中間子ー原子核束縛系の物理 - a brief summary of current interests -...

中間子ー原子核束縛系の物理中間子ー原子核束縛系の物理- A brief summary of current interests -- A brief summary of current interests -

奈良女子大学奈良女子大学比連崎　悟比連崎　悟

Pionic Atom, Kaonic Atoms(Pionic Atom, Kaonic Atoms( 代表的・歴史的なも代表的・歴史的なものの ))

Meson ( Yukawa Particle )

Large !!

Small !!

Electromagnetic

Strong

B.E.

Radius

Interactions

A(Z,N)

-

m ~ 300 me

Strong Interacting Particle System!

Observation of Pionic AtomObservation of Pionic Atom= Traditional Way : Slow Pion Trap =

X-ray DetectorX-ray

Slow

Nucleus

Absorption to Nucleus by Strong Interaction

4He 16O 40Ca

In-Medium Dispersion RelationIn-Medium Dispersion Relation

Pion – Nucleus Optical PotentialPion – Nucleus Optical Potential

with

Ericson-Ericson, Ann. Phys. 36 (66) 323Seki-Masutani, Phys. Rev. C27(83)2799

Medium Effects

Medium Effects

Nucleus Densities

Potential Parameters

Observed by Observed by

X-ray SpectroscopyX-ray Spectroscopy

Toki, Hirenzaki, Yamazaki, Hayano (1989)

Toki, Hirenzaki,

Yamazaki, Hayano (1989)

Energy

and

Width

Information on

pion-nucleus interactions

Do you believe this ?

の限界

Missing mass spectroscopyMissing mass spectroscopy

emitted particleemitted particle

Incident particleIncident particle

targettargetmesonmeson

-hole-holeprotonproton

Distortion effectDistortion effect

distortion Factor reduction of the flux due to absorption

[Eikonal approx.]

These two reactions haveThese two reactions havedifferent sensitivitiesdifferent sensitivities to systems. to systems.

Missing mass spectroscopyMissing mass spectroscopyIncident particleIncident particle

targettargetmesonmeson

-hole-holeprotonproton

emitted particleemitted particle

Deeply bound Deeply bound -- states in the states in the 208208Pb(d,3He) reactionPb(d,3He) reaction

PRC62(00)025202PRC62(00)025202

K. Itahashi et al.

Hirenzaki, Toki, Yamazaki PRC(1991)

PRL88(02)122301PRL88(02)122301

Deeply bound 1s and 2p Pionic States in the Deeply bound 1s and 2p Pionic States in the 206206Pb(d,Pb(d,33He) reactionHe) reaction

Hirenzaki, Toki PRC55(97)2791

Pionic 1s states of Sn nucleiPionic 1s states of Sn nuclei

Umemoto, Hirenzaki, Kume, Toki PRC62(00)024606Umemoto, Hirenzaki, Kume, Toki PRC62(00)024606

K. Suzuki et al. 　 Phys. Rev. Lett. 92(2004) 072302 GOR relation + Tomozawa-Weinberg RelationGOR relation + Tomozawa-Weinberg Relation

New method – Observation of Meson-Nucleus states

( 数年間の試行錯誤があった ) Information on at finite ~ 0

Eigen state observation Invariant Mass Method

Quantum number fixed Selective information

Umemoto et al., PRC62 (2000)

Further ProgressesFurther Progresses

Exotic few body systems. (core, fermion, boson)

1. Exotic Many Body Physics

2. Hadron Physics at finite density　　　　　　　 Fundamental theory (QCD)

　　　　　　　 Effective theory

　　　　　　　 Hadron property at finite 　　　　　　　有限系　　　　無限系　　　　　　　観測量計算、　データ

• Higgs mechanism

•UA(1) Anomaly Effect

Meson Mass SpectrumMeson Mass Spectrum T.Kunihiro, T.Hatsuda, PLB206(88)385 T. Kunihiro, PLB219(89)363 R.D.Pisarski, R.Wilczek, PRD29(84)338 K.Fukushima, K.Onishi, K.Ohta, PRC63(01)045203 P. Costa et al.,PLB560(03)171, hep-ph/0408177etc…

: Jp = 0-

• Spontaneous Chiral Symmetry Breaking

Junko YamagataJunko Yamagata (Nara Women’s Univ.) H. Nagahiro (RCNP, Osaka Univ.) S. Hirenzaki (Nara Women’s Univ.)

