Effects of sterile neutrinos on supernova and UHE neutrino

fluxes

Jukka MaalampiUniversity of Jyväskylä

AlbaNova, StockholmApril 16, 2004

Contents

Backgound

Sterile neutrinos?

UHE neutrinos

Supernova neutrinos

Summary

Background

Neutrino mixingWeak interactins of leptons are not diagonal

.. )( chWlUg LiiL += + µαµα γν

21CCL

Neutrino flavour states na are superpositions of mass states ni

)( ,,

∑=

==321i

iLiL e,µ,α U τνν αα

The best ways to probe U are

•Neutrino oscillations

•Neutrinoless double beta decay

Neutrino oscillationsOscillation probability

2

22

2

∑−

==→i

ELmi

ii

i

eUULLP

*)(,),( αββαβα νννν

[ ] Im2sin2Resin4,

2∑<

⋅∆−⋅∆−=

kjkj

jkjk

jkjk WW αβαβαβδ

*)(*)( , 4

2

kjkjjkjk

jk UUUUWEmL

ββαααβ =∆

=∆

For two neutrinos

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=θθθθ

cossinsincos

U

sinsin),(EmLLP

42

222 ∆

⋅=→ θνν βα

Mixing matrixStandard parametrization

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

−−−−−−

−

132313231223121323122312

132313231223121323122312

1313121312

ccescsscesccsscsesssccessccs

escscc

ii

ii

i

δδ

δδ

δ

=U

etc) cos( 1212 θ=c

Evidence of neutrino oscillations

?Dm2 scales are very different

effectively two-neutrino oscillations

Atmospheric neutrinos

232

231

2

232

232

9102107341

mmm

m

atm

atm

∆≈∆≈∆

>×−=∆ −

.sineV )..(

θ

Solar neutrinos

212

2

12

52

950710105945

mm

m

sun

sun

∆=∆

−=×−=∆ −

..sineV )..(

2

2

θ

0290132 .sin <θ Global fit

Maltoni

Mass spectrum|Ue3|2

ν2ν1

mas

s

ν1

ν2

ν3

?ν3

mas

s

∆m2sun

∆m2atm

∆m2atm

|Ue3|2

∆m2sun

Normal mass hierarchy Inverted mass hierarchy

Electron neutrinoMuon neutrinoTau neutrino A Yu Smirnov

Sterile neutrinos?

Are there sterile neutrinos lurking around?

Sterile neutrino= neutrino that lacks Standard Model interactions

Not needed for solar and atmosphere data

Active-sterile mixing not dominantSubstantial sterile component still allowed (sin2α<0.2)

LSND data (if true) needs something beyond the three-active picture, ∆m2≈1 eV2

The most stringent limits for active-sterile mixing come from Big Bang Nucleosynthesis

A recent analysis: M. Cirelli et al ph/0403158

3−= effeff NNδ

Plot: Kainulainen Olive

Allowed Allowed

Enqvist BarbieriKainulainen DolgovJM

Oscillations bring sterile neutrinos (partially) into thermal equilibrium increasing Neff and affecting BBN

Active-sterile mixings that were relevant for solar and atmospheric neutrino data are forbidden by cosmology!

Very small ∆m2

For solar neutrinos

L=1.5x1011 m =8x1017eV-1 , E=106 eV

Sensitive only for oscillations with

1 ≤∆EmL

4

2

2112 10 eV −≥∆m

Where could one test smaller ∆m2 ’s?

•Ultra-high energy (UHE) neutrinos from distant objects (AGN, GRB)Vacuum oscillations

•SupernovaeMatter effects

ModelsMass Lagrangian

..* chmCmCmDirac

LRD

Majorana

RTRRL

TLLm +++=−

434214444 34444 21νννννν 2

121L

( ) ..)(

)( chmmmm

CL

cL

RD

DLTL

cTL +⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

νν

νν21

pair neutrino degenerate-quasi a dominates saw)-(see / mixing small withsterileheavy a dominates

/ mixing small withsterile light a dominates

⇒≈⇒

≈⇒

D

RDR

LDL

mmmm

mmmϕ

ϕ

MaBeretziani, MohapatraFoot, VolkasBlinikov, Khlopov etc

We are interested in this

Ultra-high energy neutrinos

UHE neutrinos

µµ

µ

νννµνπ

eep

→→→

Produces cosmic ray Produces cosmic ray beam?beam?

active galaxy

From Halzen

021000 :::: =τµ

FFFeNeutrino flux ratiosin the source:

Oscillation of UHE neutrinosTypically

eV PeV m10Mpc 24

15

2

10110

=≈≈≈

EL

Oscillations sensitive to

2172 10 eV −≥∆m

Fluxes at the Earth are affected by oscillations

µF

τF

An old plot on the fluxes in different oscillation schemes

Bento, Keränen, JM (1999)

