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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

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


Motivations
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



Effective lagrangian
Effective Lagrangian

  • 3 light n

  • deviations from unitarity from NP at high energy


Effective lagrangian1
Effective Lagrangian

  • 3 light n

  • deviations from unitarity from NP at high energy

Diagonal mass and canonical kinetic terms:

unitary transformation + rescaling

Nnon-unitary


Effective lagrangian2
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


The effects of non unitarity

ni

ni

nj

W -

Z

The effects of non-unitarity…

… appear in the interactions

This affects electroweak processes…


The effects of non unitarity1

ni

ni

nj

W -

Z

The effects of non-unitarity…

… appear in the interactions

This affects electroweak processes…

… and oscillation probabilities…


N oscillations in vacuum

n oscillations in vacuum


N oscillations in vacuum1

  • flavour basis

with

n oscillations in vacuum


N oscillations in vacuum2

  • flavour basis

with

n oscillations in vacuum


N oscillations in vacuum3

  • flavour basis

with

n oscillations in vacuum

Zero-distance effect:


N oscillations in matter

VCC

VNC

noscillations in matter

2 families


N oscillations in matter1

VCC

VNC

n oscillations in matter

2 families

1. non-diagonal elements 2. NC effects do not disappear


N elements from oscillations e row

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


N elements from oscillations e row1
Nelements from oscillations: e-row

KamLAND:Δ23>>1

KamLAND+CHOOZ+K2K

→ first degeneracy solved


N elements from oscillations e row2
Nelements from oscillations: e-row

KamLAND:Δ23>>1

KamLAND+CHOOZ+K2K

→ first degeneracy solved

SNO:

SNO

→ all |Nei|2determined


N elements from oscillations m row

UNITARITY

  • Degeneracy

  • cannot be disentangled

N elements from oscillations: m-row

Atmospheric + K2K:Δ12≈0


N elements from oscillations only
Nelements from oscillations only

without unitarity

OSCILLATIONS

3s

with unitarity

OSCILLATIONS

González-García 04


Nn from decays

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


Nn and n n from decays

Experimentally

(NN†) and (N†N) from decays


Nn and n n from decays1

Experimentally

(NN†) and (N†N) from decays

→ N is unitary at % level


N elements from oscillations decays
Nelements from oscillations & decays

without unitarity

OSCILLATIONS

+DECAYS

3s

with unitarity

OSCILLATIONS

González-García 04


In the future
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 future1
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 future2
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


In the future3
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


In the future4
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


Conclusions
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



Adding near detectors

(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


Non unitarity from see saw
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


Number of events

nproduced and detected in CC

Number of events

  • Exceptions:

  • measured flux

  • leptonic production mechanism

  • detection via NC


Nn from decays g f

ni

Z

W

ni

nj

la

GFis measured inm-decay

Nmi

m

ni

e

N*ej

(NN†) from decays: GF

  • W decays

Info on

(NN†)aa

  • Invisible Z

  • Universality tests


Chooz
CHOOZ

10-3


Unitarity in the quark sector

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


Unitarity in the quark sector1

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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