TAUP 2015
Torino, 9/9
Sterile neutrinos
Antonio Palazzo
MPI Munich
Outline
Introduction
- Short baseline anomalies, a critical overview
-  Sterile νs and CPV: a new challenge for LBLs
-  Other potential windows onto sterile νs
Conclusions
9/9/15
Antonio Palazzo, MPI Munich
2
Sterile neutrinos
Many extensions of the SM involve sterile
neutrinos, i.e. singlets of the SM gauge group
νs investigated at several scales:
• GUT, see-saw models of ν mass, leptogenesis
• TeV, production at LHC and impact on EWPOs
• keV, dark matter candidates
✓ • eV, anomalies in SBL oscillation experiments
• sub-eV, θ13-reactors and solar neutrinos
9/9/15
Antonio Palazzo, MPI Munich
3
Light Sterile Neutrinos: A White Paper
Light νs
Wide interest in the
scientific community
K. N. Abazajian , M. A. Acero,2 S. K. Agarwalla,3 A. A. Aguilar-Arevalo,2 C. H. Albright,4, 5
S. Antusch,6 C. A. Argüelles,7 A. B. Balantekin,8 G. Barenboima ,3 V. Barger,8 P. Bernardini,9
F. Bezrukov,10 O. E. Bjaelde,11 S. A. Bogacz,12 N. S. Bowden,13 A. Boyarsky,14 A. Bravar,15
D. Bravo Berguño,16 S. J. Brice,5 A. D. Bross,5 B. Caccianiga,17 F. Cavanna,18, 19 E. J. Chun,20
B. T. Cleveland,21 A. P. Collin,22 P. Coloma,16 J. M. Conrad,23 M. Cribier,22 A. S. Cucoanes,24
J. C. D’Olivo,2 S. Das,25 A. de Gouvêa,26 A. V. Derbin,27 R. Dharmapalan,28 J. S. Diaz,29
X. J. Ding,16 Z. Djurcic,30 A. Donini,31, 3 D. Duchesneau,32 H. Ejiri,33 S. R. Elliott,34
D. J. Ernst,35 A. Esmaili,36 J. J. Evans,37, 38 E. Fernandez-Martinez,39 E. Figueroa-Feliciano,23
B. T. Fleminga ,18 J. A. Formaggioa ,23 D. Franco,40 J. Gaffiot,22 R. Gandhi,41 Y. Gao,42
G. T. Garvey,34 V. N. Gavrin,43 P. Ghoshal,41 D. Gibin,44 C. Giunti,45 S. N. Gninenko,43
V. V. Gorbachev,43 D. S. Gorbunov,43 R. Guenette,18 A. Guglielmi,44 F. Halzen,46, 8
J. Hamann,11 S. Hannestad,11 W. Haxton,47, 48 K. M. Heeger,8 R. Henning,49, 50 P. Hernandez,3
P. Huberb ,16 W. Huelsnitz,34, 51 A. Ianni,52 T. V. Ibragimova,43 Y. Karadzhov,15 G. Karagiorgi,53
G. Keefer,13 Y. D. Kim,54 J. Koppa ,5 V. N. Kornoukhov,55 A. Kusenko,56, 57 P. Kyberd,58
P. Langacker,59 Th. Lasserrea ,22, 40 M. Laveder,60 A. Letourneau,22 D. Lhuillier,22 Y. F. Li,61
M. Lindner,62 J. M. Linkb ,16 B. L. Littlejohn,8 P. Lombardi,17 K. Long,63 J. Lopez-Pavon,64
W. C. Louisa ,34 L. Ludhova,17 J. D. Lykken,5 P. A. N. Machado,65, 66 M. Maltoni,31
W. A. Mann,67 D. Marfatia,68 C. Mariani,53, 16 V. A. Matveev,43, 69 N. E. Mavromatos,70, 39
A. Melchiorri,71 D. Meloni,72 O. Mena,3 G. Mention,22 A. Merle,73 E. Meroni,17 M. Mezzetto,44
G. B. Mills,34 D. Minic,16 L. Miramonti,17 D. Mohapatra,16 R. N. Mohapatra,51 C. Montanari,74
Y. Mori,75 Th. A. Mueller,76 H. P. Mumm,77 V. Muratova,27 A. E. Nelson,78 J. S. Nico,77
E. Noah,15 J. Nowak,79 O. Yu. Smirnov,69 M. Obolensky,40 S. Pakvasa,80 O. Palamara,18, 52
M. Pallavicini,81 S. Pascoli,82 L. Patrizii,83 Z. Pavlovic,34 O. L. G. Peres,36 H. Pessard,32
F. Pietropaolo,44 M. L. Pitt,16 M. Popovic,5 J. Pradler,84 G. Ranucci,17 H. Ray,85
S. Razzaque,86 B. Rebel,5 R. G. H. Robertson,87, 78 W. Rodejohanna ,62 S. D. Rountree,16
C. Rubbia,39, 52 O. Ruchayskiy,39 P. R. Sala,17 K. Scholberg,88 T. Schwetza ,62 M. H. Shaevitz,53
M. Shaposhnikov,89 R. Shrock,90 S. Simone,91 M. Skorokhvatov,92 M. Sorel,3 A. Sousa,93
D. N. Spergel,94 J. Spitz,23 L. Stanco,44 I. Stancu,28 A. Suzuki,95 T. Takeuchi,16 I. Tamborra,96
J. Tang,97, 98 G. Testera,81 X. C. Tian,99 A. Tonazzo,40 C. D. Tunnell,100 R. G. Van de Water,34
L. Verde,101 E. P. Veretenkin,43 C. Vignoli,52 M. Vivier,22 R. B. Vogelaar,16 M. O. Wascko,63
J. F. Wilkerson,49, 102 W. Winter,97 Y. Y. Y. Wonga ,25 T. T. Yanagida,57 O. Yasuda,103
M. Yeh,104 F. Yermia,24 Z. W. Yokley,16 G. P. Zeller,5 L. Zhan,61 and H. Zhang62
arXiv:1204.5379v1 [hep-ph] 18 Apr 2012
a 1
1 University
2 Instituto
of California, Irvine
de Ciencias Nucleares, Universidad Nacional Autónoma de México
3 Instituto
de Fisica Corpuscular, CSIC and Universidad de Valencia
4 Northern
5 Fermi
Illinois University
National Accelerator Laboratory
6 University
a
b
9/9/15
of Basel
Section editor
Editor and corresponding author ([email protected] and [email protected])
Antonio Palazzo, MPI Munich
4
The short baseline anomalies,
a critical overview
9/9/15
Antonio Palazzo, MPI Munich
5
The SBL accelerator anomalies
February 25, 2013
14:7
WSPC/146-MPLA
S0217732313300048
3–11
(unexplained νe appearance in a νµ beam)
LSND
[LSND, PRL 75 (1995) 2650; PRC 54 (1996) 2685; PRL 77 (1996) 3082; PRD 64 (2001) 112007]
Phenomenology of Light Sterile Neutrino
30 m
20 MeV
Beam Excess
_
_
_
+
p(νe,e )n
12.5
2
2
p(νµ→νe,e+)n
15
10
200 MeV
E
10
Karmen
Bugey
other
10
1
7.5
KARMEN2 90% CL
LSND 90% CL
Nu
-1
0
MiniBooNE Results
0.8
2
∆mLSND ! 0 2 eV
MiniBooNE
#䃛 " #e
C. Giunti
(anti-)#e
e p (CCQE)
excess of events
ergy
ue?
9/9/15
y MicroBooNE)
more….
10
1
1.2
1.4
L/Eν (meters/MeV)
Lett. A Downloaded from www.worldscientific.com
UTE FOR PHYSICS LIBRARY on 02/28/13. For personal use only.
