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Hi again,
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PeterB agreed with the idea of repeating the fit with a constraint on the beam
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energy offset based on the arc energy measurement uncertainty. The new results
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are below.
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According to the log, each measurement has an uncertainty of about 2.6 MeV,
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independent of energy at least for the range 2.7-4.9 GeV. That corresponds to
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a fractional uncertainty of 0.59-0.87E-3, so I took +/-0.7E-3 as the constraint
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on the beam energy offset dE.
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However, one of the measurements, had a significant issue in that the arc
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energy tool gave an energy of 2.7832 GeV, which was surprisingly far from the
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expected 2.75 GeV. After some discussion in June-2019, MarkJ came up with a
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revised estimate of 2.74996 GeV, which I think Vijay is using his analysis. So
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I'll assume the uncertainty on this measurement is the same as the others for
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now, but this might need revisting.
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I also fixed an error, which was that the Heepcheck derivatives were calculated
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for a wrong setting for one of the energies.
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With this beam energy offset constraint, the global fit offset results look
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quite a bit more reasonable. As expected, the dpp(SHMS) and dpe(HMS) offsets
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are also now quite a bit smaller. The dthp(SHMS) angle offset is also quite a
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bit smaller, while the dthe(HMS) angle offset has grown slightly.
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Finally, the chi-square per energy is also more uniform. The 3.6 GeV Heep
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setting still has the largest chi-square contribution to the global fit, but by
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a lesser amount than before. Of course, the overall chi-square is slightly
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larger now, as the constrained fit no longer corresponds to the absolutely best
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fit, but the difference is not huge.
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If you have questions or comments, please let me know. We can discuss these
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further at Thursday's meeting.
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Thanks, Garth
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*** RESULTS ***
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! units are 0.1% for momenta/energy, 1 mrad for angles
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Global Offsets:
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dthe 1.3000 dpe 0.0000 dthp 0.7000 dpp 1.8000
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dE: -0.7000 0.7000 0.7000 0.0000 -0.2000
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chisq: 48.357 5.608 17.334 9.608 5.458 10.350
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Offsets for Energy: 2750.0
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dthe 2.3000 dpe 0.0000 dthp 0.3000 dpp 4.8000 dE 0.7000 chisq 3.201
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Offsets for Energy: 3660.2
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dthe 0.4000 dpe 0.1000 dthp 0.1000 dpp 1.4000 dE 0.6000 chisq 0.082
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Offsets for Energy: 3834.9
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dthe 0.1000 dpe 0.6000 dthp 0.7000 dpp 0.0000 dE -0.1000 chisq 0.603
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Offsets for Energy: 4559.7
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dthe 0.4000 dpe 1.6000 dthp 1.8000 dpp 0.0000 dE -0.1000 chisq 2.795
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Offsets for Energy: 4932.0
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dthe 0.9000 dpe 0.8000 dthp 2.2000 dpp 0.2000 dE -0.5000 chisq 4.194
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*** Expected shifts ***
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units are 0.1% for momenta/energy, 1 mrad for angles
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--- Original --- Global --- Individual Fit
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Energy 2750.0
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W 6.3945 1.2125 0.5605
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EM 4.0667 -0.5763 -1.2563
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70
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PMZ 4.0486 1.5776 1.1436
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PMX -0.5784 -1.1474 0.0186
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Energy 3660.2
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74
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W 1.0657 -3.7233 0.0367
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75
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EM 0.8051 -0.4669 -0.1919
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PMZ 0.8696 1.4406 0.2086
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PMX -0.8696 1.0854 0.0244
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Energy 3834.9
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W 3.1973 -2.1227 0.1733
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EM 1.0916 -0.6014 -0.5094
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PMZ 1.1614 1.2994 0.5594
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PMX -0.3871 1.7469 0.0269
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84
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Energy 4559.7
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86
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W 10.6576 1.8176 0.3706
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87
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EM 3.3951 -1.3749 -1.1409
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PMZ 2.5072 0.4362 1.1642
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PMX -0.7163 -0.2713 -0.0173
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90
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Energy 4932.0
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W 12.7891 2.3761 0.5001
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EM 4.0027 -1.3573 -1.4443
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PMZ 2.7100 0.7800 1.3630
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PMX -0.7743 -1.5013 -0.0113
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96
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Mean 2.7718 0.0315 0.0789
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98
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