Sterile Neutrinos: Phenomenology and Fits
Marco Laveder
Dipartimento di Fisica “G. Galilei”, Università di Padova
and
INFN, Sezione di Padova
mailto://[email protected]
Neutrino Unbound: http://www.nu.to.infn.it
16th Paris Cosmology Colloquium Chalonge 2012
25-27 July 2012, Observatoire de Paris, France
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 1/33
Three-Neutrino Mixing Paradigm
νe
νµ
ντ
m2
ν2
m2
ν3
∆m2S
ν1
∆m2A
∆m2A
ν2
∆m2S
ν1
Normal Spectrum
ν3
Inverted Spectrum
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 2/33
Beyond Three-Neutrino Mixing
νs1
ντ
νµ
νe
···
νs2
ν1
ν2
ν3
ν4
ν5
m21
m22
m23
m24
m25
∆m2SOL
∆m2ATM
∆m2SBL
3ν-mixing
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 3/33
···
log m2
Standard Model
◮
Neutrinos are the only massless fermions
◮
Neutrinos are the only fermions with only left-handed component νL
◮
Neutrinos are the only neutral fermions
Extension of the SM: Massive Neutrinos
◮
Simplest extension: introduce right-handed component νR
(singlet of SU(2)L × U(1)Y )
◮
One generation: Dirac mass mD νR νL + Majorana mass mM νRc νR
=⇒ 2 massive Majorana neutrinos
◮
Three left-handed fields + NR right-handed fields:
νeL , νµL , ντ L + ν1R , . . . , νNR R
=⇒ 3 + NR massive Majorana neutrinos
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 4/33
Sterile Neutrinos
◮
Light anti-νR are called sterile neutrinos
νRc →νsL
(left-handed)
◮
Sterile means no standard model interactions
◮
Active neutrinos (νe , νµ , ντ ) can oscillate into sterile neutrinos (νs )
◮
Observables:
◮
◮
Disappearance of active neutrinos (neutral current deficit)
◮
Indirect evidence through combined fit of data (current indication)
Short-baseline anomalies + 3ν-mixing:
ν1
νe
2 ≪ |∆m2 | ≪ |∆m2 | ≤ . . .
∆m21
31
41
ν2
ν3
ν4
...
νµ
ντ
νs1
...
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 5/33
◮
In this talk I consider sterile neutrinos with mass scale ∼ 1 eV in light of
LSND, MiniBooNE, Reactor Anomaly, Gallium Anomaly.
◮
Other possibilities (not incompatible):
◮
Very light sterile neutrinos with mass scale ≪ 1 eV: important for solar
neutrino phenomenology
[de Holanda, Smirnov, PRD 83 (2011) 113011]
◮
Heavy sterile neutrinos with mass scale ≫ 1 eV: could be Warm Dark
Matter
[Kusenko, Phys. Rept. 481 (2009) 1]
[Boyarsky, Ruchayskiy, Shaposhnikov, Ann. Rev. Nucl. Part. Sci. 59 (2009) 191]
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 6/33
Effective SBL Oscillation Probabilities in 3+1 Schemes
2
2
Pνα →νβ = sin 2ϑαβ sin
2 L
∆m41
4E
sin2 2ϑαβ = 4|Uα4 |2 |Uβ4 |2
No CP Violation!
