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Formation spectra of Formation spectra of -mesic nuclei by (-mesic nuclei by (,p) reaction,p) reactionat J-PARCat J-PARC

永廣 秀子 永廣 秀子 (( 阪大阪大 RCNP)RCNP)

Collaborators :Collaborators :慈道 大介 慈道 大介 (( 京大基研京大基研 ))

比連崎 悟 比連崎 悟 (( 奈良女奈良女 ))

H.Nagahiro, D.Jido and S.Hirenzaki, NPA761(05)92H.Nagahiro, D.Jido and S.Hirenzaki, NPA761(05)92H.Nagahiro, D.Jido and S.Hirenzaki, PRC68(03)035205H.Nagahiro, D.Jido and S.Hirenzaki, PRC68(03)035205D.Jido, H.Nagahiro and S.Hirenzaki, PRC66(02)045202D.Jido, H.Nagahiro and S.Hirenzaki, PRC66(02)045202

E.Kolomeitsev, D.Jido, H.Nagahiro, S.Hirenzaki, in preparationE.Kolomeitsev, D.Jido, H.Nagahiro, S.Hirenzaki, in preparationH.Nagahiro, D.Jido, S.Hirenzaki, in preparationH.Nagahiro, D.Jido, S.Hirenzaki, in preparation

『ストレンジネスとエキゾティクス・理論の課題』『ストレンジネスとエキゾティクス・理論の課題』3 Mar. 2007 @ 3 Mar. 2007 @ 鳥羽鳥羽 , , 三重三重

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IntroductionIntroduction

中中中中中中中中中中中中» works for works for -mesic nuclei-mesic nuclei

› ((++,p) * Liu, Haider, PRC34(1986)1845 ,p) * Liu, Haider, PRC34(1986)1845 [theo][theo] * Chrien * Chrien et al.et al., PRL60(1988)2595 , PRL60(1988)2595 [exp][exp] * Chiang, Oset, and Liu, PRC44(1988)738 * Chiang, Oset, and Liu, PRC44(1988)738 [theo][theo] * Kohno * Kohno et al.et al., NPA519(1990)755 , NPA519(1990)755 [theo][theo]

› (d,(d,33He) * Hayano, Hirenzaki, Gilltzer, EPJ.A6(1999)99 He) * Hayano, Hirenzaki, Gilltzer, EPJ.A6(1999)99 [theo][theo] * Jido, Nagahiro, Hirenzaki, PRC66(2002)045202 * Jido, Nagahiro, Hirenzaki, PRC66(2002)045202 [theo][theo] * Exp. at GSI (Yamazaki, Hayano group) 2005-6 * Exp. at GSI (Yamazaki, Hayano group) 2005-6 [exp][exp]

› ((,p) * Nagahiro, Jido, Hirenzaki, NPA761(2005)92 ,p) * Nagahiro, Jido, Hirenzaki, NPA761(2005)92 [theo][theo]› -light-nucleus system : TAPS @ MAMI(2004) -light-nucleus system : TAPS @ MAMI(2004) [exp][exp]› etc… (ex. (etc… (ex. (,,) @ Tohoku, etc …)) @ Tohoku, etc …)

» strong coupling to strong coupling to N*(1535)N*(1535) [J [JPP= ½= ½--] resonance ] resonance › 有限密度中における 有限密度中における N*(1535) N*(1535) の性質 の性質 中間子原子核中間子原子核

– カイラル二重項模型 カイラル二重項模型 … … N* mass reduction in mediumN* mass reduction in medium

– カイラルユニタリー模型 カイラルユニタリー模型 … … no change N* mass in mediumno change N* mass in medium

formation of formation of -mesic nuclei induced by -mesic nuclei induced by meson beammeson beam» and K beams are available and K beams are available at J-PARCat J-PARC ((++,p) reaction,p) reaction

› カイラル模型を用いたスペクトラム カイラル模型を用いたスペクトラム › 運動学的な考察運動学的な考察

» ““((++,p) experiment at 1988” ,p) experiment at 1988” の再考の再考› ““negative result” negative result” の意味するところ。の意味するところ。

negative resultnegative result

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核媒質中の 核媒質中の N*(1535) N*(1535) に対するカイラル模型に対するカイラル模型

Chiral doublet modelChiral doublet model

N* : Chiral partner of nucleonN* : Chiral partner of nucleon

DeTar, Kunihiro PRD39(89)2805DeTar, Kunihiro PRD39(89)2805Jido, Nemoto, Oka, Hosaka NPA671(00)471Jido, Nemoto, Oka, Hosaka NPA671(00)471

Jido, Oka, Hosaka PTP106(01)873Jido, Oka, Hosaka PTP106(01)873Kim, Jido, Oka NPA640(98)77Kim, Jido, Oka NPA640(98)77

mass difference of N* and nucleonmass difference of N* and nucleon

mas

sm

ass

C ~ 0.2 : strength of C ~ 0.2 : strength of chiral restorationchiral restoration at the saturation density at the saturation density 00

reduction of mass difference in the nuclear mediumreduction of mass difference in the nuclear medium

N* :N* : resonance dynamicallyresonance dynamically generatedgenerated in meson-baryon scatteringin meson-baryon scattering

Chiral unitary modelChiral unitary model Kaiser, Siegel, Weise PLB362(95)23Kaiser, Siegel, Weise PLB362(95)23Waas, Weise NPA625(97)287Waas, Weise NPA625(97)287Garcia-Recio, Nieves, Inoue, Oset PLB550(02)47Garcia-Recio, Nieves, Inoue, Oset PLB550(02)47Inoue, Oset NPA710(02)354Inoue, Oset NPA710(02)354

TT VV VV VV== ++ ++ …… quasi bound state of quasi bound state of KK

No mass shift of N* is expected in the nuclear mediumNo mass shift of N* is expected in the nuclear medium

coupled channel Bethe-Salpater eq. in mediumcoupled channel Bethe-Salpater eq. in mediumno Pauli blocking for no Pauli blocking for in nuclear medium in nuclear medium

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energy

/0

m

mN*-mN

-nucleus interaction -nucleus interaction ~ N* dominance model ~~ N* dominance model ~

+ (cross term)+ (cross term)

Chiang, Oset, Liu PRC44(1991)738Chiang, Oset, Liu PRC44(1991)738

Jido, Nagahiro, Hirenzaki, PRC66(2002)045202Jido, Nagahiro, Hirenzaki, PRC66(2002)045202

self-energyself-energy

optical potentialoptical potential

associated with mass reduction

mN* -m

N

11 22 33 44 55 66 77r [fm]r [fm]

potential naturepotential nature

48 MeV48 MeV

N* - NN* - N

N* - NN* - N

attractiveattractive

medium effectmedium effect

repulsiverepulsive

level crossing

Kolomeitsev, Jido, Nagahiro, HirenzakiKolomeitsev, Jido, Nagahiro, Hirenzakiin preparationin preparation

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Chiral unitary modelInoue, Oset, NPA710(02) 354, fig.6

Energy dependence of the Energy dependence of the self-energy self-energybound regionbound region

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Energy dependence of the optical potentialsEnergy dependence of the optical potentials

0

50

-50

-100

-150

100

150

V(r

) [M

eV]

0

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-50

-100

-150

100

150

doublet

unitary

- m = +100 MeV

0

50

-50

-100

-150

100

150

V(r

) [M

eV]

0

50

-50

-100

-150

100

150

- m = -100 MeV

doublet

unitary

00 5050 100100-50-50-100-100 [MeV][MeV]

0

50

-50

-100

-150

100

150

V(r

) [M

eV]

0

50

-50

-100

-150

100

150

doublet

unitary

- m = -70 MeV

2 4 6 8r [fm]

Chiral unitary modelInoue, Oset, NPA710(02) 354, fig.6

0

50

-50

-100

-150

100

150

V(r

) [M

eV]

0

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-100

-150

100

150

doublet

unitary

- m = 0 MeV

2 4 6 8r [fm]

0

50

-50

-100

-150

100

150

V(r

) [M

eV]

0

50

-50

-100

-150

100

150

doublet

unitary

- m = -50 MeV2 4 6 8

r [fm]

bound regionbound region

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Missing mass spectroscopy : one nucleon pick-upMissing mass spectroscopy : one nucleon pick-up

(d,(d,33He) : established by studies of He) : established by studies of pionic atom formationpionic atom formation– theory … S.Hirenzaki, H.Toki, T.Yamazaki, PRC44(91)2472, …theory … S.Hirenzaki, H.Toki, T.Yamazaki, PRC44(91)2472, …

– experiment … K.Itahashi et al., PRC62(00)025202, …experiment … K.Itahashi et al., PRC62(00)025202, …

› -mesic nuclei formation-mesic nuclei formation : 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.

((,p) : ,p) : smaller distortion effectsmaller distortion effect– -nucleus … Marco, Weise, PLB502(01)59-nucleus … Marco, Weise, PLB502(01)59

– -atom … Hirenzaki, Oset, PLB527(02)69-atom … Hirenzaki, Oset, PLB527(02)69

› -mesic nuclei formation-mesic nuclei formation : H.N., D.Jido,S.Hirenzaki, NPA761(05)92. : H.N., D.Jido,S.Hirenzaki, NPA761(05)92.

((,p) : could be possible at J-PARC ?,p) : could be possible at J-PARC ?› secondary meson beam, secondary meson beam, , K, …, K, …

emitted particleemitted particle

Incident particleIncident particle

targettargetmesonmeson

-hole-holenucleonnucleon

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J-PARC J-PARC で可能になると期待されるエネルギー領域で可能になると期待されるエネルギー領域

1212C(C(++,p),p)1111BB reaction reaction

momentum transfer : forward angle (0 degree)momentum transfer : forward angle (0 degree)

= m

= m– 50 MeV

= m– 100 MeV

T = 820 MeV (p ~ 950 MeV/c)

T = 650 MeV (p ~ 777 MeV/c)

elementary cross sectionelementary cross section

S.Prakhov et al., [Crystal Ball Collaboration]PRC72,015203 (2005).

angular distribution

total

~ flat

total cross sectiontotal cross section

として見積もりとして見積もり

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EEexex – E – E00 [MeV] [MeV]

((++,p) spectra : ,p) spectra : 1212C targetC target

= 820 MeV (p= 820 MeV (p = 950 MeV/c) : = 950 MeV/c) : = 0 deg. = 0 deg.

Chiral doublet model [C=0.0]Chiral doublet model [C=0.0](t-(t- approx.) approx.)

Chiral doublet model [C=0.2]Chiral doublet model [C=0.2] Chiral unitary modelChiral unitary model

productionproductionthresholdthreshold

productionproductionthreshold (s-state proton-hole)threshold (s-state proton-hole)

recoilless at recoilless at threshold threshold

EEexex – E – E00 [MeV] [MeV]

00 5050 100100 150150-50-50-100-100 00 5050 100100-50-50-100-100

2020

1010

1515

55

0000 5050 100100 150150-50-50-100-100

EEexex – E – E00 [MeV] [MeV]EEexex – E – E00 [MeV] [MeV]

150150 00 5050 100100 150150-50-50-100-100

pion proton

bound regionquasi-free

* Morimatsu, Yazaki NPA435(85)727* Morimatsu, Yazaki NPA435(85)727NPA483(88)493NPA483(88)493

by Green function method*by Green function method*

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EEexex – E – E00 [MeV] [MeV]

((++,p) spectra : ,p) spectra : 1212C target : Green function methodC target : Green function method

= 820 MeV (p= 820 MeV (p = 950 MeV/c) : = 950 MeV/c) : = 0 deg. (Lab) = 0 deg. (Lab)

Chiral doublet model [C=0.0]Chiral doublet model [C=0.0](t-(t- approx.) approx.)

Chiral doublet model [C=0.2]Chiral doublet model [C=0.2] Chiral unitary modelChiral unitary model

EEexex – E – E00 [MeV] [MeV]

recoilless at recoilless at threshold threshold

shallow b.s.shallow b.s.

EEexex – E – E00 [MeV] [MeV]

00 5050 100100 150150-50-50-100-100 00 5050 100100 150150-50-50-100-100 00 5050 100100 150150-50-50-100-100

2020

1010

1515

55

00

deep b.s. deep b.s.

0

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V(r

) [M

eV]

doublet unitary

r [fm]2 4 6 8

r [fm]2 4 6 8

V(r)V(r) V(r)V(r)

- m = -100 MeV

0

50

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-100

-150

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150

V(r

) [M

eV]

doublet

r [fm]2 4 6 8

unitary

r [fm]2 4 6 8

V(r)V(r) V(r)V(r)

at thresholdat threshold

* Total spectrum shape : 顕著な違い* 束縛状態の存在 - 浅い束縛状態 : CUM - 深い束縛状態 : CDM* ピーク構造は見えない。 - 幅が広い

quasi-free quasi-free

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((++,p) spectra : ,p) spectra : 1212C target C target : : 入射 入射 + + エネルギー依存性エネルギー依存性

EEexex – E – E00 [MeV] [MeV]00 5050 100100 150150-50-50-100-100

EEexex – E – E00 [MeV] [MeV]

00 5050 100100 150150-50-50-100-100

2020

1010

1515

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00

2020

1010

1515

55

00

Chiral doublet model [C=0.2]Chiral doublet model [C=0.2] Chiral unitary modelChiral unitary model

= 820 MeV (p= 820 MeV (p = 950 MeV/c) = 950 MeV/c)

Chiral doublet model [C=0.2]Chiral doublet model [C=0.2]

Chiral unitary modelChiral unitary model

EEexex – E – E00 [MeV] [MeV]

00 5050 100100 150150-50-50-100-100

= 650 MeV (p= 650 MeV (p = 777 MeV/c) = 777 MeV/c)

recoilless position

8080

6060

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2020

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6060

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2020

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Liu, Haider, PRC34(86)1845, Fig.7Liu, Haider, PRC34(86)1845, Fig.7

(B.E, /2) = (2.65, 4.77) [MeV]

((++,p) spectra : past experiment in 1988,p) spectra : past experiment in 1988

Chrien et al., PRL60(1988)2595Chrien et al., PRL60(1988)2595» pp = 800 MeV/c = 800 MeV/c

» proton angle : proton angle : 15 deg. (Lab.)15 deg. (Lab.)» search for predicted narrow bound state ( ex. search for predicted narrow bound state ( ex. ~ 10 MeV) ~ 10 MeV)

negative results (bound state was not observed)negative results (bound state was not observed)

Chrien at al., PRL60(88)2595, Fig.1Chrien at al., PRL60(88)2595, Fig.1

Li

C

O

Al

100

200

300

400

500

0

[Me

V]

0.8 1 1.2 1.40.60.4p [GeV/c]

momentum transfermomentum transfer

0 deg.

15 deg.

hole

quasi free quasi free

b.s. + quasi-freeb.s. + quasi-free

bound statebound state

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((++,p) spectra : past experiment in 1988,p) spectra : past experiment in 1988

quasi-free quasi-free の取り扱いの取り扱い» virtual virtual absorption (due to Imaginary potential) absorption (due to Imaginary potential) The peak structure is hidden in quasi-free contributionThe peak structure is hidden in quasi-free contribution

Difference of nucleon separation energy in Difference of nucleon separation energy in 1616OO» 1p1/2 1p1/2 1p3/2 1p3/2 1s1/2 1s1/2

~ 6 MeV~ 6 MeV ~ 23 MeV ~ 23 MeV

100

200

300

400

500

0

[Me

V]

0.8 1 1.2 1.40.60.4p [GeV/c]

momentum transfermomentum transfer

0 deg.

15 deg.

