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MDC update

MDC update. D.A. Petyt 9 th March 2005. This talk focuses on efforts to fit the ND mock data to determine the systematic beam/x-sec parameters that were inserted as part of the data challenge.

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MDC update

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  1. MDC update D.A. Petyt 9th March 2005 • This talk focuses on efforts to fit the ND mock data to determine the systematic beam/x-sec parameters that were inserted as part of the data challenge. • The method employed uses the reweighting functions developed by Chris and Hugh that are encapsulated in the MCReweight package • Since the last meeting, the required truth variables for beam weighting have now been added to the standard CC analysis PAN. • In this particular study, I am looking at these beam systematic (BMPT) parameters for the first time. • So far, the study has only been conducted on ND events. The next step is to perform a combined ND/FD fit to extract the oscillation parameters while maintaining all correlations between the systematic parameters. This fit should be available by the time of the collaboration meeting.

  2. Data samples • PDF construction: • ~50 ND files (550 snarls/file) • 10 FD numu files + ~40 ‘NC’ nutau files • Event reweighting and parameter fitting: • ND: • 179 MC files – 78875 selected events (PID parameter>-0.2) • 88 Challenge set files • MC/Data ratio=2.05/1 • FD: • 19 MC files @ 6.5e20 pot – 34992 selected events (PID parameter>-0.4) • 1 Challenge set file @ 7.4e20 pot • MC/Data ratio=16.7/1

  3. ND MC/MDC matchup – before PID cut NB – MC statistical error is not negligible in these plots! MC MDC

  4. Event length distribution All MC events True CC events True NC events Challenge set c2=49.4/46

  5. ND MC/MDC matchup – after PID cut MC MDC

  6. Reco_enu distribution – after cuts All MC events True CC events True NC events Challenge set c2=36.2/30

  7. Fit method • The ND fit is performed on the 2D E_reco vs reconstructed_y distribution, where reco_y =reco_shw/reco_enu. The reco_y dimension is necessary to provide some discrimination between QEL, RES & DIS events. It is expected that the e_reco distribution will provide discrimination between BMPT beam systematic parameters. • A total of 51 bins of variable bin-size are employed in the fit (17 in e_reco and 3 in y) and a simple chisq is calculated between the observed and expected distributions. • The fit uses the ‘many loops’ (or ‘brute force’) method to find the chisq minimum. Numerous tricks have been employed to reduce the execution time to the absolute minimum (a 5 parameter fit currently takes ~30 mins on a single node on the FNAL Linux Cluster). Other techniques, such as the Marquardt fit advocated by Brian, might be necessary if the number of free parameters becomes too large (i.e. >8) QEL RES DIS

  8. BMPT parameterization

  9. Slide from Alysia’s talk at the last NC meeting… Parameter errors were determined from a fit to NA20/NA56(SPY) data

  10. Fit parameters and ranges * can be calculated outside of MCReweight

  11. E_reco vs reco_y distribution, challenge set 3 bins 17 bins

  12. Fractional difference between MC and challenge sets Low statistics bins

  13. MDC/MC matchup – nominal parameters c2=39.1/51 Match-up is pretty good – implies that FD fit with nominal beam/xsec parameters will be OK. ND fit is required to determine the allowed range of these parameters, however.

  14. Effect of ma_qel9% MDC/nominal MC Weighted MC/nominal MC

  15. Effect of ma_res9% MDC/nominal MC Weighted MC/nominal MC

  16. Effect of disfact9% MDC/nominal MC Weighted MC/nominal MC

  17. 2 parameter fit – ma_qel & ma_res 1d Dc2 projections Best fit x 90% CL Discrimination between ma_qel and ma_res is provided by y-distribution

  18. 3 parameter fit – adding disfact • Adding extra parameters will inflate the uncertainties on the systematic parameters due to correlations and/or degeneracies between the variables. • In this case, the size of the error contour in the ma_qel, ma_res chisq projection is significantly larger than the 2 parameter fit. • The best fit value of ma_qel remains the same, although the value of ma_res is higher by 3%. This is compensated by a 3% decrease in best-fit value of disfact from nominal (0.97 instead of 1.0) Best fit x 90% CL

  19. Effect of A_pi5% MDC/nominal MC Weighted MC/nominal MC

  20. Effect of B_pi25% MDC/nominal MC Weighted MC/nominal MC

  21. Effect of alpha_pi5% MDC/nominal MC Weighted MC/nominal MC Strong correlation between B_pi and alpha_pi expected in fits

  22. Effect of a_pi6% MDC/nominal MC Weighted MC/nominal MC

  23. 5 parameter fit – Adding Ap, Ak • Two additional parameters are introduced here – the values of A (the overall BMPT cross-section normalisation term) for pion and kaon parent hadrons respectively. • This effectively adds a normalisation term to the fit (although there is some mild shape dependence due to the differing spectra of neutrinos from pi/K parents) • The addition of these variables significantly increases the uncertainty on ma_qel,ma_res. 2 parameter fit 3 parameter fit 5 parameter fit

  24. Result of 5 parameter fit Parameters: ma_qel, ma_res, disfact, A_pi, A_k Nominal Best fit c2=37.88/46

  25. Fit uncertainties 90% CL Best fit: Ma_qel = 1.09 Ma_res = 1.03 disfact = 1.2 A_pi = 59.8 A_k = 7.58 Note anti-correlation between ma_qel,disfact and A_pi,A_k

  26. Do correlations/degeneracies matter? • At the last meeting I presented this plot which shows that there is complete degeneracy between ma_qel and ma_res if only the E_reco distribution is used in the ND fit. (This degeneracy is broken by fitting to y_reco). • What effect does getting the ‘wrong’ systematic parameters have on the FD fit? Does it actually matter that the input cross-section/beam parameters are not at the nominal values as long as the resulting energy distribution is the same? • As far as fitting to the correct values of dmsq and sin2theta is concerned, I think the answer (to first order) is no: • I tested this by fitting a FD dataset generated with nominal parameters with a MC set generated with ma_qel=1.15, ma_res=0.88. The fit produced a perfectly good chisq at the input values of dmsq and sin2theta. • It’s clear though that the size of the error contours will depend on how well the systematic parameters are determined and I think this is where their real importance lies. 68% CL 90% CL

  27. First look at FD challenge set All MC events True CC events True NC events Challenge set Distribution seems consistent with numu disappearance at a level that is expected for SK-like oscillation parameters…

  28. Next steps • Decide on a minimal set of x-sec/BMPT parameters and re-do ND-only fits with finer binning. • Proposal is to use: ma_qel, ma_res, disfact, A_pi, A_k, alpha_pi, a_pi. • Try fits with c2 constraints – how much do these restrict the allowed regions? • Try FD-only fit with best-fit systematic parameters from ND. • Attempt simultaneous ND/FD fit.

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