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PMNS Matrix Elements Without Assuming Unitarity

NOW06, September 9-16, 2006, Otranto. PMNS Matrix Elements Without Assuming Unitarity. Enrique Fernández Martínez Universidad Autónoma de Madrid. hep-ph/0607020 In collaboration with S. Antusch, C. Biggio, M.B. Gavela and J. López Pavón. Thanks also to C. Peña Garay. Motivations.

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PMNS Matrix Elements Without Assuming Unitarity

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  1. NOW06, September 9-16, 2006,Otranto PMNS Matrix ElementsWithout Assuming Unitarity Enrique Fernández Martínez Universidad Autónoma de Madrid hep-ph/0607020 In collaboration with S. Antusch, C. Biggio, M.B. Gavela and J. López Pavón Thanks also to C. Peña Garay

  2. Motivations • n masses and mixing → evidence of New Physics beyond the SM • Typical explanations (see-saw) involve NP at higher energies • This NP often induces deviations fromunitarityof the PMNS at low energy We will analyze the present constraints on the mixing matrix without assuming unitarity

  3. The general idea

  4. Effective Lagrangian • 3 light n • deviations from unitarity from NP at high energy

  5. Effective Lagrangian • 3 light n • deviations from unitarity from NP at high energy Diagonal mass and canonical kinetic terms: unitary transformation + rescaling Nnon-unitary

  6. Effective Lagrangian • 3 light n • deviations from unitarity from NP at high energy Diagonal mass and canonical kinetic terms: unitary transformation + rescaling unchanged Nnon-unitary

  7. ni ni nj W - Z The effects of non-unitarity… … appear in the interactions This affects electroweak processes…

  8. ni ni nj W - Z The effects of non-unitarity… … appear in the interactions This affects electroweak processes… … and oscillation probabilities…

  9. mass basis n oscillations in vacuum

  10. mass basis • flavour basis ≠ with n oscillations in vacuum

  11. mass basis • flavour basis ≠ with n oscillations in vacuum

  12. mass basis • flavour basis ≠ with n oscillations in vacuum Zero-distance effect:

  13. VCC VNC noscillations in matter 2 families

  14. VCC VNC n oscillations in matter 2 families 1. non-diagonal elements 2. NC effects do not disappear

  15. UNITARITY • Degeneracy • cannot be disentangled Nelements from oscillations: e-row Only disappearance exps → information only on |Nai|2 CHOOZ: Δ12≈0 K2K(nm→nm):Δ23

  16. Nelements from oscillations: e-row KamLAND:Δ23>>1 KamLAND+CHOOZ+K2K → first degeneracy solved

  17. Nelements from oscillations: e-row KamLAND:Δ23>>1 KamLAND+CHOOZ+K2K → first degeneracy solved SNO: SNO → all |Nei|2determined

  18. UNITARITY • Degeneracy • cannot be disentangled N elements from oscillations: m-row Atmospheric + K2K:Δ12≈0

  19. Nelements from oscillations only without unitarity OSCILLATIONS 3s with unitarity OSCILLATIONS González-García 04

  20. ni Z W ni nj la g W la ni lb (NN†) from decays • W decays Info on (NN†)aa • Invisible Z • Universality tests • Rare leptons decays Info on(NN†)ab

  21. Experimentally (NN†) and (N†N) from decays

  22. Experimentally (NN†) and (N†N) from decays → N is unitary at % level

  23. Nelements from oscillations & decays without unitarity OSCILLATIONS +DECAYS 3s with unitarity OSCILLATIONS González-García 04

  24. In the future… MEASUREMENT OF MATRIX ELEMENTS • |Ne3|2 , m-row→ MINOS, T2K, Superbeams, NUFACT… • t-row → high energies: NUFACT • phases → appearance experiments: NUFACTs, b-beams

  25. In the future… MEASUREMENT OF MATRIX ELEMENTS • |Ne3|2 , m-row→ MINOS, T2K, Superbeams, NUFACT… • t-row → high energies: NUFACT • phases → appearance experiments: NUFACTs, b-beams TESTS OF UNITARITY • Rare leptons • decays • m→eg • t→eg • t→mg PRESENT

