Minimal Flavour Seesaw
Belén Gavela
Universidad Autónoma de Madrid and IFT
T. Hambye, D. Hernández, P. Hernández, MBG
Beyond-doubt evidence of ν masses …
MINOS 2007
KamLAND 2008
New physical states in the SM
Violation of global symmetries: Le, Lµ, Lτ
P. Hernandez Neutrino08
What are the main physics goals
in ν physics?
• To determine the absolute scale of masses
•
To determine whether they are Majorana
* To discover Leptonic CP-violation
The art of the possible:
We should at least measure the 3 active ν mass matrix
Masses
m12 < m22,
m32
Angles
θ12,θ23,θ13
CP-phases
δ, α, β
Absolute mass scale
(Karlsruhe Katrin web page)
Majorananess and ν mass scale
0νββ decay
β decay and cosmology
mββ(eV)
Next era
Next-to-next
Next era
Next-to-next
Fogli et al
Cosmo
Σ(eV)
Cosmo
eiα
eiβ
U=
1
θ13 = 0 is the key to CP violation
Entering the era of precision
neutrino oscillation physics
~ % level
νµ<−−−>νe golden channel…
θ13 future sensitivities
Example with
fixed atmosph.
parameters
( Albrow et al. 06)
Race for the CP phase δ…
ISS report
06
Work of many people …
Plenty of possibilities to reach the sin2 2θ13~10-4 realm …
What are the main physics goals
in ν physics?
• To determine the absolute scale of masses
•
To determine whether they are Majorana
* To discover Leptonic CP-violation
What is the relation of the these putative discoveries to
the matter-antimatter asymmetry of the universe?
Can leptogenesis be “proved”?
The short, and rather accurate answer
NO
Nevertheless, a positive discovery of both
2 last points
would constitute a very compelling argument
in favour of leptogenesis
What are the main physics goals
in ν physics?
• To determine the absolute scale of masses
(Tritium…., cosmo?)
•
To determine whether they are Dirac Majorana
(neutrinoless ββ decay,degenerate or inverse hierarchy)
• To discover Leptonic CP-violation
(in νµ-νe oscillations at superbeams, betabeams….
neutrino factory)
Go for those discoveries!
Neutrino masses indicate new
physics beyond the SM
Maybe new physics could appear
also in neutrino couplings ?
Neutrino masses indicate new
physics beyond the SM
?
Maybe new physics could appear
also in neutrino couplings ?
New physics scale M > v
L= LSM + cd=5 Od=5 + cd=6 Od=6 +……
Μ
M2
ν masses beyond the SM
The Weinberg operator
Dimension 5 operator:
2
λ/M (L L H H) → λv/M (νν)
d=5
O
ν masses beyond the SM
The Weinberg operator
Dimension 5 operator:
2
λ/M (L L H H) → λv/M (νν)
d=5
O
It’s unique → very special role of ν masses:
lowest-order effect of higher energy physics
ν masses beyond the SM
The Weinberg operator
Dimension 5 operator:
2
λ/M (L L H H) → λv/M (νν)
d=5
O
It’s unique → very special role of ν masses:
lowest-order effect of higher energy physics
This mass term violates lepton number (B-L)
→ Majorana neutrinos
ν masses beyond the SM
The Weinberg operator
Dimension 5 operator:
2
λ/M (L L H H) → λv/M (νν)
d=5
O
It’s unique → very special role of ν masses:
lowest-order effect of higher energy physics
This mass term violates lepton number (B-L)
→ Majorana neutrinos
d=5
O
is common to all models of Majorana
νs
ν masses beyond the SM : tree level
2x2=1+3
δL= c d=5 Od=5
3 generic types (Ma)
The Seesaw models
Ν
Δ
Σ
The Seesaw models
Y
Ν
Y
µ
Δ
Y
Y
Σ
Y
The Seesaw models
Y
µ
Ν
Δ
Y
Y
mν~ v2 YNT_1_ YΝ
MN
mν~
v2
YΔ _µ_
MΔ2
Y
Σ
Y
mν~ v2 YΣT _1_YΣ
MΣ
The Seesaw models
Y
Ν
Y
µ
Δ
Y
Y
Σ
Y
Heavy fermion singlet NR Heavy scalar triplet Δ Heavy fermion triplet ΣR
Minkowski, Gell-Mann, Ramond,
Slansky, Yanagida, Glashow,
Mohapatra, Senjanovic
Magg, Wetterich, Lazarides,
Shafi, Mohapatra,
Senjanovic, Schecter, Valle
Ma, Roy, Senjanovic, Hambye et al., …
Those fields, NR , Δ, ΣR, would mediate other
processes too….
