Neutrinos masses and ordering from Multi

Neutrinos masses and ordering from
Multi-messenger Astronomy
Kasper Langæble
In collaboration with A. Meroni and F. Sannino
MASS 2016
Gravita'onalWaves
AL REVIEW
gnal-to-
time of
graded,
o detect
vational
ition is
me and
2
(90%
t being
es—i.e.,
al black
equency
z, where
lausible
orbiting
sion. At
ized by
=5
this event, was operating
but was
not operating
in observational
this event,
but not in ob
mode. With only twomode.
detectors
positionthe
is source p
With the
onlysource
two detectors
primarily determined primarily
by the relative
arrival
timerelative
and arrival
determined
by
the
P
H
Y
S
I
C
A
L
R
E
V
I
E
W
L
E
T
T
E
R
S
2
PRL 116, 061102
(2016)
localized to an area localized
of approximately
(90%
to an area600
of deg
approximately
600 d
credible
region)
[39,46].
Observation
ofevents
Gravitational
Waves
from
a Binary
Black Hole
Merger
credible
region)
[39,46].
propagation
time,
the
have
a
combined
signal-toLIGO Scientific and Virgo Collaborations (B.P. Abbott (Caltech) et al.).
The
basic
features ofThe
GW150914
pointof toGW150914
it being point t
basic features
116
no.6,
061102
(SNR) of
24(2016)
[45].
week
ending
L E T noise
T E R SratioPhys.Rev.Lett.
12 FEBRUARY 2016
produced
by
coalescence
of
black holes—i.e.,
Only the LIGO
detectors
werethe
observing
at the time
produced
byoftwo
the coalescence
of two black h
GW150914. The
Virgo
detector
wasand
being
upgraded,
their
orbital
inspiral
and merger,
subsequent
their
orbital
inspiral
merger,
and
subsequent
final and
black
and GEO 600, hole
though
not sufficiently
to signal
detect increases
hole
ringdown.
Over 0.2 s,inthe
signal increases in
ringdown.
Oversensitive
0.2
s, the
frequency
this event, was operating but not inand
observational
amplitude
in35
about
8 cycles
from 35 to 150
and
amplitude
in
about
8
cycles
from
to
150
Hz,
where
mode. With only two detectors the source position is
thea amplitude
reaches a maximum. The mos
the amplitude
reaches
maximum.
primarily determined
by the relative
arrival
time and The most plausible
explanation
this evolution
the inspiral of tw
for this evolution
theforinspiral
of two is
orbiting
localized to anexplanation
area of approximately
600
deg2is(90%
masses,
m1 and m2 , due to
gravitational-wave
em
credible region)masses,
[39,46]. m1 and m2 , due
to gravitational-wave
emission.
At
the
lower
frequencies,
such evolution
The basic features
of GW150914
point
to
itevolution
being
the lower
frequencies,
such
is characterized
by is charac
produced by the coalescence of two black
holes—i.e.,
the chirp
mass [11]
the chirp mass [11]
their orbital inspiral and merger, and subsequent final black
;
its time
ant and
n Fig. 1,
!
3=5
3
hole ringdown. Over 0.2 s, the signal increases in frequency
!
"
ðm
m
Þ
c
5 −8=3 −11=3
1 2
FIG.f_
3=5
3
3=5
m
Þ
c
5
π
¼
f
M
¼
and amplitude in about 8 cyclesðm
from
35
to
150
Hz,
where
1 2
−8=3 f −11=3
1=5 f
_ G ;96
from
π
¼
M
¼
ðm
þ
m
Þ
1
2
the amplitude reaches a maximum.
The
most
plausible
1=5
G 96
ðm1 þ m2 Þ
band
explanation for this evolution is the inspiral of two orbiting
Theani
where
f and
masses, m1 and m2 , due to gravitational-wave
emission.
At f_ are the observed frequency
where such
f and
f_ areisthe
observed
andtheitsgravitational
time
hole
observed
the lower frequencies,
evolution
characterized
byfrequency
derivative
and
G and c are
co
frequency
the chirp mass [11]
derivative and G and cspeed
are the
gravitational
constant
Top: Estimated gravitational-wave strain amplitude
of light.
Estimating
f and f_ and
from theeffec
dat
FIG. 2.
(RS ¼
from
GW150914 projected onto H1. This shows the
full
chirpmass
totalmass
!
"
we
obtain
a
chirp
mass
of
M
≃
30M
,
implyi
FIG. 2. Top: Estimated
⊙ gravitatio
bandwidth of the waveforms, without
ðm1the
m2filtering
Þ3=5 used cfor3 Fig.5 1. −8=3 −11=3 _ 3=5
postThe inset images showM
numerical
of the blackπ
from
GW150914
projected
onto
¼
f
;
¼ relativity models
f
total
mass
M
¼
m
þ
m
is
≳70M
in
the
dete
⊙1
2
⊙
1=5
96
hole horizons as the black holesðm
coalesce.
