Neutrinos in Astrophysics and Cosmology - INFN Sezione di Ferrara

Fermion Mass Spectrum 

IDAPP 2d Meeting, 12-13 12 13 May 2006, 2006, 

University of Ferrara, Italy 

Neutrinos in 

Astrophysics and Cosmology 

Georg G. Raffelt 

Max-Planck 

Max Planck-Institut Institut für f r Physik, München, M nchen, Germany 

Georg Raffelt, Max-Planck-Institut für Physik, München, Germany IDAPP 2d Meeting, 12-13 May 2006, Ferrara, Italy

Where do Neutrinos Appear in Nature? 

Nuclear Reactors 

Sun 

 

 

 

Particle Accelerators 

Earth Atmosphere 

(Cosmic Rays) 

Earth Crust 

(Natural 

Radioactivity) 

Supernovae 

(Stellar Collapse) 

SN 1987A 

Astrophysical 

Accelerators Soon ? 

Cosmic Big Bang 

(Today 330 ν/cm /cm3 ) 

Indirect Evidence 


⎛ 

ν 

⎜ 

⎜ 

ν 

⎜ 

⎝ 

ν 

3 

2 

1 

e 

µ 

τ 

⎞ 

⎛ 

1 

⎟ 

⎜ 

⎟ 

= 

⎜ 

⎟ 

⎜ 

⎠ 

⎝ 

C 

− 

S 

23 

Three-Flavor Three Flavor Neutrino Parameters 

Atmospheric/K2K/Minos 

37 

o 

37 

o 

< 

θ 

o 

θ 54 

o 

23 < 

54 

23 

S 

C 

23 

23 

⎞ 

⎛ 

C 

13 

⎟ 

⎜ 

13 

⎜ 

⎟ 

⎜ 

⎟ 

⎜ 

⎠ 

⎝ 

− 

δ 

S 

i 

e δ 

− i 

e 

13 

1 

e 

−iδ 

S 

δ −i 

e 

C 

⎞ 

⎛ 

C 

⎟ 

⎜ 

⎟ 

⎜ 

− 

S 

⎟ 

⎜ 

⎠ 

⎝ 

⎞ 

⎛ 

ν 

⎟ 

⎜ 

⎟ 

⎜ 

ν 

1 

⎟ 

⎜ 

⎠ 

⎝ 

ν 

Georg Raffelt, Max-Planck-Institut für Physik, München, Germany IDAPP 2d Meeting, 12-13 May 2006, Ferrara, Italy 

13 

13 

= cos 

θ 

etc 

., 

δ CP-violating CP violating phase 

C 12 

12 

Normal 

µ τ 

Atmosphere 

e µ τ 

Sun 

e µ τ 

2 

1 

3 

Inverted 

e µ τ 

Sun 

e µ τ 

Atmosphere 

µ τ 

CHOOZ Solar/KamLAND 2σ ranges 

θ 

o 

θ 11 

o 

hep 

13 < 

11 30 

o 

36 

o 

12 < θ < 30 

o 

36 

o 

12 < θ < 

12 

12 

S 

C 

12 

12 

1 

2 

3 

⎞ 

⎟ 

⎟ 

⎟ 

⎠ 

hep-ph/0405172 

ph/0405172 

Solar 

75−92 75 92 

Atmospheric 

1400−3000 1400 3000 

∆ 

m 

2 

m 

2 

meV 

2 

meV 

2 

Tasks and Open Questions 

• Precision for θ12 12 and θ23 23 

• How large is θ13 13 ? 

• CP-violating CP violating phase δ? 

• Mass ordering ? 

(normal vs inverted) 

• Absolute masses? masses 

(hierarchical vs degenerate) 

• Dirac or Majorana? 