Which are the new exotic couplings,
that is, d=6 operators, in Seesaws?
(type I)
(type III)
(type II)
(Abada, Biggio, Bonnet, Hambye, M.B.G.)
(type I)
(type III)
(type II)
Cd=6~
+
Y Y
2
M
Exotic lepton
couplings
For all scalar and fermionic
Seesaw models, present bounds:
or stronger
Observable effects?
Obviously requires scale near the TeV
M~1 TeV is suggested by electroweak hierarchy problem
N
H
L
(Vissani, Casas et al., Schmaltz)
Δ
H
Σ
H
L
(Abada, Biggio, Bonnet, Hambye, M.B.G.)
Could d=6 be stronger than d=5 ?
* Loop suppression of d=5 and not d=6
Zee, Babu
De Gouvea
* Two independent scales in d=5, d=6 from a symmetry
principle: lepton number
Cirigliano et al; Kersten,Smirnov; Abada et al
Λ5~ΛLN >> Λ6 ~ ΛLFV ~ TeV
ΛLN >> ΛLF
~
~TeV
?
fl
flavour
Cirigliano, et al
There is a sensible physics motivation:
Origin of lepton/quark flavour violation linked/close to the
EW scale
Lepton number breaking scale higher and responsible
for the gap between ν and other fermions
Seesaw mechanism
vs
Minimal Flavour Violation
T. Hambye, D. Hernández, P. Hernández, MBG
Minimal Flavour Violation
The global Flavour symmetry of the SM:
without Yukawas
Minimal Flavour Violation
The global Flavour symmetry of the SM:
Minimal Flavour Violation
The global Flavour symmetry of the SM:
Minimal Flavour Violation
The global Flavour symmetry of the SM:
Quark sector
L= LSM + cd=6 Od=6 +……
Λfl2
(D’Ambrosio, Cirigliano, Isidori, Grinstein, Wise….Buras….)
Minimal Flavour Violation
The global Flavour symmetry of the SM:
Quark sector
L= LSM + cd=6 Od=6 +……
Λfl2
(D’Ambrosio, Cirigliano, Isidori, Grinstein, Wise….Buras….)
Predictivity
Minimal Flavour Violation
The global Flavour symmetry of the SM:
Quark sector
L= LSM + cd=6 Od=6 +……
2
Λ
fl
+
Yαβ Yγδ
~
Od=6 ~ Qα Qβ Qγ Qδ
(D’Ambrosio, Cirigliano, Isidori, Grinstein, Wise….Buras….)
i.e.
Cd=6
M2
A rationale for the MFV ansatz?
Not really, although:
• Flavour data (i.e. B physics) consistent with all flavour
physics coming from Yukawa
• Inspired in “condensate” flavour physics a la Nielsen
(Yukawas ~ <ΨΨ>n/Λfl), rather than in susy-like options
•It makes you think on the relation between scales:
electroweak vs. flavour vs lepton number scales
Minimal Flavour Violation
The global Flavour symmetry of the SM:
L= LSM + cd=6 Od=6 +……
Λfl2
D’ambrosio et al., Cirigliano, Isidori, Grinstein, Wise….Buras….)
What happens in the presence of neutrino masses?
