γλώσσες
Σελίδες
Νομικός
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
PHENOMENOLOGY WITH MASSIVE
NEUTRINOS
Concha Gonzalez-Garcia
(YITP Stony Brook & ICREA U. Barcelona )
UB, June 1tth, 2016
Neutrino Flavour Transition: Data and Interpretation
Some Implications for/from Cosmology
http://www.nu-fit.org
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
p
Sources of ν’s
Concha Gonzalez-Garcia
The Big Bang
ρν = 330/cm3
pν =0.0004 eVSN1987
Eν ∼ MeV
ExtraGalactic
Eν & 30 TeV
The Sun
νe
ΦEarthν = 6× 1010ν/cm2s
Eν ∼ 0.1–20 MeV
Atmospheric ν′s
νe, νµ, νe, νµΦν ∼ 1ν/cm2sHuman Body
Φν = 340× 106ν/day
Nuclear Reactors
νe
Eν ∼ few MeV
Accelerators
Eν ≃ 0.3–30 GeV
Earth’s radioactivity
Φν ∼ 6× 106ν/cm2s
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Neutrinos in the Standard Model
The SM is a gauge theory based on the symmetry group
SU(3)C × SU(2)L × U(1)Y ⇒ SU(3)C × U(1)EM
With three generation of fermions
(1, 2)− 12
(3, 2) 16
(1, 1)−1 (3, 1) 23(3, 1)− 1
3(
νee
)
L
(
ui
di
)
LeR ui
R diR(
νµµ
)
L
(
ci
si
)
LµR ciR siR
(
νττ
)
L
(
ti
bi
)
LτR tiR biR
Three and only three
There is no νR
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Neutrinos in the Standard Model
The SM is a gauge theory based on the symmetry group
SU(3)C × SU(2)L × U(1)Y ⇒ SU(3)C × U(1)EM
With three generation of fermions
(1, 2)− 12
(3, 2) 16
(1, 1)−1 (3, 1) 23(3, 1)− 1
3(
νee
)
L
(
ui
di
)
LeR ui
R diR(
νµµ
)
L
(
ci
si
)
LµR ciR siR
(
νττ
)
L
(
ti
bi
)
LτR tiR biR
Three and only three
There is no νR⇒Accidental global symmetry: B × Le × Lµ × Lτ (hence L = Le + Lµ + Lτ )⇒
ν strictly massless
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
• By 2016 we have observed with high (or good) precision:
∗ Atmospheric νµ & νµ disappear most likely to ντ (SK,MINOS, ICECUBE)
∗ Accel. νµ & νµ disappear at L ∼ 300/800 Km (K2K, T2K/ MINOS, NOνA)
∗ Some accelerator νµ appear as ντ at L ∼ 700 Km ( OPERA)
∗ Some accelerator νµ appear as νe at L ∼ 300/800 Km ( T2K, MINOS,NOνA)
∗ Solar νe convert to νµ/ντ (Cl, Ga, SK, SNO, Borexino)
∗ Reactor νe disappear at L ∼ 200 Km (KamLAND)
∗ Reactor νe disappear at L ∼ 1 Km (D-Chooz, Daya Bay, Reno)
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
• By 2016 we have observed with high (or good) precision:
∗ Atmospheric νµ & νµ disappear most likely to ντ (SK,MINOS, ICECUBE)
∗ Accel. νµ & νµ disappear at L ∼ 300/800 Km (K2K, T2K/ MINOS, NOνA)
∗ Some accelerator νµ appear as ντ at L ∼ 700 Km ( OPERA)
∗ Some accelerator νµ appear as νe at L ∼ 300/800 Km ( T2K, MINOS,NOνA)
∗ Solar νe convert to νµ/ντ (Cl, Ga, SK, SNO, Borexino)
∗ Reactor νe disappear at L ∼ 200 Km (KamLAND)
∗ Reactor νe disappear at L ∼ 1 Km (D-Chooz, Daya Bay, Reno)
All this implies that Lα are violated
and There is Physics Beyond SM
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
The New Minimal Standard Model
• Minimal Extension to allow for LFV ⇒ give Mass to the Neutrino
∗ Introduce νR AND impose L conservation ⇒ Dirac ν 6= νc:
L = LSM −MννLνR + h.c.
∗ NOT impose L conservation ⇒ Majorana ν = νc
L = LSM − 12MννLν
CL + h.c.
_ _
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
The New Minimal Standard Model
• Minimal Extension to allow for LFV ⇒ give Mass to the Neutrino
∗ Introduce νR AND impose L conservation ⇒ Dirac ν 6= νc:
L = LSM −MννLνR + h.c.
∗ NOT impose L conservation ⇒ Majorana ν = νc
L = LSM − 12MννLν
CL + h.c.
• The charged current interactions of leptons are not diagonal (same as quarks)
g√2W+
µ
∑
ij
(
U ijLEP ℓi γµ Lνj + U ij
CKM U i γµ LDj)
+ h.c.
