カイラル対称性の部分的回復とη 中間子原子核 - kekd. jido (yukawa institute,...

D. Jido (Yukawa Institute, Kyoto)

D. Jido 12.16, 2011KEK 東海１号館

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

collaboration with H. Nagahiro and S. Hirenzaki (Nara WU)

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]

Reference

LoI for GSI-SIS: Spectroscopy of η’ mesic nuclei with (p,d) reactionK. 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

Friday, 16 December 2011

D. Jido J-PARC検討会

Introduction (３つのキーワード)

2

核媒質中のカイラル対称性の部分的回復

UA(1) anomaly

中間子原子核

量子効果による対称性の破れ

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 qq∗

qq

b1

b∗1

1/2 1− γ

ρ

ρ0

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）

引力と吸収の起源が同じ s-channel N* → πN

η’の質量生成機構と密接に関連

DJ, Hatsuda, Kunihiro, PLB 670 (2008) 109.



Mesonic atoms and mesonic nuclei

3

modification of mass and width by many-body effects

interactions between meson and nucleus

extract more fundamental and universal quantities

mN → mN mN → πNmNN → NN

ex. mass shift width

in-medium self-energy of meson

qqquark condensateex.

bound systems of meson and nuclei

experimental tool to observe medium modification of meson

we do not have to remove in-vacuum contributions

mN → B∗



Low density theorem

4

qq∗ =

1 − σπN

m2πf2

π

ρ

qq +O(ρn>1)

Drukarev, Levin, Prog. Part. Nucl. Phys. 27, 77 (1991)

σπN : πN sigma term, O(mq), obtained from TπN at soft limit

model independent theoretical relation

derivation

qq∗ = qq + ρN |qq|N + O(ρn>1)

m2πf2

π = −2mqqq

2mqN |qq|N = σπN

density expansion

definition of sigma term

Gell-Mann Oakes Renner relation

30 % reduction of quark condensate at nuclear density



Partial restoration of chiral symmetry

5

effective reduction of quark condensate in nuclear medium

hadronic quantities closely connected to dynamical breaking

1) pion decay constant

2) spectrum of sigma meson

3) mass difference of chiral partners

4) mass of eta’ meson

etc.

ρ-a1 N-N*(1535)

deeply bound pionic atom

qq∗/qq < 1

DJ, Hatsuda, Kunihiro, PLB 670 (08) 109.

Hatsuda, Kunihiro, PRL55 (1985), 158.Hatsuda, Kunihiro, Shimizu, PRL82 (99) 2840.ππ production off nuclei

Weinberg, PRL18 (67) 507.

etc.DJ, Hatsuda, Kunihiro, PRD63 (01) 011901.

Kapusta, Shuryak, PRD49 (94) 4694.

etc.DeTar, Kunihiro, PRD39 (89) 2805.

K. Suzuki et al., PRL92 (04) 072302.W. Weise, NPA690 (01) 98.

etc.

H.C. Kim, DJ, Oka, NPA640 (98) 77.

DJ, Nagahiro, Hirenzaki, arXiv: 1109.0394S.H. Lee, Hatsuda, PRD57 (96) 1871

etc.

etc.

need systematic studies



Deeply bound pionic atom

6

π- bound in atomic orbit

not observed in X ray spectroscopy

deeply bound states (1s, 2p,... )

need to formation experiments

neutron picking-up process in (d, 3He)

