J-PARC における原子核中のハドロン
慈道 大介（京都大学基礎物理学研究所）
1

our aim- produce new hadron-nucleus systems
structure, hadron properties- investigate the properties- extrapolate the knowledge

dense nuclear matter (neutron star)

hadron-nucleus system (new exotics)
mesons in nuclei（中間子原子核）
hadronic molecular statesetc.
(hadronic atoms)
ex. π atom, K atom, Ξ atom, ...
(hypernuclei)
fundamental interactions
hadron spectroscopy, hadron structure
baryon resonance: mesons excite nucleons in nuclei
ultimate goal
understanding of strong interactions of QCDKaons in nuclei
one of the ultimate goals
in medium π- mass
obtain self-energy as functions of density and energy
kaon condensation in neutron star ??

Kaons are probably boundproperties of bound states give a lot of constraints
need peaks !!
a lot of subcomponents and wide width→ selective reactions for desired statespionic atom
pion-nucleus scattering
theory (ChPT)

calculate whole structure of spectra
Ohnishi, Jido, Sekihara, Tsubakihara, in preparation

mesons in nuclei（中間子原子核）
challenge of mesic nuclei

mesic atom(hypernuclei)

bindingCoulomb assisted

decay

strong int.

possible orbits

surface or outside(strong int.)(weak int.)(inside nucleus)

width

keV 〜 1 MeV

bound states

well separated

mesic nuclei
strong int.
strong int.
inside nucleus
several 10s MeV
couples to B*

overlappedmesons in nuclei（中間子原子核）
recoilless kinematics
selection rule for nucleon hole and meson statesmeson ground state is s-statecreation of s-state hole costs energy
nuclei with s-state hole are highly excited stateslarge distortion effects

as another possiblity

two-nucleon pick-up reaction(π,d), (γ,d) etc.

J=0 with “shallow” two nucleon holes and mesoncomplications in theoretical calculations

mesons in nuclei（中間子原子核）cf. hadronic atoms
meson-nucleus systems governed by strong interactions
issue: bound or unbound ?

KbarN: strong attraction

mesonsKbar, η, ω, η’, Φ, J/Ψ, ....

narrow widths in vacuum

σ, ρ, K*, ....

wide widths in vacuum

π, K, .....

repulsivebind and decay by strong interactions
wide widths naturally expected

how wide ??

suppression of widths in deeply bound systems !?

mesons excite nucleons in nuclei
creation of baryon resonances in nuclei
meson - B*-hole couplings

hadronic excitation of hypernuclei

φ中間子原子核
カイラル対称性の部分的回復を strange quark で見る
φN 相互作用は U(3) 対称性では消える (OZI rule)
OZI rule の破れとhadronic decay
核媒質効果の asymmetry

ω中間子原子核ωN と N(1520) 3/2- との結合 ?!

KbarN 引力KN 斥力ηʼ中間子原子核

Nagahiro, Hirenzaki, PRL97, 232503 (05)Nagahiro, Takizawa, Hirenzaki, PRC74, 045203 (06)UA(1) 量子異常による重い質量
QCD における operator 関係式
カイラル対称性の自発的な破れを通して質量に反映
原子核中での質量変化
η-η’ mixingEγ = 3GeVNagahiro, Hirenzaki PRL97, 232503 (2005)

η中間子原子核 (eta mesic nuclei)- ηN strongly couples to N(1535)- level crossing of η and N*-hmodes

AttractiveRepulsive- N(1535) is a candidate of chiral partner of N

Reduction of the mass difference of N and N*
Jido, Nagahiro, Hirenzaki, PRC66, 045202 (’02)
Nagahiro, Jido, Hirenzaki, PRC68, 035205 (’03), NPA761,92 (’05)
9Jido, Kolomeitsev, Nagahiro, Hirenzaki, NPA acceptedSpectral function of in-medium eta meson
Energy dependence
Infinite matter calc.

