1. Žarko Pavlović, 2 Patricia Vahle, 1 Sacha Kopp, 2 1 University College, London 2 University of Texas at Austin Flux Uncertainties for the NuMI Beam

2. How Good is our Beam MC? Beam flux starting with Fluka2005 model of particle yield off target. NuMI has run several beam energy configurations (more on this later) Error bars are from the beam systematic errors (dominated by hadron production uncertainty, but all effects are included). “Medium” Energy Beam Setting “High” Energy Beam Setting “Low” Energy Beam Setting MINOS Data Calculated flux

3. Why Hadron Production Is Important to NuMI Two-detector experiment for  disappearance measurement. Agreement ‘OK’ in ND, within model spread. But what should we use as error in predicted beam spectrum? (model correlation?)

4. Non-hadron production systematic Non-hadron production systematics affect the falling edge of the peak the most Far/near uncertainty < 2% Focusing Peak

5. Compare Hadron Production Models Model  p T  (GeV/c) GFLUKA0.37 Sanf.-Wang0.42 CKP0.44 Malensek0.50 MARS – v.140.38 MARS – v.150.39 Fluka 20010.43 Fluka 20050.36 Fluka2001 Fluka2005 MARS–v.14 MARS–v.15

6. LE10/185kA Beam Data Upon Which Models are Based Atherton 400 GeV/c p-Be Barton 100 GeV/c p-C SPY 450 GeV/c p-Be Available input data is sparse for “high energy” protons Now there is extensive data available from NA49 (not true at time of NuMI/MINOS analysis), eventually also FNAL/E907.

7. Thick-Target Effects Hadron production data largely from ‘thin’ targets. Particles are created from reinteractions in NuMI target. Approx 30% of yield at NuMI p 0 =120 GeV/c MiniBooNE NuMI CNGS J-PARC Fluka 2005

8. NuMI Variable energy beam “Low” Energy proton Horn 1 Horn 2 target “High” Energy target Horn 1 Horn 2   with p T =300 MeV/c and p=5 GeV/c p=10 GeV/c p=20 GeV/c NuMI Beam MC NuMI Beam MC

9. NuMI Beam Configurations We can vary –Horn current (p T kick supplied to pions) –Target Position (x F of focused particles) LE010/185kA LE010/0kA LE010/170kA LE010/200kA LE100/200kALE250/200kA

10. Parameterizing Hadron Production Used empirical form similar to BMPT to parameterize Fluka2005: Fit was to a MC of our thick-target yield estimated by Fluka2005. Tune parameters of the fit to match ND data.

11. ND Spectra After Reweighting (I)

12. ND Spectra After Reweighting (II)

13. ND Spectra After Reweighting (III)

14. ND Spectra After Reweighting (IV)

15. ND Spectra After Reweighting (V)

16. ND Spectra After Reweighting (VI)

17. (x F,p T ) weights Result of the fit is set of weights in (x F,p T ) plane that should be applied to  /K yields Data prefers more low p T pi’s    weights

18. Are fitted x F and p T reasonable? Model  p T  (GeV/c) GFLUKA0.37 Sanf.-Wang0.42 CKP0.44 Malensek0.50 MARS – v.140.38 MARS – v.150.39 Fluka 20010.43 Fluka 20050.36 Our Fluka2005 (reweighted) 0.36 We also tried doing a fit without  p T  constraint. Fitted  2 to ND was same with/without, so this just shows that different parameterizations give equivalent fits.

19. Final Result F/N ratio unchanged by this procedure in focusing peak (expected). Changes in high energy tail ~10%, but stable to 2% (Fluka2005) Focusing Peak

20. Kaons in NuMI LE10 ME HE

21. LE10/185kA Results (Including >30 GeV) Reconstructed Energy (GeV) Data/MC Events/bin 20 406080 0 (other beams fit simultaneously) (ovflw)

22. Conclusions “Dead-reckoned” flux using Fluka2005 particle yields off our target gave reasonably good agreement with data in MINOS Near Detector  (10-30% discrepencies, depending on E ) We had concerns about correlations between hadron production models, our inability to determine a flux “uncertainty” other than to quote “model spread”. Flexible beam configurations of NuMI permitted tuning hadron production yields to match the ND data  reduce dependence on input models. Flux uncertainty at far detector reduced (2-10)%  (1-4)% NuMI ’s at MiniBooNE can give us insight into  /K yields.

23. Backup slides

24. Hadron Production Each (x F,p T ) bin contributes with different weight in each beam configuration LE010/185kA LE100/200kA LE250/200kA LE010/185kA LE100/200kA LE250/200kA LE010/185kA LE100/200kALE250/200kA 1 2 1 2 1 2 1 2

25. Some slices in x F -p T plane

26.  Results LE010/185kA Reconstructed Energy (GeV) Data/MC Events/GeV 20 4060 0 Fluka2005 Tuned Had. Prod. (ovflw)

27. Calibration of NuMI Flux Using MiniBooNE NuMI ’s sprayed in all directions. K  and  decays at off-axis angle: p beam , K Opportunity to check the  /K ratio of yields off the target.  ~110mrad to MiniBooNE