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

Physics Potential Cambridge Off-Axis Meeting 12 January 2004 Gary Feldman. P( n m  n e ) (in Vacuum). P( n m  n e ) = P 1 + P 2 + P 3 + P 4 P 1 = sin 2 ( q 23 ) sin 2 (2 q 13 ) sin 2 (1.27 D m 13 2 L/E) P 2 = cos 2 ( q 23 ) sin 2 (2 q 12 ) sin 2 (1.27 D m 12 2 L/E)

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

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

  2. P(nmne) (in Vacuum) • P(nmne) = P1 + P2 + P3 + P4 • P1 = sin2(q23) sin2(2q13) sin2(1.27 Dm132 L/E) • P2 = cos2(q23) sin2(2q12) sin2(1.27 Dm122 L/E) • P3 = J sin(d) sin(1.27 Dm132 L/E) • P4 = J cos(d) cos(1.27 Dm132 L/E) where J = cos(q13) sin(2q12) sin(2q13) sin(2q23) x sin(1.27 Dm132 L/E) sin(1.27 Dm122 L/E) Gary Feldman Cambridge Off-Axis 12 January 2004 2

  3. P(nmne) (in Matter) • In matter, P1 will be approximately multiplied by (1 ± 2E/ER) and P3 and P4 will be approximately multiplied by (1 ± E/ER), 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 . Gary Feldman Cambridge Off-Axis 12 January 2004 3

  4. Magnitudes • For long-baseline nm ne oscillations, P1, P3, P4, and the matter effects are all the same order of magnitude. • A measurement of P(nm ne ) measures “sin2(2q13)eff” which is only a crude estimate of sin2(2q13). • Reactor experiments measure sin2(2q13) directly, but have no sensitivity to sign(Dm132) or d. Gary Feldman Cambridge Off-Axis 12 January 2004 4

  5. Probability Plots • Probability plots assumes a particular result for a measurement of P(nmne) and show • The possible values of sin2(2q13), sign(Dm132), and d consistent with this measurement, and • How another another measurement would discriminate among them. Gary Feldman Cambridge Off-Axis 12 January 2004 5

  6. P(nmne) = 0.02 at 820 km Note Effect of cos(d) term Ambiguities ( Hidden ambiguity: P1  sin2(q23); if sin2(2q23) = 0.95, sin2(q23) = 0.39 or 0.61) Rough equivalence of reactor and antineutrino measurements Gary Feldman Cambridge Off-Axis 12 January 2004 6

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

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

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

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

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

  12. Goals of the Off-Axis Experiment • Primary goal: Find evidence for nmne, determining sin2(2q13) to a factor of 2. • Longer term goal: Determine the mass hierarchy. • Ultimate goal: Precision measurement of the CP-violating phase d. Gary Feldman Cambridge Off-Axis 12 January 2004 12

  13. 3 s Discovery Potential for nmne Gary Feldman Cambridge Off-Axis 12 January 2004 13

  14. MINOS Sensitivity tonmne at 3s Discovery Off-Axis Goal Gary Feldman Cambridge Off-Axis 12 January 2004 14

  15. Sensitivities • To consider sensitivities, I consider one experiment (or one set of experiments) with the expected results and calculate 1, 2, and 3 s contours based on Dc2’s, assuming 5% systematic error on the background. Gary Feldman Cambridge Off-Axis 12 January 2004 15

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

  17. Point 1: NuMI 3 yr n, 3 yrn4 1020 and 20 1020 pot/yr Proton Driver Gary Feldman Cambridge Off-Axis 12 January 2004 17

  18. NuMI 3 yr n, 3 yrn4 1020 and 20 1020 pot/yr Proton Driver Gary Feldman Cambridge Off-Axis 12 January 2004 18

  19. NuMI 3 yr n, 3 yrn, 20 1020 pot/yr and JPARC, Phase 1 Without JPARC Phase 1 With JPARC Phase 1 Gary Feldman Cambridge Off-Axis 12 January 2004 19

  20. NuMI 3 yr n, 3 yrn, 20 1020 pot/yrand JPARC Phase 2, 2 yr n, 2 yrn JPARC Phase 2 alone Proton Driver Gary Feldman Cambridge Off-Axis 12 January 2004 20

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

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

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

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