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.