Status of the MSM (neutrino Minimal extension of the...
Transcript of Status of the MSM (neutrino Minimal extension of the...
ИIЯNИR
Status of the νMSM(neutrino Minimal extension of the SM)
Dmitry GorbunovInstitute for Nuclear Research of RAS, Moscow
Flavour Physics ConferenceXth Rencontres du Vietnam
Quy Nhon, Vietnam
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 1 / 22
Neutrino oscillations: NP is below EW scaleИIЯNИR
Outline
1 Neutrino oscillations: NP is below EW scale
2 Scheme: seesaw type I
3 νMSM: 3 in 1 flask(neutrino oscillations, dark matter, baryon asymmetry of theUniverse)
4 “Heavy” Neutral Leptons
5 Dark Matter neutrino
6 Summary
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 2 / 22
Neutrino oscillations: NP is below EW scaleИIЯNИR
Neutrino oscillations: masses and mixing angles
)23
θ(22
sin
0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1
)4
/c2
eV
3| (1
02 32
m∆|
2
2.5
3
3.5
4 90% C.L.νT2K 3
90% C.L.νT2K 2011 2
90% C.L.νMINOS 2013 2
90% C.L.νSK zenith 2012 3
90% C.L.νSK L/E 2012 2
-110 1
-410
KamLAND
95% C.L.
99% C.L.
99.73% C.L.
best fit
Solar
95% C.L.
99% C.L.
99.73% C.L.
best fit
σ1
12θ
2tan
)2
(eV
21
2m
∆
“atmospheric” 2×2sector
1308.0465
“solar” 2×2 sector
0801.4589
)π
(C
Pδ
68% CL90% CLBest fit
rangeσPDG2012 1
>0322m∆
1
0.5
0
0.5
1
13θ22sin
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
)π
(C
Pδ
<0322m∆
1
0.5
0
0.5
1
1311.4750
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 3 / 22
Neutrino oscillations: NP is below EW scaleИIЯNИR
“Normal” and “Inverted” neutrino mass hierarchies
Only two squared mass differences are determined, there are options for masses. . .
may be, the hierarchy will be fixed by T2K & Noνae & JUNO
m
0
solar~8×10−3eV
atmospheric
~4×10−2eVatmospheric
~4×10−2eV
m1
m2
m3
m
0
m2
m1
m3
νe
νµ
ντ
solar~8×10−3eV
normal invertedhierarchy
may be Cosmology will help...Planck (2014)? . . . EUCLID (galaxy survey)
neutrinoless 2β -decay Z−> (Z + 2) + 2e− CP ??
99% CLH1 dofL
Normal: Dm232 > 0
disfavoured by 0Ν2Β
disf
avou
red
byco
smol
ogy
10-4 10-3 10-2 10-1 1
10-4
10-3
10-2
10-1
1
lightest neutrino mass in eV
Èmee
ÈineV
Inverted: Dm232 < 0
|mee|=∣∣∑U2
ei mi∣∣, for Majorana masses
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 4 / 22
Neutrino oscillations: NP is below EW scaleИIЯNИR
Sterile neutrinos: NEW ingredients
One of the optional physics beyond the SM:
sterile: new fermions uncharged under the SM gauge groupneutrino: explain observed oscillations by mixing with SM (active)
neutrinosAttractive features:
possible to achieve within renormalizable theoryonly N = 2 Majorana neutrinos neededmassive sterile neutrinos can explain via seesaw why active ones are so lightsterile neutrino (Majorana) masses violate lepton symmetryproduce baryon asymmetry via leptogenesisdark matter (with N ≥ 3 at least)1 eV sterile neutrino might be responsible for neutrino anomalies. . . ?not a dark matter (N ≥ 4 ?)