In-Flight (K-,p) Reactions for the formation of Kaon-Nucleus bound systems

* J. Yamagata, H. Nagahiro, Y. Okumura, S. Hirenzaki, Prog. Theor. Phys. 114 (2005) 301; Errata 114 (2005) 905Prog. Theor. Phys. 114 (2005) 301; Errata 114 (2005) 905

* J. Yamagata, H. Nagahiro, S. Hirenzaki, arXive:nucl-th/0602021arXive:nucl-th/0602021

Kaonic Nuclei K-Nucleus bound system strong interaction Binding Energy : 10 – 100 MeV100 MeV

Formation ReactionFormation Reaction (In-flight K,N) reaction – Kishimoto Group ((In-flight K,N) reaction – Kishimoto Group (Exp.Exp.)) (Stopped K,N) reaction – Iwasaki, Suzuki Group ((Stopped K,N) reaction – Iwasaki, Suzuki Group (Exp.Exp.))

(K– light nuclei) system structure – Akaishi, Yamazaki, Dote (K– light nuclei) system structure – Akaishi, Yamazaki, Dote ((Theor.Theor.))

Critical analysis – E. Oset, H. Toki (Theor.)

Introduction for kaon KK

Very deep!!Very deep!!

We theoretically study the formation spectra of In-flight (K-,p) reactions.

• quasi-stable K-Nuclear State

• Ultra high density state Really Exist or not ?Really Exist or not ?

Cf. Kaonic Atoms

Introduction for kaon

Kaonic Nuclei case large widths

Green Function Method

Cf. Effective Number Approach (previous work)

Good for small width casesJ. Yamagata et. al., Prog. Theor. Phys. 114(05)301J. Yamagata et. al., Prog. Theor. Phys. 114(05)301

Our Study Structure of Kaonic Atoms and Kaonic Nuclei (two different K-Nucleus optical potentials) Formation spectra of In-flight (K-,p) reactions

Green Function Method

The energy dependence of the optical potential The Quasi-Free Kaon production processes

Formulation -- Structure Klein-Gordon Equation

Chiral Unitary Model

Phenomenological Model[Batty, Friedman, Gal, Phys. Rep. 287(97)385]

[A. Ramos, E. Oset, NPA671(00)481][Hirenzaki, Okumura, Toki, Oset, Ramos, PRC61(00)055205]

Phase Space Factor (for the phenomenological potential)

threshold 　・・・

threshold 　・・・

Pha

se S

pace

Fac

tor

Formulation -- Structure Klein-Gordon Equation

Chiral Unitary ModelChiral Unitary Model

Phenomenological ModelPhenomenological Model[Batty, Friedman, Gal, Phys. Rep. 287(97)385]

[A. Ramos, E. Oset, NPA671(00)481][Hirenzaki, Okumura, Toki, Oset, Ramos, PRC61(00)055205]

Energy level (examples by the potential at E=0)

Atomic StateAtomic StateSimilar

Nuclear StateNuclear StateDifferent

Formulation – Reaction

Green Function Method O. Morimatsu, K. Yazaki NPO. Morimatsu, K. Yazaki NPA435A435 (85)727 (85)727

O. Morimatsu, K. Yazaki NPO. Morimatsu, K. Yazaki NPA483A483 (88)493 (88)493

: Green function for K interacting with the nucleus

: Elementary cross section (Exp. data)

Previous work: Effective Number ApproachPrevious work: Effective Number Approach(J. Yamagata et. al., PTP114(05)301)

12C is interesting !