j
W+
l_
i
ν
W+
_
i
uj
d
Phenomenology with Massive Neutrinos Concha Gonzalez-Garciaν Mass Oscillations in Vacuum
• If neutrinos have mass, a weak eigenstate |να〉 produced in lα + N →να + N ′
is a linear combination of the mass eigenstates (|νi〉) : |να〉=n∑
i=1
Uαi |νi〉
• After a distance L it can be detected with flavour β with probability
Pαβ = δαβ − 4n∑
j 6=i
Re[U⋆αiUβiUαjU
⋆βj ]sin
2
(
∆ij
2
)
+ 2∑
j 6=i
Im[U⋆αiUβiUαjU
⋆βj ]sin (∆ij)
∆ij
2 =(Ei−Ej)L
2 = 1.27(m2
i−m2j )
eV2L/E
Km/GeV
Phenomenology with Massive Neutrinos Concha Gonzalez-Garciaν Mass Oscillations in Vacuum
• If neutrinos have mass, a weak eigenstate |να〉 produced in lα + N →να + N ′
is a linear combination of the mass eigenstates (|νi〉) : |να〉=n∑
i=1
Uαi |νi〉
• After a distance L it can be detected with flavour β with probability
Pαβ = δαβ − 4n∑
j 6=i
Re[U⋆αiUβiUαjU
⋆βj ]sin
2
(
∆ij
2
)
+ 2∑
j 6=i
Im[U⋆αiUβiUαjU
⋆βj ]sin (∆ij)
∆ij
2 =(Ei−Ej)L
2 = 1.27(m2
i−m2j )
eV2L/E
Km/GeV
No information on ν mass scale nor Majorana versus Dirac
Phenomenology with Massive Neutrinos Concha Gonzalez-Garciaν Mass Oscillations in Vacuum
• If neutrinos have mass, a weak eigenstate |να〉 produced in lα + N →να + N ′
is a linear combination of the mass eigenstates (|νi〉) : |να〉=n∑
i=1
Uαi |νi〉
• After a distance L it can be detected with flavour β with probability
Pαβ = δαβ − 4n∑
j 6=i
Re[U⋆αiUβiUαjU
⋆βj ]sin
2
(
∆ij
2
)
+ 2∑
j 6=i
Im[U⋆αiUβiUαjU
⋆βj ]sin (∆ij)
∆ij
2 =(Ei−Ej)L
2 = 1.27(m2
i−m2j )
eV2L/E
Km/GeV
No information on ν mass scale nor Majorana versus Dirac
• For 2-ν:Pαα = 1− Posc Disappear
Posc = sin2(2θ) sin2(
1.27∆m2LE
)
Appear
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Matter Effects
• If ν cross matter regions (Sun, Earth...) it interacts coherently
– But Different flavours
have different interactions :
νe, νµ, ντ only νe
Z W
ν ν ν e
e,N e,Ne ν
⇒ Effective potential in ν evolution : Ve 6= Vµ,τ ⇒ ∆V ν = −∆V ν =√2GFNe
⇒ Modification of mixing angle and oscillation wavelength ≡ MSW effect
• The mixing angle in matter
sin(2θm) =∆m2 sin(2θ)
√
(∆m2 cos(2θ)− 2E∆V )2 + (∆m2 sin(2θ))2
• For solar neutrinos in adiabatic regime P (νe → νe) =12 [1 + cos(2θm) cos(2θ)]
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia• By 2016 we have observed with high (or good) precision:
∗ Atmospheric νµ & νµ disappear most likely to ντ (SK,MINOS, ICECUBE)
∗ Accel. νµ & νµ disappear at L ∼ 300/800 Km (K2K, T2K, MINOS, NOνA)
∗ Some accelerator νµ appear as ντ at L ∼ 700 Km ( OPERA)
∗ Some accelerator νµ appear as νe at L ∼ 300/800 Km ( T2K, MINOS,NOνA)
∗ Solar νe convert to νµ/ντ (Cl, Ga, SK, SNO, Borexino)
∗ Reactor νe disappear at L ∼ 200 Km (KamLAND)
∗ Reactor νe disappear at L ∼ 1 Km (D-Chooz, Daya Bay, Reno)
• Confirmed:
SK
MINOS/T2K/NOvA
(km/MeV)eν/E0L
20 30 40 50 60 70 80 90 100
Surv
ival
Pro
babi
lity
0
0.2
0.4
0.6
0.8
1
eνData - BG - Geo Expectation based on osci. parameters
determined by KamLAND
KamLAND
Daya-Bay/RENO/D-Chooz
Vacuum oscillation L/E pattern with 2 frequencies
MSW conversion in Sun
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia3ν Flavour Parameters
• For for 3 ν’s : 3 Mixing angles + 1 Dirac Phase + 2 Majorana Phases
ULEP =
1 0 0
0 c23 s23
0 −s23 c23
c13 0 s13eiδcp
0 1 0
−s13e−iδcp 0 c13
c21 s12 0
−s12 c12 0
0 0 1
eiη1 0 0
0 eiη2 0
0 0 1
• Two Possible Orderings
M
sola
r
sola
r
atm
os
m m 1 3
∆ 2
∆ m
2
m 3
m 2
∆ m
m 1
m 2
NORMAL INVERTED
2
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia3ν Flavour Parameters
• For for 3 ν’s : 3 Mixing angles + 1 Dirac Phase + 2 Majorana Phases
ULEP =
1 0 0
0 c23 s23
0 −s23 c23
c13 0 s13eiδcp
0 1 0
−s13e−iδcp 0 c13
c21 s12 0
−s12 c12 0
0 0 1
eiη1 0 0
0 eiη2 0
0 0 1
• Two Possible Orderings
M
sola
r
sola
r
atm
os
m m 1 3
∆ 2
∆ m
2
m 3
m 2
∆ m
m 1
m 2
NORMAL INVERTED
2
Experiment Dominant Dependence Important Dependence
Solar Experiments → θ12 ∆m221 , θ13
Reactor LBL (KamLAND) → ∆m221 θ12 , θ13
Reactor MBL (Daya Bay, Reno, D-Chooz) → θ13 ∆m2atm
Atmospheric Experiments → θ23 ∆m2atm, θ13 ,δcp
Acc LBL νµ Disapp (Minos,T2K,NOvA) → ∆m2atm θ23
Acc LBL νe App (Minos,T2K,NOvA) → θ13 δcp , θ23
×
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia3 ν Flavour Parameters: Status in 6/2016
Global 6-parameter fit http://www.nu-fit.org (ArXiv:1409.5439)Maltoni, Schwetz, Martinez-Soler, Esteban, MCG-G
0.2 0.25 0.3 0.35 0.4
sin2 θ12
0
5
10
15
∆χ2
6.5 7 7.5 8 8.5
∆m221 [10
-5 eV
2]
0.3 0.4 0.5 0.6 0.7
sin2 θ23
0
5
10
15
∆χ2
-2.6 -2.4 -2.2
∆m232 [10
-3 eV
2] ∆m
231
2.2 2.4 2.6 2.8
0.015 0.02 0.025 0.03
sin2 θ13
0
5
10
15
∆χ2
0 90 180 270 360δCP
NO, IO (LEM)
NO, IO (LID)
NuFIT 2.1 (2016)
0.2 0.25 0.3 0.35 0.4
sin2 θ12
6.5
7
7.5
8
8.5
∆m2 21
[10-5
eV
2 ]
0.015 0.02 0.025 0.03
sin2 θ13
0.015
0.02
0.025
0.03
sin2
θ 13
0
90
180
270
360
δ CP
0.3 0.4 0.5 0.6 0.7
sin2 θ23
-2.8
-2.6
-2.4
-2.2
2.2
2.4
2.6
2.8
∆m2 32
[1
0-3 e
V2 ]
∆m
2 31
NuFIT 2.1 (2016)
θ23 6= 45
θ23 < 45 ?
N/I
?