Disappointing feature:Major part of parameter space is UNTESTABLE
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 5 / 22
Scheme: seesaw type IИIЯNИR
Outline
1 Neutrino oscillations: NP is below EW scale
2 Scheme: seesaw type I
3 νMSM: 3 in 1 flask(neutrino oscillations, dark matter, baryon asymmetry of theUniverse)
4 “Heavy” Neutral Leptons
5 Dark Matter neutrino
6 Summary
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 6 / 22
Scheme: seesaw type IИIЯNИR
Sterile neutrino lagrangian
Most general renormalizable with 2(3. . . ) right-handed neutrinos NI
LN = N I i/∂NI− fαILαHNI−MNI
2N
cI NI + h.c.
Parameters to be determined from experiments
9(7): active neutrino sector
2 ∆m2ij : oscillation
experiments3 θij : oscillation experiments1 CP-phase: oscillation
experiments2(1) Majorana phases: 0νee,
0νµµ
1(0) mν : 3H→3 He + e + νe,cosmology, . . .
11: N = 2 sterile neutrinos( works if mν = 0 !!!)
2: Majorana masses MNI9: New Yukawa couplings fαI
which form2: Dirac masses MD = f 〈H〉3+1: mixing angles2+1: CP-violating phases
4 new parameters in totalhelp with leptogenesis
18: N = 3 sterile neutrinos:
3: Majorana masses MNI15: New Yukawa couplings fαI
which form3: Dirac masses MD = f 〈H〉3+3: mixing angles3+3: CP-violating phases
9 new parameters in totalboth BAU and DM are possible
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 7 / 22
Scheme: seesaw type IИIЯNИR
Sterile neutrino lagrangian
Most general renormalizable with 2(3. . . ) right-handed neutrinos NI
LN = N I i/∂NI− fαILαHNI−MNI
2N
cI NI + h.c.
Parameters to be determined from experiments
9(7): active neutrino sector
2 ∆m2ij : oscillation
experiments3 θij : oscillation experiments1 CP-phase: oscillation
experiments2(1) Majorana phases: 0νee,
0νµµ
1(0) mν : 3H→3 He + e + νe,cosmology, . . .
11: N = 2 sterile neutrinos( works if mν = 0 !!!)
2: Majorana masses MNI9: New Yukawa couplings fαI
which form2: Dirac masses MD = f 〈H〉3+1: mixing angles2+1: CP-violating phases
4 new parameters in totalhelp with leptogenesis
18: N = 3 sterile neutrinos:
3: Majorana masses MNI15: New Yukawa couplings fαI
which form3: Dirac masses MD = f 〈H〉3+3: mixing angles3+3: CP-violating phases
9 new parameters in totalboth BAU and DM are possible
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 7 / 22
Scheme: seesaw type IИIЯNИR
Sterile neutrino lagrangian
Most general renormalizable with 2(3. . . ) right-handed neutrinos NI
LN = N I i/∂NI− fαILαHNI−MNI
2N
cI NI + h.c.
Parameters to be determined from experiments
9(7): active neutrino sector
2 ∆m2ij : oscillation
experiments3 θij : oscillation experiments1 CP-phase: oscillation
experiments2(1) Majorana phases: 0νee,
0νµµ
1(0) mν : 3H→3 He + e + νe,cosmology, . . .
11: N = 2 sterile neutrinos( works if mν = 0 !!!)
