京都大学21COEプログラム「物理学の多様性と普遍性の探求拠点」外国旅費補助による国際会議参加報告

Strong matter in the heavens, Johns Hopkins Workshop (satellite workshop of Quark matter 2005)

1-3, Aug 2005Quark Matter 2005, international conference, 4-9, Aug,2005

Eötvös University, Budapest, Hungary

遠藤 友樹原子核理論研究室

T

Hadron Phase

µ0

Quark Gluon Plasma

古城

津村

名和

遠藤

Hadron-quark mixed phase

HQ(Hadron-Quark)分野の動向“QCD相図を描く”

ペンタクォーク、エキゾチックバリオン

Color Superconductivity

lattice QCD

Kaonic nuclei 中性子星

RHIC

J-PARC

※簡単な相図

The candidate of quark starRX J185635-375 (2002) The pulsar in the Crab nebula

SN 1987A in the Large Magellanic Cloud

“宇宙の実験室”中性子星

D. Page

中心密度～1015 g/cm3

(1cm3で10億t)超高密度⇒“構成は核子？”

強磁場～1012 G

超強磁場中性子星（マグネター）

～1015 G

物質のエキゾチック状態

観測からの問題

グリッチ現象冷却問題他

観測からの問題

グリッチ現象

冷却問題

“星震”説 π凝縮？

“渦糸のピンはずれ”説：有力

“冷却曲線をひく”

“ハドロン・クォーク混合相？”

Neutron super-fluidity

Color superconductivity

非一様構造？

Lyne et al (1969-1993)

原子核分野からのアプローチ物質の状態方程式: “EoS” (Equation of State）を作る

核物質のEoS

クォーク物質のEoS

対称核物質の実験値の再現様々な理論計算：未だ成功せず⇒

何かが足りない？Ex.３体力の効果：扱いが難しい

Color superconductivity

BCS or BEC

強磁性相: spin polarized phase

核力が正確に分かっていない：核力は複雑

MIT Bag模型

活発に研究されている

Toki et al (2000)

Coester line

ハドロン・クォーク間の相転移

低温・高密度：1次相転移

ハドロン・クォーク混合相がどれくらい現れるか？

応用：星の物理現象にも影響する ⇒観測との比較

Q H

ハドロン・クォーク混合相(自分の仕事)

核物質：有効ポテンシャルを用いるパラメータ調節で実験値に合わせる

クォーク物質：Bagモデル、Unpaired Quark Matter

※各々の物質としては簡単なEoS

有限サイズ効果表面張力効果クーロン遮蔽効果

Hadron-quarkinterface:

unknown…

F.Weber

Strong Matter in the Heavens Budapest, August 1-3 2005 29th Johns Hopkins Workshop in Theoretical Physics (a thematic satellite workshop of the Quark Matter '05 International Conference)

Venue: Budapest, Eötvös University Faculty of Science

Registration is closed. Map Transport Information

Conference Poster

Main subjects: •Equation of State •Strange matter and other exotic phases •Structure and dynamics of compact stars •Cosmological significance •Cosmic Rays •Strong Interactions beyond Standard Model•The workshop consists of 17 invited talks of 40 min. duration + 14 short contributed talks (20 min.)

Johns Hopkins Workshop(QM2005のサテライト会議)と同じ場所（エトベシュ大学）でJHWと連続して開催。

JHW：口頭発表（２０分＋５分）QM2005：ポスター発表 ※QM2005期間中の滞在費は補助、登録料は自己負担

JHW（8月1日～3日）

QM2005（4日～9日）

約100名程度

アメリカ：＞10名ドイツ：＞10名日本：３名

ハンガリー：３～４割

イギリスイタリアオーストリアオランダ韓国

クロアチアスウェーデンスペインデンマークフランスメキシコ他

登録：784名（出席600名以上）

アメリカ：＞200名日本：30名程度

Charge screening effect on hadron-quarkmixed phase in compact stars

Strong matter in the heavens, Johns Hopkins Workshop 1-3, Aug 2005

Tomoki EndoDepartment of Physics, Kyoto University, Japan

Collaboration with

Toshiki Maruyama A, Satoshi Chiba A, Toshitaka Tatsumi B

ASRC, Japan Atomic Energy Research Institute, Tokai, Japan A,Department of Physics, Kyoto University, Japan B

