Supernova Nucleosynthesis and Physics of Neutrino Oscillation

Carpathian Summer School of Physics 2012
Exotic Nuclei & Nuclear/Particle Astrophysics IV: from Nuclei to Stars
Sinaia, Romania, June 24 - July 7 in 2012
Supernova Nucleosynthesis
and Physics of Neutrino Oscillation
θ 13 is well known now.
“Mass Hierarchy” is still far to reach!
Taka KAJINO
National Astronomical Observatory
Department of Astronomy, University of Tokyo

ニュートリノの Neutrino Masses 質 量 1
他 の 素 粒 子 の 質 量
~
10,000,000,000
Quark & Lepton Masses
Quark & Lepton
Masses
E = mc 2
Why 10 -10 ?
10 -10
This could be a signature of new physics at 10 10
times higher energy scale than the ordinary scale.
i + i e + + e - 2g (T)
Key Physics suggested by FINITE mass neutrinos:
?
ν Masses
Generation
Unification of elementary forces beyond the
standard model ?
CP violation and Lepto- & Baryo-genesis ?
Why left-handed neutrinos, Majorana or Dirac ?
Explosion Mechanism of Supernovae ?

Challenge of the Century
Universal expansion is most likely accelerating and flat !
W B + W CDM + W L = 1
● What is the CDM, W CDM = 0.23, and Dark Energy, W L = 0.73 ?
CMB including -mass: Yamazaki, Kajino, Mathews & Ichiki, Phys. Rep. (2012), in press.
● Is BARYON, W B = 0.04, well understood ?
BBN with Axions + SUSY to solve Dark Matter Problem & Li Problem:
Kusakabe, Balantekin, Kajino & Pehlivan, (2012) arXiv:1202.560.
SUSY-DM ⇒ “beyond the Standard Model” ⇒ m = 0 is the unique signal !
Total mass, Hierarchy, details of mixing nature ?
Purpose
.
“Supernova -Process Nucleosynthesis”
to determine the MASS HIERARCHY of Active Neurinos.

Physics of Neutrino Oscillation
Dirac Equation(Dirac-Pauli representation)
Eigen-State of Free Neutrinos with (E, p) (for m = 0)
L-neutrino (h=-1)
Dirac spinor
R-neutrino (h=+1)
Neutrino flavor oscillation for weak interactions (due to vacuum, MSW,
or self-interaction effects) does not change the spinor structure.
Therefore, only the propagation of energy eigen-state is important!

Neutrino Flavor Oscillation
, 1962)
n e = Electron Number Density
〇 m 2 -difference
〇 Mixing angle
〇 CP Phase : d

Exercise 1: Vacuum Oscillation (Example of 2 flavors)
Oscillation Probability
Osc. Probability depends on q.
Osc. length l
(cm)

Reactor Neutrinos
(Kashiwazaki)
KamLAND at D=0 km
(Kamioka)
Distance D from Reactors (m)

Atmospheric Neutrinos
No Oscillation
Expected from 23-mixing
SK Observation
Down coming ’s
Up going ’s

“KNOWN” of Neutrino Oscillations
KAMIOKANDE, SK, KamLand (reactor ν), SNO determined ⊿m 12
2
and θ 12 uniquely,
and also SK (atmospheric ν) determined ⊿m 23
2
and θ 23 uniquely.
23-mixing
sin 2 2q 23 = 1.0
|Δm 2 23| = 2.4×10 -3 eV 2
12-mixing
sin 2 2q 12 = 0.816 (q 12 +q C =p/2)
Δm 2 12 = 7.9×10 -5 eV 2
Cabibbo angle
“UNKNOWN”
● sin 2 2q 13 = 0.1
T2K, MINOS, RENO, Daya Bay, Double Chooz
● ⊿m
2
13 = ±2.4x10 -3 eV 2
● δ=CP-phase
● Absolute Mass 0bb, cosmology
E()=E(): Yokomakura et al., PL B544, 286.

Exercise 2: Matter (MSW)Oscillation (Example of 2 flavors)
Wolfenstein (1978), Mikheyev & Smirnov (1986)
Oscillation Probability

effective mass
effective mass
MSW Matter Effect & Mass Hierarchy
Normal
r ~ 10 3 g/cm 3
Inverted
3
H-resonance
3
~ e
2
3
3
L-resonance
2
2
~ e
2
2
1
2
1
1
2
1
1
L-resonance
2
3
3
1
H-resonance
1
3
1
ne
vacuum SN core vacuum SN core
3
~ e
ne

PURPOSE is to
solve the Mystery of Neutrino Mass Hierarchy.
-process Nucleosynthesis in Core-Collapse Supernovae
(1) Average Neutrino Temperatures/Energies
(2) -Mass Hierarchy ⊿m 13
2
(for known θ 13 )
Normal
Inverted

Number Abundance (Si = 10 6 )
Solar System Abundance
Big-Bang Nucleosynthesis 1,2 H, 3,4 He, 6,7 Li, etc.
Stellar Fusion 12 C… 56 Fe- 58 Ni, etc.
Core-Collapse SNe & AGB: 56 Fe < A
Iron peak
(r-nuclei)
(s-nuclei)
Supernova
-Nucleosynthesis
Li-Be-B
r-nuclei
p-nuclei
92
Mo, 96 Ru
p-nuclei
92
Nb 98 Tc
138
La
180
Ta
232
Th (14.05Gy)
238
U (4.47 Gy)
Cosmic Ray Spallation
Li-Be-B, F, Na, etc.
Mass Number A

Sneden, Cowan, Gallino, ARAA 46 (2008) 241.
HST-obs., Roederer et al., ApJ 747 (2012) L8.
log Fe/H
Fe/H
t
∝
10 10 y
Te
=
-3.1
-3.0
-2.1
-2.9
-2.2
Solar system
-3.0
Sr-Y-Zr Ba Eu Au Pb Th U
Metal-poor
stars
UNIVERSALITY !

Z (atomic number)
Initial Condition of the R-Process:
g,-Disintegration of “Fe”
RIKEN-RIBF
2010
Fe-Co-Ni are
g,-disintegrated!
Rapid Nautron-Capture Process
on neutron-rich nuclei in SNe
n

Proton Number Z
Supernova
Nucleosynthesis
Simulation
T. Kajino & S. Chiba
-Pair Heated Collapsar Model
K. Nakamura, et al. ApJ (2012).
235
U
208
Pb
184
56
Fe
126
82
20 28
50
Neutron Number N

R-process Nucleosynthesis
K. Nakamura, S. Sato, S. Harikae, T. Kajino and G.J. Mathews (2012), submitted to ApJ.
T e = 3.2 MeV < T e = 4 MeV
Neutron-rich condition for successful r-process:
0.2 < Y e < 0.48
Sr-Y-Zr
I-Xe
Ir-Pt
Theoretical model
Dy-Er
Pb
Observed
Solar r-abundance

Identified Important Reaction Flow Paths
Utsunomiya et al.
PRC63 (2001), 018801
35% (1s)
(3)
(1)
Hashimoto et al., PL B674 (2009) 276.
LaCognata et al., PL B664 (2008), 157.
Factor 2 ~ 4 different ! (1s)
(2)
Brune et al., PRC (1995)
35% (1s)

7
Li(n,g) 8 Li(a,n) 11 B
LaCognata et al., ApJ 706 (2009) L251.
• 8 Li(a,n) 11 B
Discrepancy
Inclusive Data >> Exclusive Sum
LaCognata et al., Phys. Lett. B664 (2008), 157.
Boyd et al. Phys. Rev. Lett. 68 (1992), 1283.
Gu et al., Phys. Lett. B343 (1995), 31.
Ishiyama et al., Phys. Lett. B640 (2006), 82.
Hashimoto et al., Phys. Lett. B674 (2009), 276.
8
Li+a
Inclusive data
11
B*
11
B gr + n
Exclusive Sum

log (Abundance)
NON-LINEAR Effect of “a-process-r-process”
(1) a(an, g) 9 Be
(2) (3) a(t, g) 7 Li(n, g) 8 Li(a, n) 11 B
x 2 artificial change
rates x 1
~ 100
rates x 2
< 1000
Mass Number A