δcp
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
3ν Analysis: Leptonic CP violation
• “Hint” CP phase around δCP = 3π2 (maximal)
0 90 180 270δCP
0
2
4
6
8
10
12
14
∆χ2
0 90 180 270 360δCP
NuFIT 2.0 (updated)
+ DeepCore
+ T2K ν+ NOνA (LEM, LID)
NuFIT 2.1 (2016)
IO NO
• Leptonic Jarslog Determinant
0.025 0.03 0.035 0.04
JCPmax
= c12 s12 c23 s23 c213 s13
0
5
10
15
∆χ2
-0.04 -0.02 0 0.02 0.04
JCP = JCPmax
sinδCP
NO, IO (LEM)
NO, IO (LID)
NuFIT 2.1 (2016)
Potentially much larger than the quark sector JCMK =(
3.06+0.21−0.20
)
× 10−5
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Issues with the Solar Fluxes
– Newer determination of abundance of heavy
elements in solar surface give lower values
– Solar Models with these lower metalicities
fail in reproducing helioseismology data
– Two sets of SSM:Starting from Bahcall etal 05, Serenelli etal 0909.2668
GS98 uses older metalicities
AGSXX uses newer metalicities
Flux GS98 AGSS09 Diff (%)cm−2 s−1
pp/1010 5.97 6.03 (1± 0.005) 0.8
pep/108 1.41 1.44 (1± 0.010) 2.1
hep/103 7.91 8.18 (1± 0.15) 3.4
7Be/109 5.08 4.64 (1± 0.06) 8.8
8B/106 5.88 4.85 (1± 0.12) 17.7
13N/108 2.82 2.07(1+0.14−0.13) 26.7
15O/108 2.09 1.47 (1+0.16−0.15) 30.0
17F/1016 5.65 3.48 (1+0.17−0.16) 38.4
Most difference in CNO fluxes
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Issues with the Solar Fluxes
– Newer determination of abundance of heavy
elements in solar surface give lower values
– Solar Models with these lower metalicities
fail in reproducing helioseismology data
– Two sets of SSM:Starting from Bahcall etal 05, Serenelli etal 0909.2668
GS98 uses older metalicities
AGSXX uses newer metalicities
Flux GS98 AGSS09 Diff (%)cm−2 s−1
pp/1010 5.97 6.03 (1± 0.005) 0.8
pep/108 1.41 1.44 (1± 0.010) 2.1
hep/103 7.91 8.18 (1± 0.15) 3.4
7Be/109 5.08 4.64 (1± 0.06) 8.8
8B/106 5.88 4.85 (1± 0.12) 17.7
13N/108 2.82 2.07(1+0.14−0.13) 26.7
15O/108 2.09 1.47 (1+0.16−0.15) 30.0
17F/1016 5.65 3.48 (1+0.17−0.16) 38.4
Most difference in CNO fluxes
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Issues with the Solar Fluxes
– Newer determination of abundance of heavy
elements in solar surface give lower values
– Solar Models with these lower metalicities
fail in reproducing helioseismology data
– Two sets of SSM:Starting from Bahcall etal 05, Serenelli etal 0909.2668
GS98 uses older metalicities
AGSXX uses newer metalicities
–Impact in Osc Parameter Determination
Neglegeable ⇒ Possible to Invert
and Extract Fluxes from Data.
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Learning how the Sun Shines with ν ′s
Results of Oscillation analysis with solar flux normalizations free: fi =Φi
ΦGS98i
Bergstrom,MCG-G,Maltoni,Pena-Garay,Serenelli, Song,
ArXiv:1601:00972
Present limit on CNO:
LCNOL⊙
< 2% (3σ)
Test of Luminosity Constraint:
L⊙(ν − inferred)L⊙
= 1.04± 0.07
Comparing with the Models:
Both statistically equally probable
New experiments needed
more sensitive to CNO fluxes
New models with new Nuclear Rates
New problems with Helioseismology
Bergstrom,MCG-G,Maltoni,
Pena-Garay,Serenelli,Song, in preparation
Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaBeyond 3ν’s: Light Sterile Neutrinos
• Several Observations which can be Interpreted as Oscillations with ∆m2 ∼ eV2
Reactor Anomaly
New reactor flux calculation
⇒ Deficit in data at L . 100 m
0.7
0.8
0.9
1
1.1
1.2
1.3
obse
rved
/ pr
edic
ted
oldnew
Bug
ey 4
RO
VN
O
Bug
ey 3
Goe
sgen
ILL
Kra
snoy
arsk
235 U
238 U
239 Pu
241 Pu
Explained as νe disappearance
Kopp etal, ArXiv 1303.3011
Gallium AnomalyAcero, Giunti, Laveder, 0711.4222Giunti, Laveder,1006.3244
Radioactive Sources (51Cr, 37Ar)
in calibration of Ga Solar Exp;
νe + 71Ga → 71Ge + e−
Give a rate lower than expected
R =Nobs
NthBahc
= 0.86± 0.05 (2.8σ)
Explained as νe disappearance
10 3
10 2
101
101
100
101
Ue42
m
412eV2
95 CL
Gallium
C12
Kopp etal, ArXiv 1303.3011
LSND, MiniBoone
νµ → νe and νµ → νe
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Light Sterile Neutrinos
• These explanations require 3+Ns mass eigenstates → Ns sterile neutrinos
• Problem: fit together
νe → νe disapp (REACT,Gallium,Solar, LSND/KARMEN)
νµ → νe app (LSND,KARMEN,NOMAD,MiniBooNE,E776,ICARUS)
νµ → νµ disapp (CDHS,ATM,MINOS,MiniBooNE)
• Generically: P (νe → νµ) ∼ |U∗eiUµi| [i =heavier state(s)]
But |Uei| constrained by P (νe → νe) disappearance data
And |Uµi| constrained by P (νµ → νµ) disappearance data⇒ Severe tension
Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaLight Sterile Neutrinos:3+1
• Comparing the parameters required to explain signals with bounds from disapp
Kopp etal, ArXiv 1303.3011
104 10 3 10 2 101101
100
101
sin 2 2 Θ Μe
m
2
disappearance
appearance
Giunti etal, ArXiv 1308.5288
sin22ϑeµ
∆m412
[e
V2 ]
10−4 10−3 10−2 10−1 110−1
1
10
+
10−4 10−3 10−2 10−1 110−1
1
10
+
3+1 − GLO
68.27% CL90.00% CL95.45% CL99.00% CL99.73% CL
3+1 − 3σνe DISνµ DISDISAPP
Somewhat different conclusions
Further Disfavoured by ICECUBE
sin
2
2θ
24
10
−1
10
0
10
1
∆m
2
41
/eV
2
SuperK
MINOS
M
B
/
S
B
ν
C
D
H
S
IceCube 90% CL
90% CL sensitivity
(68% and 95%)
Kopp et al. (2013)
10
−2
10
−1
10
0
sin
2
2θ
24
10
−2
10
−1
10
0
∆m
2
41
/eV
2
SuperK
MIN
OS
M
B
/
S
B
ν
C
D
H
S
IceCube 99% CL
99% CL sensitivity
(68% and 95%)
Kopp et al. (2013)
Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaLight Sterile Neutrinos:3+1
• Comparing the parameters required to explain signals with bounds from disapp
Kopp etal, ArXiv 1303.3011
104 10 3 10 2 101101
100
101
sin 2 2 Θ Μe
m
2
disappearance
appearance
Giunti etal, ArXiv 1308.5288
sin22ϑeµ
∆m412
[e
V2 ]
10−4 10−3 10−2 10−1 110−1
1
10
+
10−4 10−3 10−2 10−1 110−1
1
10
+
3+1 − GLO
68.27% CL90.00% CL95.45% CL99.00% CL99.73% CL
3+1 − 3σνe DISνµ DISDISAPP
Somewhat different conclusions
Further Disfavoured by ICECUBE
sin
2
2θ
24
10
−1
10
0
10
1
∆m
2
41
/eV
2
SuperK
MINOS
M
B
/
S
B
ν
C
D
H
S
IceCube 90% CL
90% CL sensitivity
(68% and 95%)
Kopp et al. (2013)
10
−2
10
−1
10
0
sin
2
2θ
24
10
−2
10
−1
10
0
∆m
2
41
/eV
2
SuperK
MIN
OS
M
B
/
S
B
ν
C
D
H
S
IceCube 99% CL
99% CL sensitivity
(68% and 95%)
Kopp et al. (2013)
More steriles help? Arguelles etal ArXiv:1602.00671
More latter...