Pνα →να = 1 − sin2 2ϑαα sin2
2 L
∆m41
4E
sin2 2ϑαα = 4|Uα4 |2 1 − |Uα4 |2
Perturbation of 3ν Mixing
|Ue4 |2 ≪ 1 ,
Ue1
U =
Ue2
Ue3
|Uµ4 |2 ≪ 1 ,
Ue4
|Uτ 4 |2 ≪ 1 ,
|Us4 |2 ≃ 1
sin2 2ϑαα ≪ 1
Uµ1 Uµ2 Uµ3 Uµ4
⇓
Uτ 1 Uτ 2 Uτ 3 Uτ 4
Us1
Us2
Us3
Us4
|Uα4 |2 ≃
sin2 2ϑαα
4
SBL
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 7/33
Effective SBL Oscillation Probabilities in 3+2 Schemes
2
φkj = ∆mkj
L/4E
∗
∗
η = arg[Ue4
Uµ4 Ue5 Uµ5
]
P(−)
(−)
νµ → νe
= 4|Ue4 |2 |Uµ4 |2 sin2 φ41 + 4|Ue5 |2 |Uµ5 |2 sin2 φ51
(+)
+ 8|Uµ4 Ue4 Uµ5 Ue5 | sin φ41 sin φ51 cos(φ54 − η)
P(−)
(−)
να → να
= 1 − 4(1 − |Uα4 |2 − |Uα5 |2 )(|Uα4 |2 sin2 φ41 + |Uα5 |2 sin2 φ51 )
− 4|Uα4 |2 |Uα5 |2 sin2 φ54
◮
More parameters: 7 (vs 3 in 3+1)
◮
CP violation
[Sorel, Conrad, Shaevitz, PRD 70 (2004) 073004; Maltoni, Schwetz, PRD 76 (2007) 093005; Karagiorgi et al, PRD 80 (2009)
073001; Kopp, Maltoni, Schwetz, PRL 107 (2011) 091801; Giunti, Laveder, PRD 84 (2011) 073008; Donini et al,
arXiv:1205.5230]
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 8/33
LSND
[LSND, PRL 75 (1995) 2650; PRC 54 (1996) 2685; PRL 77 (1996) 3082; PRD 64 (2001) 112007]
20 MeV ≤ E ≤ 200 MeV
Beam Excess
15
p(νµ→νe,e+)n
_
_
_
p(νe,e+)n
12.5
10 2
2
17.5
2
4
L ≃ 30 m
∆m (eV /c )
Beam Excess
ν̄µ → ν̄e
10
Karmen
Bugey
other
10
CCFR
1
7.5
NOMAD
5
10
2.5
-1
90% (Lmax-L < 2.3)
99% (Lmax-L < 4.6)
0
0.4
0.6
0.8
1
1.2
1.4
L/Eν (meters/MeV)
2
& 0.2 eV2
∆mLSND
10
-2
10
-3
10
-2
(≫ ∆mA2 ≫ ∆mS2 )
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 9/33
10
-1
1
2
sin 2θ
MiniBooNE Neutrinos
[PRL 98 (2007) 231801; PRL 102 (2009) 101802]
Events / MeV
νµ → νe
L ≃ 541 m
200 MeV ≤ E . 3 GeV
3
Data
νe from µ
νe from K +
νe from K 0
π0 misid
∆ → Nγ
dirt
other
Total Background
2.5
2
1.5
1
0.5
0.2
0.4
0.6
0.8
1
1.2
1.4
1.5
1.6
3.
Excess Events / MeV
EQE
ν (GeV)
0.8
data - expected background
best-fit νµ →νe
0.6
2
sin22θ=0.004, ∆ m =1.0eV 2
2
sin22θ=0.2, ∆ m =0.1eV 2
0.4
0.2
0
-0.2
0.2
0.4
0.6
0.8
1
1.2
1.4
1.5
1.6
3.
EQE
ν (GeV)
[MiniBooNE, PRL 102 (2009) 101802]
◮
◮
[Djurcic, arXiv:0901.1648]
no νµ → νe signal corresponding to LSND ν̄µ → ν̄e signal (E > 475 MeV)
low-energy anomaly
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 10/33
MiniBooNE Antineutrinos - 2009-2010
[PRL 103 (2009) 111801; PRL 105 (2010) 181801]
ν̄µ → ν̄e
L ≃ 541 m
200 MeV ≤ E . 3 GeV
102
ν e & ν e from µ +/+/ν e & ν e from K
0
ν e & ν e from K
π0 misid
∆ → Nγ
dirt
other
Constr. Syst. Error
Best Fit (E>475MeV)
Fit Region
0.4
Events/MeV
0.2
0.3
Data - expected background
0.2
Best Fit
sin 2θ=0.004, ∆ m =1.0eV
2
2
sin 2θ=0.03, ∆m =0.3eV
2
0.1
2
2
90% CL
99% CL
KARMEN2 90% CL
10
|∆m2| (eV2/c4)
Events/MeV
68% CL
0.6
BUGEY 90% CL
1
2
10-1
0.0
-0.1
0.2
LSND 90% CL
0.4
0.6
0.8
1.0
1.2
1.4 1.5 1.6 3.0
LSND 99% CL
QE
Eν (GeV)
[MiniBooNE, PRL 105 (2010) 181801]
10-2
-3
10
10-2
10-1
sin2(2θ)
◮
5.7e20 POT: agreement with LSND ν̄µ → ν̄e signal (E > 475 MeV)
◮
similar L/E but different L and E =⇒ oscillations
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 11/33
1
MiniBooNE ν̄ - Neutrino 2012 - 6 June
agreement with LSND signal is sadly vanishing
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 12/33
MiniBooNE ν and ν̄ - Neutrino 2012 - 6 June
Neutrino energy reconstruction problem?
