1. 1 Using the pHE data to measure the beam e ’s from  + decay David Jaffe and Pedro Ochoa June 14 th 2007  Reminder  Updated Statistical error  Horn 1 systematics  Summary

2. 2 Reminder x parLE (  + ) pHE ( ,K) pHE - ( ,K) LE x parHE (  + ) LE  Procedure: - Take pHE-LE difference. Correct for - Fit using MC shapes. Scale (  + ) LE and (  + ) pHE by parameters parLE and parHE.  Previous study (doc-2909) showed that pHE background is not big concern.  Main systematics associated with this measurement:  C= ( ,K) pHE - ( ,K) LE correction.  Background in nubar selection.  But the previous assessment of C was too pessimistic and done with too few statistics, so it is redone here.

3. 3 Update on statistical error  Previous study (doc-2783) assumed 2.0x10 19 POT of pHE data and a statistical error of ~13% in the measurement was quoted.  But more precisely, the pHE data taken after the 2006 shutdown corresponds to 1.6x10 20 POT. So repeated the fit with this number:  New statistical error in (  + ) LE is 15%. 90% C.L. 68.3% C.L.

4. 4 Horn 1 systematics  How well can we determine C = ( ,K) pHE - ( ,K) LE ?  So obtained ratios of spectra with systematics over nominal spectra using gnumi: Ex: horn1 current increase by 2% in pHE neutrino beam  Good agreement with pbeam  Systematics considered are: horn 1 offset1.0 mm horn current offset1% Target displacement1cm  Work by David suggests C mostly affected by horn1 & target geometry, as one would expect (minos-doc- 2841)  Obtained gnumi ratios are shown in the next 5 slides.

5. 5 Horn current -1% le010z185ile250z200i nominal with systematic (  ,K - ) (  + )

6. 6 Horn current +1% le010z185ile250z200i nominal with systematic (  ,K - ) (  + )

7. 7 Horn offset by 1mm le010z185ile250z200i nominal with systematic (  ,K - ) (  + ) (  ,K - ) (  + )

8. 8 Target in LE position -1cm le010z185i (  ,K - ) nominal with systematic (  + )

9. 9 Target in LE position +1cm le010z185i (  ,K - ) nominal with systematic (  + )

10. 10  Converted these ratios to reconstructed energy using the ntuples: Ex: target position increased by 1cm in LE Convert to E reco  Used these ratios(E reco ) to scale the spectra in our feasibility study and obtain systematic shifts.  Nominal spectra are used to do the fit which contains spectra including these systematics.  Infinite MC and LE data statistics are assumed. (no events in first bin)

11. 11  Example: Horn offset by 1mm Systematics: Results of fit: with systematics nominal with systematics result of fit pHE-LE corrected for background and nominal C  Bias of 3% (  + ) pHE  Bias of 3% (  + ) LE fit

12. 12  Summary of biases in measurement:  Also need to add the error associated with hadron production. Horn I -1%Horn I +1%Horn offset 1mmLE Target -1cmLE Target +1cm Bias in parLE -15%-9%3%1% Bias in parHE -14% 3%-6%  This assumed same horn conditions for pHE and LE running (except for target displacement). If that is not the case need to work with other combinations: Horn I -1%Horn I +1%Horn offset 1mm Applying systematics to LE beam only Bias in parLE-4%-5%6% Bias in parHE-6%-9%6% Applying systematics to pHE beam only Bias in parLE-10%-3% Bias in parHE-9%-5%-2%

13. 13  The statistical error of the measurement with 1.6x1019 POT of pHE data is ~15%. Summary & Ongoing work  Measurement of (  + ) pHE is more affected by horn1 & target systematics than (  + ) LE. Fortunately we don’t care.  Main sources of systematic errors seem to be under control. Next step: carry out the measurement

14. 14 Backup

15. 15  Horn current -1% Systematics: Results of fit: with systematics nominal with systematics result of fit pHE-LE corrected for background and nominal C  Bias of -14% (  + ) pHE  Bias of -15% (  + ) LE fit

16. 16  Horn current +1% Systematics: Results of fit: with systematics nominal with systematics result of fit pHE-LE corrected for background and nominal C  Bias of -14% (  + ) pHE  Bias of -9% (  + ) LE fit

17. 17  Target -1cm Systematics: Results of fit: with systematics nominal with systematics result of fit pHE-LE corrected for background and nominal C  Bias of -6% (  + ) pHE  Bias of 1% (  + ) LE fit

18. 18  Target +1cm Systematics: Results of fit: with systematics nominal with systematics result of fit pHE-LE corrected for background and nominal C  Bias of -6% (  + ) pHE  Bias of 7% (  + ) LE fit