According to the data neutrino mixing is bi-large:

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

−

−≈

21

212

212

21

212

212

1212 0

cs

cssc

U0423 ≈≈ 13 ,/ θπθ

Averaged over many oscillations

αββα

βαβααββα δνν

PUU

UUUULP

ji

j

ijjji

i

≡=

−=→

∑

∑>

22

2

*

*

),(

0

31

31

31

0

0

0

e

ee

F

F

FF

PFFF

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

=⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

τ

µ

τ

µFluxes at the Earth (1/L2 implicit):

111 :::: ≈τµ

FFFeLearned, PakvasaBento, Keränen, JMAthar, Jezabek, Yasuda

A model with three sterile neutrinos

Keränen, JM, Myyryläinen, Riittinen

Assume that the mass states of active neutrinos mix with sterile neutrinos:

αανν ii U=ˆ

321 ,, cosˆ sin' sinˆ cos

=

+=−=

i

siiiii

siiiii

νϕνϕννϕνϕν

”Normal” mass states

siν Sterile neutrino

3’3

2’21’1

Closely degenerate pairs with a small ∆m2

A pair appears as a single state with the full SM couplings in ordinary WI’s

Example: One sterile. U is replaced with

2

32

3442

22

2

2

12

1

121

βαβαβααβ ϕϕ UUUUUUP44 344 21

to

)sin(cos

=

+++=

Suppression factor; some of the original flux goes to sterile neutrinoThree steriles:

∑=

+=321

2244

,, )sin(cos

iiiii UUP βααβ ϕϕ

Results

.

Relative fluxes of UHE neutrinos at the Earth

Red point Bi-large mixing with θ23 =π/4, θ13=0

Gray area No-sterile case with exp errors for θij

Black area 3-sterile case with active-sterile mixing angles φivarying within (0,π/4)

Detectable effect in neutrino telescopes%

)/()/()/(

% 7040 ≤−

≤−SMe

SMesterilee

FFFFFF

µ

µµ

The same as before but with anticipated better accuracy of the standard neutrino mixing angles

.

Ranges used:

Other possible effectsNow Future

Barenboim, Quigg

Supernova neutrinos

Degenerate steriles in supernovae

Neutrinos and antineutrinos are produced in dense matter, ρ ∼ (1011 - 10 12 ) g/cc.

eF

mattereff

NGV

VU

mm

mU

EH

200000000

000000

21

23

22

21

=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛= +

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

τ

µ

ννν e

-basis

In the core V>>mi2 neutrinos start as flavour states and evolve to

mass states during their transit

Production fluxes of flavour states determine the fluxes of the mass states leaving the SN. Mass states fly to the Earth as incoherent states (wave packets do not overlap).

Active neutrino case

1m

2m

3mTwo MSW-resonancies:

high (H) corresponds to ∆m2atm

ρ≈102-104 g/cc

low (L) corresponds to ∆m2sun

ρ≈10-30 g/cc

Non-adiabaticity described by Landau- Zener probability P

θθ 232 cos/sinmP ∆∝

Normal mass hierarchy

P=0 adiabatic transition (solid lines)P=1 non-adiabatic transition (dotted lines)

Fluxes of different mass states on the surface of SN and at the Earth are

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

=⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

03

02

01

3

2

1

FFF

PFFF

Fluxes of different flavours at the Earth

Probability to find να in the mass state νi

In the presence on steriles this appears as

If active-sterile mixing angles φi differ (and are not all small), flux ratios of different flavours will change from their values in 3-active case

Also the ratio electron neutrino and electron antineutrino will change (suppressed by different angles)

ResultsSimplified analysis: PL =0

PH=0 (adiabatic)PH=1 (non-adiabatic)No active-sterile resonance adiabatic

Initial fluxes 234000 :::: =τµ

FFFe (Integrated over tha energy spectra given by Raffelt, Keil)

ττµµ FFFFFa +++=

1m

2m

3m

1

2

3

s

s

s

νν

ν

1sν

Sterile-active resonancies may have large effects

Change dominantly active mass state to dominantly sterile mass state if φi small:

sinˆ cos siiiii νϕνϕν −=

siiiii νϕνϕν cosˆ sin' +=

Depends on profileenergy∆m2

Landau-Zener

Summary

Sterile neutrinos are not needed for explaining solar and atmospheric neutrino data

Sterile neutrinos mixing with active neutrinos with ∆m2 < 10-11 eV2 not visible in these phenomena

Sterile neutrinos with 10-17 eV2 < ∆m2 < 10-11 eV2 detectable effects on UHE and supernova neutrino fluxes at the Earth

In some theoretical models (simple see-saw and mirror neutrino models) a small ∆m2 implies maximal mixing no effects on the fluxes.Generally ∆m2 and mixing angles are independent.