B.E. = 150 MeV

B.E. = 100 MeV

B.E. = 50 MeV

B.E. = 0 MeV

Kaon BindingEnergy

Momentum Transfer – =0°

Green vs. Effective (Energy Spectrum)

Nuclear States• Phenomenological

potential

• At E=0TK = 600 MeV

Target : 12C

Quasi-free regionBound regionBound region

Green vs. Effective (Energy Spectrum)

Nuclear States

• Phenomenological

potential

• At E=0

TK = 600 MeV

Target : 12C

Bound regionBound region

Energy Spectrum ( E=0 potential )

12C (K-,p) reactions – TK = 600 MeVGreenEffective Number

Atomic State

1s 2p 2s

Atomic State

1s 2p 2s

Energy Spectrum ( Energy dependence )

12C (K-,p) reactions – TK = 600 MeV

Smooth Structure?Structure?

Effect of Branching Ratio of Decay Channel Phenomenological Potential

80%80%

20%20%

Pha

se S

pace

Fac

tor

80%

20%

90%90%

10%10%

Energy Spectrum 　　　： Phenomenological Model (Energy Dependent)

80%80% 90%90%

20%20% 10%10%

Energy Spectrum 　　　： Energy Dependent

PhenomenologyChiral Unitary

Green

Effective

Number

Green

Effective

Number

J. Yamagata, H. Nagahiro, S. Hirenzaki, arXive:nucl-th/0602021J. Yamagata, H. Nagahiro, S. Hirenzaki, arXive:nucl-th/0602021

Comparison with

Kishimoto group’s data

Energy SpectrumEnergy dependent

Green

Effective Number

Chiral Unitary

Phenomenology

Please ask

Kishimoto san group.

Nuclear State : Just a tiny bump.

**Exist!!Exist!! But, it is very difficult to see. (large decay width)

*Need *Need more accurate experimental datamore accurate experimental data..

Summary for kaon

( not simple peaks )

Atomic State :

**Exist Exist as quasi-stable state.as quasi-stable state.

We studied the formation spectra of In-flight (K-,p) reactions. Target : 12C, 16O ; TK = 600 MeV Green Function Method (cf. Effective number approach)

Interesting spectrum shape.

No peak structure is expected in spectra for all cases considered here.

Nuclear structure change was not considered.

Formation of Formation of -mesic nuclei-mesic nuclei› Optical potential ~ N*(1535) dominance model ~Optical potential ~ N*(1535) dominance model ~

» Chiral Doublet modelChiral Doublet model» Chiral Unitary modelChiral Unitary model

› Numerical Results of (d,Numerical Results of (d,33He) & (He) & (,p) reactions,p) reactions

Formation of Formation of ’(958)-mesic nuclei’(958)-mesic nuclei› NJL modelNJL model

» UUAA(1) anomaly in finite density(1) anomaly in finite density

› Numerical Results of (Numerical Results of (,p) reactions,p) reactions

Hideko NgahiroHideko Ngahiro, D.Jido and S.Hirenzaki, NPA761(05)92, D.Jido and S.Hirenzaki, NPA761(05)92Hideko NagahiroHideko Nagahiro, D.Jido and S.Hirenzaki, PRC68(03)035205, D.Jido and S.Hirenzaki, PRC68(03)035205D.Jido, D.Jido, Hideko NagahiroHideko Nagahiro and S.Hirenzaki, PRC66(02)045202 and S.Hirenzaki, PRC66(02)045202

Hideko NagahiroHideko Nagahiro, S. Hirenzaki, PRL94(05)232503, S. Hirenzaki, PRL94(05)232503Hideko NagahiroHideko Nagahiro, M.Takizawa and S. Hirenzaki, in preparation., M.Takizawa and S. Hirenzaki, in preparation.