Plan of this talkPlan of this talkMaxwell construction and Gibbs conditionMaxwell construction and Gibbs conditionGeometrically structured mixed phaseGeometrically structured mixed phaseScreening effectScreening effect on the range of geometrically structured mixed phaseon the range of geometrically structured mixed phaseSummarySummary

Maxwell construction is valid in single chemical potential system.

not valid

“Gibbs conditions”

Hadronquark PP = BHadron

Bquark µµ =

quark HadronT T= e equark Hadronµ µ=

Bulk calculation with Gibbs condition(No Coulomb nor Surface)

First order Phase Transition in First order Phase Transition in more than onemore than one chemical potential systemschemical potential systems

But,But, more than one more than one chemical potential ?chemical potential ?

watervapor PP =

watervapor µµ =

watervapor TT =

water – vaporMaxwell Gibbs conditions

N.K.Glendenning,PRD46(1992)1274

ex. pion condensation, kaon condensation,hadron-quark mixed phase

“Gibbs conditions”

Naive “Maxwell construction”

Hadron matter (charge neutral)p , n , e

Quark matter (charge neutral)u , d , s(150 MeV) , e

Quark matter (charged)Hadron matter (charged)

0)1( =−+ Hadronquark QffQf Volume fraction

Uniform matter

mixedphase

≡

Total charge neutrality0)1( =−+ Hadronquark QffQ

f Volume fraction

Bulk calculation with Gibbs Condition“Bulk Gibbs”

; wide density area ,pressure is not constant

Mixed Phase

Maxwell ; narrow density area, pressure is constant

0

0

=

=

hadron

quark

Q

QLocal charge neutrality

d: dimensiond=3 : sphered=2 : rodd=1 : slab

1 dim

2 dim

)()(2 222 ffRe dQH

C Φ−= ρρπε 1)/21(1 )2]()211()2(2[)( −−− ++−−=Φ dfdfdf d

d

Rdf

Sσε =

Coulomb energy density

Surface energy density

here

CS εε +R

31

220 )()(

4⎟⎠⎞

⎜⎝⎛ Φ−= fedR d

QH ρρπ

σ

CS εε 2=

minimising with respect to

CS εε +

RRw

+-Heiselberg, Pethick and Staubo et al PRL70(1993)1355

“Quark droplet embedded in hadron matter”Including surface tension, mixed phase area become narrow.

And σ>90[MeV/fm2] , mixed phases are energetically unfavorable

: volume fraction f

Q

HBulk Gibbsσ=10

σ=60

σ=90

uniform (nucleon) , drop , rod , slab, tube, bubble, uniform(quark)“Geometrical structure appear”

drop rod slabUniform (nucleon)

CS εε +Add surface & Coulomb energy

tube bubble Uniform (quark)They didn’t solve the Poisson equation !

Voskresensky ,Yasuhira and Tatsumi, PLB541(2002)93；NPA723(2003)291

“Maxwell construction picture” ・・・solve Poisson equation with linear approximationwith screening effect

The Gibbs conditions are not fulfilled by the Maxwell construction ?e eq u a rk H a d ro nµ µ≠

e equark Hadronµ µ=

Because, If Coulomb potential is not takeninto account, density is

Here, when we deal with Coulomb potential appropriately, we can get the charged chemical equilibrium.

But, Coulomb potential is treated appropriately,

But , solved the Poisson equation analytically with RPA order approximation. They showed screening effect in some cases of mixed phase.

In this study, to include full Coulomb interaction in proper way,solve the Poisson equation numerically

without any approximation and calculate various geometrically structured mixed phases

Ⅱeµ

Ⅱen

Ⅰeµ

quark phase

nucleon phase

nucleon

quark

Quark : Phase Ⅰu , d ・・・masslesss ・・・massive ～150 [MeV]Bag constant : 120 [MeV/fm3]interaction : one gluon exchange

Nucleon : Phase Ⅱp,n ・・・nonrelativisticinteraction : effective potentialElectron : All space

RwR

Formalism We use the Wigner-Seitz approximation, space is dividedinto equal cells and each cell is charge neutral.Quark phase and nuclear phase are sharply separated by confinement picture with incorporating the MIT bag model.The most important point is electrons are in all space.