V. CONCLUDING REMARKS

In the Ericson-Ericson type formulation of the pion-nucleus optical potential the p-wave !nonlocal" part param-eters have relatively strict restrictions from existing data,while the s-wave !local" part parameters have had larger un-certainties so far. Sensitivity of a pionic state to this s-wavepart parameters is proportional to the overlap integral be-tween the pionic density and the nuclear medium#$ !%&(r)!2'(r)dr3( , and thus, the 1s and 2p pionic states inheavy nuclei are the most suitable for the study of the s-waveparameters.Since such deeply bound states could not be formed in the

conventional method of using stopped pions #33(, we devel-oped pion-transfer reactions #3(. Several experiments weretried by using !n,p" #34(, !n,d" #35,36(, (d , 2He) #37(,(d , 3He) #38(, (p ,2p) #39( reactions, resulting in no clearevidence of pionic atom formation. In the meantime, the the-oretical investigation was continued to find the optimal ex-perimental condition. Finally, the (d , 3He) reaction wasfound to be suitable in producing pionic states under therecoilless condition ()q*0). This condition was expectedto enhance the cross section for the formation of a boundpionic state of substitutional configuration (l&!"ln).This new method involved several questions. !i" Can the

optical potential deduced from shallow pionic atoms be ap-plied to deeply bound states? !ii" Are the calculated produc-tion cross sections correct? !iii" Is the intrinsic backgroundsmall enough to observe the bound-pion peaks? !iv" Can the

instrumental background be suppressed sufficiently? !v" Isthe energy resolution good enough?The present experimental setup was carefully designed

based on the previous experiences. It was optimized toachieve the highest possible resolution at sufficiently highyield and low background. In the design of the experiment,the fragment separator !FRS" #40( at the GSI was a key com-ponent. It was used as a spectrometer at forward 0°, and itstwo 30° dipole magnets after the target bending in oppositedirections swept out most of the background particles beforethey reach the dispersive focal plane. The second part of theFRS worked as a 36 m long transfer line, where the particleswere perfectly identified by the time of flight and by theenergy loss in the scintillation counters. The synchrotronSIS-18 provided a high intensity beam#1011 d/spill, with asmall momentum spread )p/p$5%10!4, which corre-sponds to an energy resolution $0.3 MeV. The experimentalresolution and the symmetric spectral response were guaran-teed by the monoenergetic peak of 3He from the two-bodyreaction of p(d , 3He)&0 by using a polyethylene #!CH2)n]target.The finally obtained energy spectrum after careful correc-

tions for the acceptance of the spectrometer, the target thick-ness, the time dependent incident beam momentum driftwithin the extraction, second order ion optical aberrations,and other contributions had a resolution of 0.48&0.06MeV, and was in notable agreement with the theoreti-cally calculated spectrum in the whole measured range.The observed absolute cross sections are found to be by a

factor of 2.5 smaller than the theoretical values, which iswithin the uncertainty of the calculation of absolute crosssections. There was a prominent peak at about 5 MeV belowthe &! production threshold, and it was assigned to the for-mation of the 2p pionic state coupled to neutron hole statesof 3p1/2 and 3p3/2 , which are separated by 0.9 MeV. Struc-ture due to the formation of shallower states was also seenbetween the 2p peak and the threshold. An additionalpeak, though unresolved, was observed in the (1s)&!

region and was assigned to the configurations of(1s)&!(3p1/2,2 f 5/2,3p3/2)n

!1.We analyzed the excitation spectrum of 208Pb(d , 3He) re-

action in terms of the formation of bound pionic states in thenuclear reaction, and deduced the binding energy and thewidth of the 2p state to be B2p"5.13&0.02 !stat"&0.12 !syst"MeV, +2p"0.43&0.06 !stat"&0.06 !syst"MeV.The formation of the 1s ground state was clearly observed,but the precise determination of the binding energy andwidth was not possible because of the incomplete separationfrom the main peak. Constraints of B1s vs +1s were pre-sented for each of assumed 1s/2p cross section ratios aslisted in Table III.The binding energies and widths are compared with the

calculated values using the existing potential parameter sets.The resolution was high enough to test the validity of themodel predictions. In their relation to the theoretically calcu-lated values, the deduced values of 1s and 2p states are inmutual accordance. The widths expected from Konijn et al.#28( in which the potential parameters were adjusted to fit tothe data showing the 3d anomaly #9,10,41( were smaller

FIG. 10. !a" The real part of local potential V(r), which isequivalent to the pion mass shift )m&

eff(r), the total real-part poten-tial including the Coulomb interaction „Vc(r)…, and the imaginarypart of the local potential „W(r)…, as obtained from the analysis ofthe measured 1s and 2p&! binding energies and widths based onthe SM-1 parameter set. Re B0 was not changed in the analysis. !b"Radial distributions of the 1s and 2p&! densities. The half densityradius is shown by the vertical dotted line.