2: Majorana masses MNI9: New Yukawa couplings fαI
which form2: Dirac masses MD = f 〈H〉3+1: mixing angles2+1: CP-violating phases
4 new parameters in totalhelp with leptogenesis
18: N = 3 sterile neutrinos:
3: Majorana masses MNI15: New Yukawa couplings fαI
which form3: Dirac masses MD = f 〈H〉3+3: mixing angles3+3: CP-violating phases
9 new parameters in totalboth BAU and DM are possible
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 7 / 22
Scheme: seesaw type IИIЯNИR
Left
Left
Right
Left
Right
Left
Left
Right
Left
Left
Right
Left
Right
Left
Right
Left
Right
Left
Right
Left
Rightu
up
2.4 MeV
⅔ ccharm
1.27 GeV
⅔ ttop
171.2 GeV
⅔
ddown
4.8 MeV
-⅓ sstrange
104 MeV
-⅓ bbottom
4.2 GeV
-⅓
νeelectronneutrino
0 νμmuon
neutrino
0 ντtau
neutrino
0
eelectron
0.511 MeV
-1 μmuon
105.7 MeV
-1 τtau
1.777 GeV
-1
ggluon
0
0
γphoton
0
0
Z091.2 GeV
0
weakforce
W±
80.4 GeV
± 1
weakforce
mass→
charge→
Qua
rks
Lept
onsThree Generations
of Matter (Fermions) spin ½
Bos
ons
(For
ces)
spi
n 1
I II III
name→
H>114 GeV
0
0Higgsboson
spin 0
<0.0001 eV ~0.01 eV ~0.04 eV
N~10 keV
1 N~GeV
2 N~GeV
3sterileneutrino
sterileneutrino
sterileneutrino
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 8 / 22
Scheme: seesaw type IИIЯNИR
Seesaw type I mechanism: MN mactive
LN = N I i/∂NI − fαILα HNI −MNI
2N
cI NI + h.c.
where I = 1,2,3 and α = e,µ,τ Ha = εabH∗b
When Higgs gains 〈H〉= v/√
2 we get in neutrino sector
LN →12
(να ,N
cI
) 0 v f√2
v f T√
2MN
(νcα ,NI
)T+ h.c.
Then for off-diag diag ( MD = v f√2MN ) we find the eigenvalues:
' MN and Mν =−MD1
MNMT
D ∝
(off-diag
diag
)2MN ≪ MN
Mixings: flavor state να = Uα i νi + θαINI
active-active mixing: (PMNS-matrix U) UT Mν U = diag (m1 ,m2 ,m3)
active-sterile mixing: θαI =MDαI
MI∝ f
vMN 1
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 9 / 22
νMSM: 3 in 1 flaskИIЯNИR
Outline
1 Neutrino oscillations: NP is below EW scale
2 Scheme: seesaw type I
3 νMSM: 3 in 1 flask(neutrino oscillations, dark matter, baryon asymmetry of theUniverse)
4 “Heavy” Neutral Leptons
5 Dark Matter neutrino
6 Summary
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 10 / 22
νMSM: 3 in 1 flaskИIЯNИR
Sterile neutrino mass scale: Mν =−v2f T M−1N f
Is not fixed: lighter sterile neutrinos with smaller YukawasWith fine tuning in MN and f we can get f ∼ 1, hierarchy in sterile neutrino masses, etc
10−13 10−7 0.1 105 1011 101710−17
10−13
10−9
10−5
0.1
1000
107
0.05 eV 1 TeV 1016
GeV
LHCLSND GUT see−sawν MSM
Majorana mass, GeV
Yu
kaw
a co
up
lin
g
neutrino masses
are too large
neutrino masses are too small
strong coupling
T.Asaka, M.Shaposhnikov(2005)νMSM implies
2 “heavy” neutralleptons of 0.1-50 GeV– responsible forseesaw– responsible forleptogenesis (must bedegenerate∆M ∼ 100 keV)
1 “light” sterileneutrinos of 2-50 keV– form dark matter
BSM is below EW scale:– no gauge hierarchy– available for direct tests
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 11 / 22
“Heavy” Neutral LeptonsИIЯNИR
Outline
1 Neutrino oscillations: NP is below EW scale