Bottom:
The G
Keplerian
gravi
1þm
2Þ
bandwidth
of theSchwarzschild
waveforms, without
This
bounds
the
sum
of
the
ra
effective black hole separation in units of Schwarzschild radii 1
2
⊙
The inset images 2show numerical
andrelM
(RS ¼ 2GM=c2 ) and the effective relative velocity given by the
speed of light. Estimating f and f_ from the data in Fig. 1,
we obtain a chirp mass of M ≃ 30M , implying that the
total mass M ¼ m þ m is ≳70M in the detector frame.
to 2GM=c
210 km. To
of thecomponents
Schwarzschild
radii of≳the
_ This bounds the sumbinary
Mul'-MessengerAstronomy
Photons,neutrinosandgravita'onalwaves
Fermi Gamma-ray Space Telescope
LISA
Gravitational waves Observatories
Borexino
Super-Kamiokande
Antares
IceCube
SNEWS:SuperNovaEarlyWarningSystem
Days Bay
In theoffollowing
the conditions
th
etection
GWs we
is explore
a crucial
test of under like the merging of a neutronbfpstar
±1 binary3 orran
constrain
the neutrino
mass ordering
and
of or
aabsoGW.
Typically
the
emission
time
ofWe
the
t
are
believed
to
follow
this pattern.
wi
2
which
multi-messenger
astronomy
can reveal
+0.013
core
bounce
of
a
core-collapsed
supernova
(SN
sin
✓
0.304
0.270
!
12
lativitylute
and,
as already discussed in
0.012
1 . Fo
mass.
and extend
the
of [14].
The
di
signals
and
⌫)2 notation
do
coincide
constrain the neutrino mass ordering and absoare(GW,
believed
to follow
thisnot
pattern.
We
will
ado
+0.052
sin ✓23
0.452 0.028
0.382 !
ure (see
e.g. [14]), it is also important
of
the
arrival
times
between
the
GWs
an
lute mass.
extend
the notation
of [14]. The
di↵eren
stanceand
in the
supernova
explosion
SN1987A
2
+0.0010
e other relevant physical properties.
sin
✓
0.0218
0.0186
!
13
trinos,
⌧
⌘
t
t
,
or
the
GW
and
ah
0.0010
of
the
arrival
times
between
the
GWs
ne
⌫
g
obs
the
neutrinos
arrived
approximately
2
–
3
II. MULTI-MESSENGER ASTRONOMY
2 observables,
information can be derived when
⌧obs⌧⌘
which
trinos,
t g , 5both
or
GW+0.19
and a 7.02
photo
[10
eVthe
] 7.50
!
g ,221are
obst ⌘ t⌫tm
0.17
before
the
associated
photons.
II.Neutrino
MULTI-MESSENGER
ASTRONOMY
masses and ordering via gravitational waves, photon
and
neutrino
detections
⌧
⌘
t
t
,
areDenmark,
observables,
which
b
positive
or
negative
an +0.047
early
or can
late
g
g, for example,
their
propagation
2 for
2both3Odense,
obs
Kasper Langaeble, Aurora Meroni, Francesco Sannino (Southern Denmark U.,
CP3-Origins & U. Southernm
DIAS).
[10
eV
]
+2.457
+2.317
!
2
The
detection of GWs is a crucialLet
testusofassume now 3`that a neutrino
0.047 is emitte
CP3-ORIGINS-2016-010-DNRF90, DIAS-2016-10
positive
or
negative
for
an
early
or time
late arriv
of
a
GW.
Typically
the
emission
of th
with those
of
photons
and
neutrinos
e-Print:
arXiv:1603.00230
The detection
of and,
GWs as
is already
a crucialdiscussed
testE of Ein ⌫
general
relativity
1.
t⌫ = t gof+a ⌧signals
and
detected
at
time
t
.
A
relativ
GW.
Typically
the
emission
time
of
the
thr
⌫
(GW,
and
⌫)
do
not
coincide
the fit to
general
relativity
and,
already
in Table I.intThree-flavor oscillation parameters from
th
from
the
same astrophysical
source.
the
literature
(see
e.g.as [14]),
it isdiscussed
also important
1
scale
2 ⌧
signals
(GW,
and
⌫) do
not
coincide
.SN1987
For
i
mass
eigenstate
neutrino
with
mass
m
c
stance
in
the
supernova
explosion
by
the
NuFIT
group
[17].
The
numbers
in
the
1st
(2nd
i
We
can
get
information
of
the
e.g.relevant
[14]), it is
also important
deduce (see
other
physical
properties.
LIGO thetoliterature
2
2
2
2
stance
[16
m3`the
⌘ inneutrinos
mthe
> supernova
0 for NO
andexplosion
mapproximately
⌘ m32SN1987A
< 0 for IO.
31
3`group
arrived
2
–
i
=
1,
2,
3
)
propagates
with
a
velocity:
to
deduce
other
relevant
physical
properties.
GW
masses:
have
Mul'-MessengerAstronomy
This new information
can be derived when
the neutrinos
arrived
approximately
2 – 3 hou
Tg
before
the
associated
photons.
new information
can be their
derived
when
0 4 8emitted
1
my. This
comparing,
for example,
propagation
before
the
associated
photons.