  26. In the future… MEASUREMENT OF MATRIX ELEMENTS • |Ne3|2 , m-row→ MINOS, T2K, Superbeams, NUFACT… • t-row → high energies: NUFACT • phases → appearance experiments: NUFACTs, b-beams TESTS OF UNITARITY • Rare leptons • decays • m→eg • t→eg • t→mg PRESENT FUTURE ~ 10-6MEG ~ 10-7 NUFACT

  27. In the future… MEASUREMENT OF MATRIX ELEMENTS • |Ne3|2 , m-row→ MINOS, T2K, Superbeams, NUFACT… • t-row → high energies: NUFACT • phases → appearance experiments: NUFACTs, b-beams TESTS OF UNITARITY • Rare leptons • decays • m→eg • t→eg • t→mg • ZERO-DISTANCE EFFECT • 40Kt Iron calorimeter near NUFACT • ne→nm • 4Kt OPERA-like near NUFACT • ne→nt • nm→nt PRESENT FUTURE ~ 10-6MEG ~ 10-7 NUFACT

  28. In the future… MEASUREMENT OF MATRIX ELEMENTS • |Ne3|2 , m-row→ MINOS, T2K, Superbeams, NUFACT… • t-row → high energies: NUFACT • phases → appearance experiments: NUFACTs, b-beams TESTS OF UNITARITY • Rare leptons • decays • m→eg • t→eg • t→mg • ZERO-DISTANCE EFFECT • 40Kt Iron calorimeter near NUFACT • ne→nm • 4Kt OPERA-like near NUFACT • ne→nt • nm→nt PRESENT FUTURE ~ 10-6MEG ~ 10-7 NUFACT

  29. Conclusions • If we don’t assume unitarity for the leptonic mixing matrix • Present oscillation experiments alone can only measure half the elements • EW decays confirms unitarity at % level • Combining oscillations and EW decays, bounds for all the elements can • be found comparable with the ones obtained with the unitary analysis • Future experiments can: • improve the present measurements on the e- and m-rows • give information on the t-row and on phases (appearance exps) • test unitarity by constraining the zero-distance effect • with a near detector

  30. Back-up slides

  31. (NN†)et <0.013 • NOMAD:(NN†)mt <0.09 • KARMEN:(NN†)me <0.05 • MINOS:(NN†)mm=1±0.05 • BUGEY:(NN†)ee =1±0.04 …adding near detectors… Test of zero-distance effect: → also all |Nmi|2determined

  32. Non-unitarity from see-saw Integrate outNR d=5 operator it gives mass ton d=6 operator it renormalises kinetic energy Broncano, Gavela, Jenkins 02

  33. nproduced and detected in CC Number of events • Exceptions: • measured flux • leptonic production mechanism • detection via NC

  34. ni Z W ni nj la GFis measured inm-decay Nmi m ni Wˉ e N*ej (NN†) from decays: GF • W decays Info on (NN†)aa • Invisible Z • Universality tests

  35. CHOOZ 10-3

  36. d d Vus* K0 p - W+ ni Uei e+ Unitarity in the quark sector Quarks are detected in the final state → we can directly measure|Vab| ex:|Vus|fromK0 →p - e+ne → ∑i|Uei|2 =1 if Uunitary With Vab we check unitarity conditions: ex:|Vud|2+|Vus|2+|Vub|2 -1 = -0.0008±0.0011 → Measurements of VCKM elements relies on UPMNS unitarity

  37. d d Vus* K0 p - W+ ne e+ • decays → only (NN†) and (N†N) • Nelements → we need oscillations • to study the unitarity of N: no assumptions on VCKM With leptons: Unitarity in the quark sector Quarks are detected in the final state → we can directly measure|Vab| ex:|Vus|fromK0 →p - e+ne With Vab we check unitarity conditions: ex:|Vud|2+|Vus|2+|Vub|2 -1 = -0.0008±0.0011 → Measurements of VCKM elements relies on UPMNS unitarity

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