1. 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/
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

6. 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

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

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

9. n oscillations in vacuum
mass basis

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

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

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

13. n oscillations in matter
VCC
VNC
2 families

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

15. 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

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

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

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

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

20. (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

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

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

23. N elements 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
~ MEG
~ 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
~ MEG
~ 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
~ MEG
~ 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. …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

32. 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

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

34. (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

35. CHOOZ
10-3

36. 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 = ±0.0011
→ Measurements of VCKM elements relies on UPMNS unitarity

37. 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 = ±0.0011
→ 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: