Tokyo Metropolitan University K.Aoki and D.Jido 2016.12.01,02 - - PowerPoint PPT Presentation

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Tokyo Metropolitan University K.Aoki and D.Jido 2016.12.01,02 - - PowerPoint PPT Presentation

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Tokyo Metropolitan University K.Aoki and D.Jido 2016.12.01,02 ELPH C015 1. INTRODUCTION Nucleus-hadron systems & par4al restora4on of

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Tokyo Metropolitan University K.Aoki and D.Jido

2016.12.01,02 ELPH 研究会 C015 マルチフレーバーで探るエキゾチックハドロンとハドロン多体系の物理

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  • 1. INTRODUCTION
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★Purpose of study. To prove spontaneous breaking of chiral symmetry from experimental fact. Chiral symmetry is parKally restored in finite density nuclear medium. We implant hadron into nucleus (hadron-nucleus system). Hadrons change their properKes in nuclear medium. ーIn-medium hadron-nucleon interacKons

  • vs. In-vacuum hadron-nucleon interacKons.

ーreducKon of magnitude of quark condensate. Prove reducKon of magnitude of quark condensate by restoring broken chiral symmetry . Nucleus-hadron systems & par4al restora4on of chiral symmetry

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  • Deeply bound pionic atoms.
  • π meson-nucleus elasKc scaTering.

＋theoreKcal consideraKon chiral symmetry is restored about 30%.

Friedman et al. PRL93, 122302 (2004)

Jido,Hatsuda,Kunihiro, PRD63,011901(2001) Kolomeitsev,Kaiser,Weise, PRL90 092501(2003) Jido,Hatsuda,Kunihiro, PLB670,109 (2008)

K.Suzuki et al. PRL92, 072302 (2004)

present status of par4al restora4on of chiral symmetry For NG boson wavefuncKon renormalizaKon

  • One of the higher order correcKon beyond tρ approximaKon
  • In-medium self-energy has strong energy-dependence

wavefuncKon renormalizaKon has large contribuKon low-energy QCD effecKve theory (chiral perturbaKon theory) NG bosons are wriTen as their energy expansion. ️ NG boson-nucleon interacKon has strong energy-dependence. wavefuncKon renormalizaKon is important as in-medium effects

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connecKon of wavefuncKon renormalizaKon & parKal restoraKon of chiral symmetry

Jido,Hatsuda,Kunihiro, PRD63,011901(2001)

low energy QCD effecKve theory [chiral perturbaKon theory] consistent with original chiral symmetry

  • angular direcKon: NG boson (pion)
  • radial direcKon: σ mode

U = exp  i~ ⇡ · ~ ⌧ F

  • angular variable = dimensionless
  • pion field has energy dimension
  • F has energy dimension

= pion decay constant =quark condensate. parKal restoraKon of chiral symmetry. F is change. renormalizaKon of pion field.

V(π, σ) π σ mσ

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Further studies. Does parKal restoraKon of chiral symmetry systemaKcally occur in

  • ther than pion-nucleus systems?

OUR STUDY K+ meson – nucleus system. ️K+N amplitude. ・elementary process of K+-nucleus interacKons. ️K+ self-energy in nuclear medium. ・Taking into account all possible medium effect.

  • nucleon Fermi moKon
  • mass modificaKon
  • vertex correcKon
  • ️wavefuncKon renormalizaKon

Our goal ・EvaluaKng reducKon of magnitude of quark condensate from in-medium K+N interacKon

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Further studies. Does parKal restoraKon of chiral symmetry systemaKcally occur in

  • ther than pion-nucleus systems?

OUR STUDY K+ meson – nucleus system. ️✔️K+N amplitude. ・elementary process of K+-nucleus interacKons. ️K+ self-energy in nuclear medium. ・Taking into account all possible medium effect.

  • nucleon Fermi moKon
  • mass modificaKon
  • vertex correcKon
  • ️✔️wavefuncKon renormalizaKon

Our goal ・EvaluaKng reducKon of magnitude of quark condensate from in-medium K+N interacKon

・large contribu4on as one of the in-medium effect. ・rela4on to par4al restora4on of chiral symmetry.

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  • 2. Overview of K+ - nucleus system.
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K+ - nucleon interac4on ★K+N interacKon is repulsive and relaKvely weak.

ーmean free path in nuclear medium is as large as 5 fm. ーcomparable to typical nucleus size.

Single step K+N interacKon should be dominant. [MulKple scaTering could be negligible.]

  • Only K+ exists in nuclear medium.
  • It is relaKvely easy to consider in-medium effect to K+.

★K+N interacKon has S= +1.

ーThere is no strong resonance.

K+ is considered to be clean hadronic prove. In contrast to S=−1 KbarN interacKon. ーStrong aTracKve interacKon and quasi bound state Λ(1405)

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K+ - nucleus interac4on. ★ExpectaKon from K+N interacKon. Single step K+N interacKon should be dominant. [MulKple scaTering could be negligible.]

σ(K+A) ' Aσ(K+N) plab < 800MeV/c

★Experimental data…total cross secKon per nucleon.

σ(K+ 12C)/12 σ(K+d)/2 > 1

linear density approximaKon is not valid.

D.V.Bugg, et al Phys.Rev. 168(1968) 1466.

★OpKcal potenKal… linear density (low density) approximaKon is not valid.

2ωK+Vopt = T(K+N)ρ

1.2 at plab=450 MeV/c

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Table 1 raKo of K+- nucleus opKcal potenKal. tρ: Fits to K+-nucleus scaTering data (experiment).

E.Friedman,A.Gal Phys.Rept. 452(2007) 89

tfreeρ: In-vacuum K+N interacKon (expectaKon). ・|tfreeρ| is increased by 14 – 34 % by in-medium effects. ・ImX is small compared to ReX.

|tρ| = X|tfreeρ|

in-medium effects

experiment expectaKon

積分を実行すると次のような方程式が得られる のとき の解を持つ 結合の強さがある程度まで大きくなるとクォークの質量は と なる 表 表 異なるポテンシャルを用いた のフィット

PLAB [MeV/c] VOP T Reb0 [fm] Imb0 [fm] X ≡ |

tρ tfreeρ|

|arg(

tρ tfreeρ)| [deg]

488 tρ

  • 0.203(26)

0.172(7) 1.14 0.33 tfreeρ

  • 0.178

0.153 531 tρ

  • 0.196(39)

0.202(9) 1.17 1.27 tfreeρ

  • 0.172

0.170 656 tρ

  • 0.220(50)

0.262(12) 1.27 2.31 tfreeρ

  • 0.165

0.213 714 tρ

  • 0.242(53)

0.285(15) 1.34 5.15 tfreeρ

  • 0.161

0.228

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  • 3. Method
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️✔️K+N amplitude. ・elementary process of K+-nucleus interacKons. ️K+ self-energy in nuclear medium. ・Taking into account all possible medium effect.

  • nucleon Fermi moKon
  • mass modificaKon
  • vertex correcKon
  • ️✔️wavefuncKon renormalizaKon

Outline

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K+N amplitude(1)

K+p → K+p K+n → K+n

Using the 3-flavor chiral perturbaKon theory up to NLO. χ2 fits to the exparimental data. I=1 (2 parameters) & I=0 (2 parameters)

Weinberg-Tomozawa Born (crossed) NLO

fK

D = 0.80, F = 0.46

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  • Tree-level calculaKon…Amplitude is real.

We want to calculate the imaginary part.

  • We want to reproduce more wide energy range data.

★ UnitalizaKon Summing up higher order diagrams to saKsfy unitarity of amplitude.

= + + +・・・

New parameter is appearing. SubtracKon constant a. K+N amplitude(2)

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χ2 fits to the experimental data. common parameter ・・・subtracKon constant a

Isospin1 Isospin0

K+N amplitude(3) I=1 DifferenKal cross secKon PLAB = 726MeV/c (many data) I=0 Total cross secKon PLAB = 350 ∼ 800MeV/c (less data)

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️K+ self-energy in nuclear medium. ・Taking into account all possible medium effect.

  • nucleon Fermi moKon
  • mass modificaKon
  • vertex correcKon
  • ️✔️wavefuncKon renormalizaKon

️✔️K+N amplitude. ・elementary process of K+-nucleus interacKons. Outline

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wavefuncKon renormalizaKon

Σ = T(K+N)ρ

  • K+ self-energy

describe interacKon with nuclear medium.

Z ' 1 + ∂Σ ∂E2

  • E2=ω2

K+

  • WavefuncKon renormalizaKon factor.

2ωK+Vopt = ZT(K+N)ρ

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  • 4. Results
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bI=1=6.18×10-4 dI=1=3.00×10-4 [MeV-1] a=-1.224

2 4 6 8 10 12 14 16 100 200 300 400 500 600 700 800 TOTAL CROSS SECTION [mb] PLAB [MeV/c] ChPT Bugg 1968 Bowen 1970 Adams 1971 Bowen 1973 Carroll 1973 Cameron 1974

  • DifferenKal cross secKon

at PLAB=726 MeV/c.

  • χ2/N =0.68

I=1 TOTAL CROSS SECTION

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bI=0=4.13×10-4 dI=0=-9.80×10-4 [MeV-1] a=-1.224

5 10 15 20 25 100 200 300 400 500 600 700 800 TOTAL CROSS SECTION [mb] PLAB [MeV/c] ChPT Bowen 1970 Bowen 1973 Carroll 1973

  • Total cross secKon

Plab = 350 ー 800 MeV/c

  • χ2/N =6.85

I=0 TOTAL CROSS SECTION

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Table 2 wavefuncKon renormalizaKon factor Z .

Z ' 1 + ∂Σ ∂E2

  • E2=ω2

K+

[evaluated at saturaKon density] Weinberg-Tomozawa term evaluated at threshold: |Z| = 1.08 ・At low-energy |tfreeρ| is increased by about 10 % only by wavefuncKon renormalizaKon.

|tρ| = |Z||tfreeρ|

[our calculaKon] [literature values]

|tρ| = X|tfreeρ|

・ImZ is small compared to ReZ.

積分を実行すると次のような方程式が得られる のとき の解を持つ 結合の強さがある程度まで大きくなるとクォークの質量は と なる 表

PLAB [MeV/c] |Z| |arg(Z)| [deg] X ≡ |

tρ tfreeρ|

|arg(

tρ tfreeρ)| [deg]

488.0 1.11 3.87 1.14 0.33 531.0 1.09 1.68 1.17 1.27 656.0 1.04 0.04 1.27 2.31 714.0 1.03 0.11 1.34 5.15

表 異なるポテンシャルを用いた のフィット

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  • 5. Summary & Outlook
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Summary

  • We have calculated wavefuncKon renormalizaKon as one of the

in-medium effect.

  • Only wavefuncKon renormalizaKon, |tfreeρ| is increased by 3- 11 %.
  • We have constructed K+N elasKc scaTering amplitude based on chiral

perturbaKon theory.

  • We have carried out unitalizaKon.
  • To determine low-energy constants and subtracKon constant , we

have carried out χ2 fit.

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Outlook Taking into account other in-medium effects. ーFermi moKon ーmass modificaKon ーvertex correcKon 3-flavor in-medium chiral perturbaKon theory. Whether wavefuncKon renormalizaKon is large compared to

  • ther in-medium effects or not.

more precise calculaKon of K+ self-energy.