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Neutrino Mass Scale: Laboratory Probes
Single β decay : Dirac or Majorana ν mass modify spectrum endpoint
νm
K (T)
QT
m2νe
=∑
m2j |Uej |2 = c213c
212m
21 + c213s
212m
22 + s213m
23
Present bound: mνe≤ 2.2 eV (at 95 % CL)
Katrin (2016?) Sensitivity to mνe∼ 0.2 eV
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Neutrino Mass Scale: Laboratory Probes
Single β decay : Dirac or Majorana ν mass modify spectrum endpoint
νm
K (T)
QT
m2νe
=∑
m2j |Uej |2 = c213c
212m
21 + c213s
212m
22 + s213m
23
Present bound: mνe≤ 2.2 eV (at 95 % CL)
Katrin (2016?) Sensitivity to mνe∼ 0.2 eV
ν-less Double-β decay: ⇔ Majorana ν′s
n
p
W
n
p
Wν
e−
e−
If mν only source of ∆L T 0ν1/2 = me
G0ν M2nucl m
2ee
mee = |∑
U2ejmj |
=∣
∣c213c212m1 e
iη1 + c213s212m2 e
iη2 + s213m3 e−iδCP
∣
∣
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
0νββ Decay: Present
Bounds from 136Xe (EXO and KamLAND-ZEN), 76Ge (Gerda) and 130Te (Cuore-0)
(eV)lightestm
4103
10 210 110
(eV
)m
310
210
110
1
IH
NH
Xe)136
KamLAND-Zen (
A
50 100 150
Ca
Ge
SeZr
Mo
CdTe
Te
Xe
Nd
KamLAND-Zen Coll. ArXiv:1505.02889
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
The Emerging Picture
• At least two neutrinos are massive ⇒ There is NP
• Oscillations DO NOT determine the lightest mass but β decay:∑
mνi≤ 2 eV/c2
⇒ Heaviest ν is at least 1 millon de times lighter than the electron
• Dirac or Majorana?: We do not know
• Three mixing angles are non-zero (and relatively large) ⇒ very different from CKM
– The two arising questions
∗ Why are neutrinos so light?
The Origin of Neutrino Mass
∗ Why are lepton mixing so different from quark’s?
The Flavour Puzzle
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Bottom-up: Light ν from Generic New Physics
If SM is an effective low energy theory, for E ≪ ΛNP
– The same particle content as the SM and same pattern of symmetry breaking
– But there can be non-renormalizable
(dim> 4) operatorsL = LSM+
∑
n
1
Λn−4NP
On
First NP effect ⇒ dim=5 operator
There is only one!L5 =
Zνij
ΛNP
(
LL,iφ)(
φTLCL,j
)
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Bottom-up: Light ν from Generic New Physics
If SM is an effective low energy theory, for E ≪ ΛNP
– The same particle content as the SM and same pattern of symmetry breaking
– But there can be non-renormalizable
(dim> 4) operatorsL = LSM+
∑
n
1
Λn−4NP
On
First NP effect ⇒ dim=5 operator
There is only one!L5 =
Zνij
ΛNP
(
LL,iφ)(
φTLCL,j
)
which after symmetry breaking
induces a ν Majorana mass(Mν)ij = Zν
ij
v2
ΛNP
Implications:
– It is natural that ν mass is the first evidence of NP
– Naturally mν ≪ other fermions masses ∼ λfv if ΛNP >> v
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Bottom-up: Light ν from Generic New Physics
If SM is an effective low energy theory, for E ≪ ΛNP
– The same particle content as the SM and same pattern of symmetry breaking
– But there can be non-renormalizable
(dim> 4) operatorsL = LSM+
∑
n
1
Λn−4NP
On
First NP effect ⇒ dim=5 operator
There is only one!L5 =
Zνij
ΛNP
(
LL,iφ)(
φTLCL,j
)
which after symmetry breaking
induces a ν Majorana mass(Mν)ij = Zν
ij
v2
ΛNP
Implications:
– It is natural that ν mass is the first evidence of NP
– Naturally mν ≪ other fermions masses ∼ λfv if ΛNP >> v
– mν >√
∆m2atm ∼ 0.05 eV for Zν ∼ 1⇒ ΛNP ∼ 1015GeV⇒ ΛNP ∼ GUT scale
⇒ Leptogenesis possible
[ But if Zν ∼ (Ye)2 ⇒ ΛNP ∼ TeV scale ]
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Implications: Leptogenesis
• Majorana mν ⇒ Lepton # violated ⇒ Matter-Antimatter asymmetry possible
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Implications: Leptogenesis
• Majorana mν ⇒ Lepton # violated ⇒ Matter-Antimatter asymmetry possible
• How? In the Early Universe via decay of heavy state N related to ν-mass generation
– If /CP : Γ(N → X l) 6= Γ(N → X l)
– And decay is out of equilibrium:
(ΓN ≪ Universe expansion rate)
∆ L is generated
SM sphaleron processes ⇒∆ L is transformed in ∆ B
• Today µB = − gtoday∗
gend∗
asph NendL ≃ − 3.92
106.752879N
endL ≃ 10−2 N end
L
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Implications: Leptogenesis
• Majorana mν ⇒ Lepton # violated ⇒ Matter-Antimatter asymmetry possible
• How? In the Early Universe via decay of heavy state N related to ν-mass generation
– If /CP : Γ(N → X l) 6= Γ(N → X l)
– And decay is out of equilibrium:
(ΓN ≪ Universe expansion rate)
∆ L is generated
SM sphaleron processes ⇒∆ L is transformed in ∆ B
• Today µB = − gtoday∗
gend∗
asph NendL ≃ − 3.92
106.752879N
endL ≃ 10−2 N end
L
• To obtain N endL : solve Boltzman Eqs. with all relevant processes
⇒ Details and connection to ν parameters are model dependent
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Leptogenesis connection to ν’s: Challenge
O5 is generated for example by tree-level exchange of singlet (Ni ≡ (1, 1)0) (Type-I) or
triplet fermions (Ni ≡ Σi ≡ (1, 3)0) (Type-III) or a scalar triplet ∆ ≡ (1, 3)1 (Type-II)
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Leptogenesis connection to ν’s: Challenge
O5 is generated for example by tree-level exchange of singlet (Ni ≡ (1, 1)0) (Type-I) or
triplet fermions (Ni ≡ Σi ≡ (1, 3)0) (Type-III) or a scalar triplet ∆ ≡ (1, 3)1 (Type-II)
• For fermionic see-saw −LNP = −iNi/DNi +12MNijN
ci Nj + λν
αjLαφNj [.τ ]
⇒ O5 =(λνTλν)αβ
ΛNP
(
Lαφ)(
φTLCβ
)
with ΛNP = MN
• For scalar see-saw −LNP = f∆αβLα ∆LCβ +M2
∆|∆|2 + κφT ∆† φ . . .
