カイラル対称性の部分的回復とη`中間子原子核 - J-PARC分室

J-PARCハドロン原子核理論検討会
カイラル対称性の部分的回復とη’中間子原子核
D. Jido
(Yukawa Institute, Kyoto)
collaboration with
H. Nagahiro and S. Hirenzaki (Nara WU)
Reference
Nuclear bound state of eta'(958) and partial restoration of chiral symmetry
in the eta' mass.
Daisuke Jido, Hideko Nagahiro, Satoru Hirenzaki. Sep 2011.
e-Print: arXiv:1109.0394 [nucl-th]
LoI for GSI-SIS: Spectroscopy of η’ mesic nuclei with (p,d) reaction
K. Itahashi, H. Outa, H. Fujioka, H. Geissel, H. Weick, V. Metag, M. Nanova,
R.S. Hayano, S. Itoh, T. Nishi, K. Okochi, T. Suzuki, Y. Tanaka,
S. Hirenzaki, H. Nagahiro, D. Jido, K. Suzuki
D. Jido
Friday, 16 December 2011
KEK 東海１号館
12.16, 2011
Introduction (３つのキーワード)
UA(1) anomaly
量子効果による対称性の破れ
η の質量生成機構と密接に関連
核媒質中のカイラル対称性の部分的回復
深く束縛されたπ中間子原子、低エネルギーπ核散乱実験 ＆ 理論
30%程度のクォーク凝縮の減少
∗
�q̄q�
�
�q̄q�
�
b1
b∗1
�1/2 �
1−γ
ρ
ρ0
�
DJ, Hatsuda, Kunihiro, PLB 670 (2008) 109.
中間子原子核
中間子-原子核束縛系、実験で観測
束縛状態はあるが、幅が広い（束縛エネルギーと幅が同程度）
s-channel N* → πN
引力と吸収の起源が同じ
D. Jido
Friday, 16 December 2011
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Mesonic atoms and mesonic nuclei
bound systems of meson and nuclei
experimental tool to observe medium modification of meson
we do not have to remove in-vacuum contributions
modification of mass and width by many-body effects
ex.
mass shift
width
mN → mN
mN → B ∗
interactions between meson and nucleus
mN → πN
mN N → N N
in-medium self-energy of meson
extract more fundamental and universal quantities
ex.
D. Jido
Friday, 16 December 2011
quark condensate
�q̄q�
3
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Low density theorem
model independent theoretical relation
�
�
σπN
∗
�q̄q� = 1 − 2 2 ρ �q̄q� + O(ρn>1 )
mπ fπ
Drukarev, Levin,
Prog. Part. Nucl. Phys. 27, 77 (1991)
σπN : πN sigma term, O(mq), obtained from TπN at soft limit
derivation
density expansion
�q̄q�∗ = �q̄q� + ρ�N |q̄q|N � + O(ρn>1 )
definition of sigma term
2mq �N |q̄q|N � = σπN
Gell-Mann Oakes Renner relation
m2π fπ2 = −2mq �q̄q�
30 % reduction of quark condensate at nuclear density
D. Jido
Friday, 16 December 2011
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Partial restoration of chiral symmetry
effective reduction of quark condensate in nuclear medium
�q̄q� /�q̄q� < 1
∗
hadronic quantities closely connected to dynamical breaking
1) pion decay constant
W. Weise, NPA690 (01) 98.
K. Suzuki et al., PRL92 (04) 072302.
DJ, Hatsuda, Kunihiro, PLB 670 (08) 109.
deeply bound pionic atom
2) spectrum of sigma meson
Hatsuda, Kunihiro, PRL55 (1985), 158.
Hatsuda, Kunihiro, Shimizu, PRL82 (99) 2840.
ππ production off nuclei
DJ, Hatsuda, Kunihiro, PRD63 (01) 011901.
3) mass difference of chiral partners
ρ-a1
N-N*(1535)
4) mass of eta’ meson
etc.
D. Jido
Friday, 16 December 2011
etc.
Weinberg, PRL18 (67) 507.
Kapusta, Shuryak, PRD49 (94) 4694.
DeTar, Kunihiro, PRD39 (89) 2805.
H.C. Kim, DJ, Oka, NPA640 (98) 77.
etc.
etc.
etc.