10Jido, Nagahiro, Hirenzaki, PRC66, 045202 (’02)
Jido, Kolomeitsev, Nagahiro, Hirenzaki, NPA acceptedK meson and Λ(1405)-h modes

Λ(1405)-hYamagata, Jido, Nagahiro, Hirenzaki
in preparation

K meson原子核中での K+
KN 相互作用 (Strong も EM も) は斥力
K+-原子核弾性散乱
KN より下には状態がない
cf. KbarN には Λ(1405) がいる
情報が clean !?
cf. π-原子核散乱
原子核中の fK や KNσ項

ハドロン励起状態
hadron resonances：produced by strong interactions
theory：many models based on diﬀerent aspects
experiment：rich and precise dataItʼs ready to investigate details of the structure ofhadron resonances from both sides

properties in vacuum : masses, widths and couplings
mesons in nuclei : meson excites nucleon
dynamical aspectdecaying resonance → large hadronic components
hadron dynamics is important
symmetry aspectsymmetry of quarks
chiral partners: N(1535) chiral partner of nucleon ??
13

DJ, Oller, Oset, Ramos, Meissner
NPA725, 181 (’03)Λ(1405) is a superposition of two states.
there are two attractive channels
group theoretically
SU(3) singlet and octet
physically

KbarN, πΣImplication of double pole structureΛ(1405) spectrum is dependent on channels

Resonance position in KbarN channel~1425 MeV with narrower width
not 1405 MeVThis 20 MeV difference is important for KbarN interactions

Subthreshold properties of KbarN
Λ(1405) spectra in KbarN channel
Sekihara, DJ, Oset, in progressΛ(1520)Λ(1405)peak position 1420 MeV
NPB129,1,(’77)

bubble chamber

N(1535) のカイラル電荷

gAN* ~ gπN*N*

バリオンのカイラル対称性と密接に関連
gAN* > 0 “naive” assignment

massless in χ restoration

gAN* < 0 “mirror” assignment

massive in χ restoration

Lattice では、 gAN* ~ 0

T.T. Takahashi, T. Kunihiro

N(1535) dominant around threshold

Jido, Oka, Hosaka, PTP106, 823 (’01)

ハドロン励起状態の大きさ
励起状態の構造
クォーク自由度 v.s. ハドロン自由度
ハドロン分子状態 ~ 原子核中の核子間距離 (~1 fm)
異なる核媒質効果Λ(1405)の荷電半径(diagonal form factor)
KbarN negativeπΣ(I=0) almost zerotransition form factor
energy dependence in production

Sekihara, Hyodo, DJ arXiv:0803.4068 [nucl-th];in priparation

hadronic molecular
新しいハドロン励起状態

K中間子が特別な役割

N* as KKbarN quasibound stateΞ* as KKbarN quasibound state
main decay modes: three-body decayΛ(1405) への doorway
N* around 1900 MeV
spacial structure

Y. Kanada-En’yo, DJ, PRC78,025212 (08).
DJ,Y. Kanada-En’yo, arXiv:0806.3601, PRC in press

20~40 MeV bound, 90~100 MeV width

hadron-hadron distances are comparablewith nucleon-nucleon distances in nuclei
r.m.s radius (1.7 fm) is larger thanthat of 4He (1.4 fm)
mean hadron density: 0.07 hadrons/(fm3)Λ(1405)N
2.1 fm(1.4)

2.8 fm(2.3)

Kbara0(980)K2.3 fm(2.1)
18

Connection to QCD
establish in-medium effective theory of QCD
in medium chiral perturbation theory
medium modifications of LEC’s
fpi, fK, sigma term etc.

LEC = low energy constantgive connections to universal parameters

exact sum rule in chiral limit

DJ, Hatsuda, Kunihiro, arXiv:0805.4453 [nucl-th]

low energy theorem

all zero modes contribute to in-medium quark condensate.