Tantalum( 180,181 Ta)
181
Ta g (stable), 180 Ta g (unstable, 1/2 = 8h), 180 Ta m (isomer, 1/2 > 10 15 y)
The rarest isotope in the Universe!
Origin of 180 Ta was unknown.
“SN -process”, overproduces 180 Ta !
p process
Burbidge 2 -Fowler-Hoyle,
Rev. Mod. Phys. 29
(1957), 547-650.
“Element Genesis”
Neutral current
in Supernovae
r process
(1990)
J. Burbidge
M. Burbidge
W. Fowler
F. Hoyle

Excitatoin Energy
180
Ta-genesis needs Quantum Phys. + SN Hydro-dyn.
Solar- 180 Ta is all “ISOMER” with T 1/2 > 10 15 y!
- Long lived 180 Ta m is excited in hot SN-photon bath.
- Intermediate states are depopulated to the ground state,
which decays in 8 hours.
We solved dynamical “explosive SN-nucleosynthesis” coupled with
“quantum transitions” simultaneously. (Hayakawa, et al. 2010, PR C81,
052801®; PR C82, 058801)
Photons
Plan
Distribution
Planckian
Distribution
Intermediate states
Intermediate States
Intermediate
states
Photon Flux
K=1 K = 1
1 + 180
Ta0
180
Ta g
Ground St.
K=9 K = 9
T 1/2
=8.15 h
9 - 75.3
T 1/2 > 10 15 y
T 1/2
> 10 15 y
Isomer
180
Ta m : solar abundance

-Process and Structure of 180 Ta
Saitoh et al. (NBI group), NPA 1999, +
Dracoulis et al. (ANU group), PRC 1998, +
J = Total Quantum
Number
Linking transitions
between K = 1 and 9 bands
are extremely weak.
K=9
K Quantum
gr. state 1 + isomer 9 - Excitation Energy [MeV]
Number
K=1
D. Belic et al., PR C65 (2002), 035801.
g i /g 0 G i G 0 /G tot

7
7
6
6
5
5
4
4
3
3
2
2
1
1
Result from
-Nucleosynthesis
138La 138La 138La
180Ta 180Ta
180Ta
180Ta isomer
180Ta
Heger et al. PLB606, 258 (2005)
(Overproduction)
(Our new result)
T. Hayakawa, T. Kajino, S. Chiba, and
G.J. Mathews, Phys. Rev. C81 (2010), 052801®
About 40% 180 Ta m
survives in supernova
explosion.
Then, both 138 La and
180
Ta abundances
can be consistently
reproduced by the
CC-int. of e and e of
T e = 3.2 MeV,
T e = 4 MeV.
0
0
solar
system
gamma
gamma
only
only
nc 6MeV cc 4MeV cc 6MeV cc 8MeV
nc
6MeV
cc
4MeV
cc
6MeV
cc
8MeV
Consistent with
the r-process !

Various roles of ’s in SN-nucleosynthesis
8
p-process
92
Mo, 96 Ru
8
MSW high-density resonance
at r ~ 10 3 g/cm 3
e
NS
Si
Layer
R-process:
Heavy Nuclei
Explo. Si-burn.
Fe-Co-Ni,
60
Co, 55 Mn, 51 V …
-process
180
Ta, 138 La, 92 Nb, 98 Tc …
-process:
6,7
Li, 9 Be, 10,11 B …

Galactic Chemical Evolution of 9 Be & 10,11 B
Livermore Model
T , = 8 MeV
Woosley -Weaver 1995, ApJS 101, 181.
s ∝ E
2
T , = 6 MeV
Consistent with SN1987A
Overproduction problem is resolved!
Yoshida, Kajino & Hartmann 2005,
PRL 94 (2005), 231101.
16
17
OLD stars
SUN
9
Be:
-Galactic Cosmic Rays
10+11
B + 11 B:
-Galactic Cosmic Rays
-Supernova -process
Yoshii, Kajino, Ryan, 1997, ApJ 486, 605.
Ryan, Kajino, Suzuki, 2001, ApJ549, 55.