0.6
#䃛 " #e
2
-2
Δm2(eV2)
10
2.5
om 2007-12
LSND 99% CL
NOMAD
5
0.4
68% CL
90% CL
95% CL
99% CL
3σCCFR
CL
MiniBooNE
17.5
L
2 4
LSND
¯e
Δm (eV /c )
Beam Excess
¯
90% (Lmax-L < 2.3)
99% (Lmax-L < 4.6)
10
(
2
∆mATM
Phenomenology of Sterile Neutrinos
-3
10
-2
2
∆mSOL
)
16 May 2011
Te
V(
90
FR
%)
(
90
MA
%)
D(
90
%)
-1
CL
10Excluded at 90%
1
2
2θ
Excludedsin
at 99%
CL
ICARUS
NO
CC
5/59
1
sin2(2θ)
Fig. 1. Regions allowed by the main published experiments sensitive to the accelerator anomal
superimposed to the limits established by the ICARUS experiment. Figure taken from Ref. 9.
nary” pieces of data, namely the solar neutrino sector experiments together with th
Antonio
Palazzo,
MPIθ13
Munich
6
new
dual-baseline
-sensitive reactor experiments Daya Bay and RENO,
are abl
to put interesting constraints on the 3 + 1 scheme. Finally we draw our conclusions
The reactor and gallium anomalies
(unexplained
νe disappearance)
CHOOZ
PaloVerde
Bugey3
Goesgen
Krasnoyarsk!2
Krasnoyarsk!3
Goesgen
Bugey3
Goesgen
1.05
1
0.95
0.9
0.85
0.8
0.75
0.7
1.1
p(measured)/ p(predicted)
NOBS/(NEXP)pred,new
ILL
1.1
ROVNO
Bugey!3/4
1.15
Krasnoyarsk
9
GALLEX Cr1
SAGE Cr
1.0
0.9
0.8
0.7
1
2
10
10
GALLEX Cr2
SAGE Ar
3
10
Distance to Reactor (m)
FIG. 4. Illustration of the short baseline reactor antineutrino anomaly. The experimental results are compared to the prediction
without oscillation, taking into account the new antineutrino spectra, the corrections of the neutron mean lifetime, and the
off-equilibrium effects. Published experimental errors and antineutrino spectra errors are added in quadrature. The mean
averaged ratio including possible correlations is 0.937±0.027. The red line shows a 3 active neutrino mixing solution fitting the
data, with sin2 (2θ13 ) = 0.06. The blue line displays a solution including a new neutrino mass state, such as |∆m2new,R | ! 1
eV2 (for illustration) and sin2 (2θnew,R )=0.16.
Mention et al. arXiv:1101:2755 [hep-ex]
[SAGE, PRC 73 (2006) 045805, nucl-ex/0512041]
SAGE coll., PRC 73 (2006) 045805
RGa = 0 86
0 issues
05
Warning: both are mere normalization
noted anomalies affecting other short baseline electron
neutrino experiments Gallex, Sage and MiniBooNE, reviewed in Ref. [43]. Our goal is to quantify the compatibility of those anomalies.
We first reanalyzed the Gallex and Sage calibration
runs with 51 Cr and 37 Ar radioactive sources emitting
∼1 MeV electron neutrinos. [44], following the method[SAGE, PRC 59
ology developed in Ref. [43, 45]. However we decided to
include possible correlations between these four measurements in this present work. Details are given in in Appendix B. This has the effect of being slightly more conservative, with the no-oscillation hypothesis disfavored at
97.73% C.L., instead of 98% C.L in Ref. [43]. Gallex and
Sage observed an average deficit of RG = 0.86±0.05(1σ).
Considering the hypothesis of νe disappearance caused by
short baseline oscillations we used Eq. (11), neglecting
the ∆m231 driven oscillations because of the very short
baselines of order 1 meter. Fitting the data leads to
|∆m2new,G | > 0.3 eV2 (95%) and sin2 (2θnew,G ) ∼ 0.26.
Combining the reactor antineutrino anomaly with the
Gallium anomaly gives a good fit to the data and disfavors the no-oscillation hypothesis at 99.7% C.L. Allowed
regions in the sin2 (2θnew ) − ∆m2new plane are displayed
Experiment(s)
sin2 (2θnew ) |∆m2new | (eV2 ) C.L. (%)
Reactors (no ILL-S,R∗ ) 0.02-0.23
>0.2
95.0
Gallium (G)
0.06-0.4
>0.3
97.7
—
—
72.4
MiniBooNE (M)
ILL-S
—
—
68.2
∗
R +G
0.07-0.24
>1.5
99.7
0.04-0.23
>1.4
97.5
R∗ + M
(1999)
2246, hep-ph/9803418]
R∗ + ILL-S
0.04-0.23
>2.0
97.1
ALL
0.06-0.25
>2.0
99.93
The culprit may be in hidden systematics
9/9/15
C. Giunti
Recent Progress in Neutrino Physics
TABLE III. Best fit parameter intervals or limits at (95%)
for (sin2 (2θnew ), ∆m2new ) and significance of the sterile neutrino oscillation hypothesis in %, for different combinations of
the reactor experiment rates only (R∗ ), the ILL-energy spectrum information (ILL-S), the Gallium experiments (G), and
MiniBooNE-ν (M) re-analysis of Ref. [43].
Antonio Palazzo, MPI Munich
eV2 and sin2 (2θnew,MB ) ∼ 0.2, but are not significant
at 95% C.L. The no-oscillation hypothesis is only disfavored at the level of 72.4% C.L., less significant than
the reactor and gallium anomalies. Combining the reactor antineutrino anomaly with our MiniBooNE re-
1 Mar 2011
21/25
7
New-generation detectors confirm deficit
Daya Bay @ Neutrino 2014 & ICHEP 2014
Definitive results appeared 3 weeks ago on arXiv:1508.04233
However, the same detectors give us a warning …
9/9/15
Antonio Palazzo, MPI Munich
8
Understanding of rea. spectrum is incomplete
Daya Bay
RENO
Observation of new reactor # component at 5 MeV!
V'$)C"/&"4&U&R(f&(@)(++&ZX[&#"&(@A()#(-&D9@&
"  #*2,%S%<;@=@%g^h%%=;B=>%A*-.*,&/*0(2FD%g^h%=;BC<%A*-.*9(*4%')2.*%*,,1,D%%%%%%%%%%%%%%%%%
"  P2,%%%%S%>;YYU%g^h%%=;Y=`%A*-.*,&/*0(2FD%g^h%=;B`V%A*-.*9(*4%')2.*%*,,1,D
Double-CHOOZ
Spectrum
distortion (1)
◾ spectral distortion above 4 MeV observed
◾ several crosschecks have shown
▸
▸
▸
Shoulder at 4-6 MeV observed in all the three experiments
θ13 measurement is not affected
energy scale at E > 4 MeV tested (e.g. n-12 C) and as cause disfavoured
unknown background disfavoured
Identical at Near & Far sites: not imputable to new osc. physics
Julia Haser (MPIK Heidelberg)
DC-III @ ICHEP 2014
2014/07/04
13 / 16
θ13 extraction is unaffected (based on near/far comparison)
9/9/15
Antonio Palazzo, MPI Munich
9
pd
fission daughters are unstable, and will decay until reaching a stable isotopic state. The cumulative yield Ypic is the
�
probability that a particular isotope AZ� Ni is produced via
the decay chain of any initial fission daughter. On average, the daughter isotopes of each fission undergo 6 beta
decays until reaching stability. For short-lived isotopes,
the decay rate Ri is approximately equal to the fission
Hayes et al.
Dwyer and Langford
`8(iM&7-/%(0*%('&13(3G(&/1/%"0'-/3(,6%#0'&(G3'(H-F%'%/0(
rate Rf of the parent isotope p times the cumulative yield
PRL p112, 202501 (2014)
PRL 114, 012502 (2015)
of the isotope i,
0'%&07%/0,(3G(0*%(G3'I-HH%/(0'&/,-13/,(
p=0
Rpf Ypic
(2)
Hayes et al.
arXiv:1306.00583 [nucl-th]
Nuclear Calculation
0.2
-
β Conversion, Huber
-p+@1-=>+0-=i+`E@8+!-k8:+
XROa+'(*+a&UV*b+
-
β Conversion, Mueller
Normalized Ratio to Huber-Mueller
Ri �
P
�
σν × S(Eν ) [MeV-1 fission-1]
Discrepancy under active investigation
1.15
Huber-Mueller uncert.
JEFF-3.1.1
ENDF/B-VII.1
Daya Bay
S(Eν ) / S
-
β conv.
(Eν )
1.1
The ENDF/B.VII.1 compiled nuclear data contains ta0.1
#4:R*M+
bles of the cumulative fission yields of 1325 fission daugh1.05
ter isotopes, including relevant nuclear isomers [17, 18]. p&:V*M+
Evaluated nuclear structure data files (ENSDF) provide p*:VM+
1
RENO
tables of known beta decay endpoint energies and branch1.1
Double CHOOZ
0.95
ing fractions for many isotopes [19]. Over 4000 beta
1
decay branches are found which have endpoints above
0.9
0.9
7
2
3
4
5
6
the 1.8 MeV threshold for inverse beta decay. The specEPrompt (MeV)
0.8 2
3
4
5
6
7
8
trum of each beta decay Sij (Eν ) was calculated includAntineutrino Energy [MeV]
%<B3+3Q+<2B2-./0123+8S-F/0.A+/3+/E-+301T12<=+e!!+8S-F/0.A+<==3J12T+
ing Coulomb [20], radiative [21], finite nuclear size, and
+>1l-0-2/+3S-0</308+/3+>3A12</-+/E-+232#.21n.-+Q30C1>>-2+/0<281B328+
weak magnetism corrections [13]. In the following calcu- FIG. 1. Upper: The ab initio nuclear calculation of the
+
E*%(G3'I-HH%/(0'&/,-13/,(-/0'3H"#%(&/(36%'&03'JH%6%/H%/0((H-,03'13/(3G(,6%#0'"7((
lations we begin by assuming that
have allowed cumulative
β − energy spectrum per
fission of 235entirely
U exposed
• Systematics
inall decays
reactor
spectra
not
under control
4(6"'%$+(0*%3'%1#&$(&/&$+,-,(-,("/$-C%$+(03('%H"#%(0*%("/#%'0&-/1%,(-/(&(73H%$J-/H%6%/H%/0(e&+(
to thermal neutrons (red), including 1-σ uncertainties due
Gamow-Teller
spectral
shapes.