2
4
t
with
respect
to
a
massless
particle,
i Let us assume
now
thatBamneutrino
isbyem
m
c
c
comparing,
for
example,
their
propagation
C
v
BB isi is
CC emitted
isource now
i that
er ex- velocity
with those of photons and neutrinos
Let
us
assume
a
neutrino
A. Set-up
the same
at
the
same
time,
E
E
⌫
+ O B@ at time
CA ,t⌫ . A rela
⌧
and
detected
⌫ with those of photons and neutrinos E t⌫E = t g⌫=+ 1
velocity
2
4
int detected
com- coming both from the same astrophysical source.
c⌧int and
2E
8Et⌫ . A relativist2
t
=
t
+
at time
⌫
g
T
⌫
eigenstate neutrino with mass2 mi c
o de- coming both from the same astrophysical source. massmass
!2with
eigenstate
neutrino
mass
mi c ⌧ E
2 c4
✓
◆
2
2
m
art by considering a potential obsermi c
E a group
L veloci
i = 1,i 2, L3 ) propagates
with
g the
wherei =we
thea group
di↵erent
speci
t1,
= 2.57thatwith
s.
3 )2propagates
velocity:
i 2,assumed
c
eV
MeV
50kpc
2E
an astrophysical catastrophe. Using
01 4 a
1 com
2
4
8
neutrinos
have
been
produced
with
0
(2)
T
m
c
m
c
B
C
2
4
4
8
v
CC
i m c
i Bm cB
CC i expann
the
notation
of [14], we A.
denote
with T g ⌘
A.Set-up
Set-up
vnot
BB+ cosmic
i take=into
i account
iO B
1
, (
B
Here
we
do
CC , is4 CAprod
@
=
1
+
O
B
energy
value
E.
If
a
given
neutrino
2
@ 8E4 A8E as
c 2E
The
neutrinos
are
produced
2 2E
mass
c
sion
since
we
consider
sources
at low redshift,
⌘ L/v⌫i and T ⌘ L/v respectively the
byobsera source
atThis
a distance
L, the
time-of-flight
d
E
E E
a de- Let’s
t
t
t
t
t
t
z
<
0.1.
causes
an
error
less
than
5%.
From
Let’s
start
by
considering
a
potential
flavor
eigenstates
but
travel
as
g
⌫
g
⌫
start
by considering
potential obseropagation of
a GW,
a given aneutrino
where
weinassumed
thatdi↵erent
the
di↵erent
sp
where
we assumed
that
the
species
the
expression
(2)
we
observe
that
larger
dise sur- vation
vation
of
astrophysical
catastrophe.
Using
of
an an
astrophysical
catastrophe.
Using
mass
eigenstates.
neutrinos
have
been
produced
with
a c
nstate
and
photons
with
group
velocineutrinos
have
been
produced
with
a
commo
tances
and
small
neutrino
energies
are
needed
in
, will the
Figure
1.notation
GW,
neutrino
and
propagation
the
same
notation
of [14],
we
denote
same
of [14],
wephoton
denote
withwith
T1g In⌘Tin
g ⌘
alternative
theory
of
gravity
the three
particles
energy
value
E.
If
a
given
neutrino
is pr
energy
value
E.
If
a
given
neutrino
is
produce
order
to
maximise
the
experimental
sensitivity.
and
v
.
Following
Fig.
1
a
GW
is
emittime.
when L/vL/v
⌘ L/v
⌘ L/v
the
T T
⌘ L/v
respectively
Tgrespectively
L/vg the
g, T
⌫i and
g ,⌫iT⌘
⌫i L/v
⌫i and
study
—aby
photons,
gravitons
neutrinos—
canan
cou
For
distances
around
50 and
kpc
(SN1987A)
and
by
source
at
a
distance
L,
the
time-of-flight
dela
a
source
at
a
distance
L,
the
time-of-fligh
E
time time
t gtime
from
apropagation
source at
La and
of of
propagation
of distance
aofGW,
a given
neutrino
a GW,
given
neutrino
di↵erent e↵ective metrics. In this case the Shapiro
energy of 10 MeV, a neutrino with a mass of 0.07
Whatdoweknowaboutneutrinos?
trivial
massive neutrinos implies
that the left-handed (L
I⌫lLThe
mixing
(x) =three
Uljneutrino
⌫neutrino
l=
e, µ,and
⌧, framework
(1.1)
jL (x), mixing
jneutrino
fields ⌫lL (x), which enter into the expression for the lepton curr
In the formalism
used tocurrent
construct
the Standard
Model
(SM), the existence
of combinations
a noncharged
weak
interaction
Lagrangian,
are
linear
of th
The three neutrino
mixing
framework
trivial neutrino
mixing and
massive neutrinos implies that the left-handed (LH) flavour
(orwhich
more)
neutrinos
⌫ja, mass
havingmmasses
mj 6=
ofthree
the
field
of ⌫enter
0 and
U 0:
is a in the
where ⌫jL (x) is the LH component
j possessing
j the
neutrino fields
⌫ (x),
into the expression
for
lepton
current
Whatdoweknowaboutneutrinos?
unitary
matrix
—thetoPontecorvo-Maki-Nakagawa-Sakata
neutrino
mixing
n the formalism used
construct the Standard Model (PMNS)
(SM), the
existence
of maa nonlL
Xcombinations of the fields of
charged current weak interaction Lagrangian, are linear
=
U(CKM)
l = e, µ, ⌧,
(or more)
⌫j , having masses⌫m
6= 0:
lLj(x)
lj ⌫jL (x),quark
UPMNS .three
Similarly
to neutrinos
the Cabibbo-Kobayashi-Maskawa
[3, 4, 9], U ⌘
ivialtrix
neutrino
mixing and massive neutrinos impliesX
that the left-handed
(LH) flavour
j
mixing matrix, the leptonic matrix UPMNS , is described (to a good approximation) by
⌫lL (x) =
Uljfor
⌫jL (x),
= e, µ, ⌧, current in the (1.1)
eutrino fields ⌫lL (x), which enter into the expression
the l lepton
a 3 ⇥ 3 unitary mixing matrix. In thewhere
widely
parametrization
[6],ofU⌫PMNS
(x) isstandard
the jLH component
of the field
0
⌫jLused
j possessing a mass mj
They
oscillate!