S.H. Lee, Hatsuda, PRD57 (96) 1871
DJ, Nagahiro, Hirenzaki, arXiv: 1109.0394
etc.
need systematic studies
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Deeply bound pionic atom
pion is one of the Nambu-Goldstone bosons
- in-medium properties of pion are directly connected to chiral symmetry in nuclear matter
- especially s-wave pion-nucleus interaction is important to chiral symmetry, since symmetry
properties are seen in soft limit (p→0),
K. ITAHASHI et al.
π- bound in atomic orbit
deeply bound states (1s, 2p,... )
not observed in X ray spectroscopy
need to formation experiments
neutron picking-up process in (d, 3He)
sensitive to nuclear effects
effective density ~ 0.6ρ0
complemental experiment
low-energy pion-nucleus scattering
GSI
20~30 MeV LAMPF, PSI
D. Jido
Friday, 16 December 2011
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FIG. 10. !a" The real part of local potential V(r), which is
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total real-part potenequivalent to the pion mass shift )m &eff(r), the
tial including the Coulomb interaction „V c (r)…, and the imaginary
Deeply bound pionic atom
level shift ΔE and width Γ → medium effect of pion
π- optical potential (s-wave part)
S
2mπ Uopt
�
= −4π 1 +
mπ
mN
�
(b0 ρ − b1 δρ) + · · ·
b1 parameter: isovector pion-nucleus scattering length
fit parameters so as to reproduce data
isoscalar density
ρ = ρ p + ρn
isovector density δρ = ρp − ρn
missing repulsion puzzle
low density theorem
S
S
Σπ = 2mπ Uopt
= −ρTπN
b0 and b1 should be in-vacuum values
bfree
1 /b1 = 0.78
pionic atom
enhancement of repulsion
D. Jido
Friday, 16 December 2011
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Reduction of pion decay constant Fπ
enhancement of s-wave repulsive interaction
'HHSO\ERXQGSLRQLFDWRP .6X]XNLHWDO35/
V\VWHPDWLFVWXG\RI/ERXQGVWDWHVLQ6QLVRWRSHV
(ODVWLFVFDWWHULQJ)ULHGPDQHWDO
This is related to in-medium reduction of pion decay constant Fπ at low density
Weinberg-Tomozawa realtion
�
�
mπ
free
mπ
4π 1 + mN b1 = − 2
in vacuum
2F
�
�
in medium
mπ
mπ
at low-density 4π 1 + mN b1 = −
2(Fπt )2
bfree
1
b1
=
�
Fπt
Fπ
�2
Kolomeitsev, Kaiser, Weise, PRL90 (03), 092501.
DJ, Hatsuda, Kunihiro, PLB 670 (08), 109.
The next question is how to conclude partial restoration of chiral
symmetry from the reduction of Fπ.
D. Jido
Friday, 16 December 2011
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Nuclear bound state of meson
neutral meson (η’) only strong interaction is relevant
nuclear many body effects
attraction
mN→mN
absorption
mN→πN
m N N→ N N
attraction and absorption come from the same mechanism
wavefunctions of meson and nucleus largely overlap
→ binding energy and width
have comparable sizes
d<PHVLFQXFOHL
d<
PHVLFQXFOHL
due to large width, bound states are
hard to see in experiment
100 MeV absorption for omega meson
(>0H9@
(>0H9@
70 MeV one-body potential in nucleus
Friday, 16 December 2011
typical energy scale
D. Jido
SLRQLFDWRP
&D
&D
&*DUFLD5HFLRHWDO3/%
9
7RNLHWDO13$
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Search for Kaonic nuclear bound states
attractive electromagnetic interaction
attractive strong interaction
K- (Kbar)
no doubt that Kbar is bound in nucleus
Kishimoto et al. PTP118, 181 (07)
KEK
12
C(K − , n)
12
K +
12
pΛ invariant mass spectrum
C→N +X
back-to-back correlation in light nuclei
some strength in bound region
D. Jido
Agnello et al. PRL94, 212303 (05)
C(K − , p)
missing mass spectra
−
FINUDA
hint of KbarNN bound state
still we have no clear signals of kaonic nuclear states
Friday, 16 December 2011
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Origin of η’ mass
symmetry in classical QCD
U(3)L ⊗ U(3)R → SU(3)V ⊗ U(1)V
no UA(1) symmetry due to quantum anomaly
symmetry in the original theory can be counted
by numbers of conserved currents
η’ is not necessarily massless
→ η’ is massive
UA(1) anomaly effect lifts η’ mass up
Vogl, Weise, Prog.Part.Nuc.Phys.270, 195 (91)
divergence of axial current
i
µ (8)
¯ 5 d − 2ms s̄γ5 s)
∂ Aµ = √ (mu ūγ5 u + md dγ
3
∂
µ
A(0)
µ
anomaly
for simplicity,
we consider SU(3) and chiral limits, and neglect η and η’ mixing
Friday, 16 December 2011
A
3αs a µν
¯
= 2i(mu ūγ5 u + md dγ5 d + ms s̄γ5 s) +
Fµν F̃a
8π
PCAC
D. Jido
a
F̃aµν ≡ �µνρσ Fρσ
11
V
V
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η’ meson in chiral restoration
DJ, Nagahiro, Hirenzaki, arXiv:1109.0394 [nucl-th]
When chiral symmetry is restored...