Majorana

Sanduleak −69 69 202 

Tarantula Nebula 

Supernova 1987A 

Large Magellanic Cloud 

Distance 50 kpc 

(160.000 light years) 

23 February 1987 



Stellar Collapse and Supernova Explosion 

Main-sequence Main Onion sequence structure 

star 

Degenerate iron core: 

ρ ≈ 10 9 g cm −3 

T ≈ 10 10 K 

MFe Fe ≈ 1.5 M sun 

RFe Fe ≈ 8000 km 

Hydrogen Burning 

Collapse Helium-burning Helium burning (implosion) 

star 

Helium 

Burning 

Hydrogen 

Burning 



Newborn Neutron Star 

~ 50 km 

Neutrino 

Cooling 

Proto-Neutron Proto Neutron Star 

ρ ≈ ρnuc nuc = 3 × 10 14 g cm −3 

T ≈ 30 MeV 

Collapse Explosion 

(implosion) 



Newborn Neutron Star 

~ 50 km 


Cooling 

Proto-Neutron Proto Neutron Star 

ρ ≈ ρnuc nuc = 3 × 10 14 g cm −3 

T ≈ 30 MeV 

Gravitational binding energy 

Eb ≈ 3 × 10 

10 53 erg 

erg ≈ 17% M SUN 

SUN c 2 

This shows up as 

99% Neutrinos 

1% Kinetic energy of explosion 

(1% of this into cosmic rays) 

0.01% Photons, outshine host galaxy 

Neutrino luminosity 

Lν ≈ 3 × 10 53 erg / 3 sec 

≈ 3 × 10 19 

19 LSUN SUN 

While it lasts, outshines the entire 

visible universe 


Neutrino Signal of Supernova 1987A 

Kamiokande (Japan) 

Water Cherenkov detector 

Clock uncertainty ±1 1 min 

Irvine-Michigan 

Irvine Michigan-Brookhaven Brookhaven (US) 

Water Cherenkov detector 

Clock uncertainty ±50 50 ms 

Baksan Scintillator Telescope 

(Soviet Union) 

Clock uncertainty +2/-54 +2/ 54 s 

Within clock uncertainties, 

signals are contemporaneous 



diffusion 

The Energy-Loss Energy Loss Argument 


sphere 

Volume emission 

of novel particles 

Emission of very weakly interacting 

particles would “steal steal” energy from the 

neutrino burst and shorten it. 

(Early neutrino burst powered by accretion, 

not sensitive to volume energy loss.) 

Late-time Late time signal most sensitive observable 

SN 1987A neutrino signal 


Large Detectors for Supernova Neutrinos 

SNO (800) 

MiniBooNE (190) 

LVD (400) 

Borexino Borexino 

(80) 

(80) 

Amanda/IceCube 

Amanda/ IceCube 

Super-Kamiokande 

Super Kamiokande (10 4 ) 

Kamland (330) 

In brackets events 

for a “fiducial fiducial SN” SN 

at distance 10 kpc 


Simulated Supernova Signal at Super-Kamiokande 

Super Kamiokande 

Accretion 

Phase 

Kelvin-Helmholtz 

Kelvin Helmholtz 

Cooling Phase 

Simulation for Super-Kamiokande 

Super Kamiokande SN signal at 10 kpc, kpc 

based on a numerical Livermore model 

[Totani Totani, , Sato, Dalhed & Wilson, ApJ 496 (1998) 216] 


The Future: A Megatonne Detector? 

Megatonne detector motivated by 

• Long baseline neutrino oscillations 

• Proton decay 

• Atmospheric neutrinos 

• Solar neutrinos 

• Supernova neutrinos 

(~10 5 events for SN at 10 kpc) kpc 

Similar discussions in 

• US (UNO project) 

• Europe (MEMPHYS project) 


Southpole Ice-Cherenkov 

Ice Cherenkov Neutrino Detectors 

AMANDA II (0.1 km 3 , 800 PMTs) PMTs Future IceCube (1 km 3 , 4800 PMTs) 

PMTs 


IceCube as a Supernova Neutrino Detector 

Each optical module (OM) picks up 

Cherenkov light from its neighborhood. 