K. ITAHASHI et al. PHYSICAL REVIEW C 62 025202

025202-10

sensitive to nuclear effects

effective density ~ 0.6ρ0

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),

low-energy pion-nucleus scatteringcomplemental experiment

20~30 MeV

GSI

LAMPF, PSI



Deeply bound pionic atom

7

level shift ΔE and width Γ → medium effect of pionπ- optical potential (s-wave part)

b1 parameter: isovector pion-nucleus scattering lengthδρ = ρp − ρn

ρ = ρp + ρnisoscalar density

isovector density2mπUS

opt = −4π1 + mπ

mN

(b0ρ− b1 δρ) + · · ·

fit parameters so as to reproduce data

low density theorem

Σπ = 2mπUSopt = −ρTS

πN

missing repulsion puzzle

b0 and b1 should be in-vacuum values

bfree1 /b1 = 0.78 pionic atom

enhancement of repulsion



Reduction of pion decay constant Fπ

8

enhancement of s-wave repulsive interaction

This is related to in-medium reduction of pion decay constant FπWeinberg-Tomozawa realtion

4π1 + mπ

mN

bfree1 = − mπ

2F 2

4π1 + mπ

mN

b1 = − mπ

2(F tπ)2

bfree1

b1=

F t

π

Fπ

2

in vacuum

in mediumat low-density

DJ, Hatsuda, Kunihiro, PLB 670 (08), 109.

The next question is how to conclude partial restoration of chiral symmetry from the reduction of Fπ.

at low density

Kolomeitsev, Kaiser, Weise, PRL90 (03), 092501.



Nuclear bound state of meson

9

m N → π N

nuclear many body effects

absorption m N N→ N N

m N → m Nattraction

neutral meson (η’) only strong interaction is relevant

attraction and absorption come from the same mechanism

→ binding energy and width have comparable sizes

due to large width, bound states are hard to see in experiment

typical energy scale

70 MeV one-body potential in nucleus

100 MeV absorption for omega meson

wavefunctions of meson and nucleus largely overlap


D. Jido

no doubt that Kbar is bound in nucleus

K- (Kbar) attractive electromagnetic interactionattractive strong interaction

J-PARC検討会

Search for Kaonic nuclear bound states

10

missing mass spectra

12C(K−, n)

12C(K−, p)

K− + 12C→ N + X

Kishimoto et al. PTP118, 181 (07)

some strength in bound region

KEK FINUDA

pΛ invariant mass spectrumback-to-back correlation in light nuclei

hint of KbarNN bound state

Agnello et al. PRL94, 212303 (05)

still we have no clear signals of kaonic nuclear statesFriday, 16 December 2011

D. Jido

divergence of axial current

PCAC anomaly

∂µA(0)µ = 2i(muuγ5u + mddγ5d + mssγ5s) +

3αs

8πF a

µνFµνa

∂µA(8)µ =

i√3(muuγ5u + mddγ5d− 2mssγ5s)

J-PARC検討会

Origin of η’ mass

11

Vogl, Weise, Prog.Part.Nuc.Phys.270, 195 (91)

