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

and chiral symmetry for baryons and chiral symmetry for baryons

Hideko Nagahiro (RCNP)Hideko Nagahiro (RCNP)

Collaborators :Collaborators :Daisuke Jido (YITP)Daisuke Jido (YITP)

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

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

International Nuclear Physics Conference “INPC2007”International Nuclear Physics Conference “INPC2007”4 June, 20074 June, 2007

Tokyo International Forum, JapanTokyo International Forum, Japan

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IntroductionIntroduction -mesic nuclei-mesic nuclei

» works for works for -mesic nuclei-mesic nuclei› ((++,p) * Liu, Haider, PRC34(1986)1845 ,p) * Liu, Haider, PRC34(1986)1845 [theo][theo]

* Chiang, Oset, and Liu, PRC44(1988)738 * Chiang, Oset, and Liu, PRC44(1988)738 [theo][theo] * Chrien * Chrien et al.et al., PRL60(1988)2595 , PRL60(1988)2595 [exp][exp]

› (d,(d,33He) * Hayano, Hirenzaki, Gilltzer, EPJ.A6(1999)99 He) * Hayano, Hirenzaki, Gilltzer, EPJ.A6(1999)99 [theo][theo] * D. Jido, H.Nagahiro, S. Hirenzaki, PRC66(2002)045202 * D. Jido, H.Nagahiro, S. 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) * H.Nagahiro, D.Jido, S.Hirenzaki, NPA761(2005)92 ,p) * H.Nagahiro, D.Jido, S.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 N*(1535) [Jstrong coupling to N*(1535) [JPP= ½= ½--] resonance ] resonance › in-medium properties of N*(1535)in-medium properties of N*(1535) -mesic nuclei-mesic nuclei

– Chiral doublet model Chiral doublet model … N* mass reduction in medium… N* mass reduction in medium

– Chiral unitary model Chiral unitary model … no change N* mass in medium… no 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

› with the chiral doublet model & chiral unitary modelwith the chiral doublet model & chiral unitary model› appropriate kinematicsappropriate kinematics

» comparison with the (comparison with the (++,p) experiment at 1988,p) experiment at 1988

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Chiral models for N*(1535) in mediumChiral models for N*(1535) in medium

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 chiral restoration at the saturation density C ~ 0.2 : strength of chiral restoration 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 shifts of N* is expected in the nuclear mediumNo mass shifts 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* - holeN* - hole

N* - holeN* - hole

attractiveattractive

medium effectmedium effect

repulsiverepulsive

level crossing

Jido,Jido, Kolomeitsev, Nagahiro, HirenzakiKolomeitsev, Nagahiro, Hirenzakiin preparationin preparationposter June 5:poster June 5: QT-111 by D. Jido QT-111 by D. Jido

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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

50

-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

50

-50

-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]

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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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energy range expected at J-PARCenergy range expected at J-PARC

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

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

= m

= m– 50 MeV

= m– 100 MeV

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

Green function methodGreen function method

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

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

= 650 MeV (p= 650 MeV (p = 777 MeV/c) = 777 MeV/c) :: = 0 deg. (Lab) = 0 deg. (Lab)

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

recoilless at recoilless at threshold - 50 MeV threshold - 50 MeV

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

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

8080

6060

4040

2020

00

production thresholdproduction threshold

production thresholdproduction threshold(s-state proton-hole)(s-state proton-hole)

pp nn

1212C targetC target

18 MeV18 MeV

bound regionbound region bound regionbound regionquasi-freequasi-free quasi-freequasi-free

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

= 650 MeV (p= 650 MeV (p = 777 MeV/c) = 777 MeV/c) : : = 0 deg. (Lab) = 0 deg. (Lab)

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

recoilless at recoilless at threshold - 50 MeV threshold - 50 MeV

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

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

8080

6060

4040

2020

00

shallow b.s.shallow b.s.

quasi-free quasi-free

unitary

0

50

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-150

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V(r

) [M

eV]

at -100 MeV

r [fm]2 4 6 8

V(r)V(r)

V(r

) [M

eV]

0

50

-50

-100

-150

100

150unitary

r [fm]2 4 6 8

V(r)V(r)

at thresholdat threshold

deep b.s. deep b.s. 0

50

-50

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-150

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V(r

) [M

eV]

doublet

r [fm]2 4 6 8

at thresholdat threshold

V(r)V(r)

0

50

-50

-100

-150

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150

V(r

) [M

eV]

doublet

at -100 MeV

r [fm]2 4 6 8

V(r)V(r)

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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.)» 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)

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

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.

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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

3030

2020

1010

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.

• The experimental data is consistent with both model The experimental data is consistent with both model This experimental set-up is not sensitive to N* in-This experimental set-up is not sensitive to N* in-

mediummedium

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

proton angle should be 0 degreeproton angle should be 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 state(s)deep bound state(s)

– 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 state(s)shallow bound state(s)

((++,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

Reconsideration of the experimental data at 1988 by Chrien Reconsideration of the experimental data at 1988 by Chrien at al.at al.» Is the 15°proton angle appropriate?Is the 15°proton angle appropriate?

› Not sensitive to the N* properties in-mediumNot sensitive to the N* properties in-medium

» 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 largeht be large

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

possible at J-PARC ?possible at J-PARC ?» realistic discussion with experimentalists [H.Fujioka, K.Itahashi]realistic discussion with experimentalists [H.Fujioka, K.Itahashi]

… … refinements and concrete discussions for a real experimentrefinements and concrete discussions for a real experiment