all the particle belonging to the same chiral multiplet should degenerate
chiral multiplet for S and PS mesons
(3̄, 3) ⊕ (3, 3̄)
q̄iL qjR
R L
q̄i qj
SUL (3) ⊗ SUR (3)
(3×3)+(3×3)=18
q̄i γ5 qj , q̄i qj
parity eigenstate
scalar and pseudoscalar
both octet and singlet contain
π, K, η8 , η0
(1+8)+(1+8)=18
σ, a0 , κ, f0
if chiral symmetry is manifest,
η8 and η0 should degenerate even though anomaly is there
axial trans.
mixes octet
and singlet
[QaA , φB
5 ]
= q̄
�
�
B
λa λ
2 , 2
q = daBC φC
σ↔π
a0 ↔ η
�
both singlet and octet belong to the same multiplet without U(3)
dynamical argument was given by Lee and Hatsuda
D. Jido
Friday, 16 December 2011
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Lee, Hatsuda, PRD54, 1871 (1996)
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η’ meson in chiral restoration
DJ, Nagahiro, Hirenzaki, arXiv:1109.0394 [nucl-th]
When chiral symmetry is restored...
9 PS
π, K, η8 , η0
9S
σ, a0 , κ, f0
get degenerate
even though UA(1) anomaly exists in the singlet axial current
η0
massive
UA(1) anomaly
π, K, η8 , η0
π, K, η8
manifest chiral sym.
massless
broken chiral sym.
the UA(1) anomaly can affect the η’ mass only through (spontaneous and/or explicit)
chiral symmetry breaking.
η-η’ mass difference comes from the anomaly effect through the
quark condensate at the chiral limit.
D. Jido
Friday, 16 December 2011
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η’ meson in nuclear matter
DJ, Nagahiro, Hirenzaki, arXiv:1109.0394 [nucl-th]
divergence of axial current
∂
µ
(0)
Aµ
3αs a µν
¯
= 2i(mu ūγ5 u + md dγ5 d + ms s̄γ5 s) +
Fµν F̃a
8π
PCAC
anomaly
nonchiral gluon field cannot couple to chiral pseudoscalar states
without explicit and/or dynamical chiral symmetry breaking.
η’
R
L
L
D. Jido
Friday, 16 December 2011
L
R
R
R
L
R
L
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2
(c) gD (ρ) = gD exp[−(ρ/ρ0 ) ],
η’
meson
in
nuclear
matter
is the vacuum strength of the determinant interaction
why the η$ mass decrease. In Fig
degenerate completely and their
density, and the mass of η$ has n
the UA (1) anomaly effects. With
n Table I. The gD (ρ) has no density dependence for
Hooft
- Kobayashi
- Maskawa
interaction
and‘t(b).
In case
(a), the meson
vacuum properties
NJL model
eproduced as shown in Table I, while there are no
use slightly
ffects in case (b). For gD = 0 case, we�q̄q�
(a)
UA(1) anomaly
parameter set as shown in Table I in Ref. [60] to
contributes η’ mass
the meson masses and the pion decay constant in
through ChSB
LD assume
ithout anomaly effect. In case (c), we simply
y dependence of gD as this form in order to examine
m effect due to density dependence of gD itself on
If partial restoration of chiral symmetry takes place
mass spectra in finite density.
in nuclear matter
may be interesting for our study to notice that there
we expectabout
strong
mass reduction
in nuclei
tical suggestions
possible
density dependence
,62]. In Ref. [62],Δm
the effective
coupling
constant
η’ ~ 150 MeV
stanton-induced interaction is suggested to have
(with 35% PRChS
- mη ≈ For
400NMeV)
potential dependence
for Nfand
=m
2 η’
systems.
f =
Nagahiro, Takizawa, Hirenzaki
, we can expect to have the similar µ dependence,
FIG. 2.
