Testing Leptogenesis

Wilfried BuchmüllerDESY, Hamburg

Symposium, University of Tokyo, May 2016

Leptogenesis

This year: 30th aniversary, opened new field of research!

Key idea: CP violating decays and scatterings of heavy Majorana neutrinosgenerate lepton asymmetry which is partially transformed into baryon asymmetry via sphaleron processes [Kuzmin, Rubakov, Shaposhnikov ’85]; observed baryon asymmetry perfectly consistent with neutrino properties!

Many versions of leptogenesis: thermal, nonthermal, resonant, soft, axion oscillations, Higgs relaxation, gravitational, ...; (historically) interesting: main activity started with about 10 years delay ...

This talk: focus on aspects most relevant to neutrino physics and testability of leptogenesis; classify models according to seesaw mass scale

Fukugita, Yanagida ’86

What is the origin of matter, i.e., the baryon-to-photon ratio

B = nBn

= (6.1± 0.1) 1010

? ? ? ?

Leptogenesis: quantum effect, requires CP violation, small Majorana neutrino masses, connection between baryon and lepton number, and an expanding universe (Sakharov’s conditions OK)

Matter in the Universe

Sphaleron

cL

τ

L

e

µ

LsLs t

b

b

ν

ν

ν

u

d

d

L

L

LL

L

GUT-scale seesaw Grand Unified Theories (GUTs) predict right-handed neutrinos:

GSM = U(1) SU(2) SU(3) SU(5) SO(10) . . .

SO(10) : 16 = (dcR, lL, qL, ucR, e

cR,

cR)

For hierarchical right-handed neutrinos and 3rd generation Yukawa couplings , light neutrino masses related to mass scale of grand unification:

RH neutrinos can have large Majorana masses , not predicted by SM gauge symmetry; electroweak symmetry breaking yields Dirac neutrino masses ; result 3 heavy and 3 light mass eigenstates (seesaw mechanism):

N ' R + cR : mN ' M ,

' L + cL : m = mD1

MmT

D

mD = hvF

M3 GUT 1015 GeV , m3 v2

M3 0.01 eV

M

O(1)

Lepton asymmetry, and subsequently baryon asymmetry is caused by CPviolation in heavy Majorana neutrino decays, magnitude determined by neutrino masses (quantum interference!):

"1 = (N1 ! H + lL)

N1 ! H† + l†L

(N1 ! H + lL) + N1 ! H† + l†L

' 3

16

M1

(hh†)11v2FIm

hmh

†11

Self-energy diagram gives “resonant enhancement” of CP asymmetry for quasi-degenerate N’s

Covi, Roulet, Vissani ’96

Rough estimate of CP asymmetry in terms of neutrino masses, assuming dominance of largest eigenvalue, phases and seesaw relation,

CP asymmetry determined by heavy neutrino mass hierarchy; mass ratioslike for quarks or charged leptons, , yield estimate . Final baryon asymmetry:

with “dilution factor” and “washout factor” (Boltzmann equations); observed value of baryon asymmetry consequence of hierarchical heavy neutrino masses and kinematical factors!

O(1)

"1 3

16

M1m3

v2 0.1

M1

M3,

M1/M3 104 . . . 105

1 105 . . . 106

d 102 f 102

B =nB nB

n= dcs"1f 109 . . . 1010

In “strong washout regime,”

baryon asymmetry rather independent of initialconditions (abundance ofheavy neutrinos & initial baryon asymmetry)

dNN1

dz= (D + S) (NN1 N eq

N1) ,

dNBL

dz= "1 D (NN1 N eq

N1)W NBL

Quantitative description via Boltzmann equations (decays “D”, scatterings “S”, washout “W”; simple for sum over lepton flavours):

10-1 100 101

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

10110 10 10

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

|NB-L|

NN1

z=M1/T

NN1

in=0 NN1

in=3/4 NN1

eq

m1 > m 103 eV

m1 =(mDm†

D)11M1

m1 (eV)

M1

(GeV

)

Detailed study of Boltzmann equations leads to bounds on light and heavy neutrino masses (and reheating temperature); in simplest approximation (sum over lepton flavours):

mi < 0.1 eV , M1 > 4 108 GeV

Preferred neutrino mass range (“strong washout regime”, independence of initial conditions):

modifications: lepton flavour effects (bounds relaxed by about one order ofmagnitude ?! ); furthermore effects from possible neutrino mass degeneracies

103 eV < mi < 0.1 eV

WB, Di Bari, Plumacher ’04

[Davidson, Nardi, Nir ’08; Blanchet, Di Bari ’12]

-dhL

+dhL

+dhL

-dhobsL

mN = 400 GeV

zc0.2 1 10 2010-9

10-8

10-7

10-6

10-5

z = mNêT

±dh

L

total, hinN=0, dhin

L=10-3I

total, hinN=0, dhin

L=0

total, hinN=heq

N , dhinL=0

N diag., hinN=heq

N , dhinL=0

N diag., analytic

L diag., hinN=heq

N , dhinL=0

N, L diag., hinN=heq

N , dhinL=0

[Dev, Millington, Pilaftsis,

Teresi ’15]

Resonant leptogenesis: strong enhancement of CP asymmetry, and baryon asymmetry, due to close degeneracy of heavy neutrino masses; flavour effects included; careful adjustment of parameters required

TeV-scale seesaw Pilaftsis et al ’03, ...

