Meeting minutes for first period:

  • New transport forward matrix is obtained:
    • For y_focal: use 56 data points and 23 parameters.
    • For phi_focal: use 56 data points and only 14 parameters (0th, 1st, 2nd and cross terms).
    • Result agree good between simulation and data, plots are here.
  • Jianping suggested to use SNAKE to go from focal plane to target plane, then project to sieve plane or HRS entrance. We know the HRS well, so we can separate HRS effect from the broken septum.
    • This will not work because the coupling of variables at target, make it becomes only 3 variables.
  • I will spend time working on Nilanga's method.
  • Dp reconstructed: dp = offset + 0.073*x_fp + 0.073*y_fp - 1.46*y_fp**2 + 0.511*theta_fp + 0.292*theta_fp*x_fp + 3.65*theta_fp**2.

  • 2D plot for all conbination of 4 variables at focal plane, which can find here.
  • From 2D plot for theta_fp vs x_fp, there is a dependent between these two variables. In dp_reconstructed (which is given above), this theta_fp vs x_fp is taken into account. So it made 4 variables become 3. But we need one more variable to tell us about y_tg?
  • The spread of x_fp (~30cm with different phi_tg) is not a big concern because in dp_res, the coefficient  theta_fp dependent is a factor of 10 bigger than that of x_fp.
  • The question still, how can we get y_tg?
  • To do:
    • Get momentum distribution and compare with simulation. Now dp_res is trusted. Can add an offset into dp_res to match with energy loss due to ice and material.
    • Plot 4 variables at focal plane for 2nd period.
    • Maybe can start to add 2 more variables at focal plane.

  • New forward matrix for both y_fp and phi_fp. Results agree pretty well, plots can find here.
    • Changes: remove dp offset in simulation when I do the optimization.
    • Use 56 data points which include: 1A, 1B, 1C, 1D and 2C, 2D, 2E.
    • 23 paramerters for y_fp, 18 parameters for phi_fp.
    • Can it be better if I use all given data points?
  • Momentum reconstruction:
    • Add in offset due to shift in ice thickness + known materials (offset=0.00405).
    • Add in x_fp^2 term to shift both -2 and +2 dp to the same direction. Result can find here.
    • The dp =-2% is not so good. Is it due to septum mismatch? Need to check with Vince. Is it due to systematic? Is it the same as the other dp =-2%?
  • y_target reconstruction:
    • y_tg
    • Vince mentioned that y_tg resolution at 1.1 GeV is 4mm. So the result make sense. The spread in y_tg for upstream and downstream foil is due to the correlation between y_tg and phi_tg become stronger for these 2 foils.
    • We can't separate the foils because there is overlap between foils.
  • 2D plot at focal plane for second period (good septum) can find here. theta_fp ~ theta_tg; y_fp ~ phi_tg.
  • To do:
    • Try to optimize forward matrix again with all given data points.
    • Reconstruct Z_target, hope can get better separation between foils.
    • Check septum setting mismatch.

  • During meeting, discuss about the complete procedure for optic study:
    • Get dp_res, y_res.
      • How to get dp_res? Each sieve hole, known: theta_tg, phi_tg, E_beam --> E' --> dp. The optimized dp =f(x_fp,y_fp,th_fp,ph_fp). It should be equal to dp calculated.
      • How to constrain y_tg? Which term to add?
    • Get forward matrix as a function of (dp,y,theta,phi)_tg.
  • Meeting with Nilanga:
    • Suppose y_tg is strongly depend on ph_fp and y_fp, 2D plot. Nilanga suggested to make a modification to y_tg to make each foil seat at the right place, by scaling y_tg. y_tg look better, but the resolution is worse. --> Need more work on this.
    • Get an universal cut which can be applied for all cases (multifoil, multi-dp). The cut will take the y_tg, dp acceptance into account. From 5 edge to 3 edge, I need to make a spline interpolation to make the cut continous. But the function depend on the y_tg range.

  • Reconstructed momentum:
    • The y_fp^2 term seem bend dp too much, that's why dp width is broaden. Vince suggested that it maybe due to the constrain on y_tg (we only have 3 foils), when we go up to 2nd order in y_fp make the dp diverge.
    • Without y_fp^2 term, dp look much better: width is smaller and the tail on high energy side is better, plot is here. Is this too good to believe?
  • To do:
    • Check dp spectra for all momentum setting and all foils target.
    • Optimize y_tg further to see the improvement.