’’(958)-Nucleus system(958)-Nucleus system

’’(958) meson …(958) meson …close connections with close connections with UUAA(1) anomaly(1) anomaly

› some theoretical workssome theoretical works» the effects of the Uthe effects of the UAA(1) anomaly on (1) anomaly on ’’ properties properties

» at finite temperature/densityat finite temperature/density T. Kunihiro, PLB219(89)363T. Kunihiro, PLB219(89)363 R.D.Pisarski, R.Wilczek, PRD29(84)338R.D.Pisarski, R.Wilczek, PRD29(84)338 Y. Kohyama, K.Kubodera and M.Takizawa, PLB208(1988)165Y. Kohyama, K.Kubodera and M.Takizawa, PLB208(1988)165 K.Fukushima, K.Onishi, K.Ohta, PRC63(01)045203K.Fukushima, K.Onishi, K.Ohta, PRC63(01)045203 P. Costa P. Costa et al.et al.,PLB560(03)171, hep-ph/0408177 etc…,PLB560(03)171, hep-ph/0408177 etc…

» the possiblethe possible character changes of character changes of ’’

› a a poor experimental informationpoor experimental information on on the Uthe UAA(1) anomaly at finite density(1) anomaly at finite density

proposal for the formation reaction proposal for the formation reaction of theof the ’’-mesic nuclei-mesic nuclei› UUAA(1) anomaly in medium from the viewpoint of “mesic nuclei”(1) anomaly in medium from the viewpoint of “mesic nuclei”

› the the ’’ properties, especially properties, especially mass shiftmass shift, at finite density, at finite density

Hideko Nagahiro, S. H, Phys.Rev.Lett.Hideko Nagahiro, S. H, Phys.Rev.Lett.9494, 232503 (2005), 232503 (2005)Hideko Nagahiro, M.Takizawa and S. H, in preparation.Hideko Nagahiro, M.Takizawa and S. H, in preparation.

Model for Model for and and ’’ meson in medium meson in medium

Nambu-Jona-Lasinio modelNambu-Jona-Lasinio model with the with the KMT interaction KMT interaction › unified treatment of the unified treatment of the and and ’’ meson meson

du s

u d s

One can reproduce the heavy One can reproduce the heavy ’’ mass mass

Kunihiro, Hatsuda, PLB206(88)385, Fig.3Kunihiro, Hatsuda, PLB206(88)385, Fig.3

Anomaly effect in vacuumAnomaly effect in vacuum

explicit breaking the Uexplicit breaking the UAA(1) sym.(1) sym.

Kobayashi, Maskawa Prog.Theor.Phys.44, 1422 (70)Kobayashi, Maskawa Prog.Theor.Phys.44, 1422 (70)G. ’t Hooft, Phys.Rev.D14,3432 (76)G. ’t Hooft, Phys.Rev.D14,3432 (76)

Masses in finite Masses in finite with with NJLNJL

==== …………

quark-anti-quark scatteringquark-anti-quark scattering

++++

Bethe-Salpeter equationBethe-Salpeter equation

==== ++++

condensate in finite condensate in finite

Fermi distribution functionFermi distribution function

== ++ ++

Gap equations for quarksGap equations for quarks

meson properties (mass)meson properties (mass)

mesonmesonmesonmeson

T. Kunihiro, PLB219(89)363,T. Kunihiro, PLB219(89)363,P. Costa P. Costa et al.et al.,PLB560(03)171. etc…,PLB560(03)171. etc…

flavor mixing termsflavor mixing terms

partial restoration in mediumpartial restoration in medium[MeV

] [MeV

]

SU(2) sym. matterSU(2) sym. matter

SU(3)SU(3)

SU(2) symmetric matterSU(2) symmetric matter

we consider the SU(2) sym. matter as the sym. nuclear matter.we consider the SU(2) sym. matter as the sym. nuclear matter.

’’

mm’’ ~ ~ -150-150 MeV @ MeV @ 00

mm ~ ~ +20+20 MeV @ MeV @ 00

and and ’’ mass shifts @ mass shifts @ 00

P. Rehberg, et al., PRC53(96)410.P. Rehberg, et al., PRC53(96)410.

parameters (in vacuum)parameters (in vacuum)

= 602.3 = 602.3 [MeV][MeV]

ggS S 22 = 3.67 = 3.67

ggDD55 = -12.36 = -12.36

mmu,du,d = 5.5 = 5.5 [MeV][MeV]

mmss = 140.7 = 140.7 [MeV][MeV]

