My time for the last few weeks has been spent working on determining the form of the corrections necessary for the vertex reconstruction and the momentum reconstruction. I have made some good progress on both of these fronts, though more work may be necessary to remove a few of the more problematic feautures. Overall, though, other than the form of the curves themselves, how these corrections should be applied has now clear. Mainly in this work we work in the bend x, bend y coordinates (which I will just refer to as x and y unless otherwise noted) which are the vertical and horizontal cooridinates of the reconstructed track at the magnetic midplane respectively. These proved to be useful such that this is where the average interaction takes place. As they are just a straight projection onto this plane which is, by design, parallel to the drift chamber planes, x_bend = x - (0.81m)*x' y_bend = y - (0.81m)*y' The vertex corrections must be done first so as to ensure proper fitting of the momentum reconstruction which is dependent upon the reconstructed scattering angle. This correction has a number of features intertwined and appears to be the most difficult to try and divine. The correction goes as (from the documentation of the script to do the corrections): The ROOT files to fit to are defined at the top of the function and are put into a TChain The fitting is done through a number of steps. The correction is ultimately of the form: XMIN to x1: c0 exp( r0 bendx ) + c1 bendx^2 + v0 x1 to x2 c1 bendx^2 x2 to XMAX c2 exp( r2 bendx ) + c1 bendx^2 + c3(bendx - x2)^2 + v2 c0-c2, v0, v2 are all of the form: m*ybend+b c3 is of the form: m*vz+b r0, r2 are constants The TH2F::ProfileX() function is not very useful in getting the profiles we'd like to fit to, so we generate a set of TGraphs that are the values of the maximum bin of each x slice. This works better in our screwy background type events that are not necessarily uniform, especially in our lower statistics regions. The THRESHOLD definitions are the minimum value for a bin to be considered. Slices that are not considered are not put in the graph. First r0 and r2 are determined. We use a 3 point derivative to get d(vz)/d(bendx) and then divide by the value of vz for the region of the center foil. Assuming that the correction primarily take an e^rx form, this gives us r. A chi^2 fit is done from all these points to fix a value for r. Then, the c exp( r bendx ) fits are done from XMIN1 to XMAX1 and XMIN2 and XMAX2 separately for a number of Y values. Fits of c0 and c2, v0 and v2 are done linearly in bendy. This correction is applied and then we fit to bendx^2 to determine c1 as a linear function of y. This correction is applied and then we fit c3 (bendx - XMIN2)^2 to find c3 as a linear function of vz. A picture of the form is given on page 1. Page 2 and 3: The uncorrected and current corrected form as described above. While I believe that all the y dependent features have been remved there is a vz dependent feature that produces a dip at about x=0.4m. The severity of this becomes more pronounced with more negative vz. Since vz is effectively a linear combination of y and y', this may suggest a y' dependence. Also, this may say that the effective interaction takes place somewhere other than the magnetic midplane. On pages 4 and 5 are the initial fit to the exponential curve for high and low x respectively. Pages 7 and 8 are the fits to the coefficients for ce^rx + v. c, r, and v are plotted against y and fit. r is fixed for low and high. These follow roughly linear shapes nicely. Page 8 is the full x cx^2 fit. There is no offset for the symmetry which probably should be introduced at some point. Since it is strictly the x^2 term the constant and linear coefficients for the second order polynomial are zero on page 9. Page 10 is the further fit to high x that is vz dependent. Since we only have 4 foils to fit to, those are all the data points we have. (The second plot is empty due to a foil missing for this run). Page 11 is fit against vz for these. Once again it seems to follow a straight line very well. We fixed the center for the parabola at 0.2m. This should be allowed to vary at some point, though proved to be a nice value. The momentum corrections applied are much more simple. We one again break it into three regions. For the high and low x region a correction of c(x-x0)^4 was applied. For the middle region no correction was applied. For the following plots, the combinations of runs 4425, 4426, and 4427 were used and have had the vertex corrections as described above applied. Pages 12 and 13 show the uncorrected and corrected momentum reconstruction. At high and low x there still appears to be distortion, though the region of good momenta has increased dramatically. It may be prudent to just take the good region and ignore the extreme x values. A very similar method to the vertex correction was used. Pages 14 and 15 show the high and low x fits, respectively. Page 16 and 17 are the coefficients of the fits against y fit to a parabola. Pages 18 and 19 are the fits to the x0 values of c(x-x0)^4 to a constant. Though they seem to demonstrate some linear behavior against y, when done in that fashion the coeffients take a different and more difficult to fit to form. I doubt it would help improve the fits in the extreme regions significantly, so I choose to stick with this form. These values still need to be put into the database for future replays. It requires roughly 20 new numbers to be entered in. Also, a study of these coeffients as a function of time and beam energy must be done. With some hope there will be little variation. Barring any major objections I will put these values that I have obtained into the code AFTER I have finished getting a value for GEn for the 4th kinematic. My goal for the next month is to generate values for GEn, at least for the 4th kinematic. I will strive to have a number at the current level of analysis that we have by the end of the year.