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



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



“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



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


Scheme: seesaw type IИIЯNИR

Outline






6 Summary



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



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



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


νMSM: 3 in 1 flaskИIЯNИR

Outline






6 Summary


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


“Heavy” Neutral LeptonsИIЯNИR

Outline






6 Summary



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>



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


Dark Matter neutrinoИIЯNИR

Outline






6 Summary



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)



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



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



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. . .


SummaryИIЯNИR

Outline






6 Summary


SummaryИIЯNИR

Searches at LHC

Finally. . .Higgs boson has been recognized


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)


ИIЯNИR


ИIЯNИR

Backup slides


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


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


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


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


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


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


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


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