PMNS Matrix Elements Without Assuming Unitarity

1
PMNS Matrix Elements Without Assuming Unitarity
NOW06, September 9-16, 2006, Otranto
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 from unitarity
  of 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
N non-unitary
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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
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The effects of non-unitarity
appear in the interactions
This affects electroweak processes
8
The effects of non-unitarity
appear in the interactions
This affects electroweak processes
and oscillation probabilities
9
n oscillations in vacuum
10
n oscillations in vacuum
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n oscillations in vacuum
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n oscillations in vacuum
Zero-distance effect
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n oscillations in matter
2 families
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n oscillations in matter
2 families
1. non-diagonal elements 2. NC effects
do not disappear
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N elements from oscillations e-row
Only disappearance exps ? information only on
Nai2
CHOOZ ?120
K2K (nm?nm ) ?23
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N elements from oscillations e-row
KamLAND ?23gtgt1
KamLANDCHOOZK2K
? first degeneracy solved
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N elements from oscillations e-row
KamLAND ?23gtgt1
KamLANDCHOOZK2K
? first degeneracy solved
SNO
SNO
? all Nei2 determined
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N elements from oscillations m-row
Atmospheric K2K ?120
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N elements from oscillations only
without unitarity OSCILLATIONS
3s
with unitarity OSCILLATIONS
González-García 04
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(NN) from decays

• W decays

Info on (NN)aa

• Invisible Z

• Universality tests

• Rare leptons decays

Info on (NN)ab
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(NN) and (NN) from decays
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(NN) and (NN) from decays
? N is unitary at level
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N elements from oscillations decays
without unitarity OSCILLATIONS DECAYS
3s
with unitarity OSCILLATIONS
González-García 04
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In the future
MEASUREMENT OF MATRIX ELEMENTS

• Ne32 , m-row ? MINOS, T2K, Superbeams,
  NUFACT
• t-row ? high energies NUFACT
• phases ? appearance experiments NUFACTs,
  b-beams

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In the future
MEASUREMENT OF MATRIX ELEMENTS

• Ne32 , 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
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In the future
MEASUREMENT OF MATRIX ELEMENTS

• Ne32 , 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
27
In the future
MEASUREMENT OF MATRIX ELEMENTS

• Ne32 , 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
28
In the future
MEASUREMENT OF MATRIX ELEMENTS

• Ne32 , 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
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Conclusions

• If we dont 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

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Back-up slides
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adding near detectors
Test of zero-distance effect
? also all Nmi2 determined
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Non-unitarity from see-saw
Integrate out NR
d5 operator it gives mass to n
d6 operator it renormalises kinetic energy
Broncano, Gavela, Jenkins 02
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Number of events

• Exceptions
• measured flux
• leptonic production mechanism
• detection via NC

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(NN) from decays GF

• W decays

Info on (NN)aa

• Invisible Z

• Universality tests

35
CHOOZ
10-3
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Unitarity in the quark sector
Quarks are detected in the final state
? we can directly
measure Vab
ex Vus from K0 ?p - e ne
? ?iUei2 1 if U unitary
With Vab we check unitarity conditions
ex Vud2Vus2Vub2 -1
-0.00080.0011
? Measurements of VCKM elements relies on UPMNS
unitarity
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Unitarity in the quark sector
Quarks are detected in the final state
? we can directly
measure Vab
ex Vus from K0 ?p - e ne
With Vab we check unitarity conditions
ex Vud2Vus2Vub2 -1
-0.00080.0011
? Measurements of VCKM elements relies on UPMNS
unitarity