MMu,du,d = 367.6 = 367.6 [MeV][MeV]

MMss = 549.5 = 549.5 [MeV][MeV]

〈〈 uuuu 〉〉 1/3 1/3 = -241.9 = -241.9 [MeV][MeV]

〈〈 ssss 〉〉 1/31/3 = -257.7 = -257.7 [MeV][MeV]

mm’’ = 958 = 958 [MeV][MeV]

mm = 514 = 514 [MeV][MeV]

mm = 135 = 135 [MeV][MeV]

We can see the large medium effect even We can see the large medium effect even at normal nuclear densityat normal nuclear density..

anomaly term anomaly term effecteffect

anomaly effect in the finite densityanomaly effect in the finite density

We simulate an extreme case.We simulate an extreme case.

’’

ggDD : constant : constant

mm’’ ~ ~ -150-150 MeV @ MeV @ 00

mm ~ ~ +20+20 MeV @ MeV @ 00

’’

mm’’ ~ ~ -250 -250 MeV @ MeV @ 00

mm ~ ~ -100 -100 MeV @ MeV @ 00

ggDD = g = gDD(() ??) ??ggDD = g = gDD((=0) exp(-(=0) exp(-(//00))22))

- & - & ’’-Nucleus optical potential-Nucleus optical potential

Real Part VReal Part V00

› evaluated by possible evaluated by possible ’’ mass shift mass shift at at 00

~ potential description~ potential description

ggDD : constant : constant

VV’’(r)(r)

VV(r)(r)

: : repulsiverepulsive’’ : : attractiveattractive

ggDD = g = gDD((=0) e=0) e-(-(//0)0) 22

VV’’(r)(r)

VV(r)(r)

: : attractiveattractive’’ : : attractiveattractive

- & - & ’’-Nucleus optical potential-Nucleus optical potential

Real Part VReal Part V00

› evaluated by possible evaluated by possible ’’ mass shift mass shift at at 00

Imaginary Part WImaginary Part W0 0 for for ’’› estimated from AIP Conf.Proc.717 (04)837(A.Sibirtsev,Ch.Elster, S.Krewald, J.Speth)estimated from AIP Conf.Proc.717 (04)837(A.Sibirtsev,Ch.Elster, S.Krewald, J.Speth)

analysis of analysis of p p ’’p datap datafix a coupling gfix a coupling g

N N*(1535)

’

gg

(only one resonance included)

› in analogy with in analogy with -hole model for the -hole model for the -nucleus system-nucleus system

’

’

~ phenomenological estimation~ phenomenological estimation

Imaginary Part for Imaginary Part for WW00 = - 40 MeV = - 40 MeV D.Jido,H.N.,S.Hirenzaki, PRC66(02)045202, D.Jido,H.N.,S.Hirenzaki, PRC66(02)045202,

H.N.,D.Jido,S.Hirenzaki, PRC68(03)035205,H.N.,D.Jido,S.Hirenzaki, PRC68(03)035205,

~ potential description~ potential description

((,p) reaction : Parameters,p) reaction : Parameters

((,p) reaction @ E,p) reaction @ E=2.7 GeV=2.7 GeV

target … target … 1212CC

Forward (Forward ( ~ 0 deg.) ~ 0 deg.)

Elementary cross section for Elementary cross section for p p ’’pp

-mesic nuclei-mesic nuclei› mm ~ 547 MeV ~ 547 MeV mm ~ 783 MeV ~ 783 MeV m m’’ ~ 958 MeV ~ 958 MeV

› plan of experiment for the formation of plan of experiment for the formation of -mesic nuclei @ SPring-8, 2005-mesic nuclei @ SPring-8, 2005› two different predictions for optical potentialstwo different predictions for optical potentials

» 【【 attractiveattractive 】】 V= - (156 + 29 i) V= - (156 + 29 i) //00 MeV MeV [Klingl, Waas, Weise NPA650(99)299][Klingl, Waas, Weise NPA650(99)299]

