Ely preview…

1. Ely preview… D.A. Petyt 8th June 2005 • ‘Brief’ progress reports on the two topics I am intending to present at Ely • Calibration question: “What are the CC analysis requirements on the hadronic energy scale” • New blessed plots: Updated versions of the CC sensitivity plots.

2. Calibration question • Current targets: • Ehad accurate to 5% absolute, 2% near-to-far • Given the current ‘state-of-the-art’ CC analysis, what effect do hadronic energy shifts have on the CC measurement? • What are realistic calibration targets for • Beam energy choice ~1e20 p.o.t • 1 year of running ~3e20 • Longer term targets 7.4e20 – 25e20 pot • This study – look at effect of energy scale uncertainties on: • Event selection  • Energy resolution  • N/F prediction – in progress • Parameter measurement  • NB – This is work-in progress. Any conclusions drawn are preliminary and are subject to change… • A similar analysis has been carried out by Jeff Hartnell and will appear in his thesis.

3. CC selection algorithm • Event selection algorithm uses 3 pdfs – event length, fraction of pulse height in the track, track pulse height per plane. • Modulo reconstruction effects - which are not studied here – the only variable that should be affected by hadronic energy scale uncertainties is the fraction of ph in the track (the second variable in the above plots) CC NC

4. Effect of energy scale shift on trkphfrac variable 2% 5% 10% • Plots are for the Near detector: solid=nominal, dot/dash=X% CC NC

5. Overall effect on selection efficiencies Near only 10% energy scale error produces a 0.5% change in CC selection efficiency and a 1% change in NC rejection Near/Far ratio N-F CC selection efficiency largely insensitive to shower energy scale factor (<0.2%). Larger (~1% effect) in NC rejection factors Conclusion: energy scale errors (<10%) produce negligible (~1%) changes in selection efficiencies

6. ND and FD samples – selected events DIS RES QEL NC >50% of selected events are DIS – mean y_reco for the entire sample is ~ 0.4

7. Energy resolution • Some general points: • SR shower energy calibration seems to be too high by ~20% • This is seen in both R1.12 and R1.16 • Effect is more pronounced for CC events (i.e. events with a track+shower) than NC events • Effect is non-linear as a function of true (or reco) Ehad • Effect is seen in both SR ntuples and reduced PAN ntuples (from MAD) • Similar effects were reported by Niki at the last NC phone meeting • In what follows, I have scaled down all shower energies by 20% • This issue should be a topic for discussion in the reco. session at Ely.

8. Effect of scale error on hadronic energy measurement 2% 5% 10% FAR NEAR Nominal negative positive

9. N/F differences • These plots – mean and rms from Gaussian fits to total energy reco-true/true distributions • The reason there is an offset in the left-hand plot is due to imperfect tuning of the energy scaling factor (1.2) • The reason there is a difference between near and far is due to slightly lower shower energies in the ND. • This will introduce second-order effects in ND/FD fits with energy scale errors, but these should be very small FAR NEAR

10. ND-only fits +5% shift • Hot off the press… • What happens if you try to fit an energy shift in the ND with other systematic parameters? c2min=63/58 68,90% C.L. contours x True point Best fit ~1.3e18 pot • Can obtain a reasonable fit with the two BMPT parameters a_pi and alpha_pi. • Doesn’t work for larger shifts though. Poor chisq obtained for fit with +10% shift. • What happens if these parameters are applied to FD fit? I predict a rather small (<<1 sigma) shift in the allowed region.

11. FD fits with energy scale error • Procedure: • MC sample: FD MC with zero energy shift • Data sample: FD MC with X% hadronic energy shift • Usual c2fit with fixed normalisation and no other systematic uncertainties • The objective here is to determine how much changes in the hadronic energy scale shift the location of the allowed regions. • A secondary objective is to see how the fit quality (i.e. c2min) is affected by these shifts (the value of c2 was observed to be OK in all the fits I have performed to date with 7.4e20 pot and energy scale shifts ranging up to 10%) • A second method is to perform a fit with the hadronic energy scale as a nuisance parameter, together with a penalty term where the value of sigma is variously 2,5,10% etc. • These fits are in progress and will be shown at Ely.

12. Fits for Dm2=0.00215 eV2 and sin22q=0.81 ‘Data’ Input parameters Input parameters Best fit

13. Shift in allowed regions – 68% C.L. contours 10% shift 5% shift • The shift is predominantly in sin22q rather than Dm2 • This can be understood by looking at the spectrum ratios in the previous slide – for a negative shift there is more feed-down of high y events from higher neutrino energies and the dip becomes somewhat ‘filled in’, resulting in a smaller fitted value of sin22q. The opposite effect occurs for a positive shift.

14. Shifts as a function of Dm2 • The size and direction of the shift does depend on the input value of Dm2. Smaller shifts are observed for larger values of Dm2, where the dip is more clearly resolved and the fits are more robust. Dm2=0.00155 eV2,sin22q=0.81 Dm2=0.00215 eV2,sin22q=0.81 Dm2=0.00345 eV2,sin22q=0.81 For 7.4e20 p.o.t, these plots suggest that the N-F energy scale should be known to better than 5%. On the assumption that the contours scale as 1/sqrt(N), this implies a requirement of ~2.5% for 25e20 pot.

15. Shifts as a function of pot Same conclusion – hadronic energy scale should be known to better than 5% for 7.4e20 p.o.t. or greater

16. Blessed Plots 2005 • The current set of Blessed plots available from the MINOS website are taken from the 5 year plan exercise that occurred in mid-2003. • The calculations at that time used selection efficiencies derived from the pdf-based method that forms the basis of the current analysis, but used parameterised smearing functions rather than full event reconstruction. • The new plots that I am creating reflect the state of the analysis post-MDC: • Full event reconstruction with R1.16 (MDC was R1.12). Some re-tuning of cuts was required in going from R1.12 to R1.16. • Systematics: • The current plots (for 1 and 3e20 pot) have the following systematics applied: • 4% overall normalisation error • 2% energy scale error • 10% NC subtraction error • Studies to incorporate x-sec/beam systematics from the MDC-era analysis are underway • Latest Super-K/K2K regions shown for comparison • The next 3 slides preview the new generation of CC Blessed plots. There will be a more complete set available at Ely.

17. Beam energy choice – 1e20 p.o.t.

18. Spectra/ratios – 1e20 p.o.t.

19. Sensitivity – 1 and 3e20 p.o.t.

20. Summary and conclusions • Calibration question: • Effect of hadronic energy scale uncertainty on selection efficiencies studied – effect is observed to be small and should not matter to the analysis. • Some tuning problems observed in SR hadron energy calibration – should be looked into further. • Observed shifts in allowed regions show some dependence on the value of Dm2 assumed. The shift tends to be more in sin22q than Dm2. • N-F shifts of 10% use up most of the error budget for 7.4e20 p.o.t. (measured relative to the 1 sigma statistical errors on the parameters). A 5% requirement therefore seems reasonable for this exposure. I expect that 1/sqrt(N) scaling is a usable rule-of-thumb for scaling to other pot values. • The effect of energy scale shifts on ND only fits (i.e. fits to x-sec & beam systematic parameters) needs to be studied. I am working on this… • Blessed plots: • New plots with up-to-date reconstruction are being generated. Some work on incorporating systematic uncertainties remains to be done. • Should have a larger complement of plots to show at Ely.