The
impact
of
forbidden
+
to fission yields and branching fractions. The measured β −
shape corrections will be discussed later in the text.
No(!%%H(H-'%#0(7%&,"'%7%/0(3G(0*%(,*&6%(3G(0*%(,6%#0'"7(03('%H"#%(0*%("/#%'0&-/1%,(
&V+
• Dissimilar
results
with
two
different nuclear databases
The upper panel of Fig. 1 shows the electron spectrum spectrum from [6] is included for reference (blue). Lower:
The corresponding ν e spectrum per fission in a nominal reper fission of 235U calculated according to Eq. 1. The β −
actor weighted by the inverse beta decay cross section (red),
• Normalization
spectral
not necessarily related
spectrum measured in the 1980s using &
the BILL
spec- compared with thatissues
obtained by the β − conversion method
trometer is shown for comparison [6]. Both spectra are (blue [12], green [11]). See text for discussion of uncertainties.
normalized
in units of electrons per MeV per needed
Measurements of the positronto
spectra (green
[22], brown [23])light on both issues
• Newabsolutely
SBL
experiments
shed
fission. The lower panel shows the calculated ν e spec- are similar to the ab initio calculation, assuming the approxtrum for a nominal nuclear reactor with relative fission imate relation Eν � Ee+ + 0.8 MeV.
9/9/15 rates of 0.584, 0.076, 0.29, 0.05 respectively for the parAntonio Palazzo, MPI Munich
10
The significant differences between the calculation and
ents 235U, 238U, 239Pu, 241Pu. The spectra have been
weighted by the cross section for inverse beta decay to BILL measurements are generally attributed to system2
3
4
5
6
7
8
No anomaly in νµ disappearance
Δm2
sin22θ
Figure 44. 90% CL sensitivity (dot-dash curve) and 90% CL
µµ
limit (solid black curve) from simultaneous
MiniBooNE/SciBooNE fit, and 90% CL limit from the spectrum fit method (red dashed curve). Previous
limits from CCFR, CDHSW, MINOS, and MiniBooNE are also shown.
only upper bounds (till now)
For the simultaneous fit, the χ2 for the null hypothesis was 45.1 for a 59% probability (48 DOF).
Using MiniBooNE Run I data, the best fit point was at ∆m2 = 43.7 eV2 , sin2 2θ = 0.60, which had
a χ2 of 39.5. The best fit point using Run II data had a χ2 of 41.5. Combining the two MiniBooNE
data run periods provided negligible improvement relative to the Run I data alone. For the spectrum
fit method, the χ2 for the null hypothesis was 41.5 for a 12% probability (32 DOF). The best fit
point was at ∆m2 = 41.7 eV2 , sin2 2θ = 0.51, which had a χ2 of 35.6. In Fig. 44, the 90% CL limit
9/9/15
Palazzo,
MPIFor
Munich
2
2
curve for
the simultaneous fit is basedAntonio
on a ∆χ
of 9.34.
the spectrum fit method, the ∆χ11
value
for the 90% CL limit curve is 8.41.
Can the sterile neutrino hypothesis
explain consistently
all the three different channels?
9/9/15
Antonio Palazzo, MPI Munich
12
Introducing a sterile neutrino
3+1 scheme
3ν scheme
|Us4| ~ 1
2
Δm14 ~ 1 eV 2
2
Δmatm
2
Δmsol
Only a small perturbation of the 3ν framework
But potential big revolution for particle physics!
9/9/15
Antonio Palazzo, MPI Munich
13
Tension in all νs models
3+1
3+2
Giunti
&
Laveder
arXiv:1107.1452
νµ ->
νe –>
νµ ->
νe positive
νe positive
νµ negative
sin2 2θeµ �
9/9/15
|Ue4||Uµ4| > 0
|Ue4| > 0
|Uµ4| ~ 0
1
sin2 2θee sin2 2θµµ � 4|Ue4 |2 |Uµ4 |2
4
Antonio Palazzo, MPI Munich
14
An undecidable problem
si n 22ϑ(4)
µµ
1,2,3 σ contours
2
However, their combination
gives a 6σ improvement
with respect to the 3ν case
10−1
+
+
Difficult to take a
decision on sterile νs !
3+1
DIS
APP
GLO
10−2
10−2
10−1
si n
he relation in
oximated rela-
2
2ϑ(4)
ee
(4)
APP. & DIS. barely
overlap at 2σ level
(4)
FIG. 2.
Allowed regions in the sin2 2ϑee –sin2 2ϑµµ plane
obtained in the global 3+1 analysis of short-baseline data
presented in Ref. [44]. The green shadowed regions are the
regions allowed at 1σ, 2σ and 3σ by the analysis of shortbaseline disappearance (DIS) data, with the best fit value
indicated by a dark-green cross. The strips enclosed by the
blue diagonal lines are allowed at 1σ, 2σ and 3σ by the analysis of short-baseline appearance (APP) data, with the central
best fit dark-blue line. The solid lines correspond to the exact relation in Eq. (9), whereas the dashed lines correspond to
the approximated relation in Eq. (10). The regions inside the
red-orange closed curves are allowed at 1σ, 2σ and 3σ by the
global (GLO) analysis of short-baseline data, with the best
fit value indicated by a dark-red cross.
Only new more sensitive
experiments can decide …
3ν limit
oosing p = 1
sin2 ∆k1
n ∆k1 sin ∆j1
Figure from Giunti & Zavanin, arXiv:1508:03172
9/9/15
Antonio Palazzo, MPI Munich
15
SOX: SHORT DISTANCE OSCILLATIONS W
The smoking gun
events
source - external
events
51Cr
!m2 = 2.0 eV2
sin2(2!s) = 0.05
200
4500
4000
150
3500
Oscillatory pattern (in energy and/or space)
100
3000
50
SOX:
SHORT DISTANCE
BOREXINO (II)
A
promising
option: νOSCILLATIONS
source closeWITH
to Borexino
2500
0
400
source - external
!m2 = 2.0 eV2
sin2(2!s) = 0.05
200
500
sensitivity of
events
events
51Cr
600
700
51Cr
800
900
1000
distance from source (cm)
144Ce
source - internal
source - external
sensiti
4500
4000
#!$
150
!m2 = 2.0 eV2
sin2(2!s) = 0.05
1 year
!!"#$%
3500
100
3000
50
2500
%&#''$(!$)%*$
%&+,&-$
./($0123$
#4$&--"$356-7&
#4$&--"$89$
#$
!"#$
0
400
500
sensitivity of
600
51Cr
700
0
800
900
1000
distance from source (cm)
100
200
300
400
500
600
distance from!"!#$
center (cm)
Neutrino 2012 - Kyoto
source - external
!"!!#$
M. Pallavicini
M. Pallavicini @ Neutrinosensitivity
2012 of 144Ce source - internal
:!4$%";" &<7=60&0$
%&#''$(!$)%*$
Several other projects under
%&+,&-$ scrutiny
#!$
./($0123$
#4$&--"$356-7&$*+,&+3*,2$
#4$&--"$89$
!!"#$%
But such an observation would be only the start
of the adventure in the sterile neutrino world…
9/9/15
#$
Antonio Palazzo, MPI Munich
!"#$
0
16
Sterile neutrinos and CPV:
a new challenge
for the LBL experiments
Based on:
- N. Klop and A.P., PRD 91 073017 (2015)
- A.P., PRD 91 091301 (2015) Rapid Communication
- A.P., in preparation
9/9/15
Antonio Palazzo, MPI Munich
17
An intrinsic limitation of SBLs
At SBL setups atm/sol oscillations negligible
L
m
∼
E
MeV
∆12 � 0
∆13 � 0
Δij =
Δm2ij L
4E
-  Not possible to observe interference phenomena
between the sterile and atm/sol frequencies
-  This is relevant because we need to observe
such phenomena in order to measure the new
CP phases that accompany the new sterile states
9/9/15
Antonio Palazzo, MPI Munich
18
ability
forDirac
Dirac
anddepend
Majorana
neutrinos
isprobnotmeasured
be measured
by neutrino
oscillation
experiments.