  • Reconstruct y_tg does not work. The resolution is so bad and I can not do better than that. So Nilanga suggested to make 4 forward matrices from target for focal plane.
  • Requirement for these matrices
    • The good ratio between number of data points and number of parameters. Over-constaint problem, oscillation between data points.
    • Try to minimize higher order terms: the 3 cross terms.
    • A reason to use a term?
    • When do optimization, each data should has a separate uncertainty. So chi square can make sense. Because hole size change with each setting.
  • Several matrices were obtained:
    • 62 data points and 60 parameters, plots and the coefficients can be found here.
    • 74 data points and 52 parameters, here.
    • 88 data points and 49 parameters, here.
    • 88 data points and 37 parameters, here.
    • 88 data points and 20 parameters (only offset and first order), here.
  • One problem with 4 forward matrix is how to get 4D cut at focal plane which does not depend on any target variable? The cut should be a function of focal plane variables only.
    • The solution is: create a look up table from simulation. In simulation we do (more detail can be found here):
      • Simulate whole phase space: (180 mrad and 100 mrad). 22 cm long target. No elastic, no radiative correction.
      • Cut at sieve plane to choose only 1CDE & 2CDE.
      • Cut momentum from -3.5 to 4.5%.
      • Cut y_tg: -18 to 18 cm.
      • Create a 4D array to store each 4D-bin, each bin has (xfoc, yfoc, phfoc, thfoc) and a content which is there is an event.
    • From experimental data, look at each bin and compare that bin with that one in simulation. If there is an event in the "look-up" table, then accept this experimental event.
      • Apply this method to simulation and experimental data with multifoil and sieve slit in, here.
      • Problem: why 11F is not cut out?
  • For 88 data and 37 parameters set, chi square from optimization for y_focal is too big, it is either uncertainty for each data point is underestimate or the fitting is bad. Suggestion: add 1 more parameter for y_focal and reduce 1 parameter from theta_focal (because chi quare for theta is too small).
  • Jianping suggested to get the functional form for each theta separately, then all theta-dependent parameters will go away. Because we only have 2 rows, which is 2 values of theta_target, and there are so many theta-dependent-parameter.
  • To do:
    • Add 1 parameter for y_focal and reduce 1 parameter for theta_focal.
    • Try with 1 value of theta functional form.

  • Add in data points from 3rd row: there are total 107 data points.
    • Remove 10 bad data points: 1863 (21D, 32D), 1866 (32A), 1869 (11A, 23E, 32A), 1809 (22F, 23E, 23F), 1816 (23E).
    • Reason for removing:
      • holes that are partly seen (small statistic, hard to know exact center hole location).
      • Points that are bending too much, strong bending effect from septum. And not stay in interested area.
  • There are 97 data points and 39 parameters at this moment.
    • With add in 3rd row, theta^2 term can be added in.
    • Issue I had before is that y_fp reduce chi square is bad. With theta^2 term add in and more data point, reduce chi square for all variables now are reasonable. Sieve plot with new matrix can be find here.
  • Use above matrix to create a look up table. There are 2 cases:
    1. Look up table for sieve slit in, no target collimator.
    2. Look up table for production run, where target collimator is in.
  • Get cross section using this look up table:
    • Simulation:
      • Simulate elastic carbon run, 1899 ( dp =0%), center foil only. Cut at x_sieve and y_sieve. Save into root file. This give me number of event (called tacc) that initially stay within cut at target.
      • Use look up table to cut event in root file. For event survive inside 4D cut (look up table cut), sum all cross sections (called xsc).
      • To get cross section, cross section = xsc/tacc.
    • Data:
      • Apply 4D cut to carbon run with PID included. Get number of event survive, called ncarbon.
      • Apply same cut to no target run. Get number of event survive, called nhe.
      • Get cross section, cross section = (ncarbon*scale_for_carbon - nhe*scale_for_he), density, Solid angle.

  • Have been trying to figure out 40% difference between simulation and data when using look-up table method.
  • I tried:
    • Change transport functions --> not help (here).
    • Get cross section with different binning: issue is that both simulation and data cross section decrease as number of binning increase, detail here and here. --> Solution for simulation is that statistic for rootfile to create the table is not enough. After increase number of simulated event, cross section from simulation is stable, cross section results can be found here.
    • Remain issue is cross section from data. Seem the acceptance cut a lot of event from data???