⇒ O5 =f∆αβ
ΛNP
(
Lαφ)(
φTLCβ
)
with ΛNP =M2
∆
κ
Very different HE physics, but same LE ν parameters
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Leptogenesis connection to ν’s: Example
• Generically in these see-saw models successfull leptogenesis
⇒ Lower bound on heavy decaying particle (for enough asymmetry)
⇒ Upper bound on light neutrino mass (for not too much washout)
• For example in Type-I see-saw
10-6
10-5
10-4
10-3
10-2
10-1
1
m 1 HeVL
109
1010
1011
1012
M1HGeVL
msol
matm
10-6
10-5
10-4
10-3
10-2
10-1
1
m 1 HeVL
108
109
1010
1011
1012
M1HGeVL
msol
matm
Abada, Josse-Michaux
Zero Initial Abundance thermal initial abundance
⇒ Lower bound on right-handed neutrino mass:
M1 & 3× 109 GeV (for zero initial abundance)
M1 & 6× 108 GeV (for thermal initial abundance)
⇒ Upper bound on neutrino mass m =√
m21 +m2
2 +m23 . O(eV)
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Light massive ν in Cosmology
Relic ν′s: Effects in several cosmological observations at several epochs
Primordial Cosmic Microwave Large Scale
Nucleosynthesis Background Structure Formation
BBN CMB LSS
T ∼ MeV T . eV
Number of ν′s (Neff ) Neff and∑
mν
Observables also depend on all other cosmological parameters
See also talk by V. Niro on Friday and posters by Cuesta and Giusarma
Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaBBN & Neff
• In general at T < me we can always write ρr =
[
1 +7
8×(
4
11
)43
Neff
]
ργ
∆Neff = Neff − 3 (exactly -3.04) parametrizes:
– Any new relativistic states (accounting for their decoupling temperature
– Possible new ν-interactions (which change the relation between Tγ and Tν )
Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaBBN & Neff
• In general at T < me we can always write ρr =
[
1 +7
8×(
4
11
)43
Neff
]
ργ
∆Neff = Neff − 3 (exactly -3.04) parametrizes:
– Any new relativistic states (accounting for their decoupling temperature
– Possible new ν-interactions (which change the relation between Tγ and Tν )
• At BBN Neff > 3 :
⇒ Faster expansion of Universe
⇒ Weak Interac freeze-out earlier
⇒ Larger nn
np⇒ Larger 4He abundance
Bu
rles
,N
oll
et,
Tu
rner
(19
99
)
Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaBBN & Neff
• In general at T < me we can always write ρr =
[
1 +7
8×(
4
11
)43
Neff
]
ργ
∆Neff = Neff − 3 (exactly -3.04) parametrizes:
– Any new relativistic states (accounting for their decoupling temperature
– Possible new ν-interactions (which change the relation between Tγ and Tν )
• At BBN Neff > 3 :
⇒ Faster expansion of Universe
⇒ Weak Interac freeze-out earlier
⇒ Larger nn
np⇒ Larger 4He abundance
Bu
rles
,N
oll
et,
Tu
rner
(19
99
)
Cyburt etal arXiv:1505.0176
BBN 4He and Deut: Neff = 2.85± 0.28
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
CMB: Effects of Neutrinos
• CMB almost unaffected by 3 ν’s if they are relativistic at recombination zrec = 1089
At recombination T recγ ≃ 3000 K≃ 0.26 eV ⇒ T rec
ν =
(
4
11
)13
T recγ ≃ 0.18 eV
The mean momenta of the neutrino 〈pν〉rec =7π4
180ξ(3)T recν = 0.58 eV
So ν’s direct effect of CMB if∑
mνi> O(eV)
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
CMB: Effects of Neutrinos
• CMB almost unaffected by 3 ν’s if they are relativistic at recombination zrec = 1089
At recombination T recγ ≃ 3000 K≃ 0.26 eV ⇒ T rec
ν =
(
4
11
)13
T recγ ≃ 0.18 eV
The mean momenta of the neutrino 〈pν〉rec =7π4
180ξ(3)T recν = 0.58 eV
So ν’s direct effect of CMB if∑
mνi> O(eV)
• For 3 lighter ν′s effect is indirect (and small):
fν = Ων
Ωm6= 0 changes background evolution
(time of matter-radiation equality)
6000
5000
4000
3000
2000
1000
01400120010008006004002002
l(l+
1) C
l / 2
π (
µK)2
l
no ν’s
fν=0
fν=0.1
J. Lesgourgues & S.Pastor Phys. Rep.(2006)
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
CMB: Effect of Neutrinos
• CMB almost unaffected by 3 ν’s if they are relativistic at recombination zrec = 1089
At recombination T recγ ≃ 3000 K≃ 0.26 eV ⇒ T rec
ν =
(
4
11
)13
T recγ ≃ 0.18 eV
The mean momenta of the neutrino 〈pν〉rec =7π4
180ξ(3)T recν = 0.58 eV
So ν’s direct effect of CMB if∑
mνi> O(eV)
• For 3 lighter ν′s effect is indirect (and small):
fν = Ων
Ωm6= 0 changes background evolution
(time of matter-radiation equality)
6000
5000
4000
3000
2000
1000
01400120010008006004002002
l(l+
1) C
l / 2
π (
µK)2
l
fν=0
fν=0.1, fixed (ωc, ΩΛ)
fν=0.1, fixed (ωc, h)
J. Lesgourgues & S.Pastor Phys. Rep.(2006)
• But parameter degeneracies:
Same effect by change of
other cosmological parameters
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
CMB: Effect of Neutrinos
• CMB almost unaffected by 3 ν’s if they are relativistic at recombination zrec = 1089
At recombination T recγ ≃ 3000 K≃ 0.26 eV ⇒ T rec
ν =
(
4
11
)13
T recγ ≃ 0.18 eV
The mean momenta of the neutrino 〈pν〉rec =7π4
180ξ(3)T recν = 0.58 eV
So ν’s direct effect of CMB if∑
mνi> O(eV)