SN appears as “correlated correlated noise”. noise 

~ 300 

Cherenkov 

photons 

per OM 

from a SN 

at 10 kpc 

Noise 

per OM 

< 500 Hz 

IceCube SN signal at 10 kpc, kpc, 

based 

on a numerical Livermore model 

[Dighe Dighe, , Keil & Raffelt, Raffelt, 

hep-ph/0303210] 

hep ph/0303210] 


Neutrino Fluxes and Spectra from Numerical Simulations 

Livermore (traditional) 

[ApJ ApJ 496 (1998) 216] 

ννx 

x 

ννe 

e 

ννe 

e 

Garching (new microphyiscs) 

microphyiscs 

[astro-ph/0303226] 

[astro ph/0303226] 


ννx 

x 

ννe 

e 

ννe 

e

Level-Crossing Level Crossing Diagram in a SN Envelope 

Normal mass hierarchy Inverted mass hierarchy 

Dighe & Smirnov, Identifying the neutrino mass spectrum from a supernova supernova 

neutrino burst, astro-ph/9907423 

astro ph/9907423 


Oscillation of Supernova Anti-Neutrinos 

Anti Neutrinos 

Measured ννe 

e spectrum at a detector like 

Super-Kamiokande 


If 13-mixing 13 mixing angle is known to be 

“large large”, , e.g. from Double Chooz, Chooz 

observed “wiggles wiggles” in energy 

spectrum signify normal mass 

ordering 

Assumed flux parameters 

Flux ratio ν e 

: 

ν 

µ 

= 

0 

. 

8 

: 

1 

E ( 

ν 

e ) 

= 

15 

MeV 

E ( 

ν 

x ) 

= 

18 

MeV 

Mixing parameters 

∆ 

m 

2 

m 

2 

2 

sun 

= 

60 

meV 

sin ( 2 ) 0. 

9 

2 sin ( 2θ) 

= 0. 

9 

2 

θ = 

No oscillations 

Oscillations in SN envelope 

Earth effects included 

Π(Dighe (Dighe, , Kachelriess, 

Kachelriess, 

Keil, Keil, 

Raffelt, Raffelt, 

Semikoz, Semikoz, 

Tomàs), Tom ), 

hep-ph/0303210, hep ph/0303210, hep-ph/0304150, hep ph/0304150, hep-ph/0307050, hep ph/0307050, hep-ph/0311172 

hep ph/0311172 


SN statistics in 

external galaxies 

Gamma rays from 

26 Al (Milky Way) 

Historical galactic 

SNe (all types) 

No galactic 

neutrino burst 

Core-Collapse Core Collapse SN Rate in the Milky Way 

0 1 2 3 4 5 6 7 8 9 10 

Core-collapse 

Core collapse SNe per century 

van den Bergh & McClure (1994) 

Cappellaro & Turatto (2000) 

Diehl et al. (2006) 

Strom (1994) 

Tammann et al. (1994) 

90 % CL (25 y obserservation) obserservation Alekseev et al. (1993) 

References: van den Bergh & McClure, ApJ 425 (1994) 205. Cappellaro & Turatto, Turatto, 

astro- 

ph/0012455. Diehl et al., Nature 439 (2006) 45. Strom, Astron. Astrophys. Astrophys. 

288 (1994) L1. 

Tammann et al., ApJ 92 (1994) 487. Alekeseev et al., JETP 77 (1993) 339 and my update. 


Local Group of Galaxies 

Events in a detector with 

30 x Super-K Super K fiducial volume, 

e.g. Hyper-Kamiokande 

Hyper Kamiokande 


250 

60 

30

Experimental Limits on Relic Supernova Neutrinos 

Super-K Super K upper limit 

29 cm -2 s-1 1 for 

Kaplinghat et al. spectrum 

[hep-ex/0209028] 

[hep ex/0209028] 

Upper-limit Upper limit flux of 

Kaplinghat et al., 

astro-ph/9912391 


Integrated 54 cm -2 s-1 Cline, astro-ph/0103138 



Improved Sensitivity with Neutron Tagging 

Beacom & Vagins, Vagins, 

hep-ph/0309300 

hep ph/0309300 

[Phys. Rev. Lett., Lett., 

93 (2004) 171101] 