harged
current
weak
interaction
Lagrangian,
are
linear
combinations
of
the
fields
of
is expressed in terms of the solar, atmospheric
and—the
reactor
neutrino mixing angles ✓12 , (PMNS) neutrino m
unitary matrix
Pontecorvo-Maki-Nakagawa-Sakata
(x)
is
the
LH
component
of
the
field
of ⌫j possessing a mass mj 0 and U is a
where
⌫
jL
hree✓(or
more)
neutrinos
⌫
,
having
masses
m
=
6
0:
j
j
and
✓
,
respectively,
and
one
Dirac
,
and
two
(eventually)
Majorana
[21] - ↵21
trix [3, 4, 9], U ⌘ U
. Similarly
to the Cabibbo-Kobayashi-Maskawa
(CK
23
13
PMNS
unitary matrix —the Pontecorvo-Maki-Nakagawa-Sakata
(PMNS) neutrino mixing mathetoleptonic
matrix UPMNS , is described
(to
a good approxim
and ↵31 , CP violating phases:
X
trix [3, 4, 9],
U mixing
⌘ UPMNSmatrix,
. Similarly
the Cabibbo-Kobayashi-Maskawa
(CKM)
quark
⌫lLmixing
(x) =
⌫3jL
(x),matrix
l =Ue,
µ,, ⌧,
(1.1) parametrization
3lj⇥leptonic
unitary
mixing
matrix.
In the (to
widely
used
standard
matrix,aU
the
is described
a good
approximation)
by
PMNS
a 3 ⇥⌘
3 unitary
widely
parametrization
[6], UPMNS
expressed
in ,In
terms
of21the
solar,
atmospheric
and(1.2)
reactor
neutrino mixing
UPMNS
U =j Vismixing
(✓
)the
Q(↵
, ↵used
) ,standard
12 , ✓matrix.
23 , ✓13
31
j atmospheric
= 1, 2, 3 and reactor neutrino mixing angles ✓12 , Majorana
is expressed in✓terms
of the solar,
23 and ✓13 , respectively, and one Dirac - , and two (eventually)
✓23 and ✓13 , respectively, and one Dirac - , and two (eventually) Majorana [21] - ↵21
andfield
↵31 , CP
phases:a mass mj
where
of violating
the
of ⌫violating
0 and U is a
here ⌫jL (x) is the LH component
j possessing
and Pontecorvo
↵31 , CP
phases:
1Maki
0
1 0(PMNS) neutrino
1 mixing manitary matrix0—the
Pontecorvo-Maki-Nakagawa-Sakata
i
1
0
0
c13
0PMNS
s13⌘e U = V (✓U12PMNS
c12
0 ,12
⌘13 ,Us)12
=
V 21
(✓
, ✓)23
, ✓13 , ) Q(↵21 ,(1.2)
↵31 ) ,
U
,
✓
,
✓
Q(↵
↵
,
23
31
Nakagawa
OSCILLATION
249
ix [3,TakaakiKajita
4, 9],
U @⌘ 0UPMNS
. Similarly
Cabibbo-Kobayashi-Maskawa
quark
A
@ to0the NEUTRINO
A @ s12 cPROBABILITY
A(CKM)
c
s
1
0
0
V
=
,
(1.3)
23
23
12
andArthurB.McDonald
Sakata
where
where
mixing matrix, the
leptonic
matrix
U
(to 0a good
by
PMNS
0
s23 c23
0 approximation)
1
s13
ei ,0is described
c13
10
11 0
coefficient
of0 |ν1widely
01 0standard
1
0
1
β ⟩, 0
i
3 ⇥ 3 unitary mixing matrix.
In the
used
parametrization
[6],
U
i
0
c
0
s
e
c
s
0
PMNS
13
13
12
12
1
0
0
c13
0 s13 e
c12 s12 0
@
A
@
A
@
A
!
0 c23 cijs23⌘
0✓ij , the
s12 c12
0 A
V =atmospheric
,✓12
and we have
used of
thethe
standard
notation
cos
✓reactor
⌘neutrino
sin@
allowed
range
ij0, sijs 1
expressed
in terms
solar,
@and
A
@ , (1.3)
A
∗0 mixing
−iEangles
0
c
1
s
c
0
V
=
k t0
23
23
12
12
i
A
(t)
≡
⟨ν
|ν
(t)⟩
=
U
U
e
,
(7.16)
βe α 0
0 ✓ s23ν
c⇡/2,
0
0 1
s13
c13
α →ν
αk i βk
23β
for
the
values
of
the
angles
being
0
and
ij
and
✓
,
respectively,
and
one
Dirac
,
and
two
(eventually)
Majorana
- ↵21 0
0
s
c
0 1
s
e
0
c[21]
23
13
23
23
13
13
k
and we have used the standard notation cij ⌘ cos ✓ij , sij ⌘ sin ✓ij , the allowed range
nd ↵31 , CP violating phases:
i↵21 /2 i↵31 /2
is for
thethe
amplitude
ofwe
→being
νeβ transitions
anotation
functioncijof⌘time.