• For more than 3 ν′s: a change in Neff changes the time of matter-radiation equality
1 + zeq =Ωm
Ωr=
Ωmh2
Ωγh2
1
1 + 0.2271Neff
• The ratio 1st/3rd peak in CMB ⇒ zeq = 3386± 69 but Neff degenerated with Ωm
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
CMB: Effect of Neutrinos
• CMB almost unaffected by 3 ν’s if they are relativistic at recombination zrec = 1089
At recombination T recγ ≃ 3000 K≃ 0.26 eV ⇒ T rec
ν =
(
4
11
)13
T recγ ≃ 0.18 eV
The mean momenta of the neutrino 〈pν〉rec =7π4
180ξ(3)T recν = 0.58 eV
So ν’s direct effect of CMB if∑
mνi> O(eV)
• For more than 3 ν′s: a change in Neff changes the time of matter-radiation equality
1 + zeq =Ωm
Ωr=
Ωmh2
Ωγh2
1
1 + 0.2271Neff
• The ratio 1st/3rd peak in CMB ⇒ zeq = 3386± 69 but Neff degenerated with Ωm
The conclusions is:
Combined analysis of Several Observables to break Degeneracies
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Matter Power Spectrum: Effects of ν’s
• Contrary to CDM, ν′s move at speed vν ∼ min
[
c, 3Tν
mν
]
⇒ They can travel freely over distances λFS ∼ vνH(t)
⇒ They affect structures formed over scales k with2πa(t)
k≤ λFS
k ≥ knr ≃ 0.018Ω1/2m
mν
1 eV
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Matter Power Spectrum: Effects of ν’s
• Contrary to CDM, ν′s move at speed vν ∼ min
[
c, 3Tν
mν
]
⇒ They can travel freely over distances λFS ∼ vνH(t)
⇒ They affect structures formed over scales k with2πa(t)
k≤ λFS
k ≥ knr ≃ 0.018Ω1/2m
mν
1 eV
• If all DM formed of ν′s (Hot Dark Matter) no structure formed with k ≥ knr
⇒ Pure HDM Ruled out by Observations
⇒ Subdominant contribution of ν′s to DM Constrained by Observations
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Matter Power Spectrum: Effects of ν’s
• In a Universe with CDM+ν′s with fν =Ων
Ωm≪ 1
∆P (k)
P (k)≃ −8fν ≃ −0.09
∑
mνi
1 eV
1
Ωmh2for k ≫ knr
0
0.2
0.4
0.6
0.8
1
1.2
110-110-210-310-4
P(k
)f ν /
P(k
)f ν=
0
k (h/Mpc)
knrknr fν
0.01
0.02
0.03
0.1
J. Lesgourgues & S.Pastor Phys. Rep.(2006)
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Cosmological Analysis by Planck
arXiv:1502.01589
−0.12
−0.08
−0.04
0.00
ΩK
0.4
0.8
1.2
1.6
Σm
ν[e
V]
2.4
3.2
4.0
4.8
Neff
0.24
0.28
0.32
YP
−0.030
−0.015
0.000
0.015
dn
s/d
lnk
0.06
0.12
0.18
0.24
r 0.0
02
0.021 0.022 0.023
Ωbh2
−2.0
−1.5
−1.0
−0.5
w
0.11 0.12 0.13 0.14
Ωch2
0.93 0.96 0.99 1.02
ns
45 60 75 90
H0
0.60 0.75 0.90 1.05
σ8
Range of Bounds
Model Observables Σmν (eV) 95%
ΛCDM+mν Planck TT + lowP ≤ 0.72
ΛCDM+mν Planck TT + lowP + lensing ≤ 0.68
ΛCDM+mν Planck TT,TE,EE + lowP+lensing ≤ 0.59
ΛCDM+mν Planck TT,TE,EE + lowP ≤ 0.49
ΛCDM+mν Planck TT + lowP + lensing + BAO + SN + H0 ≤ 0.23
ΛCDM+mν Planck TT,TE,EE + lowP+ BAO ≤ 0.17
2.4 3.0 3.6 4.2
Neff
0.0
0.2
0.4
0.6
0.8
1.0
P/P
max
Planck+WP+highL
+BAO
+H0
+BAO+H0
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Neutrino Mass Scale
Single β decay : Dirac or Majorana ν mass modify spectrum endpoint
νm
K (T)
QT
m2νe
=∑
m2j |Uej |2 = c213c
212m
21 + c213s
212m
22 + s213m
23
Present bound: mνe≤ 2.2 eV (at 95 % CL)
Katrin (2016?) Sensitivity to mνe∼ 0.2 eV
ν-less Double-β decay: ⇔ Majorana ν′s sensitive to Majorana phases
n
p
W
n
p
Wν
e−
e−
If mν only source of ∆L (T 0ν1/2)
−1 ∝ (mee)2
mee = |∑
U2ejmj |
=∣
∣c213c212m1 e
iη1 + c213s212m2 e
iη2 + s213m3 e−iδCP
∣
∣
Present Bounds: mee < 0.06−0.76 eV
COSMO Neutrino mass (Dirac or Majorana)
modify the growth of structures∑
mi
Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaNeutrino Mass Scale: The Cosmo-Lab Connection
Global oscillation analysis
⇒ Correlations mνe, mee and
∑
mν
(Fogli et al (04))
Nufit (95%)
Width due to range in oscillation
parameters very narrow
High precision determination of
mνeand
∑
mi can give informa-
tion on ordering
Wide band due to unknown Majorana
phases ⇒ Possible Det of Maj phases
If Matrix Element Uncertainty Reduced
Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaNeutrino Mass Scale: The Cosmo-Lab Connection
Global oscillation analysis
⇒ Correlations mνe, mee and
∑
mν
(Fogli et al hep-ph/0408045)
Nufit (95%)
Presently only Bounds
• From Tritium β decay (Mainz & Troisk expe)
mνe< 2.2 eV (95%)
Katrin (2016?) Sensitivity to mνe∼ 0.2 eV
• From 0νββ decay for Majorana Neutrinos
mee < 0.06− 0.15 eV (90%)
Goal of Next Decade ⇒ mee at IO
• From Analysis of Cosmological data
Bound on∑
mν changes with:cosmo parameters fix in analysis
cosmo observables considered
Model Observables Σmν (eV) 95%
ΛCDM+mν Planck TT + lowP ≤ 0.72
ΛCDM+mν Planck TT + lowP + lensing ≤ 0.68
ΛCDM+mν Planck TT,TE,EE + lowP+lensing ≤ 0.59
ΛCDM+mν Planck TT,TE,EE + lowP ≤ 0.49
ΛCDM+mν Planck TT + lowP + lensing + BAO + SN + H0 ≤ 0.23
ΛCDM+mν Planck TT,TE,EE + lowP+ BAO ≤ 0.17
See also talk by V. Niro on Friday and posters by Cuesta
and Giusarma
Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaMixed Light Sterile Neutrinos in Cosmology
One light νs mixed with 3 ν′as contributes to ρ as Neff .