[Martini, Ericson, Chanfray, arXiv:1202.4745]
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 13/33
The neutrino run
(A) electron-like neutrino data.
Comparison between the data (black
dots) and the calculated distributions
due to misidentified  events (red)
and genuine e events (blue). The sum
is indicated in black. One notices an
anomaly at low energies, which is
incompatible with LNSD predictions.
 (B) according to Giunti & Laveder
scaling of the events is applied with a
factor 1.26, within the permitted
uncertainty of F = 1.24 ±0.21 and
gives an acceptable fit to the data.
The e with and without scaling and
disappearance are also shown.

Venice_March2011
Slide# : 9
Reactor Electron Antineutrino Anomaly
[Mention et al, PRD 83 (2011) 073006; update in White Paper, arXiv:1204.5379]
new reactor ν̄e fluxes
[Mueller et al, PRC 83 (2011) 054615]
[Huber, PRC 84 (2011) 024617]
Detection:
PDG
1995
1998
2002
2011
2012
σ(ν̄e + p → n + e + ) ∝ τn−1
neutron lifetime τn
887.0 ± 2.0 sec
886.7 ± 1.9 sec
885.7 ± 0.8 sec
881.5 ± 1.5 sec
880.1 ± 1.1 sec
change of predicted event rates
235
U
+3.7%
238 U
239 Pu
241 Pu
+9.8%
+4.2%
+4.7%
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 14/33
Reactor ν̄e Disappearance
2
∆m41
L
Pνe →νe = 1 − sin 2ϑee sin
4E
sin2 2ϑee = 4|Ue4 |2 1 − |Ue4 |2
2
[Mention et al., in White Paper, arXiv:1204.5379]
102
2
[Giunti, Laveder, Li, Liu, Long, June 2012]
2
∆m 41
[eV2]
10
+
1
10−1
10−2
REA
68.27% C.L. (1σ)
90.00% C.L.
95.45% C.L. (2σ)
99.00% C.L.
99.73% C.L. (3σ)
10−2
10−1
si n 22ϑee
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 15/33
1
Gallium Anomaly
Gallium Radioactive Source Experiments
Tests of the solar neutrino detectors GALLEX (Cr1, Cr2) and SAGE (Cr, Ar)
νe + 71 Ga → 71 Ge + e −
Detection Process:
νe Sources:
e − + 51 Cr → 51 V + νe
e − + 37 Ar → 37 Cl + νe
51 Cr
E [keV]
B.R.
747
0.8163
752
0.0849
37 Ar
427
0.0895
432
0.0093
811
0.902
37Ar
37Cl
(stable)
813
0.098
(35.04 days)
813 keV ν ( 9.8%)
811 keV ν (90.2%)
[SAGE, PRC 73 (2006) 045805, nucl-ex/0512041]
[SAGE, PRC 59 (1999) 2246, hep-ph/9803418]
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 16/33
p(measured)/ p(predicted)
1.1
hLiGALLEX = 1.9 m
GALLEX Cr1
SAGE Cr
hLiSAGE = 0.6 m
1.0
0.9
0.8
0.7
GALLEX Cr2 SAGE Ar
[SAGE, PRC 73 (2006) 045805, nucl-ex/0512041]
RBGALLEX-Cr1
RBGALLEX-Cr2
RBSAGE-Cr
RBSAGE-Ar
=
=
=
=
0.953 ± 0.11
0.812+0.10
−0.11
0.95 ± 0.12
0.791+0.084
−0.078
RBGa = 0.86 ± 0.05
Bahcall cross section without
uncertainty
[Bahcall, PRC 56 (1997) 3391, hep-ph/9710491]
[GALLEX]
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 17/33
◮
Deficit could be due to overestimate of
σ(νe + 71 Ga → 71 Ge + e − )
◮
Calculation: Bahcall, PRC 56 (1997) 3391
3/2− 0.500 MeV
5/2− 0.175 MeV
1/2−
71
Ge
0.233 MeV
3/2−
71
◮
◮
◮
σG.S. from T1/2
(71 Ge)
Ga
= 11.43 ± 0.03 days
[Hampel, Remsberg, PRC 31 (1985) 666]
σG.S. (51 Cr) = 55.3 × 10−46 cm2 (1 ± 0.004)3σ
BGT175
BGT500
51
51
σ( Cr) = σG.S. ( Cr) 1 + 0.669
+ 0.220
BGTG.S.
