1. P. Vahle, Fermilab Oct. 2005 1 An Alternate Approach to the CC Measurement— Predicting the FD Spectrum Patricia Vahle University College London Fermilab Collaboration Meeting October, 2005 Outline: I. Using ND data to predict FD spectrum II. Errors in the FD

2. P. Vahle, Fermilab Oct. 2005 2 The Plan Take what we measure in the ND, use the Far/Near ratio and selection efficiencies from the MC to predict what the FD spectrum should look like in the case of no oscillations and oscillations with given values of (delta m^2, sin^2(2theta)). Use Minuit to fit for sin^2(2theta) and delta m^2. Approach different from David's method—provides an independent check Doesn't assume differences between data and MC in the ND spectrum are parameterizable Uses bin by bin differences between data and MC in the ND as basis for errors on the FD spectrum Minimization technique using Minuit is fast –Doesn't need multiple loops over nuisance parameters –Allows for 1000's of pseudo-experiments

3. P. Vahle, Fermilab Oct. 2005 3 Cuts Beam Quality Cuts tor101 > = 0.1e12 pot/spill tortgt > = 0.1e12 pot/spill horizontal beam width < = 2.9 mm vertical beam width < = 2.9 mm -2 mm < = horizontal beam position at target < = 0 mm 0 mm < = vertical beam position at target < = 2 mm closest beam monitoring record within 2 sec. of snarl time horn current > = 50 A

4. P. Vahle, Fermilab Oct. 2005 4 Cuts ND Data Quality Cuts event vertex in "The Pittsburg Fid. Region" –event vertex x position > 2.4 m –0.6 m < event vertex z position < 3.56 m –0.3 m < event vertex u position < 1.8 m –-1.8 m < event vertex v position < -0.3 m –event vertex 0.8 m away from coil hole trk.fit.pass==1 track fit chi2/NDF < 10 difference in planes between the u vertex and v vertex < 6 planes number of tracks == 1 absolute value of error in (q/p) divided by q/p <.2 if muon momentum is obtained by curvature (not a stopper). no other event with vertex time within 50 ns of event in question 90% of shower energy must be in fully instrumented planes muon charge < 1 track vertex z position > 0.6 m

5. P. Vahle, Fermilab Oct. 2005 5 Cuts FD Data Quality Cuts Event vertex in fiducial volume (0.5 m < = event vertex in z < = 14.5 m) || (16.5 m < = event vertex in z < = 29.5 m) R < = 3.5 m, R=sqrt(event vertex x^2+event vertex y^2) trk.fit.pass==1 track fit chi2/NDF < 10 difference in planes between the u vertex and v vertex < 6 planes number of tracks == 1 absolute value of error in (q/p) divided by q/p <.2 if muon momentum is obtained by curvature (not a stopper). no other event with vertex time within 50 ns of event in question muon charge < 1 track vertex z position > 0.6 m

6. P. Vahle, Fermilab Oct. 2005 6 ND Spectrum Scaled to POT

7. P. Vahle, Fermilab Oct. 2005 7 Errors 1.Find the relative difference between Data/MC in ND for each bin of reco energy. 2.Determine the error in bins of true energy by histogramming the true energy for each bin of reco energy, weighted by 1+/- the relative error from step 1, then add up these histograms. 3.Determine relative error for each bin of true neutrino energy. 4.Relative errors on the true energy applied to the true energy in the FD. 5.Add Beam syst. errors from F/N ratio (linearly) 6.Histogram reco energy in FD for each bin of true energy, weighted by 1+/- the relative error of step 4. Sum histograms. Half the spread between the 1+error and 1-error histograms is taken as the error in each bin of reconstructed energy in the FD.

8. P. Vahle, Fermilab Oct. 2005 8 FD/ND ratio

9. P. Vahle, Fermilab Oct. 2005 9 FD ν μ Spectrum Scaled to POT

10. P. Vahle, Fermilab Oct. 2005 10 FD ν τ Spectrum Scaled to POT

11. P. Vahle, Fermilab Oct. 2005 11 Summary Alternate CC analysis –“Know nothing” approach –Independent –Different PID –Fast Jenny will show the method in action