UA(1) anomaly effect lifts η’ mass up

symmetry in classical QCD

no UA(1) symmetry due to quantum anomaly

U(3)L ⊗U(3)R → SU(3)V ⊗U(1)V

A

V V

Fµνa ≡ µνρσF a

ρσ

symmetry in the original theory can be counted by numbers of conserved currents

η’ is not necessarily massless → η’ is massive

for simplicity, we consider SU(3) and chiral limits, and neglect η and η’ mixing



η’ meson in chiral restoration

12

When chiral symmetry is restored...

chiral multiplet for S and PS mesons

(3,3)⊕ (3, 3)

both octet and singlet contain

π,K, η8, η0 σ, a0,κ, f0

qiγ5qj , qiqj

if chiral symmetry is manifest,η8 and η0 should degenerate even though anomaly is there

DJ, Nagahiro, Hirenzaki, arXiv:1109.0394 [nucl-th]

qLi qR

j qRi qL

j (3×3)+(3×3)=18

(1+8)+(1+8)=18

SUL(3)⊗ SUR(3)all the particle belonging to the same chiral multiplet should degenerate

parity eigenstate scalar and pseudoscalar

dynamical argument was given by Lee and Hatsuda Lee, Hatsuda, PRD54, 1871 (1996)

axial trans.mixes octetand singlet

both singlet and octet belong to the same multiplet without U(3)

σ ↔ π a0 ↔ η[Qa

A,φB5 ] = q

λa

2 , λB

2

q = daBCφC



η’ meson in chiral restoration

13

When chiral symmetry is restored... DJ, Nagahiro, Hirenzaki, arXiv:1109.0394 [nucl-th]

manifest chiral sym. broken chiral sym.

π,K, η8, η0

π,K, η8

η0

massless

UA(1) anomaly

massive

π,K, η8, η0 σ, a0,κ, f09 PS 9 S get degenerate

even though UA(1) anomaly exists in the singlet axial current

η-η’ mass difference comes from the anomaly effect through the quark condensate at the chiral limit.

the UA(1) anomaly can affect the η’ mass only through (spontaneous and/or explicit) chiral symmetry breaking.



η’ meson in nuclear matter

14


nonchiral gluon field cannot couple to chiral pseudoscalar stateswithout explicit and/or dynamical chiral symmetry breaking.

η’

PCAC anomaly

∂µA(0)µ = 2i(muuγ5u + mddγ5d + mssγ5s) +

3αs

8πF a

µνFµνa

divergence of axial current

R

LL RL

L RR

L R



η’ meson in nuclear matter

15

qq

LD

UA(1) anomaly contributes η’ mass through ChSB

we expect strong mass reduction in nuclei

(with 35% PRChS and mη’ - mη ≈ 400 MeV)

Δmη’ ~ 150 MeV

If partial restoration of chiral symmetry takes place in nuclear matter

‘t Hooft - Kobayashi - Maskawa interaction

NAGAHIRO, TAKIZAWA, AND HIRENZAKI PHYSICAL REVIEW C 74, 045203 (2006)

TABLE I. Input parameters determined in Ref. [59] and calcu-lated results in vacuum in three-flavor NJL model.

Input parameters Calculated results [MeV]

! = 602.3 [MeV] Mu,d = 367.6 fπ = 92.4gS!

2 = 3.67 Ms = 549.5 mπ = 135.0gD!5 = −12.36 〈uu〉1/3 = −241.9 mη = 514.8

mu,d = 5.5 [MeV] 〈ss〉1/3 = −257.7 mη′ = 957.7ms = 140.7 [MeV]

q2-dependence, θ cannot be interpreted as the η − η′ mixingangle. The origin of the q2-dependence is that the η and η′

mesons have the internal structures.We obtain the dynamical quark and meson masses in

vacuum as compiled in Table I with the input parameters de-termined in Ref. [59]. In Ref. [59], the four model parameters,namely, cutoff !, four-quark coupling constant gS , six-quarkcoupling constant gD and the current s-quark mass ms havebeen fixed so as to reproduce the observed values of the pion,kaon, η′ masses and the pion decay constant, while the currentu, d-quark mass has been fixed at 5.5 MeV, which has beentaken from the results of the chiral perturbation theory andQCD sum rule approaches. This parameter set gives an ηmass of mη = 514.8 MeV, which is about 6% smaller than theobserved value mη = 547.75 MeV. One is able to fit the mass ofη instead of the η′. The reason why we have used the presentparameter set is just we are more interested in the η′-mesicnucleus than the η-mesic nucleus in this article because weconsider that the former is more suitable for observing thefinite density effect of the UA(1) anomaly.

