Hi Chris,
beautiful job!
For the estimated shifts and rotations it's also important to look at the
errors (covariance matrix) of the estimators. I agree with Doug to set
weights for rotations and shifts.
Perhaps it is a good idea to not fit for all parameters simultaneously.
Some positions or angles are more constrained than others. E.g. X can be
shifted more easily than Z because of the rails the detectors sits on.
Which parameters are the least certain ones according to the survey?
Also, I'm not quite sure at this time how the radiative tail effect
translates to the expected momentum offset for the electron.
On Tue, 28 Mar 2006, Christopher Crawford wrote:
> An update and first results on the geometrical offsets of the WC:
>
> GEOMETRY:
>
> The libraries TBLGeomWC and TBLGeometry have been updated to allow for rigid
> body transformations of either the entire left sector or right sector WC,
> through the 'blastrc' resources:
>
> GeomWC.LeftOffset: 0,0,0,0,0,0 # adjustments to left and right
> sector
> GeomWC.RightOffset: 0,0,0,0,0,0 # X,Y,Z(cm), alpha,beta,gamma(deg)
>
> or their command-line equivalents "GeomWC.LeftOffset=0,0,0,0,0,0", etc. For
> Instance, this can be added directly to the autocruncher COMMAND. Be sure to
> put no spaces between the commas, as this will confuse both the command-line
> interpreter and the parsing of the offsets. As an aside, also do not include
> comments on lines with strings, as they will be included in the string!
>
> The angles alpha, beta, gamma correspond to CCW rotations about the WC +y
> axis, the BLAST +z axis, and the WC +z axis, respectively. For small
> adjustments the order or rotations is a second-order correction. For
> example, d_alpha>0 moves the downstream end farther from the beamline;
> d_beta>0 tilts the outside edge of the left sector up and right sector down;
> and d_gamma tilts the downstream end of the left sector down and right sector
> up.
>
> Thanks, Michael, for pointing out that these adjustments cannot be applied
> uniformly to each of the three chambers. Instead, they are applied to the
> middle chamber, and the inner/outer ones are transformed explicitly as a
> single rigid body. The offsets were tested with the macro
> 'BlastLib2/test_wc_geom_adj.C', which looked at the angles between 4 points
> in each chamber spanning 3-space, before and after arbitrary transformations.
>
> There is also a new function TBLGeometry::AdjustWC to set them further in the
> code.
>
> NTUPLE:
>
> I wrote and tested a post-DST processor 'BlastLib2/geomfull.cc' to calculate
> the derivatives of each of 5 elastic kinematic offsets (along with the
> current offsets) event-by-event, using events from an elastic event-list:
> ( p_e - p_e(th_e), p_p - p_p(th_p), th_p - th_p(th_e), phi_p - phi_e
> +/- 180, z_p - z_e )
> for electrons in either the left or right sector (10 offsets), as a function
> of X,Y,Z,A,B,C in each sector (12 adjustments). A sample Jacobian for one
> event is included below. Note that the first two offsets only change for
> geometrical adjustments in the same sector, and that d(delta_z)/d(Z) = +/-1
> (at least it should) for adjustment in the proton/electron sector.
>
> There are still two problems: First dz/dZ != 1 in the electron sector. I
> haven't figured out what is wrong, but it may not be specific to the offset
> corrections. The second related problem, I expected two null eigenvectors
> corresponding to elastic scattering symmetries in Z and in Phi, but found
> neither.
>
> Command: root -l geomfull_offsets.C 12673 -n 20 -csnorm +de +dp +dt +df +dz
> +print
> Entry 0 (run 12673, event 213)
>
> _L offsets + LEFT d/dx d/dy d/dz d/dalpha d/beta
> d/dgamma + RIGHT d/dx d/dy d/dz d/dalpha d/beta d/dgamma
> pe -0.019281 0.000000 0.000000 0.000000 0.000000 0.000000
> 0.000000 0.007016 -0.001364 0.000874 0.000943 -0.004461 0.002421
> pp 0.031862 -0.006611 -0.006817 0.000285 0.023947 0.008572
> -0.007964 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
> tt 0.650497 -0.136070 -0.075535 0.001808 1.188988 0.103065
> -0.009689 -0.073448 0.032066 0.038212 0.802696 0.077736 0.020897
> ff -0.660084 0.041375 0.452306 -0.000398 -0.031691 0.214961
> 0.493497 0.071594 0.552872 0.001038 -0.021576 0.078003 0.413605
> zz 0.464627 -0.743655 -0.096612 1.003096 3.252622 0.139978
> -0.139421 -1.264678 -0.076465 -1.172769 -5.258923 -0.207254 0.144767
> +
> +
>
> ANALYSIS:
>
> I also wrote an analysis script 'exp/analysis/macros/geomfull_offsets.C'
> which fit for the WC offsets which best produced the observed kinematic
> offsets.
> The analysis cycle consists of Newton-Rhapson iterations of creating ntuples
> with the kinematic offsets and derivatives for the current WC offsets, doing
> a least-squares fit for the deviation in WC offsets, and subtracting these in
> the next iteration until convergence. The commands executed are logged in
> 'bud11:~chris2/blast/control/autocruncher/A_config' and in the header of
> 'geomfull_offsets.C', and the ntuples from each iteration are located at
> 'bud13:/scratch/bud13/chris2/geomfull/iter*' Taylan, the autocruncher came
> in real handy for this!
>
> Separate iterations were done for different weightings of the events. Plots
> of the geometrically-corrected kinematic offsets of each are included. The
> first used a flat distribution of events by weighting out the cross section
> (see plot), resulting in adjustments:
> // GeomWC.LeftOffset=0.506,2.665,-0.008,0.089,-0.503,0.399
> GeomWC.RightOffset=0.268,-2.824,-0.261,0.017,0.692,0.897
> The second set used the elastic distribution unmodified and heavily weights
> forward events:
> // GeomWC.LeftOffset=0.031,0.568,-0.688,0.140,-0.258,0.393
> GeomWC.RightOffset=0.188,-0.910,-0.182,0.011,0.021,0.736
> The three plots show offsets before corrections, after flat corrections, and
> after c.s.-weighted corrections. They don't look very good yet.
>
> This is only a preliminary analysis demonstrating the proof-of-principle.
> Physics offsets must be included before any hope of stable geometry offsets.
> Also, since the fit is a simple least-squares fit (using means) with no
> robustness added (medians or fit peaks), it is very important to handle
> momentum, which has a one-sided tail, consistently. The cuts on invariant
> mass must be used in this program must be consistent with those used to
> determine the radiative corrections to the momentum.
>
> --Chris
> _______________________________________
>
> TA-53/MPF-1/D111 P-23 MS H803
> LANL, Los Alamos, NM 87545
> 505-665-9804(o) 665-4121(f) 662-0639(h)
> _______________________________________
>
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