From evol eq for 3 + 1 ensemble one finds
⇒ So if “explaination” to SBL anomalies
1 νs contributes as much as 1 νa
But analysis of cosmo data in ΛCDM+r + νs tells us
Plank+WP+high-l+BAO
J. Bergstrom, etal, ArXiv:1407.3806
Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaLight Sterile ν ′s in Cosmology and New Interactions
• In string inspired E6 models, 3 light νR’s with new interactions
(Z ′ with coupling Y νR
Z′ = cosβ 5√40
− 1√24
sinβ)
• In these scenarios ∆Neff = 3×(
TνR
TνL
)4
= 3×(
g(TdecνR
)
g(TdecνR
)
)43
Determined by σ(νRνR → ff) mediated by Z ′ (ie MZ′ and coupling parameter β)
[GeV]Z’M
310 410
[MeV
]Rν de
cT
310
π = 0.41 βπ = 0.42 β
π = 0.5 βπ = 0.3 βπ = 0.7 βπ = 0.8 βπ = 0.1 β
= 0β
[GeV]Z’M
310 410
eff
N∆
0
0.5
1
1.5
2
2.5π = 0.41 β
π = 0.5 βπ = 0.3 βπ = 0.6 βπ = 0.7βπ = 0.2 βπ = 0.8βπ = 0.1 βπ = 0.9β
= 0β
A.
So
lag
ure
n-B
easc
oa,
MC
G-G
arX
iv:1
21
0.6
35
0
⇒ Interplay between cosmological determination of ∆Neff and Z ′ LHC searches
Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaSummary
• Neutrino oscillation searches have shown us
∆m221 = 7.49× 10−5 eV2 (2.3%)
∆m231 = 2.48× 10−3 eV2 NO
∆m232 = −2.47× 10−3 eV2 IO
(1.8%)
sin2 θ12 = 0.308 (4%) sin2 θ23 =0.579 IO
0.479 NO(7.2%) sin2 θ13 = 0.022 (4.8%)
⇒ ULEP Very different from UCKM
• mν 6= 0⇒ Need to extend SMNP breaking total L → Majorana ν : ν = νC
NP conserving total L → Dirac ν : ν 6= νC
• Still ignore or not significantly determined
Majorana/Dirac? mν scale leptonic /CP? Ordering?
Standing Puzzles: SBL anomalies light sterile ν’s?⇒ New experiments
• More physics than ν masses: VLI, NSI, Solar Physics, Cosmological effects . . .
• Majorana ν′s: generic if SM is LE effective theory and explain ν lightness
ΛNP ∼ 1015 GeV Fits OK in GUT
Leptogenesis may explain the baryon asymmetry
• ν′s example of interplay Particle Physics-Cosmology to learn about BSM physics
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Atmospheric Neutrinos
Atmospheric νe,µ are produced by the interaction of cosmic rays (p, He . . . ) with the
atmosphere
-
_
+
( )
( )
( ) ( )
Rµ/e=
Nµν
νe
N
πp , He
νµ
µ+_
e
ννµ e
+_
Nπ+_π+
2N
N
νν µ+
+~
eν
Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaAtmospheric Neutrinos: Results
• SKI+II+III+IV data:
-1 -0.5 0 0.5 10
100
200
300
400
500
Sub-GeV (e)
-1 -0.5 0 0.5 10
100
200
300
400
500
Mid-GeV (e)
-1 -0.5 0 0.5 10
100
200
300
400
Multi-GeV (e)
-1 -0.5 0 0.5 10
100
200
300
400
500
Sub-GeV (µ)
-1 -0.5 0 0.5 10
150
300
450
600
750
Mid-GeV (µ)
-1 -0.5 0 0.5 10
100
200
300
Multi-GeV FC (µ)
-1 -0.5 0 0.5 10
100
200
300
400
500
Multi-GeV PC (µ)
-1 -0.75 -0.5 -0.25 00
50
100
150
200
250
Stopping (µ)
-1 -0.75 -0.5 -0.25 00
200
400
600
800
Through (µ)
cos(zenith)
p, He
π , K
µ
e
νeνµ
detector
atmosphere
EARTH
νµ
down-going
up-going
zenithangle
L ≈1.2×104 km
L −~ 10-30 km
L ≈104 km
L ≈500 km
[not to scale]
+−
+− +−
+−
0
1
2
3
4
5
0
0.005
0.01
0.015
subGeV
multiGeV
stoppingmuons
through-goingmuons
10 10 10 10 10 10 10-1 0 1 2 3 4 5
E , GeV
dN
/dln
E, (
Kt.
yr)-1
(m .yr.ster)2
-1
ν
Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaAtmospheric Neutrinos: Results
• SKI+II+III+IV data:
-1 -0.5 0 0.5 10
100
200
300
400
500
Sub-GeV (e)
-1 -0.5 0 0.5 10
100
200
300
400
500
Mid-GeV (e)
-1 -0.5 0 0.5 10
100
200
300
400
Multi-GeV (e)
-1 -0.5 0 0.5 10
100
200
300
400
500
Sub-GeV (µ)
-1 -0.5 0 0.5 10
150
300
450
600
750
Mid-GeV (µ)
-1 -0.5 0 0.5 10
100
200
300
Multi-GeV FC (µ)
-1 -0.5 0 0.5 10
100
200
300
400
500
Multi-GeV PC (µ)
-1 -0.75 -0.5 -0.25 00
50
100
150
200
250
Stopping (µ)
-1 -0.75 -0.5 -0.25 00
200
400
600
800
Through (µ)
cos(zenith)
p, He
π , K
µ
e
νeνµ
detector
atmosphere
EARTH
νµ
down-going
up-going
zenithangle
L ≈1.2×104 km
L −~ 10-30 km
L ≈104 km
L ≈500 km
[not to scale]
+−
+− +−
+−
0
1
2
3
4
5
0
0.005
0.01
0.015
subGeV
multiGeV
stoppingmuons
through-goingmuons
10 10 10 10 10 10 10-1 0 1 2 3 4 5
E , GeV
dN
/dln
E, (
Kt.