BGTG.S.
Contribution of Excited States only 5%!
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 18/33
Krofcheck et al.
PRL 55 (1985) 1051
71
Haxton
PLB 431 (1998) 110
Frekers et al.
PLB 706 (2011) 134
◮
Ga(p, n)71 Ge
Shell Model
71
BGT175
BGTG.S.
BGT500
BGTG.S.
< 0.056
0.13 ± 0.02
0.19 ± 0.18
Ga(3 He, 3 H)71 Ge 0.039 ± 0.030 0.202 ± 0.016
Haxton:
[Haxton, PLB 431 (1998) 110]
“a sophisticated shell model calculation is performed ... for the transition
to the first excited state in 71 Ge. The calculation predicts destructive
interference between the (p, n) spin and spin-tensor matrix elements”
◮
2.7σ discrepancy of BGT500 /BGTG.S. measurements
◮
Anyhow, new
71 Ga(3 He, 3 H)71 Ge
data support Gallium Anomaly!
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 19/33
Gallium νe Disappearance
102
102
[Giunti, Laveder, Li, Liu, Long, June 2012]
10
10
10−1
1
10−1
GAL − Haxton
68.27% C.L. (1σ)
90.00% C.L.
95.45% C.L. (2σ)
99.00% C.L.
99.73% C.L. (3σ)
10−3
+
[eV2]
2
∆m 41
2
∆m 41
[eV2]
+
1
10−2
[Giunti, Laveder, Li, Liu, Long, June 2012]
10−2
10−1
10−2
1
GAL − Frekers et al.
68.27% C.L. (1σ)
90.00% C.L.
95.45% C.L. (2σ)
99.00% C.L.
99.73% C.L. (3σ)
10−3
10−2
si n 22ϑee
No Osc.
3+1
χ2min
NDF
GoF
χ2min
NDF
GoF
2
∆m41
[eV2 ]
sin2 2ϑee
10−1
si n 22ϑee
14.9
4
0.5 %
4.7
2
9.5 %
2.24
0.51
No Osc.
3+1
χ2min
NDF
GoF
χ2min
NDF
GoF
2
∆m41
[eV2 ]
sin2 2ϑee
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 20/33
18.2
4
0.1 %
7.9
2
1.9 %
2.14
0.32
1
Reactor ν̄e and Gallium νe Disappearance
102
102
[Giunti, Laveder, Li, Liu, Long, June 2012]
+
1
2
∆m 41
2
∆m 41
[eV2]
10
[eV2]
10
10−1
10−2
[Giunti, Laveder, Li, Liu, Long, June 2012]
10−1
REA + GAL − Haxton
68.27% C.L. (1σ)
90.00% C.L.
95.45% C.L. (2σ)
99.00% C.L.
99.73% C.L. (3σ)
10−2
+
1
10−2
10−1
1
REA + GAL − Frekers et al.
68.27% C.L. (1σ)
90.00% C.L.
95.45% C.L. (2σ)
99.00% C.L.
99.73% C.L. (3σ)
10−2
10−1
si n 22ϑee
No Osc.
3+1
χ2min
NDF
GoF
χ2min
NDF
GoF
2
∆m41
[eV2 ]
sin2 2ϑee
1
si n 22ϑee
45.6
42
32.3 %
30.8
40
85 %
1.95
0.16
No Osc.
