0] + a[1]*b[1] + a[2]*b[2];
+}
+
+double norm(double *a)
+{
+    return sqrt(dot(a,a));
+}
+
+void normalize(double *a)
+{
+    double n = norm(a);
+    a[0] /= n;
+    a[1] /= n;
+    a[2] /= n;
+}
+
+/* Rotate a vector x around the vector dir by an angle theta. */
+void rotate(double *result, double *x, double *dir, double theta)
+{
+    double a = dot(dir,x);
+    double b[3];
+
+    double sin_theta = sin(theta);
+    double cos_theta = cos(theta);
+
+    /* Make sure the direction vector is normalized. */
+    normalize(dir);
+
+    cross(x,dir,b);
+
+    result[0] = x[0]*cos_theta + dir[0]*a*(1-cos_theta) + b[0]*sin_theta;
+    result[1] = x[1]*cos_theta + dir[1]*a*(1-cos_theta) + b[1]*sin_theta;
+    result[2] = x[2]*cos_theta + dir[2]*a*(1-cos_theta) + b[2]*sin_theta;
+}
+
+/* Rotate a vector in earth centered coordinates to SNO coordinates (doesn't do
+ * the translation). */
+void rotate_earth_to_sno(double *x_earth, double *x_sno)
+{
+    double dir[3];
+    double z[3] = {0,0,1};
+
+    cross(x_sno, z, dir);
+
+    /* Normalize. */
+    normalize(dir);
+
+    double theta = acos(dot(x_sno,z)/norm(x_sno));
+
+    rotate(x_sno, x_earth, dir, theta);
+}
+
+/* Integral over phi. */
+double f3(double phi, void *params)
+{
+    double result, error;
+    gsl_function F;
+    double *data = (double *) params;
+    data[5] = phi;
+    double x[3];
+    double r[3];
+    double distance;
+
+    /* Compute cartesian position in local SNO coordinates. */
+    sphere2cartesian(data[3], data[4], data[5], &x[0], &x[1], &x[2]);
+
+    /* Cartesian coordinates of gamma production offset in earth centered
+     * coordinates .*/
+    double *gamma_offset = data+6;
+
+    /* Vector distance between integration in local coordinates and gamma
+     * production point .*/
+    r[0] = x_sno[0] + x[0] - gamma_offset[0];
+    r[1] = x_sno[1] + x[1] - gamma_offset[1];
+    r[2] = x_sno[2] + x[2] - gamma_offset[2];
+
+    distance = norm(r);
+
+    return exp(-distance/decay_length)/(4*M_PI*distance*distance*decay_length)*data[3]*data[3]*sin(data[4]);
+}
+
+/* Integral over theta. */
+double f2(double theta, void *params)
+{
+    double result, error;
+    gsl_function F;
+    double *data = (double *) params;
+    data[4] = theta;
+
+    gsl_integration_workspace *w = gsl_integration_workspace_alloc(1000);
+
+    F.function = &f3;
+    F.params = params;
+
+    gsl_integration_qags(&F, 0, 2*M_PI, epsabs, epsrel, 1000, w, &result, &error);
+
+    gsl_integration_workspace_free(w);
+
+    return result;
+}
+
+/* Integral over r. */
+double f1(double r, void *params)
+{
+    double result, error;
+    gsl_function F;
+    double *data = (double *) params;
+    data[3] = r;
+
+    gsl_integration_workspace *w = gsl_integration_workspace_alloc(1000);
+
+    F.function = &f2;
+    F.params = params;
+
+    gsl_integration_qags(&F, 0, M_PI, epsabs, epsrel, 1000, w, &result, &error);
+
+    gsl_integration_workspace_free(w);
+
+    return result;
+}
+
+double f4_earth(double phi_earth, void *params)
+{
+    double result, error;
+    gsl_function F;
+    double *data = (double *) params;
+    data[2] = phi_earth;
+    double gamma_offset[3];
+
+    /* Compute the cartesian coordinates of the gamma production point in the
+     * earth centered coordinates. */
+    sphere2cartesian(data[0], data[1], data[2], &data[6], &data[7], &data[8]);
+
+    gsl_integration_workspace *w = gsl_integration_workspace_alloc(1000);
+
+    F.function = &f1;
+    F.params = params;
+
+    gsl_integration_qags(&F, 0, radius_fiducial, epsabs, epsrel, 1000, w, &result, &error);
+
+    gsl_integration_workspace_free(w);
+
+    /* For now we assume the event rate is constant throughout the earth, so we
+     * are implicitly assuming that the cross section is pretty small. */
+    double flux = dm_velocity*dm_density/mass;
+
+    return dm_cross_section*number_density*flux*result*data[0]*data[0]*sin(data[1]);
+}
+
+double f3_earth(double theta_earth, void *params)
+{
+    double result, error;
+    gsl_function F;
+    double *data = (double *) params;
+    data[1] = theta_earth;
+
+    gsl_integration_workspace *w = gsl_integration_workspace_alloc(1000);
+
+    F.function = &f4_earth;
+    F.params = params;
+
+    gsl_integration_qags(&F, 0, 2*M_PI, epsabs, epsrel, 1000, w, &result, &error);
+
+    gsl_integration_workspace_free(w);
+
+    return result;
+}
+
+double f2_earth(double r_earth, void *params)
+{
+    double result, error;
+    double data[9];
+    gsl_function F;
+    data[0] = r_earth;
+
+    gsl_integration_workspace *w = gsl_integration_workspace_alloc(1000);
+
+    F.function = &f3_earth;
+    F.params = (void *) data;
+
+    gsl_integration_qags(&F, 0, M_PI, epsabs, epsrel, 1000, w, &result, &error);
+
+    gsl_integration_workspace_free(w);
+
+    return result;
+}
+
+/* Returns the event rate in SNO for a self-destructing dark matter particle
+ * with a mass of dm_mass, a dark photon decay length of gamma_length, and a
+ * cross section of cs (in mm^2). */
+double get_event_rate(double dm_mass, double gamma_length, double cs)
+{
+    double result, error;
+    gsl_function F;
+
+    gsl_integration_workspace *w = gsl_integration_workspace_alloc(1000);
+
+    F.function = &f2_earth;
+    F.params = NULL;
+
+    /* For now we just use global variables. */
+    mass = dm_mass;
+    decay_length = gamma_length;
+    dm_cross_section = cs;
+
+    gsl_integration_qags(&F, 0, radius_earth, epsabs, epsrel, 1000, w, &result, &error);
+
+    gsl_integration_workspace_free(w);
+
+    return result;
+}
+
+int main(int argc, char **argv)
+{
+    /* Spherical angles for the SNO detector in the earth frame which has z
+     * along the north and south poles and the x axis passing through Greenwich.
+     * Should double check this. */
+    double sno_theta = deg2rad(latitude + 90.0);
+    double sno_phi = deg2rad(longitude);
+
+    sphere2cartesian(radius_earth - sno_depth, sno_theta, sno_phi, x_sno, x_sno+1, x_sno+2);
+
+    /* Calculate the event rate for a standard DM candidate with a mass of 1
+     * GeV, and a mediator decay length of 1 m. */
+    printf("event rate = %.18e Hz\n", get_event_rate(1000, 1000e9, 1e-30));
+
+    return 0;
+}