Qvalues
= Diag(1,
eναhave
,used
and
cos(1.4)
✓ijThe
, sij transition
⌘ sin ✓ij , the allo
of the
angles
0 the
 ✓)ij.standard
 ⇡/2,asand
probability is, then,
by of the angles being 0  ✓ij  ⇡/2, and
for thegiven
values
i↵
/2
i↵,31 /2
21
UPMNS ⌘ U = V (✓12 , ✓23 , ✓13Q,= )Diag(1,
Q(↵
,
↵
)
(1.2) (1.4)
21
31
e
,
e
).
!years, allowed
The neutrino oscillation data, accumulated
over"2many
to
determine
"
∗
∗ i↵
−i(E
−E )t
"Aνα →ν (t)" =
21 /2k i↵j31 /2
P
(t)
=
U
U
U
U
e
. ).
(7.17)
ν
→ν
βk
αj
Q
=
Diag(1,
e
,
e
α
αk
βj
β
β
the frequencies and the amplitudes
(i.e.
the angles
the mass
di↵erences)
The neutrino
oscillation
data, and
accumulated
over squared
many years,
allowed to determine
herewhich drive the solar andthe
k,j
frequencies and
the amplitudes
(i.e. the
angles
and thehigh
mass precision
squared di↵erences)
atmospheric
neutrino
oscillations,
with
a rather
The
oscillation
data,
accumulated
overhigh
many
years, allowed to
0 [6]). Furthermore,
1
0
1
0
1
which
drive the
solar
andneutrino
atmospheric
neutrino
oscillations,
with
a rather
precision
(see, e.g.,
there
were
spectacular
developments
in
the
period
June
i
ultrarelativistic
neutrinos,
the dispersion
eqnangles
(7.8) can be
approxi1
0
0For(see,
c13the
0 s13 ethere
c12 relation
sdevelopments
0the
frequencies
and
thespectacular
amplitudes
(i.e.in
theJune
mass squared d
12
e.g., [6]).
Furthermore,
were
in the and
period
2011 -@
June 2012 year in
what
concerns
theinCHOOZ
angle
. In June
of✓ 2011
the
T2K the with
A
@by
Aand
@✓13
AJune
2011
- June 0
2012
year1drive
what
the
CHOOZ
of 2011
which
the
solar
atmospheric
0 c23 s23mated
0concerns
s12 2 angle
c12 neutrino
V =
, oscillations,
(1.3) T2K a rather hig
130. In
Whatdoweknowaboutneutrinos?
Normal Ordering
bfp ±1
3 range
Inverted Ordering
bfp ±1
3 range
sin2 ✓12
0.304+0.013
0.012
0.270 ! 0.344
0.304+0.013
0.012
0.270 ! 0.344
sin2 ✓23
0.452+0.052
0.028
0.382 ! 0.643
0.579+0.025
0.037
0.389 ! 0.644
sin2 ✓13
0.0218+0.0010
0.0186 ! 0.0250 0.0219+0.0011
0.0188 ! 0.0251
0.0010
0.0010
m221 [10
5
eV2 ]
m23` [10
3
eV2 ] +2.457+0.047
+2.317 ! +2.607
0.047
7.50+0.19
0.17
7.02 ! 8.09
7.50+0.19
0.17
2.449+0.048
0.047
7.02 ! 8.09
2.590 ! 2.307
www.nu-fit.org
Table I. Three-flavor oscillation parameters from the fit to global data after the NOW 2014 conference pe
by the NuFIT group [17]. The numbers in the 1st (2nd) column are obtained assuming NO (IO). N
m23` ⌘ m231 > 0 for NO and m23` ⌘ m232 < 0 for IO.
ti with respect to a massless particle, emitted by
B. Neutrino orderings: current statu
Whatdoweknowaboutneutrinos?
The time delay between mass eigenstates
t
i j
=
ti
m2ij
tj =
L
2
2E
i, j = 1, 2, 3
Normal Ordering
bfp ±1
3 range
Inverted Ordering
bfp ±1
3 range
sin2 ✓12
0.304+0.013
0.012
0.270 ! 0.344
0.304+0.013
0.012
0.270 ! 0.344
sin2 ✓23
0.452+0.052
0.028
0.382 ! 0.643
0.579+0.025
0.037
0.389 ! 0.644
sin2 ✓13
0.0218+0.0010
0.0186 ! 0.0250 0.0219+0.0011
0.0188 ! 0.0251
0.0010
0.0010
m221 [10
5
eV2 ]
m23` [10
3
eV2 ] +2.457+0.047
+2.317 ! +2.607
0.047
7.50+0.19
0.17
7.02 ! 8.09
7.50+0.19
0.17
2.449+0.048
0.047
7.02 ! 8.09
2.590 ! 2.307
www.nu-fit.org
Table I. Three-flavor oscillation parameters from the fit to global data after the NOW 2014 conference pe
by the NuFIT group [17]. The numbers in the 1st (2nd) column are obtained assuming NO (IO). N
m23` ⌘ m231 > 0 for NO and m23` ⌘ m232 < 0 for IO.
ti with respect to a massless particle, emitted by
B. Neutrino orderings: current statu
Whatdoweknowaboutneutrinos?