yr)-1
(m .yr.ster)2
-1
ν
νe
inag
reem
ent
wit
hS
M
→ νµ Deficit
grows with L
→ νµ Deficit
decreases with E
Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaAtmospheric Neutrinos: Results
• SKI+II+III+IV data:
-1 -0.5 0 0.5 10
100
200
300
400
500
Sub-GeV (e)
-1 -0.5 0 0.5 10
100
200
300
400
500
Mid-GeV (e)
-1 -0.5 0 0.5 10
100
200
300
400
Multi-GeV (e)
-1 -0.5 0 0.5 10
100
200
300
400
500
Sub-GeV (µ)
-1 -0.5 0 0.5 10
150
300
450
600
750
Mid-GeV (µ)
-1 -0.5 0 0.5 10
100
200
300
Multi-GeV FC (µ)
-1 -0.5 0 0.5 10
100
200
300
400
500
Multi-GeV PC (µ)
-1 -0.75 -0.5 -0.25 00
50
100
150
200
250
Stopping (µ)
-1 -0.75 -0.5 -0.25 00
200
400
600
800
Through (µ)
cos(zenith)
Best explained by νµ → ντ
0.3 0.5 1 2 3
tan2 θ
0
1
2
3
4
5
∆m2 [1
0-3 e
V2 ]
∆m2 ∼ 2.4 × 10−3 eV2
tan2 θ ∼ 1 ⇒ θ ∼ π4
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
νµ Disappearance in Accelerator ν Fluxes
T2K:
νµ produced in Tokai (Japan)
detected in SK at ∼ 250 Km
MINOS, NOνA
νµ produced en Fermilab (Illinois)
detected in Minnesota at ∼ 800 Km
Lectures by G. Feldman
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Long Baseline Experiments: νµ Disappearance
K2K/T2K 2004–: spectral distortion MINOS 2006–: spectral distortion
NOνA: 2015–
νµ oscillations with ∆m2 ∼ 2.5× 10−3 eV2 and mixing compatible with π4
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Solar Neutrinos
• Sun shines by nuclear fusion of protons into He
And only νe are produced
• Two main chains of nuclear reactions
pp Chain : CNO cycle:
N13
C12 C13
N15 N14
O15
O16 O17
F17
<E >=0.707MeV
<E >=0.999MeV
<E >=0.997MeV
He4
p p
p p
p p
e+
e+
e+
He4
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Solar Neutrinos: Fluxes
PP CHAIN Eν (MeV)
(pp)
p + p →2 H + e+ + νe ≤ 0.42
(pep)
p + e− + p →2 H + νe 1.552
(7Be)
7Be + e− →7 Li + νe 0.862(90%)
0.384 (10%)
(hep)
2He + p →4 He + e+ + νe ≤ 18.77
(8B)
8B →8 Be∗ + e+ + νe ≤ 15
CNO CHAIN Eν (MeV)
(13N)
13N →13 C + e+ + νe ≤ 1.199
(15O)
15O →15 N + e+ + νe ≤ 1.732
(17F)
17F →17 O + e+ + νe ≤ 1.74
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Solar Neutrinos: Results
radio
-ch
emic
alre
alti
me
Experiment Detection Flavour Eth (MeV)
Homestake 37Cl(ν, e−)37Ar νe Eν > 0.81
Sage + 71Ga(ν, e−)71Ge νe Eν > 0.23Gallex+GNO
Kam ⇒ SK ES νxe− → νxe− νe, νµ/τ
(
σµτ
σe≃ 1
6
)
Ee > 5
SNO CC νed → ppe− νe Te > 5
NC νxd → νxp n νe, νµ/τ Tγ > 5
ES νxe− → νxe− νe, νµ/τ Te > 5
Borexino νxe− → νxe− νe, νµ/τ Eν = 0.862
Experiments measuring νe observe a deficit
Deficit is energy dependent
Deficit disappears in NC
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
• Real Time experiments can also give information on Energy and Direction of ν′s
and can search for Energy and Time variations of the effect
• From SK (also from SNO)
Energy Dependence
0.2
0.4
0.6
0.8
5 10 15 20Energy(MeV)
Dat
a/S
SM
BP
2004
Deficit indep Eν & 5 MeV
Day-Night Variation
Not significant
Seasonal Variation
1
2
3
4
1998 2000 2002 2004 2006YEAR
Flu
x (x
106 /c
m2 /s
)
Nothing beyond 1R2
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Solar Neutrinos: Oscillation Solutions
10-12
10-11
10-10
10-9
10-8
10-7
10-6
10-5
10-4
10-3
10-4 10-3 10-2 10-1 1 10.
RATES ONLY GLOBALSK and SNO E and t dependence
SMA
LMA
LOW
VAC
LMA
∆m2 ∼ 5× 10−5 eV2
tan2 θ ∼ 0.4 ⇒ θ ∼ π6
Different frequency and flavour
than ATM and LBL
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Terrestrial test of LMA: KamLAND
Lectures by K. Heeger
KamLAND: Detector of νe produced in nuclear reactors in Japan at an average distance
of 180 Km
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Terrestrial test of LMA: KamLAND
KamLAND: Detector of νe produced in nuclear reactors in Japan at an average distance
of 180 Km
Results of KamLAND
compared with Pee for
θ = 35 y ∆m2 = 7.5× 10−5 (eV/c2)2
(km/MeV)eν/E0L
20 30 40 50 60 70 80 90 100
Surv
ival
Pro
babi
lity
0
0.2
0.4
0.6
0.8
1
eνData - BG - Geo Expectation based on osci. parameters
determined by KamLAND
Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaMedium Baseline Reactor Experiments
Lectures by K. Heeger
• Searches for νe → νe disappearance at L ∼ Km (E/L ∼ 10−3 eV2)
• Relative measurement: near and far detectors
Daya-Bay Reno
Phenomenology with Massive Neutrinos Concha Gonzalez-GarciaDaya-Bay and Reno Reactor Experiments
• Searches for νe → νe disappearance at L ∼ Km (E/L ∼ 10−3 eV2)
• Relative measurement: near and far detectors
Daya-Bay: 4 Near+ 4 Far
Described with ∆m2 ∼ 2.5× 10−3eV2
(as νµ ATM and LBL acc but for νe)
and θ ∼ 9
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
Long Baseline Experiments: νe Appearance
• Observation of νµ → νe transitions with E/L ∼ 10−3 eV2
T2K MINOS
NOνA also
Well described with νµ → νe oscillations with ∆m2 ∼ 2× 10−3 eV2 and θ ∼ 11
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
ν Oscillations: Lab Searches at Short Distance
Lectures by B. Louis
Appearance Experiment
L
αν sourceν ν detectorSearches for β
β
αdiff
Experiment 〈E/MeV
L/m〉 α β
CCFR 100 νµ, νe ντ
E531 25 νµ, νe ντ
Nomad 13 νµ, νe ντ
Chorus 13 νµ, νe ντ
E776 2.5 νµ νe
Karmen2 2.5 νµ νe
LSND 3 νµ νe
Miniboone 3 νµ νeνµ νe
ICARUS 1 νµ νe
Disappearance Experiment
αν sourceν να
detector ναdetectorI II
Φα Ι Φα ΙΙLL
I
II
α Ι α ΙΙandCompares ΦΦ to look for loss
Experiment 〈E/MeV
L/m〉 α
CDHSW 1.4 νµ
BugeyIII 0.05 νe
Chooz 0.005 νe
Phenomenology with Massive Neutrinos Concha Gonzalez-Garcia
LSND and MiniBooNE
• LSND: Main signal for νµ → νe with Eν ∼ 0.03 GeV and L = 30 m
• MiniBooNE: Search for νµ → νe and νµ → νe with Eν = 0.3− 2 GeV and L = 540 m
Compatibility (?)
for ∆m2 ∼ eV2
a third osc frequency?
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