Hi again,

PeterB agreed with the idea of repeating the fit with a constraint on the beam
energy offset based on the arc energy measurement uncertainty.  The new results
are below.

According to the log, each measurement has an uncertainty of about 2.6 MeV,
independent of energy at least for the range 2.7-4.9 GeV.  That corresponds to
a fractional uncertainty of 0.59-0.87E-3, so I took +/-0.7E-3 as the constraint
on the beam energy offset dE.

However, one of the measurements, had a significant issue in that the arc
energy tool gave an energy of 2.7832 GeV, which was surprisingly far from the
expected 2.75 GeV.  After some discussion in June-2019, MarkJ came up with a
revised estimate of 2.74996 GeV, which I think Vijay is using his analysis.  So
I'll assume the uncertainty on this measurement is the same as the others for
now, but this might need revisting.

I also fixed an error, which was that the Heepcheck derivatives were calculated
for a wrong setting for one of the energies.

With this beam energy offset constraint, the global fit offset results look
quite a bit more reasonable.  As expected, the dpp(SHMS) and dpe(HMS) offsets
are also now quite a bit smaller.  The dthp(SHMS) angle offset is also quite a
bit smaller, while the dthe(HMS) angle offset has grown slightly.

Finally, the chi-square per energy is also more uniform.  The 3.6 GeV Heep
setting still has the largest chi-square contribution to the global fit, but by
a lesser amount than before.  Of course, the overall chi-square is slightly
larger now, as the constrained fit no longer corresponds to the absolutely best
fit, but the difference is not huge.

If you have questions or comments, please let me know.  We can discuss these
further at Thursday's meeting.

Thanks, Garth


 *** RESULTS *** 
! units are 0.1% for momenta/energy, 1 mrad for angles

 Global Offsets:
   dthe  1.3000   dpe  0.0000   dthp  0.7000   dpp  1.8000
   dE: -0.7000    0.7000    0.7000    0.0000   -0.2000
   chisq:  48.357     5.608    17.334     9.608     5.458    10.350

 Offsets for Energy:   2750.0
   dthe  2.3000   dpe  0.0000   dthp  0.3000   dpp  4.8000   dE  0.7000  chisq   3.201

 Offsets for Energy:   3660.2
   dthe  0.4000   dpe  0.1000   dthp  0.1000   dpp  1.4000   dE  0.6000  chisq   0.082

 Offsets for Energy:   3834.9
   dthe  0.1000   dpe  0.6000   dthp  0.7000   dpp  0.0000   dE -0.1000  chisq   0.603

 Offsets for Energy:   4559.7
   dthe  0.4000   dpe  1.6000   dthp  1.8000   dpp  0.0000   dE -0.1000  chisq   2.795

 Offsets for Energy:   4932.0
   dthe  0.9000   dpe  0.8000   dthp  2.2000   dpp  0.2000   dE -0.5000  chisq   4.194

 *** Expected shifts *** 
 units are 0.1% for momenta/energy, 1 mrad for angles

 --- Original --- Global --- Individual Fit 

Energy   2750.0
 W    6.3945      1.2125      0.5605
 EM   4.0667     -0.5763     -1.2563
 PMZ  4.0486      1.5776      1.1436
 PMX -0.5784     -1.1474      0.0186

Energy   3660.2
 W    1.0657     -3.7233      0.0367
 EM   0.8051     -0.4669     -0.1919
 PMZ  0.8696      1.4406      0.2086
 PMX -0.8696      1.0854      0.0244

Energy   3834.9
 W    3.1973     -2.1227      0.1733
 EM   1.0916     -0.6014     -0.5094
 PMZ  1.1614      1.2994      0.5594
 PMX -0.3871      1.7469      0.0269

Energy   4559.7
 W   10.6576      1.8176      0.3706
 EM   3.3951     -1.3749     -1.1409
 PMZ  2.5072      0.4362      1.1642
 PMX -0.7163     -0.2713     -0.0173

Energy   4932.0
 W   12.7891      2.3761      0.5001
 EM   4.0027     -1.3573     -1.4443
 PMZ  2.7100      0.7800      1.3630
 PMX -0.7743     -1.5013     -0.0113

Mean  2.7718      0.0315      0.0789