2 Scheme: seesaw type I
3 νMSM: 3 in 1 flask(neutrino oscillations, dark matter, baryon asymmetry of theUniverse)
4 “Heavy” Neutral Leptons
5 Dark Matter neutrino
6 Summary
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 12 / 22
“Heavy” Neutral LeptonsИIЯNИR
Production and decays (if MN < 5 GeV)
µ
νµN
2,3
π
sµ
νµ
D
N2,3
D
<H>
<H>
N2,3
µ
π
νµ
N2,3
e
µνµ
νe
<H>
<H>
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 13 / 22
“Heavy” Neutral LeptonsИIЯNИR
Probing leptogenesis SHiP upgrading to Aerocarrier
For 1020 PoT at 400 GeV (SPS) detectors have tocover l|| ∼ 3 km D.G., M.Shaposhnikov (2012)
to explore the entire region
target
beam
detector
hadrons
l target
l
l
PTPT
L
N
µ
π
D.G, M.Shaposhnikov (2007)
lower bound at ×10−4
Br(D→ lN) . 2×10−8
Br(Ds → lN). 3×10−7
Br(D→ KlN). 2×10−7
Br(Ds → η lN) . 5×10−8
Br(D→ K ∗lN) . 7×10−8
Br(B→ DlN) . 7×10−8
Br(B→ D∗lN). 4×10−7
Br(Bs → D∗s lN). 3×10−7
0.3 0.5 0.7 1 1.5 2
0.00001
0.0001
0.001
0.01
0.1
1
BBNSee-saw
PS191
CHARM,BEBC,
NuTeVBAU
M2
τ , s
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 14 / 22
“Heavy” Neutral LeptonsИIЯNИR
Probing leptogenesis SHiP upgrading to Aerocarrier
For 1020 PoT at 400 GeV (SPS) detectors have tocover l|| ∼ 3 km D.G., M.Shaposhnikov (2012)
to explore the entire region
target
beam
detector
hadrons
l target
l
l
PTPT
L
N
µ
π
D.G, M.Shaposhnikov (2007)
lower bound at ×10−4
Br(D→ lN) . 2×10−8
Br(Ds → lN). 3×10−7
Br(D→ KlN). 2×10−7
Br(Ds → η lN) . 5×10−8
Br(D→ K ∗lN) . 7×10−8
Br(B→ DlN) . 7×10−8
Br(B→ D∗lN). 4×10−7
Br(Bs → D∗s lN). 3×10−7
0.3 0.5 0.7 1 1.5 2
0.00001
0.0001
0.001
0.01
0.1
1
BBNSee-saw
PS191
CHARM,BEBC,
NuTeVBAU
M2
τ , s
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 14 / 22
Dark Matter neutrinoИIЯNИR
Outline
1 Neutrino oscillations: NP is below EW scale
2 Scheme: seesaw type I
3 νMSM: 3 in 1 flask(neutrino oscillations, dark matter, baryon asymmetry of theUniverse)
4 “Heavy” Neutral Leptons
5 Dark Matter neutrino
6 Summary
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 15 / 22
Dark Matter neutrinoИIЯNИR
SubEW sterile neutrinos: MN ' 1 keV-50 GeV νMSMT.Asaka, S.Blanchet, M.Shaposhnikov (2005)
At T > 100 GeV active-sterile neutrino oscillations produce lepton asymmetry in the earlyUniverse, if ∆MN MN −→ baryogenesis E.Akhmedov, V.Rubakov, A.Smirnov (1998)
Lightest sterile neutrino may comprise Dark MatterI production in primordial plasma due to mixing with active neutrinos is ruled out from
searches at X-ray telescopes
sin
2(2
θ 1)
M1 [keV]
10-15
10-14
10-13
10-12
10-11
10-10
10-9
10-8
10-7
10-6
5 50 1 10
ΩN1 < ΩDM
Ph
as
e-s
pa
ce
de
ns
ity
co
ns
tra
ints
X-ray constraints
ΩN1 > ΩDM
L6=25L6=70
NRP
L6max
=700BBN limit: L6
BBN = 2500
ΓN→νγ ' 5.5×10−22θ
21
(M1
1 keV
)5s−1
a narrow line (δEγ/Eγ ∼ v ∼ 10−3)
at Eγ = MN/2
I Possible for 1-50 keV (WDM-CDM range) either with fine-tuning in MNI
(∆MN ∼ 10−7 eV) to get L B and use the resonant productionor with ANOTHER source of production, e.g. inflaton decays..