Detection of DSNB limited by 

• Solar neutrinos for E ν ≲ 18 MeV 

• Sub-Cherenkov 

Sub Cherenkov muons from atm nus 

µ → 

e 

+ 

ν 

e 

+ 

ν 

µ 

• Solution: neutron tagging from 

ν 

e + p → e 

+ 

e + p → e 

+ 

+ 

n 

• 2.2 MeV gamma from n + p → d 

invisible in water Cherenkov detector 

Add gadolinium to Super-Kamiokande 


• Efficient neutron capture on Gd 

• 8 MeV gamma cascade easily visible 

• 0.1% (100 tons of Gd Cl 3 ) 

achieves > 90% tagging efficiency 

• Diffuse SN nu background (DSNB): 

a few events per year in Super-K Super 

with no background at all 

Status of R & D (04/2006) 

[Mark Vagins, Vagins, 

private communication] 

Nov 05: Gd Cl 3 added to K2K test tank 

(kiloton or KT detector) 

• Gd Cl 3 is easy to dissolve 

• Gd Cl 3 does not significantly affect 

the light collection 

• Choice of detector materials critical 

(old rust in KT with Gd Cl 3 badly 

affected transparency) 

• The 20 inch Super-K Super K PMT's operate 

well in conductive water 

• Gd filtration works as designed at 

3.6 tons/h, can easily be scaled up 

• Looks promising for Super-K, Super K, 

conceivable within next few years 

• Capital cost negligible for future 

megatonne-class megatonne class detectors 


DSNB Measurement with Neutron Tagging 

Beacom & Vagins, Vagins, 

hep-ph/0309300 

hep ph/0309300 

[Phys. Rev. Lett., Lett., 

93:171101, 2004] 

Future large-scale large scale scintillator 

detectors (e.g. LENA with 50 kt) kt 

• Inverse beta decay reaction tagged 

• Location with smaller reactor flux 

(e.g. Pyhäsalmi Pyh salmi in Finland) could 

allow for lower threshold 

Pushing the boundaries of neutrino 

astronomy to cosmological distances 


Portion of the Hubble Ultra Deep Field 

Dark Energy 73% 

(Cosmological Constant) 

Normal Matter 4% 

(of this about 10% 

luminous) 

Dark 

Matter 23% 

Neutrinos 

0.1−2% 0.1 2% 

Georg Raffelt, Raffelt, Max-Planck-Institut für für Physik, München, Germany IDAPP 2d Meeting, 12-13 May 2006, Ferrara, Italy

Formation of Structure 

Smooth Structured 

Structure forms by 

gravitational instability 

of primordial 

density fluctuations 

A fraction of hot dark matter 

suppresses small-scale small scale structure 


Power Spectrum of Cosmic Density Fluctuations 


Neutrino Free Streaming – Transfer Function 

Power suppression for λFS FS ≲ 100 Mpc/h 

Σm ν 

Σm ν 

Σm ν 

Hannestad, Hannestad, 

Neutrinos in Cosmology, hep-ph/0404239 

hep ph/0404239 

Transfer function 

P(k) P(k) 

= T(k) T(k) 

P 0 (k) 

Effect of neutrino free 

streaming on small scales 

T(k) T(k) 

≈ 1 − 8Ων /ΩM M 

valid for 

8Ων /ΩM M ≪ 1 


= 0 

= 0.3 eV 

= 1 eV

Some Recent Cosmological Limits on Neutrino Masses 

Σmν /eV 

(limit 95%CL) Data / Priors 

Hannestad 2003 

[astro-ph/0303076] 

[astro ph/0303076] 1.01 WMAP-1, WMAP 1, CMB, 2dF, HST 

Spergel et al. (WMAP) 2003 

[astro-ph/0302209] 

[astro ph/0302209] 0.69 WMAP-1, WMAP 1, 2dF, HST, σ8 Crotty et al. 2004 

[hep-ph/0402049] 