Zl

d

l−βu

q

q

N

du

W−

q

q

N

W−

'

0.2 0.4 0.6 0.8 1.0 1.2 1.410-10

10-8

10-6

10-4

10-2

MN (TeV)

|VℓN|

Br(μ→eγ)=5.7⨯10-13

10-20

10-28

LLHC=1 mm

1 m

Δmsol2 < |VℓN2MN < 0.3 eV

Direct test: heavy neutrino production at the LHC (assume additional vector bosons), with lepton-flavour violation, displaced vertices; strong constraints from out-of-equilibrium condition in leptogenesis

[Depisch, Dev, Pilaftsis ’15]

GeV-scale seesaw Canetti, Drewes & Shaposhnikov ’13

νΜ(inimal)S(tandard)M(odel) [Asaka, Blanchet, Shaposhnikov ’05]: NO’s, DM and baryon asymmetry just from SM with 3 N’s; baryon asymmetry from N-oscillations and sphaleron conversion; resonant enhancement of CP asymmetry:

thermal history:

=|M2 M3||M2 +M3|

1013

T 100 GeV : |µ↵| 1010

T 100 MeV : |µ↵| & 8 106

1 2 5 10 20 5010!14

10!12

10!10

10!8

M1 !keV"

"Αsin

2 #2ΘΑ1$

Excluded by X!ray observations%ΜΑ% & 0

%ΜΑ% & 1.24 10!4

Excludedbyphasespaceanalysis

0.2 0.5 1.0 2.0 5.0 10.010!12

10!10

10!8

10!6

M !GeV"

U2

BAU

DM

BAUBAU #constrained $MSM%

Seesaw

BBN

PS191

NuTeV

CHARM

Dark Matter (keV mass, small active-sterile mixing):

3.5 keV line welcome!!

Lower bound on masses of heavier RH neutrinos:

can be searched for at SHiP

Prediction for lightest ν-mass:

1 keV < M1 < 50 keV

= mDM1, U2 = tr(†)

1013 . sin2(2↵1) . 107

M2,3 & 2 GeV

m1 ' 0

Leptogenesis - piece of a puzzleFor GUT scale seesaw, RH neutrinos very heavy, cannot be produced in laboratory experiments (in principle direct tests possible in cosmology via gravitational waves!). Indirect tests:

• Majorana nature of neutrinos

• lepton flavour violating processes (e.g. in supersymmetric GUTs, μ -> eγ, ...)

• connection with dark matter

• properties of light neutrino masses, using relations between quark, charged lepton and neutrino mass matrices; key observables: neutrino mass differences and mixings, CP violation ν-less ββ-decay: absolute neutrino mass scale: baryon asymmetry, magnitude and sign: , |B |, sign[B ]

m0 = |P

i U2eimi| (. 0.2 eV)

mtot

=P

i mi ( . 0.5 eV)

Anarchy with U(1) flavour symmetry

Instructive example: leptogenesis by Monte Carlo; input: anarchy & U(1) flavour symmetry:

with and fixed by ; random coefficients (Gaussian measure, independent of basis); data (mixing-split cuts):

L abLaH†byR 1

2cRmRR + h.c.

y O(1) , mR M

0

@4 3 2

3 2 2 1

1

A

' 0.1 M m2l = 2.5 103 eV2

sin2223

= 1.0

sin2212

= 0.857

sin2213

= 0.095

R =m2

s

m2

l

2 Rexp

(1 0.05, 1 + 0.05)

Lu, Murayama ’14

me↵ PimiU2

v,ei

Normal hierarchy dominant, inverted hierarchy only 0.1%; ν-less ββ-decay: ; baryon asymmetry peaks at observed value! me↵ 2 4 meV

For comparison: semi-anarchy & U(1) flavour symmetry; input:

with ; 39 real parameters, random numbers O(1), uniform on logarithmic scale; data:

h() a

0

@d+1 c+1 b+1

d c b

d c b

1

A , MR

0

@2d 0 00 2c 00 0 2b

1

A ,

! m 2a

0

@2 1 1 1 1

1

A , h(e) a

0

@3 2 2 12 1

1

A

0 a 1 (tan); b c d; a+ d = 2

2.07 103 eV2 |m2

atm

| 2.75 103 eV2 ,

7.05 105 eV2 m2

sol

8.34 105 eV2 ,

0.75 sin2(212

) 0.93 ,

0.88 sin2(223

) 1

Semi-Anarchy with U(1) flavour symmetryWB, Domcke, Schmitz ’12

10!4 10!3 10!20.00

0.04

0.08

0.12

m0ΝΒΒ !eV"

relativefrequency

10!3 10!2 10!1 1000.00

0.04

0.08

0.12

!1!!max

relativefrequency

effective neutrino mass:

mean corresponds to

observed baryon asymmetry obtained for hierarchical heavy neutrinos (strong washout regime favoured)!