M.Shaposhnikov, I.Tkachev (2006), F.Bezrukov, D.G. (2009)
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 16 / 22
Dark Matter neutrinoИIЯNИR
νMSM parameter space with resonant DM
Not an easy task (coherence, plasma, expansion, etc. . . )concentrating in a particular region of parameter spacepeople calculated what happens and foundwhere inside that region BAU & Dark Mattercan be both explained for sure
0.2 0.5 1.0 2.0 5.0 10.010-12
10-10
10-8
10-6
M @GeVD
U2
BAU
DM
BAUBAU Hconstrained îMSML
Seesaw
BBN
PS191
NuTeV
CHARM
0.2 0.5 1.0 2.0 5.0 10.010-12
10-10
10-8
10-6
M @GeVD
U2
BAU
DM
BAUBAU Hconstrained îMSML
Seesaw
BBN
PS191
NuTeV
CHARM
L.Canetti, M.Drewes, M.Shaposhnikov 1208.4607
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 17 / 22
Dark Matter neutrinoИIЯNИR
Inflation and νMSM: dark matter production ?
X+3HX + V ′ (X ) = 0
Xe > MPl
scale-invariant scalar perturbations fromexponentially stretched quantumfluctuations of X
δρ/ρ ∼ 10−5 requiresV = βX 4 : β ∼ 10−13 X
Chaotic inflation, A.Linde (1983)
DM production (inflaton gives mass)from inflaton decays in plasma at T ∼mχ M.Shaposhnikov, I.Tkachev (2006)
MNI NcI NI ↔ fIXNINI
Can be “naturally” Warm (250MeV < mχ < 1.8GeV) F.Bezrukov, D.G. (2009)
M1 . 15×(
mχ
300 MeV
)keV
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 18 / 22
Dark Matter neutrinoИIЯNИR
Higgs Inflation and νMSM: dark matter ?
If λ (∼MPl) > 0 & if non-minimally coupled to gravity H†HR the SMHiggs field may serve as the inflaton
F.Bezrukov, M.Shaposhnikov (2007)
Then DM sterile neutrino may be produced via dim-5 operator
L =β
ΛH†HNcN + h.c.
where Λ is either MPl or Λ = Λ(h)
and no need for DM sterile-active neutrino (?) mixing. . .
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 19 / 22
SummaryИIЯNИR
Outline
1 Neutrino oscillations: NP is below EW scale
2 Scheme: seesaw type I
3 νMSM: 3 in 1 flask(neutrino oscillations, dark matter, baryon asymmetry of theUniverse)
4 “Heavy” Neutral Leptons
5 Dark Matter neutrino
6 Summary
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 20 / 22
SummaryИIЯNИR
Searches at LHC
Finally. . .Higgs boson has been recognized
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 21 / 22
SummaryИIЯNИR
Searches at LHC
Finally. . .Higgs boson has been recognized
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 21 / 22
SummaryИIЯNИR
Summary: intensity frontier
We definitely need New Physics
There are arguments in favour of NP below EW scale. . .