3+1
χ2min
NDF
GoF
χ2min
NDF
GoF
2
∆m41
[eV2 ]
sin2 2ϑee
48.9
42
21.5 %
32.2
40
80 %
1.95
0.16
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 21/33
Global νe and ν̄e Disappearance
102
[Giunti, Laveder, Li, Liu, Long, June 2012]
+
10
2
∆m 41
[eV2]
+
+
+
1
10−1
10−2
95% C.L.
Gallium
Reactors
νe−C
Sun
Combined
10−2
10−1
1
si n 22ϑee
KARMEN + LSND
νe + 12 C → 12 Ng.s. + e −
SUN&KamLAND + ϑ13
[Conrad, Shaevitz, PRD 85 (2012) 013017]
[Palazzo, PRD 83 (2011) 113013]
[Giunti, Laveder, PLB 706 (2011) 200]
[Palazzo, PRD 85 (2012) 077301]
[Giunti, Li, PRD 80 (2009) 113007]
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 22/33
SUN&KamLAND + ϑ13 bound on |Ue4|2
[Giunti, Li, PRD 80 (2009) 113007; Palazzo, PRD 83 (2011) 113013, PRD 85 (2012) 077301]
3+1 with simplifying assumptions: Uµ4 = Uτ 4 = 0, no CP violation
Ue1 = c12 c13 c14
Ue2 = s12 c13 c14
Ue3 = s13 c14
Ue4 = s14
Us1 = −c12 c13 s14
Us2 = −s12 c13 s14
Us3 = −s13 s14
Us4 = c14
4 4
4
4 4 2ν
c14 + s14
c14 Pνe →νe + s13
Pνe →νe = c13
4
4
2 2
+1
Pν2νe →νs + s13
s14 c13
Pνe →νs = c14
2 2
2 2
V = c13
c14 VCC − c13
s14 VNC = (|Ue1 |2 + |Ue2 |2 )VCC − (|Us1 |2 + |Us2 |2 )VNC
∆χ 2
[Giunti, Laveder, Li, June 2012]
Fit with Uµ4 and Uτ 4 free:
θ 14
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 23/33
Global νe and ν̄e Disappearance
[Giunti, Laveder, Li, Liu, Long, June 2012]
10
2
∆m 41
[eV2]
+
1
GAL+REA+νeC+SUN
68.27% C.L. (1σ)
90.00% C.L.
95.45% C.L. (2σ)
99.00% C.L.
99.73% C.L. (3σ)
10−1
10−2
10−1
1
2
si n 2ϑee
No Osc.
3+1
χ2min
NDF
GoF
χ2min
NDF
GoF
2
∆m41
[eV2 ]
sin2 2ϑee
57.1
53
32.6 %
46.0
51
67 %
7.59
0.12
No Osc.
3+1
χ2min
NDF
GoF
χ2min
NDF
GoF
2
∆m41
[eV2 ]
sin2 2ϑee
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 24/33
318.4
331
68%
306.0
329
80%
1.71
0.099
Testable Implications
β Decay
10
10
(ββ)0ν Decay
[Giunti, Laveder, Li, Liu, Long, June 2012]
[Giunti, Laveder, Li, Liu, Long, June 2012]
99.73%
8
8
99.73%
EXO
99%
95.45%
4
4
∆χ2
∆χ2
6
6
99%
95.45%
90%
2
2
90%
68.27%
68.27%
GAL+REA+νeC+SUN
10−2
0
0
GAL+REA+νeC+SUN
10−1
(4)
mβ
|Uek |2 mk2
q
2
= |Ue4 | ∆m41
mβ =
(4)
mβ
qP
1
[eV]
k
10−3
10−2
(4)
mββ
10−1
[eV]
P 2
mββ = k Uek
mk q
(4)
2
mββ = |Ue4 |2 ∆m41
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 25/33
KK
1
Global 3+1 Fit: Disappearance Constraints
◮
νe disappearance experiments:
sin2 2ϑee = 4|Ue4 |2 1 − |Ue4 |2 ≃ 4|Ue4 |2
◮
νµ disappearance experiments:
sin2 2ϑµµ = 4|Uµ4 |2 1 − |Uµ4 |2 ≃ 4|Uµ4 |2
◮
νµ → νe experiments:
sin2 2ϑeµ = 4|Ue4 |2 |Uµ4 |2 ≃
◮
1 2
sin 2ϑee sin2 2ϑµµ
4
Upper bounds on sin2 2ϑee and sin2 2ϑµµ =⇒ strong limit on sin2 2ϑeµ
[Okada, Yasuda, Int. J. Mod. Phys. A12 (1997) 3669-3694]
[Bilenky, Giunti, Grimus, Eur. Phys. J. C1 (1998) 247]
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 26/33
νµ and ν̄µ Disappearance
102
99% C.L.