Liu, Haider, PRC34(86)1845, Fig.7Liu, Haider, PRC34(86)1845, Fig.7

(B.E, /2) = (2.65, 4.77) [MeV]

50

40

30

20

10

green function methodgreen function method (V0,W0) = -(34,23) [MeV]

quasi free quasi free

Liu, Haider, PRC34(86)1845Liu, Haider, PRC34(86)1845

0

bound statebound state

bound region

green function methodgreen function method (V (V00,W,W00) = -(34,) = -(34,1515) [MeV]) [MeV]

002020404060608080 -20-20 -60-60-40-40100100

EEexex – E – E00 [MeV] [MeV]

b.s. + quasi-freeb.s. + quasi-free

[Also commented in Kohno et al, NPA519(90)755] [Also commented in Kohno et al, NPA519(90)755]

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((++,p) spectra : comparison of our calc. with the exp. data,p) spectra : comparison of our calc. with the exp. data

Chrien at al., PRL60(88)2595, Fig.1Chrien at al., PRL60(88)2595, Fig.1

Li

C

O

Al

Chrien et al., PRL60(1988)2595Chrien et al., PRL60(1988)2595» pp = 800 MeV/c = 800 MeV/c

» proton angle : proton angle : 15 deg. (Lab.)15 deg. (Lab.)

chiral unitary modelchiral doublet model8080

4040

00

EEexex – E – E00 [MeV] [MeV]00 5050 100100-50-50-100-100

EEexex – E – E00 [MeV] [MeV]00 5050 100100-50-50-100-100

3030

2020

1010

00

EEexex – E – E00 [MeV] [MeV]005050100100 -50-50 -100-100

EEexex – E – E00 [MeV] [MeV]005050100100 -50-50 -100-100

0 deg.0 deg. 0 deg.0 deg.

15 deg.15 deg. 15 deg.15 deg.

bound regionbound region

bound regionbound region bound regionbound region

bound regionbound region

Chiral doublet model

Chiral unitary model

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EEexex – E – E00 [MeV] [MeV]005050100100 -50-50 -100-100

Chrien at al., PRL60(88)2595, Fig.1Chrien at al., PRL60(88)2595, Fig.1

Li

C

O

Al

Chrien et al., PRL60(1988)2595Chrien et al., PRL60(1988)2595» pp = 800 MeV/c = 800 MeV/c

» proton angle : proton angle : 15 deg. (Lab.)15 deg. (Lab.)

chiral unitary modelchiral doublet model8080

4040

00

3030

2020

1010

00

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2020

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00

EEexex – E – E00 [MeV] [MeV]005050100100 -50-50 -100-100

0 deg.0 deg. 0 deg.0 deg.

15 deg.15 deg. 15 deg.15 deg.

• どちらの模型も実験データとは矛盾しない。どちらの模型も実験データとは矛盾しない。

((++,p) spectra : comparison of our calc. with the exp. data,p) spectra : comparison of our calc. with the exp. data

proton angle ~ 0 degreeproton angle ~ 0 degree

bound regionbound region

bound regionbound region bound regionbound region

bound regionbound region

[Also commented in Kohno et al, NPA519(90)755] [Also commented in Kohno et al, NPA519(90)755]

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SummarySummary

formation of formation of -mesic nuclei-mesic nuclei» In-medium properties of N*(1535) resonanceIn-medium properties of N*(1535) resonance

› Chiral doublet model : Chiral doublet model : deep bound statedeep bound state

– pocket-like potential, level crossing of pocket-like potential, level crossing of and N*-hole modes and N*-hole modes

› Chiral unitary model : Chiral unitary model : shallow bound stateshallow bound state

((++,p) reaction,p) reaction» incident pion kinetic energyincident pion kinetic energy

› TT = 820 MeV (p = 820 MeV (p ~ 950 MeV/c) : recoilless at ~ 950 MeV/c) : recoilless at threshold threshold

› TT = 650 MeV (p = 650 MeV (p ~ 777 MeV/c) : recoilless at ~ 777 MeV/c) : recoilless at threshold – 50 MeV threshold – 50 MeV

» possible at J-PARC ?possible at J-PARC ?

((++,p) ,p) 実験結果実験結果 (Chrien at al., 1988)(Chrien at al., 1988) の再考の再考» 15°proton angle 15°proton angle は妥当かは妥当か ??

› It is hard to observe the peak structures of the bound states, It is hard to observe the peak structures of the bound states, even if it existeven if it exist..

» We should discuss We should discuss the whole shape itselfthe whole shape itself in the case that the imaginary part mig in the case that the imaginary part might be large like ht be large like -mesic nuclei-mesic nuclei

The proton angle ~ 0 deg.The proton angle ~ 0 deg.