1. 1 Cross-section systematics Broad aims of this study: –Evaluate the effect of cross-section uncertainties on the all-event CC analysis (selection efficiencies, energy resolution, parameter measurement errors) using NEUGEN reweighting package. –Develop a procedure that uses ND data to constrain systematics in FD oscillation fit. D. A. Petyt 15 th Dec 2004

2. 2 The CC-like sample A CC-like event is defined by the following cuts: –At least 1 reconstructed track with trkpass=1 –Pid parameter>-0.4 (>-0.1 in ND) Selected sample consists of: –55.4% (61.1%) DIS –25.9% (23.0%) RES –16.5% (13.2%) QEL –2.2% (2.7%) NC (numbers in parentheses are for dmsq=0.002,s2t=1.0) NC QEL RES DIS

3. 3 Event reweighting Cross-section weighting is performed on an event-by- event basis using the NeugenInterface package. The cross-section parameters that can be changed are: –ma_qel, ma_res, RES-DIS acceptance factors, PDFs Events are reweighted according to the following parameters: –True enu, initial_state, CC/NC, flavour, target nucleus and the following kinematic variables: –q 2 (QEL) –q 2, W (RES) –x,y (DIS) ma_qel+10%ma_res+10% Disfact-25%

4. 4 Shape & normalisation The plot at right shows the weighting factors for QE,RES&DIS events as a function of visible energy calculated for the following parameters: –ma_qel + 5% –ma_res + 5% –Disfact + 5% The QEL (and to a lesser extent, the RES) weights are approximately flat versus Evis. DIS weights much smaller than QEL/RES QEL RES DIS Visible energy (GeV) weight

5. 5 Overall CC-like normalisation Parameter change (%)QELRESDISALL +101.1091.1551.0141.063 +201.2231.3241.0291.131 -100.8980.8590.9860.941 -200.8040.7340.9710.888 These factors are #weighted/#unweighted events in the three event categories

6. 6 CC efficiencies/purities QuantityValue CC efficiency NC inefficiency CC purity ALLDEFAULTS89.66%20.01%97.59% Ma_qel+10%89.78%20.09%97.61% Ma_qel-10%89.54%19.95%97.56% Ma_res+10%89.79%21.15%97.48% Ma_res-10%89.52%19.03%97.68% Disfact+10%89.56%20.01%97.61% disfact-10%89.76%20.01%97.57% Reconstruction efficiencies not included in these numbers

7. 7 “Error band” for ma_qel  10% nominal  10% unoscillated dmsq=0.002,s2t=1 NC included NC subtracted 19.5e20 p.o.t FD only Note asymmetry. Protons?

8. 8 “Error band” for ma_res  10% Lots of NC RES in this bin? 19.5e20 p.o.t

9. 9 “Error band” for disfact  10% 19.5e20 p.o.t

10. 10 Fits with ma_qel  10% Far-only fits – fit with ‘unweighted’ MC Nominal ma+10% ma-10% 6.5e20 p.o.t. 90%CL  m 2 =0.002, sin 2 2  =1

11. 11 Fitting cross-section uncertainties Cross-section uncertainties can be treated as nuisance parameters in oscillation fit. – Define   as a function of oscillation parameters and cross-section parameters. Minimise chisq with respect to cross-section 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.

12. 12 FD fit – ma_qel Simulated oscillation signal with dmsq=0.002, s2t-1 –3 parameter fit: dmsq, s2t, ma_qel –Plots show ma_value that minimises chisq for each dmsq,s2t point –‘band’ structure evident – positive correlation between ma_qel and oscillation probability unconstrained  mA =5% s2theta dmsq 6.5e20 p.o.t

13. 13 Parameter measurement nominal  ma =5%  ma =10% unconstrained 6.5e20 p.o.t note positive correlation

14. 14 ND-FD fit – constrained ma_qel 6.5e20 p.o.t FD, ~10000 ND snarls FD only ND only ND+FD

15. 15 ND-FD fit – unconstrained ma_qel FD only ND only ND+FD

16. 16 Future work Need to look at other cross-section parameters. Only considered QEL weights so far and these affect just ~15% of the total CC-like dataset –What are the correlations/degeneracies between the various parameters? To what extent can ND data resolve them? How much ND data will be required? –Should increase size of FD dataset. At what pot value do systematic errors exceed statistical errors? –Resolve question mark hanging over DIS weights Can then perform a MDC-style study with 3 of the 4 systematics in place (the 3 cross-section parameters) to test the fitting machinery - in advance of tackling the real MDC once beam weighting code is available.