1. Beam Extrapolation Fit Peter Litchfield  An update on the method I described at the September meeting  Objective;  To fit all data, nc and cc combined, with the minimum of cuts  To use the beam MC extrapolation parameters event by event to produce a far detector prediction from the near detector data  Not to need beam, cross-section and/or reconstruction error fitting  Status  John Marshall is developing an independent program on the same lines. John (Mark) is reporting his results in the cc session  I have used MDC MC both raw and tweaked to develop and verify my program  I will show that it works, at least on MC data

2. Reminder of the method GNuMI Beam particle Near MC truth event Near MC reco E  - E s Weight: near data reco/ near MC reco Far MC truth event E - y Weight: Oscillation Beam extrapolation Gen/Extrapolated ratio Far flattening weight Xsec ratio Far MC truth event weighted Far MC reco event E  - E s Far data reco E  - E s distribution compare  many beam particles Predicted Far reco E  - E s distribution

3. Data  All data is MC, I have not looked (for a long time) at any real data  MDC data, R18.2 reconstruction  Pure MC, no tweaking, far data oscillated (original MDC)  Near “data” 385 files : 0.03955 10 20 pot  Near MC 382 files : 0.03934 10 20 pot  Far “data” 100 files : 102.7 10 20 pot  Far MC 177 files : 514.2 10 20 pot  Tweaked MC, far data oscillated (MDC3)  Near “data” 396 files : 0.3996 10 20 pot  Near MC 379 files : 0.3893 10 20 pot  Far “data” 100 files : 103.2 10 20 pot  Far MC 177 files : 514.2 10 20 pot

4. Near detector E  v E shw weight  Plot reconstructed E  v E shw  Only cut is that the reconstructed vertex should be in the fiducial volume  No nc/cc separation  Sign of E  is that of the reconstructed   One bin for events with no   Bins of 1 GeV 0-10 Gev, 10 GeV 10-60 GeV EE E shw Tweaked “data” Untweaked MC

5. Near detector E  v E shw weight  Weight the beam MC event by the ratio of near data to near mc in the bin of E  v E shw  For untweaked MC should be 1, Could do with more statistics Ratio near data/near mc E shw (GeV) E  (GeV) +ve momentum -ve momentum

6. Tweaked Near E  v E shw weight  Tweaked MC, ratio different from 1  Weights the near MC to allow for beam, cross-section and reconstruction differences Ratio near data/near mc E shw (GeV) E  (GeV) +ve momentum -ve momentum

7. Extrapolation to the far detector  Near-far extrapolation is done with only truth quantities  Each near detector mc event has a truth energy that a neutrino hitting the far detector from the same beam particle decay would have, together with the probabilities that the near and far detectors are hit.  Use far detector mc events with the same truth characteristics as the extrapolated near detector event  Problem: the far detector energy is different from the near therefore cannot use E  and E shw. Instead extrapolate in truth E and y which should at least approximately scale.  Select events with the same truth initial state (nc,cc,qel,dis etc) and in the same bin of E v y  Apply the far detector reconstructed fiducial volume cut and plot the reconstructed E  v E shw distribution with the weights on the next slide  Again the only cut is on the reconstructed fiducial volume

8. Far detector extrapolation  Each selected far detector MC event has the following weights applied  The ratio of the probability of the neutrino hitting the far detector to the probability of hitting the near detector  The ratio of the far to near fiducial volumes  The ratio of the pot in the far and near detector samples  The ratio of the cross section at the energy of the far detector event to that at the energy of the near detector event  A weight to flatten the far detector events as a function of E and y. Necessary to remove the cross-section dependence in the far MC  A weight to allow for the difference in truth distributions of accepted events in the near and far detectors (see next slides)  The near detector data/MC weight  An oscillation weight, dependent on  m 2, sin 2 2 , f s

9. Far detector extrapolation  `Problem: the truth MC distributions in the far detector are not the same as the extrapolated MC near detector spectrum  `Due to split and superimposed events in the near detector  MC truth finder usually associates bigger MC event with the event  Split events, the MC event gets extrapolated twice  Superimposed events, the bigger event gets extrapolated twice, the smaller event is lost Far MC Extrapolated ND Truth E All events -60.0 0.0 E 60.0

10. Far detector extrapolation  `Effect bigger for vertex selected events,  Differences in reconstruction efficiencies?  Non uniform vertex distribution in near detector + vertex resolution?  ?  Weight events with the ratio far/near of events in the E -y bin Far MC Extrapolated ND Selected events -60.0 0.0 E 60.0

11. Far detector weight  The extrapolation weight for the near to far truth should be close to 1.0  Could do with more statistics E (Gev) Far MC/Near MC projected y

12. Raw MC fit  Fit to oscillated but untweaked MC, test that the program works.  Use the MDC MC, oscillated with parameters  m 2 =0.0238, sin 2 2  =0.93  Fitted to E  v E shw but difficult to see effects, project onto E  No cc/nc selection but plot E for data divided into nc/cc by Niki’s ann nc cc Far data Extrapolated near data  No oscillations -60.0 0.0 E 60.0

13. Raw MC fit  True oscillated parameters within the 68% confidence contour  MC statistics is lacking, still contributions to likelihood from MC 68 and 90% contours ▲ truth * best fit point 0.9 0.95 sin 2 2  1.0 0.002  m 2 0.0025 Oscillated nc cc -60.0 0.0 E 60.0

14. Tweaked MC, Near data/MC Ratio near data/near mc E shw (GeV) E  (GeV) +ve momentum -ve momentum  MDC3 data. Note ratio now generally > 1.

15. Tweaked MC, no oscillations nc cc Far data Extrapolated near data  No oscillations -60.0 0.0 E 60.0  Prediction from near data includes correction for tweaking  Truth oscillations have different parameters

16. Tweaked MC, best fit ▲ truth * best fit point 0.75 0.80 sin 2 2  0.85 0.0025  m 2 0.003 Oscillated nc cc -60.0 0.0 E 60.0

17. Include sterile oscillations  Fits well with no sterile component, therefore don’t expect much in fit ▲

18. Summary and Conclusions  The beam event-by-event extrapolation works.  It works (on MC) without beam or cross-section fitting/adjustments  It works (on MC) without any cuts except a fiducial volume cut.  It works (on MC) for a fit to  m 2, sin 2 2  and f s  It should work for a CPT separated and fit  Fitting to reconstructed E  v E shw includes the detector resolution in a simple manner  I haven’t thought much about systematics but since it makes very few assumptions and cuts, the systematic errors should be small  It will work as far as there are no effects unique to one detector which are not represented by the MC  Need to compare far and near detector data to check that no such effects are present.