True Extension of the Standard Model should at least
I Reproduce the correct neutrino oscillationsI Contain the viable DM candidateI Be capable of explaining the baryon asymmetry of the UniverseI Have the inflationary mechanism operating at early times
νMSM can do it
and be directly tested right now (GeV mass scale) or later (for 10-100 GeVmasses)
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 22 / 22
ИIЯNИR
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 23 / 22
ИIЯNИR
Backup slides
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 24 / 22
ИIЯNИR
Leptogenesis in 2+1 scheme: 0ν2β decay region|m
eff | [
10
-2eV
]
MN [MeV]
1
2
3
4
5
200 250 300 350 400
Inverse hierarchy 1308.3550
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 25 / 22
ИIЯNИR
Present limits 0901.3589: 1) 0νββ -bound is stronger by 10, 1205.3867 2) limits from LHCb and CMS
10-8
10-7
10-6
10-5
10-4
10-3
10-2
m4 (GeV)
10-6
10-5
10-4
10-3
10-2
10-1
100
|Ve4
|2
0νββπ --> e ν
Borexino
Bugey
Fermi2
20F
35S
63Ni
187Re
3H
0.1 1 10 100m
4 (GeV)
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
|Vµ4
|2
L3
NA3
PS 191
NuTeV
BEBC
CHARM II
FMMF
K --> µ ν
DELPHI
0.01 0.1 1 10 100m
4 (GeV)
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
|Ve4
|2
π --> e ν
L3
DELPHI
PS 191
NA3
CHARM
K --> e ν
0νββ
0.01 0.1 1 10 100m
4 (GeV)
10-5
10-4
10-3
10-2
10-1
100
|Vτ4
|2
DELPHIBased on CHARM
NOMAD
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 26 / 22
ИIЯNИR
RG evolution of the SM couplings 1305.7055
yt
Λ
gY
g2
g3
mB2
I1
ΒΛ
0 5 10 150.0
0.5
1.0
1.5
log10
Μ
GeVDmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 27 / 22
ИIЯNИR
How “natural” the 126 GeV. . .
107 108
109
1010
1011
1012
1013
1014
1016
120 122 124 126 128 130 132168
170
172
174
176
178
180
Higgs pole mass Mh in GeV
Top
pole
mas
sM
tin
GeV
1017
1018
1019
1,2,3 Σ
Instability
Stability
Meta-stability
6 8 10
0 50 100 150 200
0
50
100
150
200
Higgs pole mass Mh in GeV
Top
pole
mas
sM
tin
GeV
LI =104GeV5
67
8910
1214
1619
Instability
Non
-pertu
rbativ
ity
Stability
Meta-sta
bility
1307.7879
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 28 / 22
ИIЯNИR
Active neutrino masses without new fields
Dimension-5 operator ∆L = 2
L (5) =Fαβ
4ΛLαHH†Lc
β+ h.c.
Lα are SM leptonic doublets, α = 1,2,3, Ha = εabH∗b , a,b = 1,2; in a unitary gauge
HT =(
0,(v + h)/√
2)
and
L(5)
νν =v2 Fαβ
4Λ× 1
2ναν
cβ
+ h.c. = mαβ ×12
νανcβ
+ h.c.
where
Λ is the scale of new dynamics only their ratio is fixed
Fαβ is the strength of new dynamics by the scale of active neutrino masses
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 29 / 22
ИIЯNИR
νMSM: Heavy neutral lepton lifetime (1208.4607)
0.2 0.5 1.0 2.0 5.010-8
10-6
10-4
0.01
1
M @GeVD
Τ@sD BAU N
BAU I
Seesaw NHSeesaw I
BBN
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 30 / 22
ИIЯNИR
νMSM: Heavy neutral lepton mixing (1208.4607)
0.2 0.5 1.0 2.0 5.0 10.010-12
10-10
10-8
10-6
M @GeVD
U2
BAU
BAU
Seesaw
BBN
PS191
NuTeV
CHARM
0.2 0.5 1.0 2.0 5.0 10.010-12
10-10
10-8
10-6
M @GeVD
U2
BAU
BAU
Seesaw
BBN
PS191
NuTeV
CHARM
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 31 / 22
ИIЯNИR
We get dim-5 operator at small momentum transfer
LN = N I i/∂NI − fαILα HNI −MNI
2N
cI NI + h.c.
lβ lα
hh
h
lβh
lα
NI NI
fIα f ∗Iβ
fIα
f ∗Iβ
at |Q2N | M2
N we arrive at effective interaction (dim-5 operator)
=⇒ L (5) =Fαβ
4ΛLα HH†Lc
β+ h.c. where
FΛ
= f T M−1N f
Dmitry Gorbunov (INR) Status of the νMSM 01.08.2014, ICISE 32 / 22