Incoherent detection probability
2
)i = |U i | |U i |
P(
2
i, j = 1, 2, 3
,
= e, µ,
Normal Ordering
bfp ±1
3 range
Inverted Ordering
bfp ±1
3 range
sin2 ✓12
0.304+0.013
0.012
0.270 ! 0.344
0.304+0.013
0.012
0.270 ! 0.344
sin2 ✓23
0.452+0.052
0.028
0.382 ! 0.643
0.579+0.025
0.037
0.389 ! 0.644
sin2 ✓13
0.0218+0.0010
0.0186 ! 0.0250 0.0219+0.0011
0.0188 ! 0.0251
0.0010
0.0010
m221 [10
5
eV2 ]
m23` [10
3
eV2 ] +2.457+0.047
+2.317 ! +2.607
0.047
7.50+0.19
0.17
7.02 ! 8.09
7.50+0.19
0.17
2.449+0.048
0.047
7.02 ! 8.09
2.590 ! 2.307
www.nu-fit.org
Table I. Three-flavor oscillation parameters from the fit to global data after the NOW 2014 conference pe
by the NuFIT group [17]. The numbers in the 1st (2nd) column are obtained assuming NO (IO). N
m23` ⌘ m231 > 0 for NO and m23` ⌘ m232 < 0 for IO.
ti with respect to a massless particle, emitted by
B. Neutrino orderings: current statu
Whatisunknown?
2
0.307+0.018
0.016
3
+0.024
0.021
+0.039
0.022
0.30 ± 0.013
perimental
data
we
have
summarized
in
Table
1.1
are
compa
The0.386
experimental
0.41 data we have summarized in Table 1.1 are co
Whatisunknown?
rino neutrino
mass patterns
(see Figure
1.1): 1.1):
0.392
0.41
0.59
rent
mass patterns
(see Figure
+0.037
0.025
+0.037
0.025
+0.021
0.022
0.0241 ± 0.0025
0.0244+0.0023
0.0025
0.023 ± 0.0023
MassHierarchy
comparable to that of LBNE.
European long-baseline projects (LAGUNA-LBNO) involve an intense neutrino source
at CERN, a near detector, and a (phased) 100 kT underground LAr detector at Pyhäsalmi
in Finland, at a baseline of 2300 km. The long baseline, large detector mass, underground
location, near detector, and a broad-band neutrino beam from a 2 MW proton source make
LAGUNA-LBNO an ultimate neutrino oscillation experiment, with outstanding sensitivity
to both the neutrino mass hierarchy and CP . However, the timescale, costs, and priority to
host such an experiment in Europe are not well defined at present.
JUNO is a 20 kT liquid scintillator detector to be located at the solar oscillation maximum, approximately 60 km away from two nuclear power plants in China. This experiment
plans to exploit subtle distortions in the neutrino energy spectrum sensitive to the sign of
rum
with normal
ordering
(NO), (NO),
m1 < m
m12 <<mm2 3<
, correspond
• spectrum
with normal
ordering
m3 , corresp
e summarizes two
recent global 2
fit analysis for the
neutrino os- 2
2
2
2
?
> 0m
and
>✓m
0;31 > 0;
⌘
to 1 uncertainty.
For ⌘
m ,m
sinm
✓ 31
and
sin
1orresponding
A
21 > 0mand
A
3
2
31
2
23
2
13
corresponds to normal (inverted) neutrino mass ordering. These
ds to extract them from experimental data are discussed in re[30].
1 Motivations and Goals
8!
• spectrum
with inverted
(IO),
m2 , corresp
rum
with inverted
(IO),
m
m31 <<mm1 2<
, correspond
1ordering
Motivationsordering
and
Goals
3 <m
ata we have summarized
in Table 1.1 are compatible
with dif2
2
2 < 0.
2
2
m
>
0
and
m
⌘
m
> (see
0 Figure
and
m
21 1.1): mA ⌘
A32 < 0.32
2
1tterns
6
6
PINGU
7!
Long Baseline
m221
?
1 62
22 ⌘
6
m
mal ordering (NO), m1 < m2 < m3 , corresponding
to
m
?
21
1
2
2
mA ⌘ m31 > 0;
m232
erted ordering (IO), m3 < m1 < m
m232
m2 ⌘
2 , corresponding to
2
2 m0.
21
m2A ⌘ m6
?32 <
?3
2
Inverted Ordering
m
6
Normal Ordering
21
?
?
3
of the light neutrino mass min(mj ), the neutrino mass spectrum
Stated MH Sensitivity
6!
5!
JUNO /
RENO-50
4!
epending
on the
of the
light neutrino
mass min(m
the neutr
j ),neutrino
on the value
of value
the light
neutrino
mass min(m
),
the
j
n be:
q
q
2
• normal
hierarchical
(NH):
m1 ⌧ m2 < m3 so m2 ⇠ 2 m , m
Hierarchy
(NH)normal
q left)
q
possible Normal
neutrino mass
spectra: with
ordering (NO,
3!
NO!A+T2K
2!
PINGU
1!