The on
oscillation
ability
for
and
Majorana
neutrinos
isidentica
identic
be
by neutrino
oscillation
experiments.
The
oscillation
probHence,
neutrino
oscillations
do not
the
Majorana
phas
them
as
different
cases
anymore.
them
different
cases
anymore.
Dirac
Majorana
neutrinos
is identical,
so from
now
on
wenot
willtreat
not treat
phases
cannot
be
measured
by neutrino
oscillation
experiments.
c and and
Majorana
neutrinos
is identical,
so as
from
now
on
we
will
fferent
anymore. ability for Dirac and Majorana neutrinos is identical, so from now
nt casescases
anymore.
Themixing
mixingmatrix
matrix UU can
can be
be parameterized
The
parameterizedby
bythe
them
Mixing matrix in 3+1 scheme
them as different cases anymore.
matricesRRjkjk. . These
These matrices
matrices perform
matrices
perform aa rotation
rotationo
matrix
U be
canparameterized
be parameterized
by
multiplication
ofreal
theby
real
orthogonal
a2 2×
2matrix,
matrix,
they
are
simply
given
by:
trix
U can
by the
multiplication
of
the
orthogonal
athe
they
are
simply
given
by:
The mixing
matrix
U×2can
be parameterized
the
multiplication
jk
jk of anof
. These
matrices
perform
a rotation
an 23
angle
θjk
theplane.
j–kofplane.
For
These
matrices
perform
a 34
rotation
θjkperform
in13
theinaj–k
Forangle
matrices
R24
. These
matrices
rotation
an
θjk
14angle
12
�
�
�
a 2 ×by:
2 matrix, they are simply given by: � c
trix,
are simply
theythey
are simply
givengiven
by:
s
= cijij sijij , ,
R̃R̃ijij
3ν
RRijij =
−s
c
ij
ij
−sij cij
�
�
�
�
−iδ
ij
�
� �
� �
�
�cij s�ijssij =
−iδ
c
s̃
=
sin
θ
s̃
=
s
e
ij
ij
ij
ij
ij
sin
θ
s̃
=
s
e
ij = ij
ij
R̃
cijRij =cs̃ijij−s s̃ijc ij ,
cij csijij sij
ij
∗
−s̃
cij
ij
ij cij = cos θij
Rij =
,
(72) ij(72)
Rij =
,R̃ij =R̃ij =∗
c
=
cos
θ
∗
ij
ij
−s̃ij −s̃
c ij cij
−sij −s
cijij cij
sij = ij
sin θij
s̃ij = sij e−iδij
−iδ
Formixing
matrices with higher dimensions, the ma
ijmixingmatrices
sij =sij
sin=θijsin θij s̃ij =s̃sijij=
e−iδ
sijijeFor
cij = cos θij with higher dimensions, the m
R
∼R
R
∼R
R
{
U =∼
R
cij =cij
cos=
cos
θij Forangles
3θij
mixing
mixing matrices with higher dimensions, the matrices Rjk can
{
{
{
6
3+3N
19
1
Dirac
CP-phases
19
3ν
3+1 jk 3
3+N 1+2N
jk
rices
withwith
higher
dimensions,
the matrices
R 3can
constructed
from: from:
2 Majorana
phases
matrices
higher
dimensions,
the matrices
R be
can
be constructed
2+N
19
θ14 = θ24 = θ34 = 0
19
9/9/15
19
➜
3-flavor case
Antonio Palazzo, MPI Munich
19
baseline QP bea
A narrow-band,
longOutline
of T2K & NOνA
baseline QP beam
‡
‡
810 km away, 14 mrad (0.84o) off-axis,
is narrow and at a good L/E for oscillati
NuMI beam has operated routinely at u
± NOQA upgrades will put it to 700 kW in 20
(compared to 1.2 MW eventually in new b
± Plans are to run in both neutrino and anti-
‡ 810 km away,off-axis
14 mrad (0.84o) off-axis, the beam spectra
is narrow and at a good L/E for oscillation physics
beam
‡ NuMI beam has operated routinely at up to 500 kW
± NOQA upgrades will put it to 700 kW in 2016
(compared to 1.2 MW eventually in new beam for DUNE)
± Plans are to run in both neutrino and anti-neutrino modes
∆m213 L π
∆=
�
4E
2
First
oscillation
maximum
9/9/15
E = 0.6 GeV
E = 2 GeV
L = 295 km
L = 810 km
Antonio Palazzo, MPI Munich
20
α → −α ∆ → −∆
(159)
−α
(159)
α∆ → α∆α →
(unchanged).
α∆ → α∆ (unchanged).
o probability in vacuum for LBL experiments can be written as the sum
inct
components:
the atmospheric
term,
theexperiments
solar term and
that
he
neutrino
probability
in vacuum for
LBL
can the
be term
written
as the sum
the
interference
between
the
two:
three distinct components: the atmospheric term, the solar term and the term that
mes from the interference between the two:
Pν3νµ →νe = P ATM + P SOL + P INT ,
(160)
Pν3νµ →νe = P ATM + P SOL + P INT ,
(160)
3-flavor transition probability
here
In vacuum:
→ νe appearance
in2 T2K,2 the three-neutrino case in
ATM
SOL
2 2
2
P212
=
4s
P
=
4c
c
s
(α∆)
(161)
23 s13 sin ∆
23 12
uum
P ATM = 4s223 s213 sin2 ∆
2 2 2
2
c23(α∆)
s12 (α∆)
P
= 8sP23SOL
s13 c=12 c4c
s12
sin ∆
cos(∆ + δCP ).
2312
ion, the transition INT
probability for νµ → νe is derived in the LBL approxiP
=use
8s23that
s13 c12|∆m
c s212|(α∆)
sin 2∆| cos(∆
+ δCP
). | is small.
this approximation,
|Ue3
onents
are plotted inwefigure
14 as a23 function
of 21sinand
2θ13that
, where
the other
31 � |∆m
INT
32
31
21
ATM
INT
SOL
Pµe
best θ13
estimate
(161)
ulation,
the
following
definitions
aretable
used:2 and the neutrino energy is fixed
are fixed
at the
best
valuesin
from
hese
components
arefit
plotted
figure
14 as a function of sin 2θ13 , where the other
INT
GeV.
The
interference
term
P
is
taken
at his maximal
value
2
Δ∼
π/2by fixing
rameters are fixed at the
fit values from
neutrino
energy is fixed
∆mbest
∆m221table 2 and the
31 L
at
cos(∆
+
δ
)
=
1.
INT
CP The
∆ =interference
, term
α =P
.
(146)by fixing
Eν = 0.6 GeV.
is
taken
at
his
maximal
value
4E
∆m231
α
∼
0.03
P such that cos(∆ + δCP ) = 1.
nt three-flavour global fits we know that α ∼ 0.03. For normal hierarchy
2
2 > 0
PATM∆m
leading
à∆m
θ13
= ∆m2 −
.
E = 0.6 GeV
sin 2θ13
NH
(147)
o account that in the T2K setup ∆ is O(1), we can use the approximate
PINT subleading à δ dependence
sin ∆α � ∆α.
PSOL negligible
ng goniometric identities are used:
(148)
IH
Matter effects break the
degeneracy
sin(a − b) = sin a cosbetween
b − cos a sin b NH & IH
(149a)
cos(a + b) = cos53a cos b − sin a sin b
(149b) (a) The results from T2K. The figure is taken from
[65].
(b) Our reproduc
2
cos 2a = 1 − 2 sin a 53
(149c)
2
Figure 19: The allowed regions for sin 2θ13 as a function of δC P in
including matter effects. The upper panels refer to normal hierar
sin
2a
=
2
sin
a
cos
a.
(149d)
21 T2K, th
9/9/15
Antonio Palazzo, MPI
Munich
inverted
hierarchy. The left panel shows the results from
reproduction.
that |α| and s13 have similar magnitude � as described in [66]. Using
The CP-violating phase and the value of θ
were varied while
First hints of CPV and NMH
-
T2K (νe+νe) & NOνA (νe)
First hint of
manifest CPV
CP-conservation (δ = 0, π)
disfavored at
~ 90% C.L.