tot surface e VEΩ = Ω +Ω +Ω +Ω +Ⅰ Ⅱ

0=Ω

i

tot

δρδWe can get “equation of motion” from

VQii

i −=δρδεµ

gauge invariant form

Density profile (droplet case)

With screening

RwR

Screening effect

[MeV]

Surface tension : [MeV/fm2]

Decreasing or increasing of Charged particle densities

Rearrangement of charged particles

Hadron( + )Quark( - )

u

d

s

Quark( - )↑↓↓

Quark( 0 )

Without screening

60=σ

1189=Bµ

uρdρsρ

Debye screening lengthand structure size

R and Rcell become large

Debye screening lengthand structure size (droplet case)

R

surfaceenergy

Coulomb energy without screening

coulomb + surface

Coulomb energy with screening

Droplet become large(Ec+

Es)

/ dr

ople

t

σπ 24 R 3

34 Rπsurface energy (Es) droplet volume (Vq)

Es / Vq Ec / Vq 2R∝Rσ3

With Screening Without Screening

Screening length

Coulomb interaction

No Coulomb interaction“charge-neutral phase”

R

RwScreening length

R

Rw

qλ

eλ

qλ

eλ

“charge-neutral phase” means local charge neutrality Maxwell construction

Preliminary results

Surface tension

Lattice QCD (finite temperature)10 ~ 100 [Mev/fm2]

Kajantie et al NPB357 (1991)693Huang et al PRD42(1990)2864

DGL theory (hadron bubble)25~50 [Mev/fm2]

Monden et al PRC57(1998)2564

Maxwell Gibbs

“ Density discontinuity ”“Mixed Phase”

Hybrid star

Physical Implication

Non-radial oscillation modes as a probe of density discontinuities in neutron starsG. Miniutti, J. A. Pons, E. Berti, L. Gualtieri, V.Ferrari, Mon.Not.Roy.Astron.Soc. 338 (2003) 389

“the relation with gravitational waves”

Neutrino scattering by geometricallystructured mixed phase.

“glitch phenomena”; mixed phase should be narrow

M. Bejger, P. Haensel and J.L. Zdunik, astro-ph/0502348

Neutrino opacity

Summary and Future plans

Summary ;We studied geometrically structured hadron-quark mixed phase . Screening effect is important that it changes the picture of mixed phases. It could be said that the mixed phase path is nearly Maxwell construction picture. Equation of state for mixed phases in hadron-quark deconfinement transition

Physical Implication; Glitch Phenomena – “density discontinuity” Neutrino opacity – neutron star cooling

Future plans ; Other phase transition. ex. between hadron matter and CFL state Including kaon phase. Nuclear matter to Kaonic matter to quark matter. Finite Temperature effect

聴衆の反応

口頭発表＠JHW

Surface tensionは最近のLatticeの結果では小さいのではないか？ A. Patkos氏 (Eötvös)

幾何学的構造は実際には現れないのではないか？ F. Weber氏 (San Diego)

次はSurface tensionを出すのが仕事だね M. Alford氏(Washington)

ポスター発表＠QM2005

Maxwellの場合の密度不連続性と観測（グリッチ）との関連が興味深い A. Drago氏 ( Ferrara )

クォーク相をカラー超伝導状態とした場合の結果を見てみたい K. Rajagopal氏（MIT）

他にも貴重な質問・コメントをもらった

まとめ

自分の仕事の宣伝ができた。“こういうのは他で見たことがない、面白い。” D. Blaschke氏(Bielefeld)

QM2005は実験分野中心の会議：RHIC（STAR, FHENIX…）らの院生とも交流がもてた

日本の会議では会ったことが無い人、特に著名な研究者達と議論が出来たのは幸運。

⇒Fridolin Weber 氏(San Diego)とは後日、メールでプレゼンファイルを交換

…. It was really nice to meet you in Budapest, and I hope that we‘ll stay in touch.

Best wishesFridolin

貴重な機会となった

F. Weber 著 “Pulsars as Astrophysical Laboratoriesfor Nuclear and Particle Physics”

補助して頂きましてありがとうございました。