Density (2006)
dependence of
PRC74,045203
is not easy to show explicitly. We are interested in
panels corresponds to the cases (a)
also, P. Costa, M. C. Ruivo, and Y. L. Kalinovsky,
he effect of such density dependence discussed in See
respectively.
The nucleon density ρ
Phys. Lett.
B560, 171 (2003).
on meson mass spectra as future works.
normal nuclear density ρ0 = 0.17 f
D. Jido
Friday, 16 December 2011
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Narrow width ??
nuclear many body effects
absorption
attraction
η’ N → π N
η’ N → N*
η’ N N→ N N
attraction coming from suppression of anomaly effect
contact interaction
in hadronic level
no hadronic
imaginary part
UA(1) anomaly
contributes η’ mass
through ChSB
�q̄q�
LD
suppression of anomaly effect selectively affects η’ channel
elastic
η’ N → η’ N
This mass reduction does not directly come from nuclear many-body interaction.
Thus the width may be smaller than binding energy.
Δm ~ 150 MeV > Γ
D. Jido
Friday, 16 December 2011
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Current experimental status
!" in-medium width
RHIC: phenix/star (low energy pion)
compared
theoretical
calculations
and E. Oset of "‘ meson
η’with
mass
reduction
of at leastA.Ramos
200 MeV
in-medium
properties
⇒in-medium width:
in the medium:
= quasiparticle;
properties
reflect interaction with the medium;
Csorgo,
Vertesi,!"Sziklai,
PRL 105 (2010)
182301
TA
TA
additional inelastic channels remove !"-mesons, e.g. !" N# $ N
pp →Ea=2.1
η’ppGeV
final
COSY
Ea=1.9state
GeV interaction
transparency ratio:
1
1
0.8
"#A $ %' X
0.9
E =1200-2200 MeV
in the medium:
TA et
= al, PLB482(2000)
Moskal
365 !" = quasiparticle; propertiesa reflect interaction with the
1
A& "#N $ additional
%' X
inelastic channels remove !"-mesons, e.g. !" N# $ N
0.8
data
transparencyd’exp
ratio:
normalized to 12C
K(l )=10 MeV
d’exp data
K(l0)=10 MeV
K(l0)=15 MeV
K(l0)=20 MeV
K(l0)=25 MeV
K(l0)=30 MeV
K(l0)=35 MeV
K(l0)=40 MeV
CB-ELSA/TAPS
0.7
!
properties of "‘ mes
0
0.7
K(l0)=15 MeV
K(l0)=20 MeV
K(l%0')=25
#A $
X MeV
K(l0)=30 MeV
K(l0)=35 MeV
#NK(l$
%' XMeV
0)=40
"
transparency
ratio Tprocesses
secondary production
?
=
A
A& "
($N#!’N)
0.9
0.8
0.7
0.6
lim
in
y
r
a
TA
0.9
TA
pη’ scatt. length ~ 0.1 fm (Δm~10MeV)
in-medium
1
0.9
0.8
0.7
Ea=1200
e
"’ reproduced with
smaller
T
kin
r
2
2
10
p
normalized to 12C
10
0.4
comparison with TA for A! meson
Ad’
A
"" absorption weaker than ! absorption
d’ for Tkin> (Ea-md’)/2
o data #($0,<|p!’|> % 0.9 GeV/c)
% 25-30
MeV
0.6
secondary
production
processes ? t
0.3
!
($N#!’N)
d for Tkin>0.5
(Ea-md)/2
" absorption
properties
ened in Nanova,
the
medium
talk at Baryon2010
"’ reproduced
T. Mertens et al., EPJA
38 (2008) with
195 smaller Tkin
2
Γinel
10
0.4
d’
comparison with TA for ! meson 10
A
=
=
14
mb
!(T)
!
%(T,A)
∝
A
;
A
scaling
law
17
D.
Jido
J-PARC検討会
ρ·β·�·c
"" absorption weaker than ! absorption
d’ for Tkin> (
Friday, 16 Decemberfor
2011& and ": '=0.67
for !"-?
0.6
0.6
0.5
Missing mass spectroscopy
formation reaction of bound states
observe spectra of final nucleon (missing mass)
identification of meson in nuclei (energy, isospin,decay,...) P
1
P
%
observing decays helps to reduce the background
η: N(1535)→πN
K: Λ(1405)→πΣ
nucleon pick-up
convolution of hole states and meson partial waves
recoilless
selection rule
−1
s−1
⊗
s
,
p
m
N
N ⊗ pm , . . .