2010
2015
2020
Cosmology
2025
2030
al hierarchical (NH): m1 ⌧ m2 < White
m3Paper:
so Measuring
m2 ⇠the Neutrino Mass
m , m3 ⇠
al
(NH):
m1neutrino
⌧ m2 <mass
m3 spectra:
so m2 ⇠with normal
m2 , mordering
m2A left)
ring
(IO, right).
two
possible
(NO,
3 ⇠
ordering (IO, right).
Inverted Hierarchy (IH) q
al (IH): m3 ⌧ m1 < m2 so m1,2 ⇠
m
q2A
hical (IH): m3 ⌧ m1 < m2 so m1,2 ⇠
m2A
QD): m1 Quasi
u m2 uDegenerate
m3 u m0 , m2j(QD)
| m2A |, i.e. m0 > 0.1eV
e (QD): m1 u m2 u m3 u m0 , m2j
| m2A |, i.e. m0 > 0.1eV
that the global fit analyses we are referring to, [29] and [30],
Year
Figure 23: Summary of sensitivities to the neutrino mass hierarchy for various experimental
approaches,Hierarchy
with timescales, as claimed by the proponents in each case. In the case of
PINGU, forR.N.
which
multiple
the proponents’
sensitivity
Cahn,
D.A.studies
Dwyer,exist,
S.J. Freedman,
W.C.stated
Haxton,
R.W. [29] is shown in
the dark blue
region,
with
the larger blue
analysis of
Kadel,
Yu.G.
Kolomensky,
K.B.region
Luk, P.representing
McDonald, the
G.D.independent
Orebi
Ref. [7]. One di↵erence between the two is the consideration of a wider range of oscillation
parameters in [7] (see Section 6 for details). The vertical scale of each region represents the
spread in the expected sensitivity after the full exposure. We do not attempt to project the
natural increase in sensitivity over time. Note: the “long baseline” region represents the
inclusive range of sensitivities for individual long-baseline experiments (LBNE, HyperK, and
LBNO) rather than a combined sensitivity.
d CERN,
Theory Division, CH-1211 Geneva 23, Switzerland
e LAPTh, Univ. de Savoie, CNRS, B.P.110, Annecy-le-Vieux F-74941, France
f DGA, 7 rue des Mathurins, 92221 Bagneux cedex, France
g INAF, Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34131 Trieste, Italy
h INFN/National Institute for Nuclear Physics, Via Valerio 2, I-34127 Trieste, Italy
i Department of Physics and Center for Cosmology and Astro-Particle Physics, Ohio State UniverI The three neutrino mixing framework
sity, Columbus, OH 43210, USA
E-mail: nathalie.palanque-delabrouille@cea.fr, christophe.yeche@cea.fr,
julien.baur@cea.fr, christophe.magneville@cea.fr, graziano@kias.re.kr,
Planck temperature power spectrum with a WMAP polarization low
Julien.Lesgourgues@cern.ch
Whatisunknown?
AbsoluteMass
and ACT high-multipole (`
2500) data. We refer to this CMB da
0.20
0.15
0.10
TRIN
S mi @eVD
KATRIN
Σ m i [eV]
Abstract. We present constraints on neutrino masses, the primordial fluctuation spectrum from
Planck+WP.
In Measuring
this case Ly↵-forest
the upperpower
limitwith
on athe
sum of the neutrin
inflation, and other parameters of the ⇤CDM model,
using the one-dimensional
neutrino masses
future galaxy survey
Jan Hamann, Steen Hannestad, Yvonne Y.Y. Wong.
1 measured by Palanque-Delabrouille et al. [1] from the Baryon
spectrum
Oscillation
Spectroscopic
⌃m
0.66 eV at 95% C.L. (Planck + WP),
JCAP 1211
(2012)
i <052
Planck+WP
Survey (BOSS)
of the Sloan Digital Sky Survey (SDSS-III), complemented by Planck 2015 cosmic
Combining
the latter
withimproves
the Barion
microwave background (CMB) data and other cosmological
probes.
This paper
on theAcoustic Oscillation data (
Planck 2013 results. XVI. Cosmological parameters
0.50 analysis by Palanque-Delabrouille
QD
significantly
lowered
at set of calibrating
previous
et al. [2]
by using a more
powerful
Astron.Astrophys. 571 (2014) A16
hydrodynamical simulations that reduces uncertainties associated with resolution and box size, by
⌃ mi <of0.23
eV at 95% C.L. (Planck + WP + BAO
adopting a Planck+WP+BAO
more flexible set of nuisance parameters for describing the evolution
the intergalactic
medium, by including additional freedom to account for
uncertainties,
using
Planck into limits on the absolut
Thesystematic
above upper
limits and
canbybe
converted
Neutrino masses and cosmology with Lyman-alpha forest
2015 constraints in place of Planck 2013.
masses that readpower
respectively
spectrum mmin . 0.22 eV in the more conserva
Fitting
Ly↵ data
leads
to cosmological parameters in excellent
agreement
the values
BOSS
Lyα alone
+ Planck
CMB
Palanque-Delabrouille
(IRFU, SPP,
Saclay)
et al..1.10). This is
and mmin . 0.07Nathalie
eV
in
the with
more
stringent
case
(eq.