SN1987A constraint
on E ,tot & Grav. Energy
SN-Boron calculations and
constraints on SN-
Woosley & Weaver
ApJS 101 (1995), 181.
T = 8 MeV
GCE constraints on 11 B
& meteoritic 11 B/ 10 B
T = 6 MeV
Yoshida, Kajino & Hartman,
Phys. Rev. Lett. 94 (2005),
231101.
Consistent with
recent numerical
simulation by
Thomas-Janka
et al. (MPA group)
2004-2011.

( ) /
-temperatures are known!
0.25
0.2
0.15
0.1
Supernova -Process to estimate T , and T
R-process, 180 Ta/ 138 La
Astron. GCE of 11 B & 11 B/ 10 B
e
T( e ) < T( e ) < T( x )
e
3.2 4.0 6.0
MeV
T e = 3.2 MeV, T e = 4 MeV
T , = T = 6 MeV
0.05
, , ,
0
0 10 20 30 40 50 60
(MeV)

-A reaction cross sections?
Haxton’s SM cal. (Woosley et al. ApJ. 356 (1990), 272)
Suzuki’s new SM cal. with NEW Hamiltonian
Suzuki, Chiba, Yoshida, Kajino & Otsuka, PR C74 (2006), 034307.
Suzuki, Fujimoto & Otsuka, PR C67, 044302 (2003)
12
C: New Hamiltonian = Spin-isospin flip int. with
tensor force to explain neutron-rich exotic nuclei.
- -moments of p-shell nuclei
- GT strength for 12 C 12 N, 14 C 14 N, etc. (GT)
- DAR (,’), (,e-) cross sections
Cheoun et al., PRC81 (2010), 028501; J. Phys. G37 (2010) 055101: QRPA Cal.
SFO
12
C( e ,e - ) 12 N
12
C( e ,e - ) 12 N(gs,1 + ) GT

- 180 Ta, 138 La, 92 Nb, 42 Ca, 12 C, 4 He… X-sections
in Quasi-particle Random Phase Approximation (QRPA)
Cheoun, Ha, Hayakawa, Kajino & Chiba, PRC82 (2010), 035504;
Cheoun, Ha, Kim, & Kajino, J. Phys. G37 (2010) 055101; Cheoun, Ha & Kajino,
PRC 83 (2011), 028801
GT + Spin-Multipole transitions !
181
Ta + → 180 Ta + n + ’ (NC)
180
Hf + → 180 Ta + e - (CC)
Total sum
Total sum
GT
Spin-Mutipole
GT
Spin-Mutipole

Counts
● -beam is not yet available !
● EM-PROBE (CEX hadrons, g’s) !
c.f. Harakeh, Shima
Similarity between Electro-Magnetic & Weak Interactions
58
Ni( 3 He, t) 58 Cu
E = 140 MeV/u
Y. Fujita et al., EPJ A 13 (’02) 411.
Y. Fujita et al., PRC 75 (’07)
58
Ni(p, n) 58 Cu
E p = 160 MeV
J. Rapaport et al., NPA (‘83)
EM-current = V, Weak-current = V - A
IV i gV
V gV
s q ( p p')
2m
2m
A
g
A
s
Weak operator in non-relativistic limit
Gamow-Tellar operator =
Spin-Multipole operator =
s
J J
[
[ s r Y r (L) ] ]
0 2 4 6 8 10 12 14
Excitation Energy (MeV)
Charge-Exchange Reaction
Photo-induced Reaction

Double b decay - mass - Astro-Cosmology Connection
K. Yako et al., PRL 103 (2009) 012503.
Experiment
(RCNP, Osaka)
Shell model (theory)