Best fit δ ~ - π/2
Hint of NH
Δχ2 ~ -1.3
Two existing trends tend to consolidate:
-  Slight preference for NH
-  Slight preference for sin δ < 0
Next data releases should be more informative
9/9/15
Antonio Palazzo, MPI Munich
22
4-flavor transition probability
- Δm214 >> Δm213 : fast Δm214 osc. are averaged out
- Phase info. (Δm214) gets lost (in contrast to SBL)
- Unlike SBL, interf. of Δm214 & Δm213 is observable
4ν
Pµe
�P
{
ATM
+ PIINT
+ PIIINT
s13 ~ s14 ~ s24 ~ ε
α = δm2/Δm2 ~ ε2
P ATM � 4s223 s_213 sin2 ∆
PIINT � 8s_
13 s23 c23 s12 c12 (α∆)
_ sin ∆ cos(∆ + δ13 )
PIIINT � 4s_
14 s24
_ s_13 s23 sin ∆ sin(∆ + δ13 − δ14 )
9/9/15
Ο(ε2)
Ο(ε3)
Ο(ε3)
Sensitivity to the new CP-phase δ14
Antonio Palazzo, MPI Munich
23
New int. term is as large as the standard one
T2K: θ13 = 9o E = 0.6 GeV
PATM
Pµe
SBL
sin2 2θµe = 4|Ue4|2|Uµ4|2
|PII|max
PSTR
|PI |max
|PIII |max
Psol
sin 2θµe
3ν limit
9/9/15
Antonio Palazzo, MPI Munich
24
Results of the 4ν analysis (LBL,IH)
3ν: T2K + NOνA (IH)
4ν
-  For δ14 = -π/2 perfect agreement of LBL & Rea
-  As a consequence no hint of NH in a 3+1 scheme
- Fragility of the LBL discovery potential of the NMH ?
9/9/15
Antonio Palazzo, MPI Munich
25
Constraints on the two CP-phases
NH
IH
- Comparable sensitivity to δ13 & δ14
-  Best fit values: δ13 ~ δ14 ~ -π/2
- This information cannot be achieved with SBLs !
9/9/15
Antonio Palazzo, MPI Munich
26
8
OPERA, JHEP 1307 (2013) 036
oscillated ν e by 3 flavor oscillation
7
ν e beam contamination
6
BG from τ → e
BG from NC with π0
5
overflow
Number of events / 10 GeV
CP-phases matter also in CNGS expts.
Data
4
3
2
1
0
0
20
40
60
80
100
120
140
160
Reconstructed energy (GeV)
Figure 6. Distribution of the reconstructed energy of the νe events, and the expected spectrum
from the different sources in a stack histogram, normalized to the number of pot analysed for this
paper.
OPERA, JHEP 1307 (2013) 036
<E> = 17 GeV
oscillation parameters θnew and ∆m2
new :
Pνµ →νe = sin2 (2θnew ) · sin2 (1.27∆m2
new L(km)/E(GeV))
L = 732 km
Note however that this approach does not allow a direct comparison between experiments
working in different L/E regimes [25].
2
The νµ flux at the detector, normalized
to the integrated-3
statistics used in our anal13
ysis, is weighted by the oscillation probability,
by the CC cross-section and by the energy
dependent detection efficiency, to obtain the number of νe CC events expected from this
oscillation.
2
As the energy spectrum of the oscillated νe with large ∆m2
new (>0.1 eV ) follows the
spectrum of νµ , which is basically vanishing above 40 GeV (see figure 1), a cut on the
reconstructed energy is introduced. The optimal cut on the reconstructed energy in terms
of sensitivity is found to be 30 GeV. We observe 6 events below 30 GeV (69% of the
oscillation signal at large ∆m2
new is estimated to remain in this region), while the expected
number of events from background is estimated to be 9.4 ± 1.3 (syst) (see table 1). Note
that we choose to include the three-flavour oscillation induced events into the background.
In this case, the oscillation probability does not contain the θ13 driven term.
The 90% C.L. upper limit on sin2 (2θnew ) is then computed by comparing the expectation from oscillation plus backgrounds, with the observed number of events. Since we
observed a smaller number of events than the expected background, we provide both, the
Feldman and Cousins (F&C) confidence intervals [26] and the Bayesian bounds, setting a
prior to zero in the unphysical region and to a constant in the physical region [27]. Uncertainties of the background were incorporated using prescriptions provided in [17]. The
results obtained from the two methods for the different C.L. are reported in table 2. We
Δm
= 2.4 x 10
∆m213 L
∆=
� 0.13
4E
3ν oscillations
play a minor role
Good place where
to look for sterile νs
9/9/15
Antonio Palazzo, MPI Munich
– 8 –
27
∆ m2new (eV2)
Official bounds from OPERA & ICARUS
LSND 90% C.L.
102
LSND 99% C.L.
KARMEN 90% C.L.
NOMAD 90% C.L.
BUGEY 90% C.L.
10
CHOOZ 90% C.L.
MiniBooNE 90% C.L.
MiniBooNE 99% C.L.
ICARUS 90% C.L.
1
OPERA 90% C.L. (Bayesian)
10-1
10-2
-3
10-2
10
10-1
1
sin2 (2θnew )
Figure 7. The exclusion plot for the parameters of the non-standard νµ → νe oscillation, obtained
from this analysis using the Bayesian method, is shown. The other limits shown, mostly using
frequentist methods, are from KARMEN (ν µ → ν e [28]), BUGEY (ν e disappearance [29]), CHOOZ
2
(ν e disappearance [30]), NOMAD (νµ → νe [31]) and ICARUS (νµ → νe 2
[10]). The regions
corree µ → ν e [8]) and MiniBooNE
µe
14
sponding to the positive indications reported byµLSND (ν
(ν
µ → νe
and ν µ → ν e [9]) are also shown.
2-flavor
P(ν -> ν ) = 4 sin 2θ sin Δ
treatment
+ small Atm. term
adopted
byparameter
both space available for a non-standard ν appearance sugOPERA limits the
gested by the results of the LSND and MiniBooNE experiments. It further constrains the
P(ν -> νe) large
= 1 ∆m
(νe bck
fixed)
still collaborations
allowed region around ∆m
= 5 × 10 e eV . For
values, the 90% C.L.
2
new
{
e
−2
2
2
new
upper limit on sin2 (2θnew ) reaches 7.2 × 10−3 . This result is still affected by the statistical
underfluctuation, the sensitivity corresponding to the analysed statistics being 10.4 × 10−3 .
A Bayesian statistical treatment has therefore been adopted for determining the 28
upper
limit.
9/9/15
Antonio Palazzo, MPI Munich
Various improvements are expected for the future. The statistics will be increased
by a factor of 3.4 by completing the analysis of the collected data. The reconstructed
Impact of the 4ν interference term
A.P., PRD 91 091301 (2015) Rapid Communication
4
4
FIG. 3: Upper
bounds
(90%
C.L.)(90%
obtained
a fixed (large)
FIG. 4: Upper
(90%
C.L.)(90%
obtained
the caseinofthe case of
FIG.
3: Upper
bounds
C.L.)for
obtained
for a fixed (large)
FIG. bounds
4: Upper
bounds
C.L.) inobtained
2
!
2 cases of NH and IH. The effect of the
!
value of ∆m
the
two
NH.
The CP-phase
δCP-phase
is marginalized
away. The away.
effect The
of the
14 in of
value
∆m
in
the
two
cases
of
NH
and
IH.
The
effect
of
the
NH.
The
δ
is
marginalized
effect of the
14
oscillationsoscillations
on the νe component
is neglectedissetting
Pee setting
= 1. Pee
oscillations
on the νe component
is neglectedis setting
Peesetting
= 1. Pee = 1.
on the νe component
neglected
= 1.
oscillations
on the νe component
neglected
After marginalization of the unknown CP-phases
solid contour
the upperthe
bounds
in
solidrepresents
contour represents
upperobtained
bounds obtained
in
the 4-flavor
scheme,
assuming
|U
|
=
|U
|
and
P
=
1. Pee = 1.
e4
µ4
ee
the 4-flavor scheme, assuming |Ue4 | =! |Uµ4 | and
As expected,
a dependence
on the CP-phase
δ appearsδ ! appears
As expected,
a dependence
on the CP-phase
In our analysis
use theweresults
of results
the νµ of
→ the
νe apIn ourwe
analysis
use the
νµ → νe apthat
is
different
in
the
two
cases
of
NH
and
IH.
that
is
different
in
the
two
cases
of
NH The
and IH. The
pearance searches
[7, 8] for
ICARUS
and
pearance provided
searches in
provided
in [7,
8] for ICARUS
and
4-flavor upper
limits
are limits
substantially
stronger (weaker)
4-flavor
upper
are
substantially
stronger
(weaker)
in [9] for OPERA.