[hep ph/0402049] 

Hannestad 2004 

[hep-ph/0409108] 

[hep ph/0409108] 

1.0 

0.6 

0.65 

Seljak et al. 2004 

[astro astro-ph/0407372] 

ph/0407372] 0.42 

Hannestad et al. 2006 

[hep-ph/0409108] 

[hep ph/0409108] 

Spergel et al. 2006 

[hep-ph/0409108] 

[hep ph/0409108] 

0.30 

Seljak et al. 2006 

[astro-ph/0604335] 

[astro ph/0604335] 0.14 

WMAP-1, WMAP 1, CMB, 2dF, SDSS 

& HST, SN 

WMAP-1, WMAP 1, SDSS, SN Ia gold sample, 

Ly-α Ly data from Keck sample 

WMAP-1, WMAP 1, SDSS, Bias, 

Ly-α Ly data from SDSS sample 

WMAP-1, WMAP 1, CMB-small, CMB small, SDSS, 2dF, 

SN Ia, BAO (SDSS), Ly-α Ly (SDSS) 

0.68 WMAP-3, WMAP 3, SDSS, 2dF, SN Ia, σ8 WMAP-3, WMAP 3, CMB-small, CMB small, SDSS, 2dF, 

SN Ia, BAO (SDSS), Ly-α Ly (SDSS) 


Sensitivity Forecasts for Future LSS Observations 

Lesgourgues, 

Lesgourgues, 

Pastor 

& Perotto, Perotto 

hep-ph/0403296 

hep ph/0403296 

Abazajian & Dodelson 



Kaplinghat, Kaplinghat, 

Knox & Song, 



Wang, Wang, 

Haiman, Haiman, 

Hu, Hu, 

Khoury & May, May 



Planck & SDSS 

Ideal CMB & 40 x SDSS 

Future weak lensing 

survey 4000 deg 2 

CMB lensing 

Weak-lensing 

Weak lensing selected 

sample of > 10 5 clusters 


Σm ν 

Σm ν 

> 0.21 eV detectable 

at 2σ 2 

> 0.13 eV detectable 

at 2σ 2 

σ(mν ) ~ 0.1 eV 

σ(mν ) ~ 0.15 eV (Planck) 

σ(mν ) ~ 0.044 eV (CMBpol ( CMBpol) 

σ(mν ) ~ 0.03 eV

Tritium β-decay decay 

3 

3 

H 

3 

H → 

He 

+ 

e 

− 

e 

− 

+ 

ν 

e 

Electron spectrum 

“Weighing Weighing” Neutrinos with KATRIN 

Endpoint 

energy 

18.6 keV 

m 

http://www-ik.fzk.de/katrin 

http://www ik.fzk.de/katrin/ 

E 

• Sensitive to common mass scale m 

for all flavors because of small mass 

differences from oscillations 

• Best limit from Mainz und Troitsk 

m < 2.2 eV (95% CL) 

• KATRIN can reach 0.2 eV 

• Under construction 

• Data taking foreseen to begin in 2009 


Extending the Mass Bound to Other Low-Mass Low Mass Particles 

Assume a generic hot dark matter particle that was in thermal equilibrium equilibrium 

at 

some cosmological epoch 

• Internal particle degrees of freedom (e.g. spin states) gX • Mass mX • Effective number of thermal degrees of freedom at freeze-out freeze out g * 

Contribution to cosmic 

mass density 

Free-streaming Free streaming length 

m g 10. 

75 ⎧ 1 for fermions 

Ω h 

2 m 

= XgX 

10. 

75 ⎧ 1 for fermions 

Ω Xh 

2 

= X X 

X 

× 

⎨ 

183 

eV 

g 

* 

X 

⎩ 

4 

/ 

3 

for 

bosons 

λ 

FS 

4 

⎛ ⎞ 

⎡ ⎛ 2 

20 Mpc ⎛ T 

⎞⎤ 

⎢ ⎜ Ω 

≈ ⎜ X ⎞ 

⎡ ⎛ 2 

20 Mpc T 

⎟ + 

X T 

⎞⎤ 

⎢1 

log 

⎜ Ω 

≈ ⎜ X ⎟ + 3. 

