Pmns matrix elements without assuming unitarity
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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

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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


Pmns matrix elements without assuming unitarity

The general idea


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

  • mass basis

n oscillations in vacuum


N oscillations in vacuum1

  • mass basis

  • flavour basis

with

n oscillations in vacuum


N oscillations in vacuum2

  • mass basis

  • flavour basis

with

n oscillations in vacuum


N oscillations in vacuum3

  • mass basis

  • 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


Back up slides

Back-up slides


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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