CDHSW (1984): νµ
ATM: νµ + νµ
MINOS (2011): νµ
[eV2]
10
◮
2
∆m 41
1
ATM constraint on |Uµ4 |2
[Maltoni, Schwetz, PRD 76 (2007) 093005]
◮
MINOS constraint on |Uµ4 |2
[Giunti, Laveder, PRD 84 (2011) 093006]
−1
10
10−2
10−2
10−1
1
si n 22ϑµµ
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 27/33
νe and ν̄e Disappearance
102
99% C.L.
Bugey3
Bugey4+Rovno
Gosgen+ILL
Krasnoyarsk
νe − 12C
Gallium
SUN
[Mention et al., PRD 83 (2011) 073006]
[Huber, PRC 84 (2011) 024617]
◮
1
2
∆m 41
New Reactor ν̄e Fluxes
[Mueller et al., PRC 83 (2011) 054615]
[eV2]
10
◮
KARMEN + LSND
νe + 12 C → 12 Ng.s. + e −
[Conrad, Shaevitz, PRD 85 (2012) 013017]
[Giunti, Laveder, PLB 706 (2011) 200]
−1
10
◮
SUN&KamLAND + ϑ13
[Giunti, Li, PRD 80 (2009) 113007]
[Palazzo, PRD 83 (2011) 113013]
[Palazzo, PRD 85 (2012) 077301]
10−2
10
−2
10
−1
1
[Giunti, Laveder, Li, Liu, Long, in preparation]
2
si n 2ϑee
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 28/33
3+1 with SUN&KamLAND+ϑ13
10
3+1 − 3σ
2
∆m 41
[eV2]
νe Dis
νµ Dis
Dis
App
GoF = 38%
1
PGoF = 0.3%
10−1
10−4
10−3
10−2
10−1
1
si n 22ϑeµ
◮
3+1 & 3+2: Appearance-Disappearance tension
Tension reduced in 3+1+NSI [Akhmedov, Schwetz, JHEP 10 (2010) 115]
◮
No tension in 3+1+CPTV
◮
[Barger, Marfatia, Whisnant, PLB 576 (2003) 303]
[Giunti, Laveder, PRD 82 (2010) 093016, PRD 83 (2011) 053006]
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 29/33
10
3+2 with SUN&KamLAND+ϑ13
8
3+2 − 3σ
App
Dis
4|U e5|2|U µ5|2
10−1
0
2
4
∆χ2
6
3+2
68.27% C.L. (1σ)
90.00% C.L.
95.45% C.L. (2σ)
99.00% C.L.
99.73% C.L. (3σ)
10−2
+
10−3
1
1
2
∆m 51
[eV2]
+
10−1
10
−1
0
1
2
∆m 41
[eV2]
2
4
6
8
10
10−4
+
10−4
10−3
GoF = 46%
10−2
10−1
4|U e4|2|U µ4|2
∆χ2
PGoF = 0.29%
◮
3+2 is preferred to 3+1 only if there is CP-violating MiniBooNE
neutrino-antineutrino difference
◮
almost disappeared with 2012 MiniBooNE antineutrino data
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 30/33
3+1 Global Fit
10
3+1 − GLO+SUN
68.27% C.L. (1σ)
90.00% C.L.
95.45% C.L. (2σ)
99.00% C.L.