9 

X T 

1 log 3. 

9 ν 

⎟ 

⎥ 

Ω 

2 

Ω 

2 

⎝ Tν 

⎠ ⎢ ⎜ Ω 2 ⎟ 

Xh 

⎝ ν ⎠ ⎢ ⎜ Ω 2 ⎥ 

⎣ ⎝ m T 

⎟ 

Xh 

T 

⎥ 

⎣ ⎝ m T 

X 

⎠ 

⎦ 

Perform maximum likelihood analysis for different choices of gX to derive cosmological limit on mX and g and g * 


L 

a 

π 

π 

Cosmic thermal degrees of 

freedom 

C 

= 

a 

f 

f 

π 

a 

π 

( 

π 

π 

π a 

0 

π 

+ 

∂ 

µ 

C a 

π 

π 

− 

− 

2 

π 

+ 

π 

+ 

0 

π 

− 

Axion Freeze-Out 

Freeze Out 

π 

− 

∂ 

∂ 

µ 

µ 

π 

π 

0 

+ 

) 

∂ 

µ 

Chang & Choi, Choi, 

PLB 316 (1993) 51 

a 

1 

− 

z 

= 

≈ 

0 

. 

094 

3 

( 

1 

+ 

z 

) 

Freeze-out Freeze out temperature 

Cosmic thermal degrees of 

freedom at axion freeze-out freeze out 


Mass Limits on Hot Dark Matter Axions and Neutrinos 

Hannestad, 

Hannestad, 

Mirizzi & Raffelt 

hep-ph/0504059 

hep ph/0504059 

m a 

Axions 

95% 95 CL 

< 1.05 eV (95% (95 CL) 

Hannestad, Hannestad, 



(Seesaw proceedings, Paris, 2004) 

95% 95 CL 


Σm ν 

Σ 


< 0.65 eV (95% (95 CL)

Quarks (Q = −1/3) 1/3) 

Quarks (Q = +2/3) 2/3) 

Fermion Mass Spectrum 

d s b 

u c t 

Charged Leptons (Q = −1) 1) e µ τ 

All flavors 

ν 3 


1 10 100 

1 10 100 

1 10 100 

1 10 100 

1 10 100 

1 

meV eV keV MeV GeV TeV 


Dirac masses 

from coupling 

to standard 

Higgs field φ 

Lagrangian for 

particle masses 

⎛ 

See-Saw See Saw Model for Neutrino Masses 

Charged Leptons 


L = 

− l L 

φ 

g l 

e 

R 

− 

l 

L 

φ 

g 

ν 

N 

R 

− N 

+ 

h 

. 

c 

. 

