1 MDC status Overall concept: –The FarDet Mock data challenge ‘dataset’ has been generated with unknown values of  m 2 and sin 2 2  which are to be determined by a fit to the FD CC-like energy spectrum –In addition, systematic ‘tweaks’ to various cross-section and beam parameters have been introduced into the ND and FD challenge sets, and these must be determined by fits to sensitive distributions in the Near Detector and then applied to the oscillation fit. These parameters are Quasi-elastic axial vector mass (3% variation) Resonance production axial vector mass (3% variation) Dis-resonance scale factor (4% variation) BMPT hadron production uncertainties (~25 parameters, 1  variations) Tools available –Mad package encapsulates ‘standard’ CC event selection algorithm and energy reconstruction. (see talks from previous meetings for a description of the standard CC analysis method) –MCReweight package provides cross-section and beam weights (see Chris’s talk) –Physics Analysis Ntuple (PAN) contains all relevant CC quantities to perform event reweighting and oscillation fits. D.A. Petyt 17 th March 2005

2 CC MDC Analysis Procedure Perform match-up between ND MC and MDC datasets to assess the level of agreement with nominal systematic parameters Perform a fit with a reduced set of systematic parameters to: –Determine if the level of agreement between MC/MDC samples can be improved –Obtain best-fit values and uncertainties on the systematic parameters Use central values of these parameters in an oscillation fit to the FD MDC data set Perform match-ups between FD MDC distributions and best- fit FD MC Perform simultaneous ND/FD fit with systematics as ‘nuisance parameters’ *Oscillation parameters will be revealed in Saturday morning MDC talk *This has not yet been done

3 Data samples used in this analysis 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 – selected events (PID parameter>-0.2) 88 Challenge set files MC/Data ratio=2.05/1 –FD: 19 MC 6.5e20 pot – selected events (PID parameter>-0.4) 1 Challenge set 7.4e20 pot MC/Data ratio=16.7/1

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

5 Event length distribution All MC events True CC events True NC events Challenge set   

6 ND MC/MDC matchup – after PID cut MC MDC

7 Reco_enu distribution – after cuts All MC events True CC events True NC events Challenge set   

8 MDC/MC matchup – nominal parameters    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.

9 Overall fit philosophy Cross-section and beam uncertainties can be treated as nuisance parameters in oscillation fit. – Define   in the FD as a function of oscillation parameters and beam/cross- section parameters. Minimise chisq with respect to these systematic parameters to yield dmsq,s2theta contours –Can also apply ‘penalty terms’ to   in order to constrain the values of these nuisance parameters. FD   therefore looks like this: –Can add additional    term for ND which depends only on the nuisance parameters. The idea here is that the ND will help to constrain these parameters since they will, in general, be correlated with dmsq,s2t in FD- only fits. –In the fits presented here, I just fit the ND distributions to determine the systematic parameters and apply them to the FD MC. The combined ND/FD simultaneous fit is in development…

10 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

11 BMPT parameterization

12 Slide from Alysia’s talk at the March 4th NC meeting… Parameter errors were determined from a fit to NA20/NA56(SPY) data

13 Effect of ma_qel  9% MDC/nominal MC Weighted MC/nominal MC

14 Effect of ma_res  9% MDC/nominal MC Weighted MC/nominal MC

15 Effect of disfact  9% MDC/nominal MC Weighted MC/nominal MC

16 Effect of A_pi  5% MDC/nominal MC Weighted MC/nominal MC

17 Effect of B_pi  25% MDC/nominal MC Weighted MC/nominal MC

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

19 Effect of a_pi  6% MDC/nominal MC Weighted MC/nominal MC

20 Fit parameters and ranges ParameterNominal valueRangeconstraint ma_qel1.032  30% 3% ma_res1.032  30% 3% Disfact * 1.0  30% 4% A_pi * 62.7  20% 20% Alpha_pi3.45  10% 5% a_pi6.10  20% 3% * can be calculated outside of MCReweight In ‘unconstrained’ fits, the parameters are allowed to vary freely within the ranges specified above, with no chisq penalty applied if they range far from the nominal values In ‘constrained’ fits, a chisq penalty is applied when parameters deviate from their nominal values – the 1 sigma error is given by the ‘constraint’ column in the table above. (BMPT errors are taken from Alysia’s fits

21 2 parameter fit – ma_qel & ma_res x Best fit 90% CL Discrimination between ma_qel and ma_res is provided by y-distribution 1d   projections

22 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) x Best fit 90% CL

23 Result of 5 parameter unconstrained fit Best fit: Ma_qel = Ma_res = alpha_pi = a_pi = A_pi =

24 Parameter correlations ma_qel ma_res alpha_pi a_pi ma_res alpha_pi a_pi A_pi x 68% CL 90% CL Best fit

25 Comparison with ND MDC spectrum    Fit was already pretty good – additional parameters don’t improve it significantly nominal best fit

26 Result of constrained fit Best fit: Ma_qel = Ma_res = alpha_pi = a_pi = A_pi =

27 Constrained fit MDC matchup    nominal best fit

28 Near and Far ratios unconstrained constrained Near unconstrainedFar unconstrained Ratio of weighted/nominal Individual components Overall

29 Comments on the fits Firstly, the fits as currently implemented are very slow –This limits the number of parameters that can be varied and the step size (about 5 or 6 is the current practical limit). –The ND/FD fit is much slower as it involves the two additional oscillation parameters – this is the main reason why I do not have this fit ready at this time. –We will need to implement a more time-efficient fitting method (such as Brian’s fit method) if we want to include additional parameters. Some degeneracy/reduncancy between parameters –Using e_reco and y factorises some of the dependencies, but further studies into sensitive variables and event sub-samples are needed. –This fit used a zeroth order set of systematic parameters (inspired by some trial fits of my own and advice from Alberto on the important BMPT parameters). A more detailed study to determine what the minimal set of important parameters are would be useful.

30 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…

31 FD matchup (nominal) – PID parameter All MC events True CC events (oscillated) True NC events Challenge set All MC events (oscillated)

32 FD matchup (nominal) – Reconstructed y

33 FD matchup (nominal) – Event length Some ‘notchiness’ in the MDC distribution. Is this pathological, or just statistics?

34 FD matchup (best fit syst) – PID parameter This is caused by best-fit values of ma_qel and ma_res 3% higher than nominal.

35 FD matchup (constrained fit) – PID parameter Problem alleviated in constrained fit. Get slightly better chisq than nominal.

36 Conclusions/Next steps I have made a first pass at using the ND to constrain the values of several of the systematic parameters used in the generation of the MDC Fits to the 2D ND (ereco,y) distribution with nominal systematic parameters yield acceptable values of chisq. This implies that the systematic shifts are either small, or conspire in such a way to cancel each other out in these variables. –This also implies that performing a FD fit with nominal systematic parameters is not an unreasonable thing to do. Fardet-only oscillation fits with either nominal or best-fit systematic parameters yield good agreement with the MDC challenge sets in most of the variables I have examined. –Oscillation parameter values will be revealed at Saturday’s MDC talk Future work should be focussed in the following areas: –Techniques to speed up the fits – this will allow us to add additional parameters and reduce the step size –Look for variables/data-sets that can further constrain fits. –Determine some minimal set of systematic parameters that are needed for the fit. Some generalisation of the BMPT parameters in terms of a reduced set of shape/normalisation variables would also be useful –Perform combined ND/FD fit where N/F correlations are properly accounted for