99.73% C.L. (3σ)
[eV2]
+
+
+
2
∆m 41
1
DIS
10
DIS
APP
−1
10−4
10−3
10−2
si n 22ϑeµ
10−1
DIS
[Giunti, Laveder, May 2012]
10−2
10−1
si n 22ϑee
◮
MiniBooNE 2011 data (E > 475 MeV)
◮
More time is needed to fit MiniBooNE 2012 data
10−2
10−1
si n 22ϑµµ
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 31/33
New Neutrino Facility in the CERN North Area�
Near position
(330 m)
Mid position
(1100 m)
Far position
(1600 m)
100 GeV primary beam fast extracted from SPS; target station
next to TCC2; decay pipe l =100m, ø = 3m; beam dump: 15m of Fe
with graphite core, followed by µ stations.
Neutrino beam angle: pointing upwards; at -3m in the far detector
~5mrad slope.
SPSC_Open Presentation April 2012�
Slide 16�
LAr + NESSiE νμdisappearance
LAr +
Cosmology
◮
Ns = number of thermalized sterile neutrinos (not necessarily integer)
◮
CMB and LSS in ΛCDM:
Ns = 1.3 ± 0.9
ms < 0.66 eV (95% C.L.)
[Hamann, Hannestad, Raffelt, Tamborra, Wong, PRL 105 (2010) 181301]
Ns = 1.61 ± 0.92
ms < 0.70 eV
(95% C.L.)
[Giusarma, Corsi, Archidiacono, de Putter, Melchiorri, Mena, Pandolfi, PRD 83 (2011) 115023]
Ns = 1.12+0.86
−0.74
◮
◮
(95% C.L.)

Ns = 0.22 ± 0.59
BBN: Ns = 0.64+0.40
−0.35

Ns ≤ 1 at 95% C.L.
CMB+LSS+BBN:
[Archidiacono, Calabrese, Melchiorri, PRD 84 (2011) 123008]
[Cyburt, Fields, Olive, Skillman, AP 23 (2005) 313]
[Izotov, Thuan, ApJL 710 (2010) L67]
[Mangano, Serpico, PLB 701 (2011) 296]
Ns = 0.85+0.39
−0.56
(95% C.L.)
[Hamann, Hannestad, Raffelt, Wong, JCAP 1109 (2011) 034]
◮
Standard ΛCDM: 3+1 allowed, 3+2 disfavored
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 32/33
A.G. Riess et al. astro-ph 1103.2976
Conclusions
◮
Short-baseline neutrino oscillation anomalies =⇒ sterile neutrinos
◮
Short-Baseline ν̄µ → ν̄e Signal is not feeling well:
◮
◮
◮
◮
◮
◮
MiniBooNE 2011 antineutrino data were more similar to neutrino data than
those of 2010 (LSND signal diminished and low-energy anomaly appeared)
MiniBooNE 2012 antineutrino data are even more similar to neutrino data
Probably there is no CP violation =⇒ no need of 3+2
The decrease of MiniBooNE-LSND agreement is discouraging
Better experiments are needed to clarify situation
Short-Baseline νe and ν̄e Disappearance is in good health:
◮
◮
◮
◮
Reactor ν̄e anomaly is alive and exciting
Gallium νe anomaly has been strengthened by new cross-section
measurements
Many promising projects to test short-baseline νe and ν̄e disappearance in a
few years with reactors and radioactive sources
Independent tests through effect of m4 in β-decay and (ββ)0ν -decay
M. Laveder − Sterile Neutrinos: Phenomenology and Fits − 25 July 2012 − 33/33
Backup slides
Parameter Goodness-of-fit (PG)
• The goodness-of-fit is the probability to obtain a worse fit under the assumption that the
model under consideration is correct. It is the standard statistic used for the estimation
of the quality of a fit obtained with the least-squares method, assuming the validity of
the approximation in which χ2min has a χ2 distribution with NDF
= ND − NP degrees of
freedom, where ND is the number of data points and NP is the number of fitted
parameters. The fit is usually considered to be acceptable if the goodness-of-fit is larger
than about 1%.
• The value of (Δχ2min )A+B corresponding to the Parameter Goodness-of-fit (PG) of two
experiments A and B is given by (χ2min )A+B − [(χ2min )A + (χ2min )B ]. It has a χ2
distribution with number of degrees of freedom NDF = PA + PB − PA+B , where PA , PB
and PA+B are, respectively, the number of parameters in the fits of A, B and A+B data.
[M. Maltoni and T. Schwetz, Phys. Rev. D68 (2003) 033020 (hep-ph/0304176).]