mass 

⎞ 

⎛ ν 

ν 

L 

( ν 

L 

) ⎜ 

⎟ ⎜ ⎟ ⎠ 

⎞ 

c 

2 R R 

1 c 

− 

2 R MNR 

1 MN 

Heavy 

Majorana 

masses 

Mj > 1010 10 10 GeV 

N R 

⎜ 

⎟ ⎜ Diagonalize 

( ν 

L ) ⎟ 

⎝g 

g ν φ 

M 

⎠ ⎝ 

N 

L N 

R 

⎜ 

NR 

R 

⎜ 

⎟ 

⎝N 

N R 

⎠ 

⎝ 

0 

ν 

g 

φ 

⎠ 

Light Majorana mass 

⎛ 2 

⎜ ν φ 

2 

⎜ 

g 

2 

g φ 

2 

g 

2 2 

g 

2 

ν 

ν φ 

⎜ M 

L 

( ) ⎜ M 

M 

L 

⎟ 

⎠ 

⎞ 

0 

⎟ 

⎟ 

⎛ ν 

⎝ 

M 

⎟ 

M 

⎟ 

⎠ 


⎜ 

⎝ 

0 

⎞

See-Saw See Saw Model for Neutrino Masses 

Light Majorana mass 

⎛ ⎜ 

g 

g 

ν 

ν 

φ 

⎞ 

0 

⎟ 

⎛ ν 

( ) ⎜ ⎟ L 

( νL 

NR 

) ⎜ M ⎟ L 

νL 

N M 

M 

R 

⎜ 

⎟ ⎜ 

⎟ 

⎝N 

N R 

⎠ 

⎝ 

M 

⎟ 

M 

⎟ 

⎠ 


⎜ 

⎝ 

2 2 φ 

0 

2 

2 

⎞

Leptogenesis by Majorana Neutrino Decays 

A classic paper 


Leptogenesis by Out-of Out of-Equilibrium 

Equilibrium Decay 

Equilibrium 

Equilibrium 

Equilibrium 

abundance abundance abundance of 

of 

of 

heavy heavy 

heavy Majorana 

Majorana 

Majorana 

neutrinos 



Real Real abundance 

abundance 

determined determined by 

by 

decay decay rate 

rate 

Created 

lepton-number 

lepton number 

abundance 

M. Fukugita & T. Yanagida: Yanagida 

Baryogenesis without Grand 

Unification 

Phys. Lett. Lett. 

B 174 (1986) 45 

CP-violating CP violating decays by 

interference of tree-level tree level 

with one-loop one loop diagram 

= ν 8π M 2 

Decay = gν 

8π M 2 

Decay g 

W. Buchmüller 

Buchm ller & M. Plümacher Pl macher: : Neutrino masses and the baryon asymmetry 

Int. J. Mod. Phys. A15 (2000) 5047-5086 5047 5086 


Γ

Leptogenesis by Majorana Neutrino Decays 

In see-saw see saw models for neutrino masses, out-of out of-equilibrium 

equilibrium 

decays of right-handed right handed heavy Majorana neutrinos provide 

source for CP- CP and L-violation L violation 

Cosmological evolution 

• B = L = 0 early on 

• Thermal freeze-out freeze out of heavy Majorana neutrinos 

• Out-of Out of-equilibrium equilibrium CP-violating CP violating decay creates net L 

• Shift L excess into B by sphaleron effects 

Sufficient deviation from 

equilibrium distribution of 

heavy Majorana neutrinos 

at freeze-out freeze out 

Limits on 

Yukawa 

couplings 

Requires Majorana neutrino masses below 0.1 eV 

Buchmüller, Buchm ller, Di Bari & Plümacher Pl macher, , hep-ph hep ph/0209301 /0209301 & hep-ph hep ph/0302092 /0302092 

Limits on 

masses of 

ordinary 



Some nuclei decay only 

by the ββ mode, e.g. 

O + O + 

76 Ge 

76 As 

2 – 2 – 

Half life ~ 1021 Half life ~ 10 yr 21 yr 

Neutrinoless ββ Decay 

76 Se 

2 + 2 + 

O + O + 

Standard 2ν 2 mode 

Measured 

quantity 

Best limit 

from 76 76Ge Ge 

= ∑ 

= 

N 

mee = ∑ 

i= 

1 

N 

mee 

i 1 

0ν mode, enabled 

by Majorana mass 


λ 

i 

U 

m ee < 

0 

. 

35 

eV 

2 

ei 

m 

i


Dark Energy 73% 

(Cosmological Constant) 

Ordinary Matter 4% 

(of this only about 

10% luminous) 

Dark Matter 

23% 


0.1−2% 0.1 2% 

Georg Raffelt, Raffelt, Max-Planck-Institut für Physik, München, Germany IDAPP 2d Meeting, 12-13 May 2006, Ferrara, Italy


Elementary Elementary Particle Physics 

Astrophysics Astrophysics & & Cosmology Cosmology 

Cosmic Cosmic Rays Rays

Neutrinos in Astrophysics and Cosmology - INFN Sezione di Ferrara

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