» 【【 repulsiverepulsive 】】 V= - ( - 42.8 + 19.5i) V= - ( - 42.8 + 19.5i) //00 MeV MeV [Lutz, Wolf, Friman NPA706(02)4[Lutz, Wolf, Friman NPA706(02)4

31] 31]

› elementary cross section ~ 150 nb/srelementary cross section ~ 150 nb/sr» event # [event # [] ~ [] ~ [] ~ [] ~ [’’]]@ test experiment at SPring-8 @ test experiment at SPring-8

[N.Muramatsu, private communication] [N.Muramatsu, private communication]

-mesic nuclei-mesic nuclei› elementary cross section ~ 150 nb/srelementary cross section ~ 150 nb/sr

Data:SAPHIR collaboration, PLB444(98)555-562

Chiang, Yang, PRC68(03)045202

Numerical results : Numerical results : 1212C(C(,p),p)1111BB,,,,’’

quasi-freequasi-free


’’

We only We only observe the observe the quasi-free quasi-free ’’

peakpeak

no medium effectno medium effect




’’VV00= - (- 42.8 + 19.5i) [MeV]= - (- 42.8 + 19.5i) [MeV]

(NPA706(02)431)(NPA706(02)431)





’’




VV00= - (156+29i) [MeV]= - (156+29i) [MeV](NPA650(99)299)(NPA650(99)299)




’’



ggDD = -12.36/ = -12.36/55




’’



mass reductionmass reductiondue to the medium due to the medium

effect througheffect throughanomaly termanomaly term

ggDD = -12.36/ = -12.36/55



’’


ggDD = -12.36/ = -12.36/55 quasi-freequasi-free

VV00= - (- 42.8 + 19.5i) [MeV]= - (- 42.8 + 19.5i) [MeV](NPA706(02)431)(NPA706(02)431)

Quasi-free Quasi-free overlap with bound overlap with bound

’’

Quasi-free Quasi-free overlap with bound overlap with bound

’’




’’ and and ’’ mass reductions mass reductions


VV00= - (- 42.8 + 19.5i) [MeV]= - (- 42.8 + 19.5i) [MeV](NPA706(02)431)(NPA706(02)431)

density dependent gdensity dependent gDD




density dependent gdensity dependent gDD



’’

Summary for Summary for and and ’ : ’ : mesic nuclei … hadron properties in finite mesic nuclei … hadron properties in finite

-mesic nuclei by (d,-mesic nuclei by (d,33He) and (He) and (,p) reactions,p) reactions» Chiral doublet modelChiral doublet model» Chiral unitary modelChiral unitary model

Different pictures for the N*(1535) in mediumDifferent pictures for the N*(1535) in medium

’’-mesic nuclei by (-mesic nuclei by (,p) reactions,p) reactions» NJL modelNJL model

UUAA(1) anomaly in finite density(1) anomaly in finite density

Future worksFuture works› -mesic nuclei-mesic nuclei

» (d,(d,33He) experiment for He) experiment for -mesic nuclei formation @ GSI -mesic nuclei formation @ GSI

› ’’-mesic nuclei -mesic nuclei » ((,p) experiment for ,p) experiment for -mesic nuclei @ SPring-8 -mesic nuclei @ SPring-8 Coming soon ?Coming soon ?

» What is the density dependence of gWhat is the density dependence of gDD ?? ??

» Other treatment ?Other treatment ?» relation with other models for relation with other models for & & ’’

chiral doublet model & chiral unitary approach for the chiral doublet model & chiral unitary approach for the -mesic nuclei-mesic nuclei

SummarySummary Mesic Atoms and Mesic Nuclei A finite density Laboratory 観測量の物理的意味をキッチリ抑えたい　　微視的な理解から実際のハドロン反応の計算まで、

統一的にやりたい

by (d,3He) Hayano (Tokyo group) @GSI (,’) by (,p) Muramatsu (LEPS group) @SPring8 k by In-Flight (K,p) Kishimoto (Osaka group)

+Many Others

いろいろな事が、まだまだ不十分でわからない

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中間子ー原子核束縛系の物理 - a brief summary of current interests -...

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