  • One problem from experimental analysis: get solid angle. Solid angle is changing with number of binning. As number of binning increase, the shape at target look better (as what it is supposed to be).
    • Solid angle get from run phase space for central foil, then use 4D table to cut at focal plane and then look at target phase space.
    • Depend on number of bin, solid angle is different.
    • --> This solid angle help to solve part of the data cross section dropping as a function of number of binning. But problem still there.
  • Tried:
    • Cut in theta, make the cut become smaller, but results are the same, still 40% difference.
    • Different transport functions --> not help.
    • Limit of each focal plane variables in the table??? --> not this.
    • Create table for single  foil at center only --> not help.
  • To do:
    • Check 2D vs 4D: result from 2D cut was good within 10%. --> Check the consistent between 2 methods.

  • Look-up table method does not work well. The boundary is well-behaved but too many events were cut inside the boundary. Less events are accepted as the number of binning increase.
  • I did a comparison just to get the sense of cross section from data and simulation with 2D cutting at focal plane (phifp vs yfp). and 4D cut at focal plane using look-up table. Detail can be found here.
  • In the plot, the distribution between 2D and 4D are different. So many events loss in 4D even they have the same boundary.
  • Now we have another new method, which using the transport function directly.

  • 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 (phi-y)+ 2D(theta-y) + 2D(x-y) 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?

  • Figure out the problem with experimental cross section using look-up table.
  • The problem is:
    • Only a small area in focal plane is covered for all kinematic (especially in y focal, as well as theta and phi focal).
    • Another limitation is the resolution of sieve holes at focal plane. From optic information in each dimension, there is an associate resolution.
    • Combine above 2 information, we can not make binning as many as we want. There is a limit for each dimension. As shown in here.
  • With these limitation, we can not get cross section better than 20% agreement between data and simulation.

  • Uncertainty in sieve survey was quoted as 0.5 mm but the final number should be use is around 0.2 mm. This uncertainty in sieve slit will transfer into uncertainty in target angles.
  • Number of binning in focal plane is determined by uncertainty in how well we know the sieve center. This is done by select 5 samples each with 5k events from 1 sieve slit hole at focal plane. This uncertainty is much better than the resolution. So, the table still not work.
  • Another method is to reconstructed 2 angles at target: theta and phi. Apply a cut at reconstructed quantities on both simulation and data to select events.
  • Comparing cross section result for central foil with different momentum settings are shown here.

  • Reconstructed 2 angles and W (invariant mass). Analysis cuts are: cut to choose 1C 1D 2C 2D (square).
    • Cut on both reconstructed variables + momentum (dp) from simulation and data, as shown here. For dp=2%, 2D&2E was chosen instead of 2C&2D. Both results from 2 beam energy are ~40% off compare with simulation.
    • W cut was applied and Choose 2C&2D for all settings, one of the dp=2% (1.5GeV) become better but still the same for other beam energy, here.
    • W cut was applied in wider range (-0.005,0.01) instead of (-0.002, 0.004). And correct for the contribution from carbon excited state, here. The problem with dp=2% is still there for 1.1 GeV. Suggestion is that maybe the background contribution, normalization for bkgd is not right.
    • So far I have worked on single carbon elastic at center.

  • Fix problem with 1.1 GeV, dp =2%. The reason is that run 1888 was used instead of run 1889. There is no end for run 1888. Updated result with run 1889 is shown in here.
  • Several problems has been appeared:
    • I figure out I used spectrometer angle 5.99 deg (which is Vince used in 2nd period) instead of 5.91 (which is from 1st period survey). The above slide have cross section with both angles.
    • We can not study multifoil. Reason: combination of mis-wired septum and target collimator block most of upstream and downstream foil.
    • I did try to optimize theta_rec with higher order (include cross terms) but results are bad.
    • 0% dp seem different from the rests. So I start to use sieve's center from run 1805 (single foil) instead of run 1866(multifoil). Then when I change the central angle, 5.91 deg, the cross section different between data and sim seem the same for both sieve position sets.
  • Uncertainty budget for simulation and data are listed in above slide.

  • Study inelastic dp: choose inelastic carbon run.
    • Dp spectrum from simulation is obtained by using Peter Bosted model with internal/external radiation length (include the equivalent radiator). From dp shape of simulation and data, as shown in here, we can extract the acceptance.
    • To do: add in elastic tail from ROSETAIL to correct for the contribution from elastic tail.
  • Study extended target: we have problem with extended target. We took multifoil carbon with z=+/-10,0 cm but with target collimator IN. With this collimator, it will block most of upstream and downstream foil. Hence, multifoil with target collimator IN can not be used to study ytg acceptance. Instead, we do the following:
    • Choose a sieve hole which is seen by all target positions (get the count with target collimator IN). Only hole 2D is seen by both downstream and center carbon foil. The count is shown in this slide.
    • In above slide, run 1900 (multifoil with target collimator OUT) and run 1899 (single carbon foil with target collimator OUT) ytg are plotted with the 2D (theta vs phi reconstructed angle) cut. We see that, seem there is no contribution from upstream and downstream.
    • To do: Get cross section from sieve slit run (with sieve slit in but target collimator OUT).