In
order
to
calculate
the
theoretical
exin [9] for OPERA. In order to calculate the theoretical exthan thosethan
obtained
in
the 2-flavor
case
whencase
the interferthose
obtained
in
the
2-flavor
when
the
interferpectation for
the
total
number
of
events,
we
convolve
the
pectation for the total number of events, we convolve the
ence term ence
assumes
positive
(negative)
values. The
maxi-The maxiterm
assumes
positive
(negative)
values.
product ofproduct
the νµ flux,
the
cross-section,
and
the
ν
→
ν
µ
e
of the
νµ flux, the cross-section, and the νµ → νe
2
mal excursion
from the 2-flavor
basically
mal excursion
from theresult,
2-flavor
result, identical
basically identical
transition transition
probabilityprobability
with the2 energy
resolution
funcwith the
energy resolution
func- MPI
!
! as expected
9/9/15
Antonio
Palazzo,
Munich
for
NH
and
IH,
is
obtained
for
δ
#
±π/2,
for
NH
and
IH,
is
obtained
for
δ
#
±π/2,
as expected
tion and the
detection
efficiency.
A
similar
computation
tion and the detection efficiency. A similar computation
from the discussion
made in Sec.
II.in Sec. II.
from the discussion
made
is performed
for the νe for
beam
incorporating
is performed
the component,
νe beam component,
incorporating
Figure 4 shows
upperthe
bounds
the usual
plane
the νe → νthe
We have checked
Figurethe
4 shows
upperinbounds
in the
usual plane
e survival
ν → ν probability.
survival probability.
We havethat
checked that
III.
NUMERICAL
ANALYSIS
III. NUMERICAL
ANALYSIS
the upper bounds get relaxed by a factor of two
29
Other potential windows
onto sterile νs
9/9/15
Antonio Palazzo, MPI Munich
30
What solar exp. have to say on νss ?
A.P., Review for Mod. Phys. Lett. A 28, 1330004 (2013)
• Solar + θ13 reactors:
sin2 θ14 < 0.04 (90% C.L.)
• Bound indep. of reactor fluxes (KamLAND only shape)
• It constitutes the only robust information on |Ue4|2
9/9/15
Antonio Palazzo, MPI Munich
31
Information from atmospheric ν in IceCube
Smoking gun: Dip at E ~ TeV due to MSW resonance
IceCube sensitivity to sterile neutr
Impact
of sterile
neutrinos on atm
ʋ flux
Nunokawa,
Peres,
Zuchanovich-Funchal
PLB 562,
279 (2003)
3 x IceCube-79 data (available now)
2
∆m2
41 = 1 eV
A.
E.,
A.
Yu.
Smirnov,
mantle crossing
sin2 2θ24 = 0.04
JHEP
1312
(2013)
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JHEP 1312, 014 (2013)
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,2sin2 2Θ24 1
"50.04
#1
100.4
27/June/2014
$ 0.6
$
$ 0.2
cos Θz 2
sin 2Θ24
10
0.0
1
TeVPA/IDM-Amsterdam
Esmaili & Smirnov JHEP 1312, 014 (2013)
events should be smeared in energy bins
Data
already
there
& wait to be analyzed!
width of are
smearing
can reach ~ 0.3
x Log (E/GeV)
as a conservative assumption we assume %E = E
Arman Esmaili
9/9/15
TeVPA/IDM-Amsterdam
Antonio Palazzo, MPI Munich
27/June/2014
32
Impact of a light sterile neutrino in β-decay
mβ =
��
�
�1/2
|Uei |2 m2i = �c212 c213 c214 m21 + s212 c213 c214 m22 + s213 c214 m23 + s214 m24 �
Phenomenology of eV steriles
Phenomenology of eV steriles
Present: Mainz
Future:
Neutrino mass observables:
β decays KATRIN
Neutrino mass observables: β decays
Mainz
Kraus et al., arXiv:1105.1326
Mainz
Sejersen Riis, Hannestad;
Formaggio
& Barrett,
arXiv:1105.1326
Sejersen
Riis, Hannestad;
Formaggio, Barret
Formaggio, Barret
9/9/15
Antonio 47
Palazzo, MPI Munich
47
33
Impact of a light sterile in 0ν2β-decay
mββ
10
0
for double beta decay. . .
� usual� plot
�The
�
�
2
=�
Uei mi � = �c2 c2 c2 m1 + s2 c2 c2 m2 eiα + s2 c2 m3 eiβ + s2 m4 eiγ �
12 13 14
12turned
13 14
13 14
. . . gets completely
around!
Normal Normal
Hierarchy
14
Inverted
Inverted
Hierarchy
3 ν (best-fit)
1+3 ν (best-fit)
3 ν (best-fit)
1+3 ν (best-fit)
<mee> (eV)
-1
10
-2
10
10
-3
0.001
0.01
0.1
mlight (eV)
0.001
0.01
0.1
Figure from Barry, Rodejohann,
Zhang,
Barry, W.R.,
Zhang JHEP 1107, 091 (2011)
See also Girardi, Meroni, Petcov, JHEP 1311, 146 (2013)
50 JHEP 1507, 171 (2015)
Giunti and Zavanin,
9/9/15
Antonio Palazzo, MPI Munich
34
What cosmology tells us?
Planck (2015)
Planck Collaboration: Cosmological parameters
photon density ργ at T � 1 MeV by
0.900
H0 [km s−1 Mpc−1 ]
78
� �4/3
7 4
ργ .
ρ = Neff
8 11
0.885
0.870
(59)
The numerical factors in this equation are included so that
Neff = 3 for three standard model neutrinos that were thermal0.840
ized in the early Universe and decoupled well before electronpositron annihilation. The standard cosmological prediction is
0.825
66
actually Neff = 3.046, since neutrinos are not completely de0.810
coupled at electron-positron annihilation and are subsequently
slightly heated (Mangano et al. 2002).
0.795
In this section we focus on additional density from mass60
0.780
less particles. In addition to massless sterile neutrinos, a variety
of other particles could contribute to Neff . We assume that the
2.0
2.5
3.0
3.5
4.0
4.5
additional massless particles are produced well before recombiNeff
nation, and neither interact nor decay, so that their energy density scales with the expansion exactly like massless neutrinos.
Fig. 31. Samples from Planck TT+lowP chains in the Neff –H0 An additional ∆Neff = 1 could correspond to a fully thermalplane, colour-coded by σ8 . The grey bands show the constraint ized sterile neutrino that decoupled at T <
∼ 100 MeV; for exH0 = (70.6 ± 3.3) km s−1 Mpc−1 of Eq. (30). Note that higher ample any sterile neutrino with mixing angles large enough to
neutrino
Neff brings H0 into better consistency with direct measurements, provide a potential resolution to short-baseline reactoreff
but increases σ8 . Solid black contours show the constraints from oscillation anomalies would most likely thermalize rapidly in the
Planck TT,TE,EE+lowP+BAO. Models with Neff < 3.046 (left early Universe. However, this solution to the neutrino oscillation
of eff
the solid vertical line) require photon heating after neutrino anomalies requires approximately 1 eV sterile neutrinos, rather
in this section; exploration of
decoupling or incomplete thermalization. Dashed vertical lines than the massless case considered
�
correspond to specific fully-thermalized particle models, for ex- the two parameters Neff and mν is reported in Sect. 6.4.3. For
ample one additional massless boson that decoupled around the a review of sterile neutrinos see Abazajian et al. (2012).
More generally the additional radiation does not need to be
same time as the neutrinos (∆Neff ≈ 0.57), or before muon
annihilation (∆Neff ≈ 0.39), or an additional sterile neutrino fully thermalized, for example there are many possible models
that decoupled around the same time as the active neutrinos of non-thermal radiation production via particle decays (see e.g.,
Hasenkamp & Kersten 2013; Conlon & Marsh 2013). The radi(∆Neff ≈ 1).
ation could
be produced at temperatures T > 100 MeV,
9/9/15
Antonio Palazzo,
MPIalso
Munich
in which case typically ∆Neff < 1 for each additional species,
since heating by photon production at muon annihilation (at
A larger range of neutrino masses was found by Beutler et al. T ≈ 100 MeV) decreases the fractional importance of the ad72
0.855
σ8
Small room for extra
relativistic content
• A "standard” eV sterile neutrino fully thermalizes (ΔN
• ΔN
= 1)
= 0 requires a mechanism that prevents thermalization
• Several possibilities (lepton asymmetry, self-interactions, …)
35
Summary
• Several SBL anomalies point to sterile neutrinos
but the global picture is not clear (internal tension)
• New SBL experiments needed to shed light
• Sterile neutrinos are sources of additional CPV
• LBLs unique interferometers sensitive to CP-phases
• T2K and NOνA give already interesting information
• Sterile neutrinos may manifest in many other places
Be ready for a discovery!