B 5 1010

m0 = 1.5+0.90.8 meV

Occam’s razorKaneta, Shimizu, Tanimoto, Yanagida’16

ME =

0

@me 0 00 mµ 00 0 m

1

A

LR

, mD =

0

@0 A 0A0 0 B0 B0 C

1

A

LR

,

MR =

0

@M1eiA 0 0

0 M2eiB 00 0 M3

1

A

RR

More ambitious: predict sign of baryon asymmetry! Ansatz: restrict mass matrices by “texture zeros”; light-neutrino mass matrix can be completely reconstructed from experiment, includes 2 phases which determine signof baryon asymmetry (vary parameters consistent with present data)

0

50

100

150

200

250

300

350

400

5 6 7 8 9 10 11

frequ

ency

|mee|[meV]

0

100

200

300

400

500

600

700

800

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

frequ

ency

sinφA

Results of Monte Carlo analysis (random numbers, linear scale):neutrino mass for ν-less ββ-decay: sign of baryon asymmetry: improved measurements will eventually resolve ambiguity

mee ' 7 8 meVsign[B ] = sign[sinA]

Independence of initial conditionsDi Bari, King, Fiorentin ’14

Red: demand washout of initial B+L asymmetry (“independence” of initial B+L asymmetry); NH: for 99% of scatter points !! (IH less restrictive); experimental progress: soon ?? Would exclude seesaw with 2 N’s, νMSM and Affleck-Dine leptogenesis !!

iB 107B

Pm = 90± 10 meV

m1 & 10 meV

0.00 0.15 0.30 0.45 0.60m [eV]

0.0

0.2

0.4

0.6

0.8

1.0

P/P

max

Planck+WP+BAOPlanck+WP+BAO+Lensing

Planck+WP+BAO+Lensing+SZ

mΩ0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44

ν m

Σ

0

0.2

0.4

0.6

0.8

1

1.2 Planck (TT+lowP) 0 + Hα Ly-

+ Planck (TT+lowP) α Ly-

Palanque-Delabrouille et al ’15

CMB & Lyman-alpha:

Battye & Moss ’14

CMB, BAO, lensing & galaxy counts :

thermal leptogenesis ruled out ??

mtot

< 0.12 eV

mtot

= (0.320± 0.081) eV

Towards a theory of leptogenesis Leptogenesis is “simple” nonequilibrium process: weakly coupled heavy neutrino in large SM thermal bath, close to thermal equilibrium; rigrous treatment in nonequilibrium QFT? [Bodeker et al; Garbrecht et al; Garny et al; Iso et al; Ramsey-Musolf et al; Hutig, Mendizabal, Philipsen ’13]; Schwinger-Keldysh formalism for spectral functions and statistical propagators of lepton doublets and heavy Majorana neutrino:

thermal production of heavy neutrinos (Higgs decay, production from lepton-Higgs pair, soft gauge bosons ...); resummation of soft gauge bosons; result very different from naive estimate with thermal masses!

generation of lepton asymmetry (CP violation!) starts at two loops; cut: interference of tree-level and one-loop diagrams

difficult problem: resummation of soft gauge bosons; compact analyticalexpressions obtained, numerical analysis in progress; expected result:thermal damping in the bath leads to local (in time) equation for lepton density matrix, including corrections from quantum statistics and propagator effects; systematic expansion in couplings...; it is importantto obtain rigorous prediction for baryon asymmetry with error bar!

• Thermal leptogenesis elegant and natural mechanism for explanation of baryon asymmetry, supported by small neutrino masses

• Low-scale leptogenesis (TeV or GeV seesaw scale) possible; potentially interesting signature: lepton-number violation at LHC; problem: scenarios rather fine-tuned (theoretical motivation?)

• Very important: more precise measurement of neutrino masses and mixings, CP violation, in particular 0νββ decay and absolute neutrino mass scale,

• Cosmological determination of absolute neutrino mass scale would rule out several classes of leptogenesis scenarios and support GUT-scale thermal leptogenesis

• Rigorous treatment of thermal leptogenesis in thermal QFT within reach

Conclusions & Outlook