1. f Axis Off Axis Physics Potential Cambridge Off-Axis Meeting 12 January 2004 Gary Feldman

2. Off Axis Gary Feldman Cambridge Off-Axis 12 January 2004 2 P(   e ) (in Vacuum) P(   e ) = P 1 + P 2 + P 3 + P 4 P 1 = sin 2 (  23 ) sin 2 (2  13 ) sin 2 (1.27  m 13 2 L/E) P 2 = cos 2 (  23 ) sin 2 (2  12 ) sin 2 (1.27  m 12 2 L/E) P 3 = J sin(  ) sin(1.27  m 13 2 L/E) P 4 = J cos(  ) cos(1.27  m 13 2 L/E) where J = cos(  13 ) sin (2  12 ) sin (2  13 ) sin (2  23 ) x sin (1.27  m 13 2 L/E) sin (1.27  m 12 2 L/E)

3. Off Axis Gary Feldman Cambridge Off-Axis 12 January 2004 3 P(   e ) (in Matter) l In matter, P 1 will be approximately multiplied by (1 ± 2E/E R ) and P 3 and P 4 will be approximately multiplied by (1 ± E/E R ), where the top sign is for neutrinos with normal mass hierarchy and antineutrinos with inverted mass hierarchy. About a ±23% effect for NuMI, but only a ±10% effect for JPARC.

4. Off Axis Gary Feldman Cambridge Off-Axis 12 January 2004 4 Magnitudes For long-baseline   e oscillations, P 1, P 3, P 4, and the matter effects are all the same order of magnitude. A measurement of P(   e ) measures “sin 2 (2  13 ) eff ” which is only a crude estimate of sin 2 (2  13 ). Reactor experiments measure sin 2 (2  13 ) directly, but have no sensitivity to sign(  m 13 2 ) or .

5. Off Axis Gary Feldman Cambridge Off-Axis 12 January 2004 5 Probability Plots Probability plots assumes a particular result for a measurement of P(   e ) and show The possible values of sin 2 (2  13 ), sign(  m 13 2 ), and  consistent with this measurement, and l How another another measurement would discriminate among them.

6. Off Axis Gary Feldman Cambridge Off-Axis 12 January 2004 6 P(   e ) = 0.02 at 820 km Note (1)Effect of cos(  ) term (2)Ambiguities ( Hidden ambiguity: P1  sin 2 (  23 ); if sin 2 (2  23 ) = 0.95, sin 2 (  23 ) = 0.39 or 0.61) (1)Rough equivalence of reactor and antineutrino measurements

7. Off Axis Gary Feldman Cambridge Off-Axis 12 January 2004 7 P(   e ) = 0.05, 0.02, 0.01, and 0.005 at 820 km

8. Off Axis Gary Feldman Cambridge Off-Axis 12 January 2004 8 P(   e ) = 0.02 at 820 and 295 km JPARC

9. Off Axis Gary Feldman Cambridge Off-Axis 12 January 2004 9 P(   e ) = 0.02 at 820 km Note ambiguities between normal hierarchy and inverted hierarchy. Can combining JPARC and NuMI data help?

10. Off Axis Gary Feldman Cambridge Off-Axis 12 January 2004 10 P(   e ) = 0.02 at 820 km vs. P(   e ) at 295 km Ambiguous points are still fairly close together

11. Off Axis Gary Feldman Cambridge Off-Axis 12 January 2004 11 A 2nd Detector at the 2nd Maximum?

12. Off Axis Gary Feldman Cambridge Off-Axis 12 January 2004 12 Goals of the Off-Axis Experiment Primary goal: Find evidence for   e, determining sin 2 (2  13 ) to a factor of 2. l Longer term goal: Determine the mass hierarchy. Ultimate goal: Precision measurement of the CP-violating phase .

13. Off Axis Gary Feldman Cambridge Off-Axis 12 January 2004 13 3  Discovery Potential for   e

14. Off Axis Gary Feldman Cambridge Off-Axis 12 January 2004 14 MINOS Sensitivity to   e at 3  Discovery Off-Axis Goal

15. Off Axis Gary Feldman Cambridge Off-Axis 12 January 2004 15 Sensitivities To consider sensitivities, I consider one experiment (or one set of experiments) with the expected results and calculate 1, 2, and 3  contours based on  2 ’s, assuming 5% systematic error on the background.

16. Off Axis Gary Feldman Cambridge Off-Axis 12 January 2004 16 Study Points 1 2

17. Off Axis Gary Feldman Cambridge Off-Axis 12 January 2004 17 Point 1: NuMI 3 yr, 3 yr  4 10 20 and 20 10 20 pot/yr Proton Driver

18. Off Axis Gary Feldman Cambridge Off-Axis 12 January 2004 18 NuMI 3 yr, 3 yr  4 10 20 and 20 10 20 pot/yr Proton Driver

19. Off Axis Gary Feldman Cambridge Off-Axis 12 January 2004 19 NuMI 3 yr, 3 yr  20 10 20 pot/yr and JPARC, Phase 1 Without JPARC Phase 1With JPARC Phase 1

20. Off Axis Gary Feldman Cambridge Off-Axis 12 January 2004 20 NuMI 3 yr, 3 yr  20 10 20 pot/yr and JPARC Phase 2, 2 yr, 2 yr  Proton DriverJPARC Phase 2 alone

21. Off Axis Gary Feldman Cambridge Off-Axis 12 January 2004 21 NuMI 3 yr, 3 yr  2 Detectors and Proton Driver

22. Off Axis Gary Feldman Cambridge Off-Axis 12 January 2004 22 95% CL Resolution of the Mass Hierarchy

23. Off Axis Gary Feldman Cambridge Off-Axis 12 January 2004 23 95% CL Resolution of the Mass Hierarchy with 2 Detectors