D. Jido
Friday, 16 December 2011
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Formation spectrum
12
C(π , p)
+
pπ=1.8 GeV/c
H. Nagahiro, PTPS 186, 316 (2010)
DJ, Nagahiro, Hirenzaki, arXiv:1109.0394 [nucl-th]
q=200MeV/c
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elementary cross section (reference)
η’ potential (Wood-Saxon type)
π + n → pη �
ρ(r)
Vη� (r) = V0
ρ0
�
dσ
dΩ
�lab.
= 100µb/st
Δm = 150 MeV
Γ/2 = 20 MeV
p3/2 hole
s1/2 hole
D. Jido
Friday, 16 December 2011
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Formation
spectrum
+
12
H. Nagahiro, PTPS 186, 316 (2010)
DJ, Nagahiro, Hirenzaki, arXiv:1109.0394 [nucl-th]
(S ,p) spectra : C target : incident energy dependence
12
+
GeV/c
C(π
, p)MeV p(pπS=1.8
J-PARC
7S = 820
= 950
MeV/c) q=200MeV/c
7S = 650 MeV
(pS = 777 MeV/c)
Chiral doublet model [C=0.2]
elementary cross section (reference)
�
π + n15 → pη �
�lab.
dσ recoilless position
= 100µb/st
dΩ
80
40
5
20
0
Chiral unitary model
20
Δm = 150 MeV
Γ/2 = 20 MeV
ρ(r)
Vη� (r) = V0
ρ0
60
10
0
Chiral doublet
model [C=0.2]
η’ potential
(Wood-Saxon
type)
Chiral unitary model
60
15
-100
10
-50
0 40 50
Eex – E0 [MeV]
100
150
p3/2 hole
20
5
NFQCD10, Joint Symposium of theory and experiment in “Hadrons in nulei”
20
s1/2 hole
0
-100
-50
0
50
100
150
0
-100
Eex – E0 [MeV]
D. Jido
Friday, 16 December 2011
-50
0
50
100
Eex – E0 [MeV]
19
150
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Formation spectrum
12
C(π , p)
+
pπ=1.8 GeV/c
H. Nagahiro, PTPS 186, 316 (2010)
DJ, Nagahiro, Hirenzaki, arXiv:1109.0394 [nucl-th]
q=200MeV/c
J-PARC
elementary cross section (reference)
η’ potential (Wood-Saxon type)
π + n → pη �
ρ(r)
Vη� (r) = V0
ρ0
�
dσ
dΩ
�lab.
= 100µb/st
Δm = 150 MeV
Γ/2 = 20 MeV
p3/2 hole
s1/2 hole
D. Jido
Friday, 16 December 2011
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Formation spectrum
12
C(π , p)
+
pπ=1.8 GeV/c
H. Nagahiro, PTPS 186, 316 (2010)
DJ, Nagahiro, Hirenzaki, arXiv:1109.0394 [nucl-th]
q=200MeV/c
J-PARC
elementary cross section (reference)
η’ potential (Wood-Saxon type)
π + n → pη �
ρ(r)
Vη� (r) = V0
ρ0
Re V0
Im V0
s
p
d
�
dσ
dΩ
�lab.
= 100µb/st
−150 MeV
−20 MeV
(93.5, 34.0)
(21.9, 19.1)
(56.3, 27.7)
(21.0, 20.8)
Δm = 150 MeV
Γ/2 = 20 MeV
p3/2 hole
s1/2 hole
D. Jido
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Conclusion
η 質量生成は、カイラル対称性の破れと UA(1) anomaly の 共演
η 質量に対する UA(1) anomaly の効果は、カイラル対称性の破れを伴う必要がある。
カイラル対称性が回復するとη 質量は減少すると予想される。
大きな吸収効果を伴うことなく、大きな質量減少が期待される
クォーク・グルーオンのダイナミクスによる引力
フレーバー１重項への選択的な相互作用
100 MeV オーダーの質量減少と30 MeV 程度の吸収幅
η 中間子原子核系の束縛状態を観測できる可能性がある
UA(1)問題に対して、有益な実験的情報を得ることを期待
outlook
理論的考察：クォーク凝縮との関係、質量公式、カイラル有効理論の構築
現象論的情報：η N 相互作用
実験：12C(p,d)反応 @ GSI, LoI 提出（板橋さん、藤岡さんら）
D. Jido
Friday, 16 December 2011
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