Summary
our aim- produce new hadron-nucleus systems- investigate the properties- extrapolate the knowledgemesons in nuclei
baryon resonance in nuclei
B* hypernuclei
complex but interesting systems !!
a lot of things can be learnt
challenges
observe bound states !!

wide widths and many subcomponents

calculate spectra in detail !!
necessary to establish in-medium effective theory
to connect observation to QCDη- mesons in nuclei
opening new states

experimental feasibility- interests of hadrons in nuclear medium

in-medium dynamics of hadronproperties of hadron, bound states in nuclei
modification of nuclear structure
partial restoration of chiral symmetry

universal proparties

high density physics, ex. neutron star
experimental observations
finite systembound states
infinite system

hadron properties in finite densities
effective theory

QCDη中間子原子核 (eta mesic nuclei)chiral doublet model と chiral unitary model の違いの詳細
どちらも N*-hole 模型
N* の取り扱い（picture）が異なる
chiral doublet model
N と N* が chiral doublet
N と N* の質量差が減少 → level crossing
chiral unitary model
N* : dynamically generated resonanceKΣ channel が重要 → Pauli blocking effect が小さい
23

Jido, Nagahiro, Hirenzaki, PRC66, 045202 (’02)

Optical potential of η in nucleus

ηNN* coupling
η-nucleus reduced mass
η energy

Real part of optical potential depends on eta energy and mass difference of N and N*.

We have seen reduction of N-N* mass difference in nuclear medium in chiral doublet model.
attraction
repulsion

Density dependence

level crossing

Energy dependence
24

Jido, Nagahiro, Hirenzaki, PRC66, 045202 (’02)

Optical potential of η in nucleus
Density dependence

fixing energy at

Repulsive
Attractive25

Jido, Kolomeitsev, Nagahiro, Hirenzaki, NPA acceptedGreen function of in-medium eta mesonEnergy dependence
potential strongly depends on energy→ bound states calculated in self-consistent way

propagation of modes as poles
pole position: in-medium “mass”
Two modes of propagation
Eta meson mode
N*-hole mode

couple in nuclear mediumchange places
if level crossing takes place26

Jido, Kolomeitsev, Nagahiro, Hirenzaki, NPA acceptedSpectral function of in-medium eta meson
Energy dependence
Infinite matter calc.

27

What is hadronic molecular state ?
- system of multiple hadrons described by hadron dynamics

ex. Λ(1405)
as KbarN QBS

possible constituents are ground states hadrons
octet baryons: N, Λ, Σ, Ξ octet meson: π, K, η

- constituents keep their identity
typical binding energy ~ 10-20 MeV

weakly bound systemdecay width ~ 50 MeV (strong interactions)- spatially extended (large size)
typically more than 1 fm

- softer form factors
strong energy dependence
in productionquasi-bound statecharge radiusof Λ(1405) as
KbarN bound state

Sekihara, Hyodo, DJ
arXiv:0803.4068 [nucl-th]

quark degrees of freedom may be less important28K meson in Λ(1405)
small binding energy ~ 10-30 MeV- heavy particle ~ half of nucleon mass

isospin averaged mass

non-relativisitc treatment
cf. pion- Nambu-Goldstone bosonstrong s-wave attraction in KbarN
chiral effective theory

momentum expansions-wave int. proportional to K energy
Kaons are different from pions in the energies of our interest !!

29

Result KKbarN

N* around 1900 MeV

spacial structureΛ(1405)

hadron-hadron distances are comparablewith nucleon-nucleon distances in nuclei
r.m.s radius (1.7 fm) is larger thanthat of 4He (1.4 fm)
mean hadron density: 0.07 hadrons/(fm3)N
2.1 fm(1.4)

2.8 fm(2.3)

Kbara0(980)K
2.3 fm(2.1)

KN repulsion importantthreshold of KKbarN 1930 MeV
30system with I=1/2, JP=1/2+ (N*)
Interactions in KKbarN system
attraction

I=0

I=1

thresholdweak attraction

1434.6 MeV
991.4 MeV

repulsionvery weekstrong repulsion

1434.6 MeV

Λ(1405), f0(980) and a0(980) are assumed to be quasi-bound states
naturally expect KKbarN bound state below Λ*+K and f0(a0)+N

questions- does KN repulsion spoil bound state ?

- are the attractions too strong to hadronic molecular picture ?
31