Neutrino Mass in Physics & Cosmology
0bb
COUORE:
|∑U 2 ebm b | < 0.3 eV
CMB Anisotropies + LSS
Σm ν < 0.28 eV (95% C.L.): WMAP-7yr +SPT (Benson et al. arXiv:1112.5435)
< 0.36 eV (95%C.L.): WMAP-7yr + HST + CMASS (Putter et al. arXiv:1201.1909)
Recent more complete analysis:
Cosamic Magnetic Field + Neutrino Mass
(+ SZ effect + integrated SW effect
+ Neutrino free streaming)
∑ m < 0.2 eV (2s, B

Oscillation (MSW) Effect on Supernova -Process
SN II: Yoshida, Kajino & Hartman, Phys. Rev. Lett. 94 (2005), 231101.
SNIc + II: Nakamura, Yoshida, Shigeyama, Kajino, ApJL 718 (2010), L137.
Abundance X A
~85%
~15%
MSW high-density resonance
Suzuki, Chiba, Yoshida,
Kajino & Otsuka, PRC74
(2006), 034307
x → e

SN-Neutrino Oscillation (MSW) Effect on -Process
Adiabatic
Conversion Probability
Non-Adiabatic
e
e
e
e
Center Radius/R sun Center Radius sun
- sin 2 2q 13 = 0.04
Parameters:
25M solar SN model (Hashimoto & Nomoto 1999)
- ⊿m 13
2
= 2.4x10 -3 eV 2
- L = 3x10 53 erg, = 3 sec Fermi-Dirac distr. of -spectrum,
so that the observed 11 B abundance
- E e =12MeV, E e =20MeV, E =24MeV in Supernova Nucleosynthesis is reproduced.

Mass Fraction
Mass Fraction
SN Nucleosynthesis with Neutrino Oscillations
Supernova nucleosynthesis (-process)
16.2 M star supernova model corresponding to SN 1987A
Normal mass hierarchy, sin 2 2q 13 = 0.01
10 -7
O-rich O/C He/C He/N
7 Be
mix 7 Li
10 -6
O-rich O/C He/C He/N
11 B
10 -8
10 -7
10 -9
10 -6 2 3 4 5 6
no mix
10 -5 2 3 4 5 6
10 -8
11 C
10 -10
10 -9
Mr / M
Mr / M
7
Be, 11 C abundance Increase by a factor of 2.5 and 1.4
Increase in the rates of charged-current reactions
4
He( e ,e - p) 3 He and 12 C( e ,e - p) 11 C in the He layer

larger effect !
Yoshida, Kajino, Yokomakura, Kimura,Takamura & Hartmann,
PRL 96 (2006) 09110; ApJ 649 (2006), 349.
T e < T e < T ,
=
=
=
3.2MeV 4.0MeV 6.0MeV
smaller effect !
Normal
L
H-Resonance
m
L
Normal
Mass Hierarchy
N e
Inverted
Inverted
m
H-Resonance
10 -6 10 -4 10 -2
NO 13-mixing
N e

Predicted 7 Li/ 11 B-Ratio
Our Theoretical Prediction
Yoshida, Kajino et al . 2005, PRL94, 231101;
2006, PRL 96, 091101; 2006, ApJ 649, 319; 2008, ApJ 686, 448.
7
Li/ 11 B
Normal Mass
Hierarchy
Excluded by T2K and MINOS ++
No Mixing
Inverted
10 -6 10 -5 10 -4 10 -3 10 -2 10 -1
Astrophysics:
Mass Hierarchy
⊿m 13
2
13-Mixing Angle
q 13
Long BaselineExp.
in 2011:
・T2K (Kamioka)
・MINOS
Reactor Exp. in
2012:
・Double CHOOZ
・Daya Bay
・RENO (KOREA)
sin 2 2q 13
sin 2 2q 13 = 0.1

T2K & MINOS results (2011)
Sin 2 2q 23 =1
Mass hierarchy is still unknown !
sin 2 2q 13 = 0.1

RENO, Daya Bay and Double Chooz results (2012)
Measuring q 13 with
Reactor Anti-neutrinos
sin 2 2q 13 = 0.103+-0.013(st)
+-0.011(sys)
→ q 13 = 8.88 deg
Small-amplitude
oscillation due to q 13
integrated over E
q 13
Large-amplitude
oscillation due to q 12
Reactor neutrino energies are
too low to produce muons.
Hence this is an antineutrino
disappearance experiment
(also no matter effects).
~1-1.8 km
> 0.1 km
m 2 13≈ m 2 23
detector 1 detector 2
Mass hierarchy is still unknown !