In this paper, we investigate the finite density effects onthe meson mass spectra for the following three cases with thedifferent strengths gD of the determinant KMT interaction as

(a) gD(ρ) = gD

(b) gD(ρ) = 0 (19)

(c) gD(ρ) = gD exp[−(ρ/ρ0)2],

where gD is the vacuum strength of the determinant interactionas shown in Table I. The gD(ρ) has no density dependence forcases (a) and (b). In case (a), the meson vacuum propertiesare well reproduced as shown in Table I, while there are noanomaly effects in case (b). For gD = 0 case, we use slightlydifferent parameter set as shown in Table I in Ref. [60] toreproduce the meson masses and the pion decay constant invacuum without anomaly effect. In case (c), we simply assumethe density dependence of gD as this form in order to examinethe medium effect due to density dependence of gD itself onthe meson mass spectra in finite density.

Here it may be interesting for our study to notice that thereare theoretical suggestions about possible density dependenceof gD [61,62]. In Ref. [62], the effective coupling constantof the instanton-induced interaction is suggested to havechemical potential dependence for Nf = 2 systems. For Nf =3 systems, we can expect to have the similar µ dependence,though it is not easy to show explicitly. We are interested instudying the effect of such density dependence discussed inRef. [62] on meson mass spectra as future works.

(a) (b) (c)

FIG. 1. Density dependence of the quark condensates in theSU(2) symmetric matter, ρu = ρd and ρs = 0, where 〈uu〉 = 〈dd〉.Three panels correspond to the cases (a), (b), and (c) defined inEq. (19), respectively. The nucleon density ρ is defined in Eq. (7) andρ0 is the normal nuclear density ρ0 = 0.17 fm−3.

In Fig. 1, we show the calculated quark condensates asfunctions of density for three types of gD(ρ) defined inEq. (19). In case (b), we have switched off the effect of theinstanton-induced flavor mixing interaction and therefore thes-quark condensate has not changed in the SU(2) symmetricmatter. The absolute values of the u,d-quark condensatedecreases significantly faster in case (c) than in case (a) whenthe density goes up. It means that the contribution of theinstanton-induced interaction on the u,d-quak condensate issizable.

In Fig. 2, we show the calculated density dependence of themeson mass spectra for three cases defined in Eq. (19). In thecase of constant gD (a), we find that the mass of η′ decreasesrapidly as a function of the density, while the masses of π and ηgradually increase. The instanton-induced interaction is repul-sive for the flavor singlet qq channel and the effective couplingstrength is gD(〈uu〉 + 〈dd〉 + 〈ss〉)/3. Since the absolute val-ues of the quark condensates decrease as the density increase,the effective repulsive interaction in the flavor singlet qq chan-nel becomes small as the density increases. That is the reasonwhy the η′ mass decrease. In Fig. 2(b), we find that π and η aredegenerate completely and their masses increase gradually asdensity, and the mass of η′ has no density dependence withoutthe UA(1) anomaly effects. Without the UA(1) anomaly effects,

(a) (b) (c)

FIG. 2. Density dependence of the meson mass spectra. Threepanels corresponds to the cases (a), (b), and (c) defined in Eq. (19),respectively. The nucleon density ρ is defined in Eq. (7) and ρ0 is thenormal nuclear density ρ0 = 0.17 fm−3.

