Hi Chris,
It's excellent that you have done this but I have some problems with
the results of your fits.
The first set had offsets of 2.6 and 2.8 cm !!! in the vertical. If
these were mm I could maybe go along with them but there is no way
this can in cm. Similarly the X offsets were .5 and .26 cm which are
also much too large to be physically compatible with the surveys.
The angle offsets are fine. The second analysis is a bit better in X
and Y offsets but still too large.
When doing such fits you need to weight the contributions from the
spacial offsets and angular offsets. What weights do you use? I
think a tolerance or uncertainty in spacial offsets of 0.1 or 0.2 cm
would be fine ie. a change of 0.1 cm is one STD. For angular offsets
I think 1 STD corresponds to about 0.5 degrees.
What do others think?
Maybe you can search just over the angular offsets and see what
improvements arise.
Cheers,
Douglas
26-415
M.I.T. Tel:
+1 (617) 258-7199
77 Massachusetts Avenue Fax: +1
(617) 258-5440
Cambridge, MA 02139, USA E-mail:
hasell@mit.edu
On Mar 28, 2006, at 11:35 AM, 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)
> _______________________________________
>
> <cs_weight.gif>
> <geomfull_offsets_orig.gif>
> <geomfull_offsets_flat.gif>
> <geomfull_offsets_cs.gif>
>
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