03/01/2017
 New method to get cross section. This use the transport function, which is the lastest version, to make the cut at focal plane.
 Detail how to make this cut:
 The cut is combine of 2D (phiy)+ 2D(thetay) + 2D(xy)
at focal plane, where these 2D are defined by the sieve positions from
the transport functions.
 Use transport function: x, y, theta, phi (at focal plane)
= function( y, dp, theta,phi  at target). By fix 3 variables, we can
get, i.e. xfoc = f(phi_target) with phi_target run from phi_min to
phi_max
 For a fix ytarget, dp, we can know limits of theta_target
and phi_target. Keep one of the angle (either phi_target or
theta_target) constant and make a "continous" point on the other
variables, i.e. phi(i) = phi_min + i*delta_phi, phi run from phi_min to
phi_max.
 Do the same, then we can get the boundary of 4 lines.
 There are 2 ways to make this cut:
 From phi_min to phi_max, there are npoints, we can do
fitting in this range and then just use a linear line ( y = a*x+b) to
cut. Combine all 4 lines together to define 4D cut at focal plane.
 Or we can use TCutG from ROOT to apply a polygon cut (which is a closed area defined by the points).
 Detail how to get cross section:
 Simulation:
 Get solid angle by: run phase space + no radiation
effect, apply cut at focal plane, look at target angle and get solid
angle. In addition, this also give the boundary at target.
 Run elastic carbon, count how many events inside the boundary at target (which is mentioned above) called "tacc".
 Count how many events survived after focal plane cut, called "cacc". Sum cross section inside this cut called xsc.
 Cross section = xsc/tacc.
 Data:
 Apply PID + dp cut, and 4D cut.
 Subtract background. Result between simulation and data can be found here.
 To do:
 Why 25%, 32% different between data and simulation?
 Check dp plot for simulation and data.
 Why 4D cut at focal plane with the right boundary still can not reproduce an exact boundary at target?
