1. 1 MDC post-mortem Now that we know most (if not all) of the input MDC parameters, I thought it would be useful to conduct a post- mortem of the CC MDC analysis, for the following reasons: –To see how close we were to the “right” answers –To uncover any flaws in the analysis – was there something we missed/got wrong? –To understand how sensitive we are to particular systematic shifts (how much data is needed to measure them?) –To find something interesting to do while I was on shift last week… D. A. Petyt 27 th April 2005

2. 2 MDC parameters Generally good agreement between true and fitted values, although fitted x-sec parameters are correlated with BMPT parameters whose values are not shown here We do not know as yet what the BMPT input parameters are. It would be useful to know these to take this sort of study further, but for now it is just modelled as an extra normalisation factor. Robert revealed at Argonne that the effect of beam reweighting was to reduce the MDC flux by roughly 7%. ParameterMDC valueFitted value ma_qel1.0123 1.06 +0.04 -0.044 ma_res1.06051.06 +0.05 -0.042 Disfact * 1.0251Not fitted dmsq2.123e-3 (2.175  0.15)e-3 sin2theta0.881 0.925  0.07

3. 3 Robert’s slide on BMPT weighting from Argonne Both Near & Far spectra are suppressed by almost the same amount (7%?). Effect on F/N ratio is negligible

4. 4 ND post-mortem Goals: –Can we see any significant discrepancies between MDC and MC datasets? Argonne MDC result used a fraction of the MDC files available (~1/3). This analysis uses all existing files. –Can we observe the effect of the ~7% decrease in the MDC flux? –Can we observe the effect of the individual x-sec parameter tweaks. Use MC to determine how much data is needed for this.

5. 5 ND match-up – full sample                 Everything looks good… MC MDC

6. 6 ND and FD samples – xsec reweighting DIS RES QEL NC InteractionUnweightedWeightedFraction NC918 2.6% QEL6016 589817.2% RES9127946326.0% DIS189311911554.2% InteractionUnweightedWeightedFraction NC2404 3.1% QEL13737 1347117.6% RES209832175126.9% DIS408524126352.4% X-sec reweighting changes norm by +1.15%X-sec reweighting changes norm by +1.17%

7. 7 ND MC-MDC match-up Reweight MC by true MDC x-sec parameters. This changes the overall normalisation by +1.15%. Plots shown above are normalised to the total number of p.o.t. A fit to the MDC energy distribution with floating normalisation should therefore yield the flux normalisation factor (expected to be ~0.95) Curiously, this is not observed in the fit. Would be useful to know the BMPT parameters in order to check this more thoroughly.

8. 8 MC study – effect of x-sec reweighting These plots are for 2.36  10 18 p.o.t. These plots show how the values of the x-section parameters used in the MDC affect the shape and normalisation of the neutrino energy spectrum. The   values quoted here (1 d.o.f.) indicate the significance of these shifts for an exposure of 2.3e18 p.o.t. QELDISRES Reconstructed True       

9. 9 Combined effect of x-sec weights Effect is visible at the ~3 sigma level in this distribution for 2.3e18 pot. Of course, it may be possible to improve the sensitivity to individual x-sec parameters by using subsets of the data (i.e. QEL enriched datasets) and alternative variables, such as q 2 and y. This is something that should be studied in more detail…    RECONSTRUCTEDTRUE

10. 10 Mea culpa… In the course of looking through the MAD code the other week, we discovered a bug which affects the muon momentum measurement in the ND Physics Analysis Ntuples –The basic problem was that the criterion that determines whether a track is exiting (i.e. whether to use range or curvature) was incorrect for the ND and the curvature measurement was used most (all?) of the the time. –This will result in additional smearing of the reconstructed neutrino energy. Note that this bug did not affect FD events so the oscillation fit was not compromised –I think this bug is my fault, but I don’t remember doing it – perhaps I was asleep when I wrote that piece of code… old new truth

11. 11 Mea maxima culpa Using curvature for stopping tracks obviously degrades the muon momentum resolution. There is also an apparent bias towards higher reconstructed energies when using curvature instead of range. old new

12. 12 After fix… Although the bug introduced additional energy smearing, I don’t think it affected the ND fit much as: –The same ‘mistake’ was applied to both “DATA” and “MC” –The systematic distortions I was fitting were slowly-varying functions of energy I haven’t re-done the fit, but can show various distributions that show that things do not change significantly now that the fix is in place.      MC MDC

13. 13 After fix – fitting normalisation factor… No surprise that this is the same as before. The fix only affects (and mildly at that) the shape of the energy distribution, not the normalisation.

14. 14 After fix – effect of x-sec re-weighting… RESQEL DISALL           new old

15. 15 FD post-mortem Goals : –What are the effects of the parameters we know (x-sec) and those we think we know (flux normalisation) on the  m 2,sin 2 2  allowed region when we fit the MDC spectrum? –Can we get a better fit if we use the true values of these parameters? –Is there a reason why the MDC fit produced slightly larger values of  m 2 and sin 2 2  than the input values, or was it just a statistical fluctuation?

16. 16 MDC fit with “true” systematic parameters x MDC input parameters nominal MDC x-sec parameters MDC x-sec parameters + -7% flux normalisation Fit was already OK (x within 68% C.L. contour). Interesting that contours move in the ‘right’ direction when systematic parameter shifts are applied. Fit chisq actually gets worse by a few units.

17. 17 1D chi-square projections   minima are almost bang-on the true values for the blue curve. Is this luck or judgement? nominal MDC x-sec parameters MDC x-sec parameters + -7% flux normalisation

18. 18 MC sensitivity – fits with/without systematic parameter shifts MC with nominal parameters MC weighted by –7% flux MC weighted by true x-sec parameters + -7% flux  m 2 =2.12  10 -3,sin 2 2  x input parameters o MDC best-fit Moving from the black contour to the grey one would require a 2.2 sigma statistical fluctuation on the total number of events…

19. 19 MDC fit with floating normalisation Assume correct MDC x-sec parameters and fit with normalisation allowed to float freely within the range +/- 10% Interestingly, fit prefers a larger normalisation and a larger value of sin 2 2  than the true MDC parameters. There seems to be no preference in either the ND or FD to fit to a MC normalisation of ~0.95, which is the expected scale factor for the product of x-sec and BMPT reweighting…

20. 20 Conclusions Overall, the CC fit did a reasonable job of determining the MDC parameters within errors. –If we were to do the exercise again (…) we should ensure that the systematic shifts are larger so that we would have something to fit – here we were able to get away with assuming nominal systematic parameters for the oscillation fit. –There is obviously work to be done to determine the best way of extracting the various systematic parameters. What was done for the MDC was fairly quick and crude in this regard It is curious that we don’t see the claimed –7% flux normalisation for the MDC events –Knowing the BMPT parameters should help to track this ‘problem’ down – I’ll ask Mark/Robert if they can be resurrected.

21. 21 Other topics… I have looked at the combined ND/FD fit (with correlated systematic uncertainties) a bit more. The main problem with this is that the FD fits (using 6 parameters) are much too slow (2 CPU-weeks on the FNAL farm). My plan is to implement the oscillation fit in MINUIT to speed up this process and have just started to work on this. As part of the overhaul of the blessed plot system, we should update our collection of physics plots: –The current plots we use date from May 2003 and contain a number of outdated assumptions about reconstruction and systematic errors. –We can use the MDC analysis as the baseline for the production of the new plots. –I plan to work on this and aim to have a new set of plots available before Ely.