9/9/15
Antonio Palazzo, MPI Munich
36
Thank you
for your attention!
9/9/15
Antonio Palazzo, MPI Munich
37
Back up slides
9/9/15
Antonio Palazzo, MPI Munich
38
The 3-flavor scheme
NH
ν3
α=
+Δm2
δm2
Δm2
IH
ν2
ν1
ν3
CP-phase δ
δm2
(Hints of δ ≠ 0,
-Δm2
νe
νµ
θ23 ~ 41º
9/9/15
unknowns:
= 0.03
NMH
(Hints of NH)
ντ
θ13 ~ 9º
π)
θ12 ~ 34º
Antonio Palazzo, MPI Munich
39
Fitting the reactor anomaly
with sterile νs
11
1 dof "#2 profile
90.00 %
95.00 %
99.00 %
5
2
10
5
10
2 dof "#2 contours
4
2
0
8
6
4
2
!1
"m2
(eV2)
new
1 dof "#2 profile
"m2
(eV2)
new
10
8
6
8
6
4
2
0
10
8
6
4
Pee = 1 − 4
2
!1
10
8
6
4
4
2
!2
!2
2
3
4 5 6 78
!2
10
2
3
2
4 5 6 78
sin (2!new)
!1
10
2
3
4 5 6 78
0
10
5
"#2
10
10 !3
10
2
2
Uej
Uek
j>k
∆m2jk L
sin
4E
2
∆m2sol � ∆m2atm � ∆m2new
8
6
2
�
1 dof "#2 profile
In a 3+1 scheme:
1
10 !3
10
4E
2 dof "#2 contours
2
1
10
8
6
90.00 %
95.00
2 %
L
new
2 ∆m
99.00
%
sin
4
2
10
Pee � 1 − sin2 2θnew
2
8
6
4
10
1 dof "#2 profile
In a 2ν framework:
10
"#2
"#2
10
2
2
2
sin210θnew
�
U
=
sin
5 θ14
10
10
10
e4
2
2
3
4 5 6 78
!2
2
3
4 5 6 78
sin (2!new)
!1
2
3
4 5 6 78
0
"#
Mention
al.,inPRD
(2011)
FIG. 6. Allowedetregions
the sin283
(2θnew073006
)−∆m2new plane
obtained from the fit of the reactor neutrino data to the 3+1 neutrino
2
hypothesis, with sin (2θ13 ) = 0. The left panel is the combination of the reactors and the gallium experiment calibration results
with 51 Cr and 37 Ar radioactive sources. The right panel is the combination of the reactors and our reanalysis of the MiniBooNE
data following the method of Ref. [56]. In both
cases the
ILL energy
spectrum
information is not included.
9/9/15
Antonio
Palazzo,
MPI
Munich
40
CPV is a genuine 3-flavor effect
Δij =
ACP
αβ ≡ P (να → νβ ) − P (ν̄α → ν̄β )
Δm2ij L
4E
12
ACP
=
−16J
αβ
αβ sin ∆21 sin ∆13 sin ∆32
ij
Jαβ
≡
∗
∗
Im [Uαi Uβj Uαj
Uβi
]
≡J
�
γ=e,µ,τ
�αβγ
�
�ijk
k=1,2,3
J is parameterization independent (Jarlskog invariant)
In the standard parameterization:
1
J = sin 2θ12 sin 2θ23 sin 2θ13 cos θ13 sin δ
8
Conditions for CPV:
9/9/15
- No degenerate (νi,νj)
- No θij = (0, π/2)
- δ/
= (0, π)
Antonio Palazzo, MPI Munich
✔
✔
?
41
CPV and averaged oscillations
ACP
αβ ≡ P (να → νβ ) − P (ν̄α → ν̄β )
{
12
ACP
=
−16J
αβ
αβ sin ∆21 sin ∆13 sin ∆32
if
∆ ≡ ∆13 � ∆23 � 1
Osc. averaged out by finite E resol.
It can be:
→ �sin2 ∆� = 1/2
ACP
αβ �= 0
(if sin δ /
= 0)
The bottom line is that if one of the three νi is ∞ far
from the other two ones this does not erase CPV
(relevant for the 4ν case)
9/9/15
Antonio Palazzo, MPI Munich
42
Numerical examples of 4ν probability
10
may help to further simplify the expression of the transition probability in Eq. (37), which, for small values of
the two mixing angles θ14 and θ24 , takes the form
3ν
4ν
" (1 − s214 − s224 )P̄µe
Pµe
− 2s14 s24 Re(e
−iδ14
(38)
∗
S̄ee S̄eµ
)
3ν
+ s214 s224 (1 + P̄ee
).
First, it can be noted that for small values of s13 ∼ $ and
α∆ ∼ $2 one has [37]
S̄ee " 1 − O($2 ) .
FIG. 7: Probability of νµ → νe transition in the 3+1 scheme.
The thin blue line represents the numerical result, while the
red line represents the averaged probability obtained using
Eq. (37). In both cases the hierarchy is normal and the mixing
angles are fixed at the values s214 = s224 = 0.025.
The fast oscillations get
averaged out due to the
finite energy resolution
(solid), δ14 = π (long-dashed), δ14 = π/2 (short-dashed),
and δ14 = −π/2 (dotted).
While the 3-flavor elements S̄ee and S̄eµ can be evaluated numerically (as we have done) approximate expressions already existing in the literature in various limits
(39)
Since we are interested to terms up to O($4 ), we can
assume S̄ee = 1. Moreover, as discussed above, the
nonstandard matter effects are completely negligible and
only the small standard matter effects are relevant. In
this approximation, the 3-flavor amplitude S̄eµ has the
well-known (see, for example, [37]) form
Different line styles
(40)
⇔
where A and BDifferent
are two complex coefficients
withof
O(1) δ
values
14
modulus, given by
m
S̄eµ " Asm
13 sin ∆ + B(α∆) ,
A = −2 i s23 e−i(∆+δ13 ) ,
B = −2 i c23 s12 c12 ,
(41)
(42)
sm
13 " (1 + v)s13 ,
∆m " (1 − v)∆ ,
(43)
(44)
The modifications induced by δ14 are as large
and (s , ∆ ) are the approximated expressions of
(s , ∆) standard
in matter
as those induced by the
CP-phase δ13
m
13
m
13
Completely analogous conclusions for NOνA
9/9/15
Antonio
with v = VCC /|k13 | " 0.05. Making use of Eqs. (39)(44) in the expression of the transition probability in
Eq. (38), in the limit case v = 0 we recover, in an alPalazzo,
MPI
ternative
way, Munich
the fourth-order expansion of the vacuum
formula in Eq. (13) presented in Sec. II. For v $= 0, one
sees that the structure of the transition probability re-
43
Some sensitivity to δ already from T2K + Rea
Slight θ13 mismatch
T2K vs Reactors
No CPV (δ = 0, π)
disfavored at
~ 90% C.L.
Best fit δ ~ - π/2
NH slightly
favored Δχ2 ~ -0.8
(similar finding in
SK atmospheric νs)
Note that δ is not extracted from observation of manifest CPV
Combination of
9/9/15
Pee (δ-independent), LBL Reactors
{
Pµe (δ-dependent), LBL Accelerators (T2K)
Antonio Palazzo, MPI Munich
44
Results of the 4ν analysis (T2K, NH)
3ν: T2K
PHYSICAL REVIEW D 91,
N. KLOP AND A. PALAZZO
4ν
-  Big impact on T2K “wiggles”
the confidence levels 68% and 90% (1 d.o.
those used by the T2K Collaboration, so a
comparison. Our results are basically supe
those obtained by the collaboration (see Fig.
thin vertical band displayed in both panels
range allowed at 68% C.L. for θ13 by the r
ments. As already noticed in the global analy
in partial fits performed by various experim
rations, the T2K-allowed bands lie at values
are somewhat larger compared to the range
reactors. As a result, as evident in the two rig
combination of the reactor experiments with
select values
of δ ∼ −π=2,
Similar
findings
in IHdisfavoring the ca
(δ13 ¼ 0; π) at roughly the 90% C.L. In add
preference for the case of normal hiera
(χ 2NH − χ 2IH ≃ −0.8).
- 4ν gives better agreement of T2K & Reactors
D. Results of the 4-flavor analy
FIG. 2 (color online). Left panels: Regions allowed by T2K and
As discussed in detail in the Appendix,
by reactor experiments for normal hierarchy (upper panel) and
inverted
panels:Palazzo,
Regions allowed
9/9/15 hierarchy (lower panel). Right
Antonio
MPI Munichscheme, the role of matter effects
45 is very
by their combination. The mixing angle θ23 is marginalized away.
