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 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 from unitarity of the PMNS at low energy We will analyze the present constraints on the mixing matrix without assuming unitarity

The general idea

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

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

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

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

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

n oscillations in vacuum mass basis

n oscillations in vacuum mass basis flavour basis with ≠

n oscillations in vacuum mass basis flavour basis with ≠

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

n oscillations in matter VCC VNC 2 families

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

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

N elements from oscillations: e-row KamLAND: Δ23>>1 KamLAND+CHOOZ+K2K → first degeneracy solved

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

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

N elements from oscillations only without unitarity OSCILLATIONS 3s with unitarity OSCILLATIONS González-García 04

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

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

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

N elements from oscillations & decays without unitarity OSCILLATIONS +DECAYS 3s with unitarity OSCILLATIONS González-García 04

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

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

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 ~ 10-6 MEG ~ 10-7 NUFACT

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 ~ 10-6 MEG ~ 10-7 NUFACT

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 ~ 10-6 MEG ~ 10-7 NUFACT

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

Back-up slides

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

Non-unitarity from see-saw Integrate out NR d=5 operator it gives mass to n d=6 operator it renormalises kinetic energy Broncano, Gavela, Jenkins 02

Number of events n produced and detected in CC Exceptions: measured flux leptonic production mechanism detection via NC

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

CHOOZ 10-3

Unitarity in the quark sector Quarks are detected in the final state → we can directly measure |Vab| K0 p - d W+ Vus* ni e+ Uei ex: |Vus| from K0 →p - e+ ne → ∑i|Uei|2 =1 if U unitary 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

Unitarity in the quark sector Quarks are detected in the final state → we can directly measure |Vab| K0 p - d W+ Vus* ne e+ ex: |Vus| from K0 →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 decays → only (NN†) and (N†N) N elements → we need oscillations to study the unitarity of N: no assumptions on VCKM With leptons: