First order corrections are made to the vertex based upon calibration to carbon foil data. The carbon foils allow us to identify fixed points along the beamline. First order corrections are applied:
- ::v_z = c_0*v0 + c_x*B.tr.x + c_x'*B.tr.xp + c_y*B.tr.y + c_y'*B.tr.yp
+ ::v_z = c_0*v0 + c_x*B.tr.x + c_x'*B.tr.xp + c_y*B.tr.y + c_y'*B.tr.yp::
Where v0 is the naive point found by assuming no change of the track in the nondispersive direction. B.tr.x, B.tr.y are the x and y positions on the detector z = 0 plane (in detector coordinates in meters). B.tr.xp, B.tr.yp are the tanget values of the track in detector coordinates, x' and y'.
Momentum reconstruction is determined by a simple dipole model with (effectively) first order corrections. Elastic events on a hydrogen target is used for calibration.
- ::p = (c0 + c_bendx*B.tr.bendx)/B.tr.defang + c_theta*atan(B.tr.fT.xp) + c_y*B.tr.y + c_y'*B.tr.yp
+ ::p = (c0 + c_bendx*B.tr.bendx)/B.tr.defang + c_theta*atan(B.tr.fT.xp) + c_y*B.tr.y + c_y'*B.tr.yp::
Where B.tr.bendx is the vertical position on the magnetic midplane (in meters in detector coordinates), B.tr.fT.xp is the x tanget in the TARGET coordinate system. B.tr.y and B.tr.yp are the same y and y' variables in the vertex reconstruction.
Using hydrogen data, one is able to determine the scattered electron momentum from an elastic event soley from the scattering angle (given that the beam energy is known). This is given from the equation:
- ::p = (m_p * E_beam)/(m_p + E_beam*(1.0 - B.tr.pz/B.tr.p))
+ ::p = (m_p * E_beam)/(m_p + E_beam*(1.0 - B.tr.pz/B.tr.p))::
where m_p is the mass of the proton (938MeV), E_beam is the beam energy, B.tr.pz is the z component of the scattered electron momentum in LAB coordinates and B.tr.p is the momentum of the electron. While B.tr.p and B.tr.pz are not well calibrated, the ratio is well defined and momentum independent (assuming the momentum B.tr.p is non-zero). This ratio is equivalent to cos(theta_e) where theta_e is the scattering angle.
The database description can be found here [http://hallaweb.jlab.org/experiment/E02-013/offline/BBoptics.txt|here].
- !Vertex
+ !!Vertex
An additional correction to v_z is done:
- v_z += correction(bend_x, bend_y)
+ ::v_z += correction(bend_x, bend_y)::
- !Momentum
+ !!Momentum
All 5 coefficients are interpolated based upon the magnetic midplane position. They in theory have the dependence c(bend_x, bend_y). In practice it is useful to remove some of this freedom to stabilize fitting. For example, the bend_x coefficient is not allowed to vary over bend_x.
+
+ !Calibration
+
+ Attached are calibration scripts. They require a few parameters to be adjusted and things such as a path to the ROOT files needs to be added, so they will not run on their own. They provide a framework that has been used to do calibrations in the past. There is a number of defined values that are required and can be found in a mwdc_defs.h header. (See ((BigBite Analysis Scripts|BigBite Analysis Scripts)) for a copy)
+
+ The vertex calibration is done by allowing just an offset to the applied.
+
+ The momentum calibration is done as described above, by allowing all coefficients to vary over the face of the magnet.
+
+ The low statistics calibration is done by just allowing the leading coefficient to vary over the face of the magnet. It requires that the rest of the coefficients already have reasonable values and that the fitting in the good central region is already done. It works by creating a histogram of the c0 value that would be necessary to give a momentum identical to pex(theta_e) for each magnet x,y bin and the appropriate c0 value is the value of the maximum bin of that histogram.
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