1511
(2015)nno.11,
011
derived
weak tension on theJCAP
scalar
index
s . Combining
0.10 independently from CMB data, except for a 1.2.
P
BOSS Ly↵ IH
with Planck CMB constrains the sum of neutrino masses to m⌫ < 0.12 eV (95% C.L.)
including all identified systematic uncertainties, tighter than our previous limit (0.15
1.50 eV) and more
robust.
to reionization
0.05 Adding
NH Ly↵ data to CMB data reduces the uncertainties on the optical depth
1.00
⌧, through the correlation of ⌧ with 8 . Similarly, correlations between cosmological
parameters
-4
10
0.001
0.010 ratio
0.100
1 fluctuations r. The tension
0.70 on n s canPlanck+WP
help in constraining
the tensor-to-scalar
of primordial
be
accommodated by allowing for
a running dn s /d ln k. Allowing running as a free parameter
in the fits
0.50
m
Pmin [eV]
does not change the limit on m⌫ . We discuss possible interpretations of these results in the context
0.30
of slow-roll inflation.
Planck+WP+BAO
Setup
We need a distant source of GW, neutrinos and photon, e.g. a core
collapse SN, that emits a short burst.
Real Signal
Simplified Signal
Simplification
L
L
Burst
int
Burst
Time
Time-dependent luminosity
and energy distribution
int
Time
Box signal characterized only
by the mean energy
Setup
We need a distant source of GW, neutrinos and photon, e.g. a core
collapse SN, that emits a short burst.
Simplified Signal
Distance
L
Prob.
1
Burst
Time
int
Box signal characterized only
by the mean energy
3
Time
{
{
int
2
t1
t12
t13
Whatinforma'oncanweget?
Prob.
When t1 can be
disentangled from int and
detector timing uncertainties,
we can get information on the
absolute mass.
1
int
3
Time
{
{
2
t1
t12
t13
When t13 can be
disentangled from int and/or
detector timing uncertainties,
we can get information on the
hierarchy.
Whatdoesitrequire?
int
O(10) ms
Super K
O(1) ms
detector
O(10
detector
1
Hyper K
) ms
Absolute Mass
1
for E = 10 MeV
QD
Planck+WP+BAO
BOSS Lyα + Planck CMB
0.10
0.05
KATRIN
mmin = 0.2 eV −→ 0.5 Mpc
0.50
Σ m i [eV]
mmin = 0.07 eV −→ 4 Mpc
Planck+WP
IH
NH
10-4
0.001
0.010
mmin [eV]
0.100
1
Whatdoesitrequire?
int
O(10) ms
detector
detector
O(1) ms
O(10
Hierarchy (high statistics)
Super K
−→ 0.8 Mpc
Hyper K
−→ 0.08 Mpc
Hierarchy (low statistics)
Normal Ordering
∆t13 > τint −→ 8 Mpc
1
) ms
Super K
Hyper K
ExpectednumberofeventsforHyperK
2
Low number of events at
required distances
What can improve the
number of events:
Detection Probability
1
in Super-Kamiokande (22.5 kton) is ∼ 104 , corresponding
P(≥1) ; 12-38 MeV
to 1 event at 1 Mpc, 0.1 events at 3 Mpc, and so on. For
P(≥1) ; 18-30 MeV
an expected number of events µ, the Poisson probability
P(≥2) ; 15-35 MeV
to detect n events is Pn = µn e−µ /n!; for small µ, we
0.8
scale P1 ≃ µ by the number of supernovae. As shown in
Fig. 2, for each supernova within, say 4 Mpc, the chance
of detecting a single neutrino (or a background event; see
0.6
below) in Super-Kamiokande is ∼ 3%. While small, this
should motivate a careful analysis of their data.
To make this technique more efficient, detectors larger
0.4
than Super-Kamiokande are needed. We consider a sim• Larger
(Linear)
ilar detector
with detector
a 1-Mton fiducial
volume, which is
somewhat larger than the proposed detectors, but if two
• Less uncertainty on int (Quadratic) 0.2
are built, the combined mass could exceed 1 Mton. In
Fig. 2, we show the detection probabilities for at least
• Better time resolution (Quadratic)
one or two events from a single supernova versus distance, along with the calculated supernova rate, which
0
coincidentally also varies from 0 to 1. For a 1-Mton de0
2
4
8
10
6
Distance D [Mpc]
tector, both the detection probability per supernova and
the relevant supernova rate are quite favorable, so that
Detection
of neutrinos
supernovae
in nearby
galaxies
FIG.
2: Probability
of from
detecting
at least
one (dotted
and
the supernova neutrino spectrum could be constructed,
Shin'ichiro Ando (Ohio State U. & Tokyo U.), John F. Beacom (Ohio State U. &
dashed
curves)
or Astron.),
at leastHasan
two Yuksel
(solid(Ohio
curves)
neutriOhio State
U., Dept.
State supernova
U. & Wisconsin
U.,
slowly but (almost) steadily. Additionally, the detection
Madison).
2005. 4 pp. Background considerations restrict the
nos
versusMar
distance.
of even a single neutrino could fix the start time of the
Published in Phys.Rev.Lett. 95 (2005) 171101
useful
energy intervals, labeled here, and explained in the
supernova to ∼ 10 seconds instead of ∼ 1 day, greatly retext. The upper set of curves is for a 1-Mton detector, and
Thankyou!