045203-4

NJL model

Nagahiro, Takizawa, HirenzakiPRC74,045203 (2006)

See also, P. Costa, M. C. Ruivo, and Y. L. Kalinovsky,Phys. Lett. B560, 171 (2003).



Narrow width ??

16

qq

LD

UA(1) anomaly contributes η’ mass through ChSB

This mass reduction does not directly come from nuclear many-body interaction. Thus the width may be smaller than binding energy.

contact interaction in hadronic level

elastic η’ N → η’ N

η’ N → π N

nuclear many body effects

absorption η’ N N→ N N

η’ N → N*attraction

attraction coming from suppression of anomaly effect

suppression of anomaly effect selectively affects η’ channel

Δm ~ 150 MeV > Γ

no hadronic imaginary part



Current experimental status

17

RHIC: phenix/star (low energy pion)η’ mass reduction of at least 200 MeV

Csorgo, Vertesi, Sziklai, PRL 105 (2010) 182301

CB-ELSA/TAPS

in the medium: !" = quasiparticle; properties reflect interaction with the medium;additional inelastic channels remove !"-mesons, e.g. !" N# $ N

transparency ratio:

!

TA ="#A$%'X

A& "#N$%'X

normalized to 12C

comparison with TA for ! meson"" absorption weaker than ! absorption

%(T,A) ∝ A!(T) ; A! scaling lawfor & and ": '=0.67 for !"-?

" absorption properties

T. Mertens et al., EPJA 38 (2008) 195

secondary production processes ?($N#!’N)"’ reproduced with smaller Tkin

’’ for Tkin> (E -m ’)/2

A

T A E =1200-2200 MeV

0.3

0.4

0.5

0.60.70.80.91

10 102

’’ for Tkin> (E -m ’)/2

A

T A E =1200-2200 MeV

0.3

0.4

0.5

0.60.70.80.91

10 102

’’ for Tkin> (E -m ’)/2

A

T A E =1200-2200 MeV

for Tkin> (E -m )/20.3

0.4

0.5

0.60.70.80.91

10 102

in-medium properties of "‘ meson

17

Nanova, talk at Baryon2010

in the medium: !" = quasiparticle; properties reflect interaction with the medium;additional inelastic channels remove !"-mesons, e.g. !" N# $ N

transparency ratio:

!

TA ="#A$%'X

A& "#N$%'X

normalized to 12C

comparison with TA for ! meson"" absorption weaker than ! absorption

prelim

inary

%(T,A) ∝ A!(T) ; A! scaling lawfor & and ": '=0.67 for !"-?

" absorption properties

T. Mertens et al., EPJA 38 (2008) 195

secondary production processes ?($N#!’N)"’ reproduced with smaller Tkin

’’ for Tkin> (E -m ’)/2

A

T A E =1200-2200 MeV

0.3

0.4

0.5

0.60.70.80.91

10 102

’’ for Tkin> (E -m ’)/2

A

T A E =1200-2200 MeV

0.3

0.4

0.5

0.60.70.80.91

10 102

’’ for Tkin> (E -m ’)/2

A

T A E =1200-2200 MeV

for Tkin> (E -m )/20.3

0.4

0.5

0.60.70.80.91

10 102

in-medium properties of "‘ meson

17

transparency ratio

!" transparency ratio compared with theoretical calculations A.Ramos and E. Oset

E =2.1 GeV

A

T A

’exp data( 0)=10 MeV( 0)=15 MeV( 0)=20 MeV( 0)=25 MeV( 0)=30 MeV( 0)=35 MeV( 0)=40 MeV

0.6

0.7

0.8

0.9

1

102

E =1.9 GeV

A

T A


0.6

0.7

0.8

0.9

1

102

TA =σγA→V X

AσγN→V X

⇒in-medium width:

comparison to data #($0,<|p!’|> % 0.9 GeV/c) % 25-30 MeV !’ is broadened in the medium

!" in-medium width

E =1.7 GeV

A

T A


0.6

0.7

0.8

0.9

1

102

19

= 14 mb⇒ σηN =Γinel

ρ · β · · c

COSY

Moskal et al, PLB482(2000) 365

pη’ scatt. length ~ 0.1 fm (Δm~10MeV)

final state interaction pp → η’pp



Missing mass spectroscopy

18

observe spectra of final nucleon

identification of meson in nuclei (energy, isospin,decay,...)