Mass Hierarchy, Normal or Inverted ?
Mathews, Kajino, Aoki and Fujiya, Phys. Rev. D85,105023 (2012).
Predicted 7 Li/ 11 B-Ratio
Normal Mass
Hierarchy
Excluded by T2K, MINOS, RENO,
Daya Bay & Double Chooz
Excluded by
SiC X-Grains
First Detection of 7 Li/ 11 B
W. Fujiya, P. Hoppe, and
U. Ott, ApJ 730, L7 (2011).
11
B and 7 Li were measured
in SiC presolar
X-grains which are made
of Supernova dusts.
Inverted Mass
Hierarchy
“Inverted Mass Hierarchy”
is more preferred !

Murchison SiC X-grains
SiC X grains exhibit
- 12 C/ 13 C > Solar
- 14 N/ 15 N < Solar
- Enhanced 28 Si
- Decay of 26 Al (t 1/2 = 7x10 5 yr)
& 44 Ti (t 1/2 = 60 yr)
Originates from Core Collapse Supernovae

Supernova ν-nucleosynthesis
is a weakly-interacting process, and
preturbative treatment is possible!
Nucleosynthetic yields for various physical conditions
(stellar mass, explosion energy, decay time of neutrino
luminosity, etc.) are averaged over IMF of stellar birth rate
to compare with observed abundance yields.
(Claim by Austin, Heger & Tur, PRL 106 (2011), 152501 )
-nucleosynthesis in well studied SN1987A
model can scale to various SN models:
- T. Shigeyama & K. Nomoto 1990, ApJ 360, 242.
- R. Hofman, S. Woosley & A.A. Weaver 2001,
ApJ 549, 1085; T. Rauscher, A. Heger,
R. Hofman & S.E. Woosley 2002, ApJ 576, 323.

Neutrino Hamiltonian: H tot = H + H
H = Mixing and Interaction with Background Electrons
MSW (Matter) Effect: Mikeheev-Smirnov-Wolfebstein (1978, 1985)
p 1 e
p 1 x
H = Self-Interaction
Self-Interaction
x
N e = electron density
p 1 e p 2 e
p 2 x
p 1 x
Quest for EXACT Many-Body SOLUTION !
“Invariants of collective neutrino oscillations”
Y. Pehlivan, A.B. Balantekin, T. Kajino & T. Yoshida
Phys. Rev. D84, 065008 (2011)

self-interaction (Quantum Effect)
neutrino-phere
H. Duan, G.M. Fuller, J. Carlson, Y.-Z. Qian,
PRL 97 (2006), 241101.
G. Fogli, E. Lisi, A. Marrone, & A. Mirizzi,
JCAP 12, (2007) 010.
A. B. Balantekin, Y. Pehlivan, J. Phys.G34, (2007) 47.
r = 200km
Swapping !
High-energy

CONCLUSION
We propose a new astrophysical method to determine
the unknown -mass hierarchy m 13
2
in terms of the
supernova -nucleosynthesis by taking account of the MSW
effects.
Combining the recent detection of 7 Li/ 11 B isotopic ratio
measured in presolar Supernova X-grains and the q 13 value
determined from the long-baseline and reactor neutrinooscillation
experiments, we can conclude that the “inverted
mass hierarchy” is statistically more preferred.
We need to study the neutrino-nucleus cross sections and
the nature of neutrino oscillation due to the MSW matter
effects and the effects of self interactions.