Cirigliano, Isidori, Grinstein, Wise
L=
+
LSM
Requirements for a model of MFV with mν
Cirigliano, Isidori, Grinstein, Wise
An unsuccessful model: simplest type I
N
mν
Hambye, Hernandez2, Gavela
A successful model: Scalar-triplet Seesaw
(type II)
Δ
MΔ 2
L
L
A successful model: Scalar-triplet Seesaw
(type II)
µΔ
Δ
YΔ
MΔ 2
L
L
A successful model: Scalar-triplet Seesaw
(type II)
L
µΔ
Δ
Δ
YΔ
YΔ
MΔ 2
L
YΔ L
L
A successful model: Scalar-triplet Seesaw
(type II)
L
µΔ
Δ
Δ
YΔ
YΔ
Λfl = MΔ
ΛLN = MΔ2 / µΔ
MΔ 2
L
YΔ L
L
L
L
mν∼
* Neutrino masses OK
* Measurable flavour OK
* Predictivity OK
Successful fermionic-mediated Seesaws:
One more mediator, one more scale…. i.e. Inverse seesaws
0
Instead of
Lm =
YN v
YN T v
ΜΝ
Successful fermionic-mediated Seesaws:
One more mediator, one more scale…. i.e. Inverse seesaws
0
0
0
0
Successful fermionic-mediated Seesaws:
One more mediator, one more scale…. i.e. Inverse seesaws
0
0
0
0
Lepton number conserved
U(1)
Λfl = Λ
ΛLN = ∞
Successful fermionic-mediated Seesaws:
One more mediator, one more scale…. i.e. Inverse seesaws
0
0
0
Lepton number violated
Successful fermionic-mediated Seesaws:
One more mediator, one more scale…. i.e. Inverse seesaws
0
0
0
Lepton number violated
mν~
v2
T
YN _µ_ YΝ
Λ2
Λfl = Λ
ΛLN = Λ2 / µ
Successful fermionic-mediated Seesaw:
One more mediator, one more scale…. i.e. Inverse seesaws
Lepton number violated
by any of those 3 entries
Successful fermionic-mediated Seesaw:
One more mediator, one more scale…. i.e. Inverse seesaws
0
0
Lepton number violated
Analyze first:
-- one massless neutrino
-- just one low-energy Majorana phase
Analyze first:
Normal hierarchy:
Inverted hierarchy:
α
α
For the general case with all entries:
N
N
N
N
Summarizing:
A Seesaw with only 2 heavy right-handed neutrinos N, N’
(or 2 fermion-triplets)
obeys automatically Minimal Flavour Violation:
* Neutrino masses OK
* Measurable flavour maybe OK
* Predictivity OK
… and is the simplest viable model of neutrino masses
Conclusions
•Simple seesaw models with at least two separate scales are
realizations of the MFV hypothesis. Ex: Scalar (type II); Inverse
Flavour effects predicted in terms of
ν masses and mixings
•The SM+ only two heavy neutrinos is a minimal model of mν,
which automatically respects MFV:
:
* Separation of flavour and lepton number scales
* Yukawas determined from mν up to an overall factor.
* Only 3 parameters to be yet determined: a CP phase δ,
a Majorana phase and θ1
One light neutrino massless and many predictions
Scalar triplet seesaw
Bounds on cd=6
Scalar triplet seesaw
Combined bounds on cd=6
ΜΔ ∼ TeV: direct searches at LHC ?
See-saw II:Pair-production of charged triplet scalars
pp-> Δ++ Δ-- -> l+l+l-lFlavour structure one-to-one to mν ! BR(Δ++ -> lα+lβ+ ) ~ |Mαβ|2
Han et al;Garayoa, Schwetz; Kadastik,et al ; Akeroyd, et al; Fileviez et al
For the Singlet-fermion Seesaws:
(NN+-1)αβ=
Y’s <
- 1
(Antusch et al. 06)
for MN ~ 1 TeV possible
Stronger bounds for the triplet-fermion seesaws
* Recently: Goswami+ Ota; Altarelli+Meloni, Tang+Winter at nufact, Antusch et al.
What are non-standard
neutrino interactions (NSI)?
Four-fermion interactions that do not preserve flavour, i.e.