η: N(1535)→πN K: Λ(1405)→πΣ

formation reaction of bound states

(missing mass)

observing decays helps to reduce the background

nucleon pick-up

recoilless

s−1N ⊗ sm, p−1

N ⊗ pm, . . .

selection rule

convolution of hole states and meson partial waves



Formation spectrum

19

pπ=1.8 GeV/c12C(π+, p)

dσ

dΩ

lab.

= 100µb/st

H. Nagahiro, PTPS 186, 316 (2010)

π+n→ pη

q=200MeV/c

p3/2 hole

s1/2 hole

elementary cross section (reference)

Vη(r) = V0ρ(r)ρ0

η’ potential (Wood-Saxon type)


Δm = 150 MeVΓ/2 = 20 MeV

J-PARC



Formation spectrum

19


dσ

dΩ

lab.

= 100µb/st

H. Nagahiro, PTPS 186, 316 (2010)

π+n→ pη

q=200MeV/c

p3/2 hole

s1/2 hole


Vη(r) = V0ρ(r)ρ0



16 NFQ

CD

10, J

oint

Sym

posi

um o

f the

ory

and

expe

rimen

t in

“Had

rons

in n

ulei

”

(( ++,p,p) spectra : ) spectra : 1212C target C target : incident energy dependence: incident energy dependence

EEexex –– EE00 [[MeVMeV]]00 5050 100100 150150--5050--100100

EEexex –– EE00 [[MeVMeV]]00 5050 100100 150150--5050--100100

2020

1010

1515

55

002020

1010

1515

55

00

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

Chiral unitary modelChiral unitary model

= 820 = 820 MeVMeV (p(p

= 950 = 950 MeV/cMeV/c))

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

Chiral unitary modelChiral unitary model

EEexex –– EE00 [[MeVMeV]]00 5050 100100 150150--5050--100100

= 650 = 650 MeVMeV (p(p

= 777 = 777 MeV/cMeV/c))

recoilless position

8080

6060

4040

2020

00

6060

4040

2020

00

Δm = 150 MeVΓ/2 = 20 MeV

J-PARC



Formation spectrum

19


dσ

dΩ

lab.

= 100µb/st

H. Nagahiro, PTPS 186, 316 (2010)

π+n→ pη

q=200MeV/c

p3/2 hole

s1/2 hole


Vη(r) = V0ρ(r)ρ0



Δm = 150 MeVΓ/2 = 20 MeV

J-PARC



Formation spectrum

19


dσ

dΩ

lab.

= 100µb/st

H. Nagahiro, PTPS 186, 316 (2010)

π+n→ pη

q=200MeV/c

p3/2 hole

s1/2 hole


Vη(r) = V0ρ(r)ρ0



Re V0 −150 MeVIm V0 −20 MeV

s (93.5, 34.0)(21.9, 19.1)

p (56.3, 27.7)d (21.0, 20.8)

Δm = 150 MeVΓ/2 = 20 MeV

J-PARC



Conclusion

20

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

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。

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

η’ 質量生成は、カイラル対称性の破れと UA(1) anomaly の”共演”

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

100 MeV オーダーの質量減少と30 MeV 程度の吸収幅

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

UA(1)問題に対して、有益な実験的情報を得ることを期待

実験：12C(p,d)反応 @ GSI, LoI 提出（板橋さん、藤岡さんら）


カイラル対称性の部分的回復とη 中間子原子核 - kekd. jido (yukawa institute,...

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