  • Study the acceptance with target collimator OUT:
  • To do:
    • Get acceptance function from these data point.

  • Obtain acceptance of all sieve holes, shown in here. Seen holes are labeled in red color, not seen ones are labeled in black color.
  • After get the acceptance for each hole. Need to determine acceptance function. Acceptance function is determined by:
    • For 1 momentum setting, determine boundary for 3 foils together. And the chosen holes should be the same for all momentum setting. Determine 6 corners.
    • For each corner (from dp =-3.0%), get a linear line which go through these 2 points. Similarly get the rests 5 corners.
    • The acceptance function is then applied to sieve slit multifoi run (1866, dp=0 and 1869, dp=-3%).
    • Reasonable results are obtained, as shown here.
  • To do:
    • How to extend this acceptance to dp=+2%?

  • The acceptance function works in dp range from (-3% , 2%).
    • The function is y_fp(dp) and ph_fp(dp). With each y_fp and ph_fp corner is a function of dp. For example: for 1st corner:
      • y_fp = -0.227*dp +0.010
      • ph_fp = -0.121*dp +0.027
      • There are 6 corners. From 6 corners, form a boundary, only accept event stay inside, throw events stay outside.
    • This function is added into simulation and data to apply same cut on both.
  • Different ice thicknesses were used for 1.1 GeV and 1.5 GeV: 1.5 GeV was taken before 1.1GeV. In my analysis, I used 8mm ice for 1.5 GeV and 15mm ice for 1.1 GeV. Cross section for 2 beam energies can be found here.
Then I start with extended target: He3.
  • Tried to get asymmetry, experimental asymmetry was extracted using this formula. Seem this formula is not right. Using this formula, dilution is corrected with N_0 term. This way, we don't need to get into N2 and He3 cross section ratio in order to extract the dilution factor. However, this solution did not give right answer for asymmetry with all dp and 2 beam energies. Asymmetry from simulation is not right either.
  • He3 spectra: ytg, phitg, thetatg, W are shown here.

  • Get elastic 3He cross section for 1.1 GeV (dp = -2, 0, +2%), 1.5 GeV (dp=0%) and 2.2 GeV (dp=0%)
    • 1.1 GeV result agree between simulation and data are within 5%, results shown here. For this energy setting, I used 15mm of ice for simulation . These  ata were taken during 05/11/2003.
    • 1.5 GeV result is ok as well, as shown here.  W plot is not so good. On the low W side and high W side have problem. But cross section result is good within 5%. These data were taken during 05/04/2003 so I used less ice, 8 mm of ice.
    • 2.2 GeV has problem, a 30% disagreement. This run was taken on  05/17/2003, so I should have added more ice, ice thickness was used is 15 mm. There are several suggestions:
      • Septum settings were changed, I checked the set and read back value of septum current, it seems ok.
      • W plot is not so good, suggestions: angle reconstruction is not so good. So I can look at dp instead.
      • Optic is not good enough? The reason why I did not include 2.2 GeV optic into my optimization is because at that point, I did not have reconstructed W, so I can't determine the sieve center well because of the huge contribution from quasi elastic (of carbon).
      • Wrong normalization?
      • Use different runs.
      • Correct for quasi elastic contribution.
  • To dos:
    • Get n2 density inside 3he target.
    • From 2.2 GeV acceptance run (carbon target without sieve) determine ice thickness?
    • Add 2.2 optic data into optimization ??? Then, need to redo everything :(
Meeting minutes for second period:
  1. Weekly meetings and Target lab status:
            August 2002     September 2002     October 2002    November 2002    February 2003    March 2003
            April 2003       September 2003     October 2003     December 2003    January 2004      February 2004
            March 2004     April 2004             August 2004
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April 10, 2006
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October 18, 2006                 April 08, 2005
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October 21, 2005
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Minutes(May 20-21, 2004) (May (May
September 13, 2004
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(last updated: 06/13/2007, maintained by Vincent Sulkosky)