3-flavor case. Basically (in comparison to
2
The confidence levels refer to 1 d.o.f. (Δχ ¼ 1.0; 2.71).
case), they tend to increase (decrease) the
Results of the 4ν analysis (LBL,NH)
3ν: T2K + NOνA (NH)
4ν
-  LBL combination more stable than T2K alone
9/9/15
Antonio Palazzo, MPI Munich
46
4ν effects at the CNGS beam
3
2
sum of three
atmospheric
ing, and the
eline of L =
GeV probed
L/4E ∼ 0.13
the solar one
atmospheric
(4)
# 0.15 and
der !.
quared-mass
expressed as
(5)
ing, the sterging over the
cy ∆m214 , we
For relatively small values of the two new mixing angles (|Ue4 |2 , |Uµ4 |2 ! 0.2), this assumption is almost irrelevant and for whatever choice of |Ue4 |2 != |Uµ4 |2 the
plot would be almost identical. For very large values of
|Ue4 |2 (or |Uµ4 |2 ) sizable deviations would appear in the
atmospheric and interference terms if |Ue4 | " |Uµ4 | (or
|Ue4 | # |Uµ4 |). It is important to stress that, in any case,
their amplitude would be always smaller than that obtained for |Ue4 | = |Uµ4 | displayed in Fig. 1 (see footnote
1 and discussion of Fig. 5).
As expected from Eq. (10), for small values of θµe , the
sterile term (solid line) and the interference one (dashed
line) display a power-law behavior. For very large values
of θµe , the interference term deviates from the power-law
behavior
because of the effect of the suppressing factor
√
F, which becomes appreciably smaller than one. In the
atmospheric term (dotted line), F is the sole source of the
dependence on θµe . This terms assumes the maximum
value of
inthe
thethree
3-flavor
limit
(θµeνµ=→0)νeand
decreases with
FIG. 1: Behavior
terms
of the
transition
2
θµe . parameters
In the region
2θµekm,
" 0.1,
probability increasing
for the CNGS
(L sin
= 732
E =the factor
becomesofvery
small
drastically
both
17 GeV) as F
a function
sin2 2θ
the case
|Ue4 | =suppresses
|Uµ4 |.
µe inand
the atmospheric and the interference terms.
For values of s14 and s24 similar to that of s13 (% 0.15),
the atmospheric
interference
terms
respectively
which and
are favored
by the
SBL are
global
fits [2, 3], we can
2 2
proportional
to thethat
factor
≡ cmixing
to its
assume
the F
three
angles
andsquared
the atmospheric
14 c24 and
root. Therefore,
Eq. (6)
can∆be%recast
in theallform
oscillating
phase
0.13 have
the same order of
magnitude
". In this regime, corresponding roughly to
4ν
3ν
−3
Pµe
= 2F2θPµe
(10)have the
µe % f ew × 10 , all the three terms
sin
√
4
!
same
transition probability
is below
F sin "2θ,µeand
s13 sthe
+ 2 order
23 sin ∆ sin(∆ + δ )
the current sensitivity of the two experiments.
1
+ As sin
.
can2 2θ
beµededuced
from Fig. 1, for the values of the
2
transition probability currently probed by ICARUS and
−3
OPERA
(Pµe
∼| f=ew|U×µ410
), suppression
roughly corresponding
to
In the particular
case
|Ue4
|, the
fac2
−2
1
9/9/15
Antonio
Palazzo,
sin 2θµeof∼the
10sole
, the
absolute
size of the
interference
tor F is a function
effective
appearance
angle
term is comparable to (approximately one half of) the
2
2
F ≡ c214 csterile
− |Ue4 This
|2 − |U
1 − sin
(11) of the
means
for 2θ
those
µ4 | =that,
µe , values
24 = 1term.
FIG. 2: Transition probability as a function of the neutrino
energy. The dotted curve represents the atmospheric term,
while the dotted-dashed (horizontal) line is the sterile one.
The sum of these two contributions, represented by the dashed
curve, is the probability implemented in the official analyses.
µ 4ν probabil-e
The two solid lines correspond to the (averaged)
ity in the NH case for the two values δ ! = ±π/2.
• Interference has substantial impact on P (ν -> ν )
(6)
!
∆+δ )
• The official analyses neglect the interference term
The discussion made above makes it clear that the
inclusion of the interference effects in the analysis is
expected to introduce substantial modifications of the
bounds obtained in their absence. In particular, the upper limits on θµe should become weaker since the interference term, when negative, decreases the predicted signal.
This qualitative expectation will be quantified by the nuMPI
Munich
merical
analysis presented in the next section.
An important remark is in order before presenting the
results of the analysis. Both ICARUS and OPERA op-
• Proper inclusion of such effects is necessary
(6) coincides
multiplying
interference
negative valthe averaged
description.
eutrino mass
hich is posi-
47
A further remark on 4ν effects
νe bkg is not fixed!
Relevant because
ICARUS & OPERA
are bkg-dominated
8
OPERA, JHEP 1307 (2013) 036
oscillated ν e by 3 flavor oscillation
7
ν e beam contamination
6
BG from τ→ e
BG from NC with π0
5
overflow
Number of events / 10 GeV
In a 4ν scheme:
Pee ~ 1 - 2 Ue42 < 1
Data
4
3
2
Measured # of events
smaller than bkg
1
0
0
20
40
60
80
100
48
120
140
160
Reconstructed energy (GeV)
Figure 6. Distribution of the reconstructed energy of the νe events, and the expected spectrum
Expected from
bkg
tends
lower
for
the different
sources in to
a stackbe
histogram,
normalized to
the number of pot analysed for this
paper.
U ≠0 allowing
for a larger signal
e4
oscillation parameters θnew and ∆m2new :
9/9/15
Antonio Palazzo, MPI Munich
48
Pνµ →νe = sin2 (2θnew ) · sin2 (1.27∆m2new L(km)/E(GeV))
General analysis with (Ue4, Uµ4) free
5
Fit prefers big
values of |U |2
appearance mixing angle θµe are now allowed by the fit.
More precisely, from Fig. 5 we derive the upper bound
sin2 2θµe ! 1.7×10−2, which is a factor ∼ 3/2 bigger than
that found in the case Pee = 1 (sin2 2θµe ! 1.2 × e4
10−2 )
and an overall factor ∼ 3 weaker than that derived using
the 2-flavor approximation (sin2 2θµe ! 5.2 × 10−3). The
reasons of this behavior can be traced to the fact that the
fit has now more flexibility and to the circumstance that
the number of νe events measured by OPERA (and also
by ICARUS) is appreciably lower than the theoretical
(non-oscillated) background prediction. When including
in the fit the possibility2of having Pee < 1, a large nonzero value of |Ue4 |2 is preferred,µe
since this suppresses the
background prediction and provides a better agreement
with the observations. In this case, larger values of the
νµ → νe signal are naturally permitted by the fit and, as
a consequence, bigger values of θµe are allowed.
Larger values of
sin 2θ tolerated
sin22θµe < 1.7 x 10-2
at the 90% C.L.
long-baseline experiments ICARUS and
IV.
CONCLUSION
The two
OPERA have recently performed sterile neutrino
searches using the νµ → νe measurements. Both collaborations have presented upper bounds on the effective appearance mixing angle θµe obtained with analyses which
make use of an effective 2-flavor description. We have
ting is fixed at ∆m214 = 1 eV2 , while the CP-phase δ ! is
shown that a consistent treatment
marginalized away. In the 2-flavor approximation (dot2 of the results must include genuine 4-flavor interference effects,
ted line) we re-obtain the bound sin2 2θµe ! 5.2 × 10−3 ,
µewhich develop
on the long distances involved in the CNGS setup. Our
which in the log-log plot of Fig. 5 is represented by a
quantitative study shows that their inclusion weakens the
diagonal line with a negative slope of 45° (we recall
upper bounds on θµe approximately by a factor of two.
that sin2 2θµe ≡ 4|Ue4 |2 |Uµ4 |2 ). The solid curve repreWe have also pointed out that, in a 4-flavor scheme, the
sents the bounds obtained when the interference term
9/9/15
Antonio
Palazzo,
MPI Munich
sterile-induced
νe disappearance is of high relevance. Its
is “switched on” in the conversion probability. It can
inclusion
in
the
data analysis leads to a further weakenbe clearly seen that the weakest bound is obtained for
ing of the upper bounds on θµe , which overall are relaxed
|Ue4 | = |Uµ4 | as anticipated, in which case we re-obtain
FIG. 5: Upper bounds (90% C.L.) obtained from the OPERA
experiment for the case of normal hierarchy. The CP-violating
phase δ ! is marginalized away. See the text for details.
Overall, bounds relaxed by a factor of 3 with
respect to the 2-flavor case (sin 2θ < 5 x 10-3)
49