Suenaga-Murakami-Itou-Iida,
PRD 107, 054001 (2023)

1/21

有限密度2カラーQCDにおける線形シグマ模型の構築とその応用

末永 大輝 (理研 仁科センター)

Suenaga-Murakami-Itou-Iida,
PRD 107, 054001 (2023)

1. イントロダクション

2/21

・有限密度系QCD- 有限密度系のQCDの理解は、学術的にも天体物理的にも重要<latexit sha1_base64="DRyqCOvFqCK+/oDB9fqEDoYYr8Q=">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</latexit>

T

相図: Fukushima-Hatsuda (2017)

超新星爆発, 中性子星等µB<latexit sha1_base64="0N+T0u/RhsaR82d72Y7WDu9iv4E=">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</latexit>

クォーク非閉じ込め? カイラル対称性の回復? カラー超伝導相? etc.

- 問題点: 有限密度系QCDの理解は、有限温度系に比べて進んでいない(要因の一つ: 符号問題により格子QCD計算が容易でない)

Suenaga-Murakami-Itou-Iida,
PRD 107, 054001 (2023)

1. イントロダクション

3/21

・有限密度系の格子QCD?
- 2カラー (かつ偶数フレーバー) のQCDは符号問題を持たない→ 有限密度系での格子QCD計算が可能！

eg, G Aarts (2016) J. Phys.: Conf. Ser. 706 022004- 2カラーQCD相図のシミュレーション結果は、例えば・・・

Boz-Cotter-Fister-Mehta-Skullerud (2013)

Buividovich-Smith-Smekal (2020)

Suenaga-Murakami-Itou-Iida,
PRD 107, 054001 (2023)

1. イントロダクション

4/21

・有限密度系の格子QCD?
- 2カラー (かつ偶数フレーバー) のQCDは符号問題を持たない→ 有限密度系での格子QCD計算が可能！

eg, G Aarts (2016) J. Phys.: Conf. Ser. 706 022004- 2カラーQCD相図のシミュレーション結果は、例えば2カラーQCDの特徴
6 0
ダイクォーク凝縮相 (バリオン超流動相) hqqi =<latexit sha1_base64="3GSZTIx06mwO2op9kwWFPyg8oXM=">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</latexit>

・・・

Boz-Cotter-Fister-Mehta-Skullerud (2013)

Buividovich-Smith-Smekal (2020)

1. イントロダクション

Suenaga-Murakami-Itou-Iida,
PRD 107, 054001 (2023)

5/21

・有限密度系2カラーQCD研究- 相図に加え、ハドロン質量・輸送係数・グルーオン二点関数・ h ¯ i, h<latexit sha1_base64="UtUr3BPYeAu2VIHxBLT/+vrcA0U=">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</latexit>の密度依存性のシミュレーション結果もいくつかある

i, hLi 等

飯田さん伊藤さんのグループ···<latexit sha1_base64="2ctn5cm3kP4ifYT7S+av/6yPqGc=">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</latexit>

自身の研究アプローチ- 2カラー格子QCD計算を有益な有限密度系QCDの数値実験とみなしその結果に対して有効模型による理解を与える
有効模型による2カラー物質中のこれまでの研究
グルーオン二点関数: Suenaga-Kojo(2019), Kojo-Suenaga(2021), CSE効果: Suenaga-Kojo(2021),
音速のピーク: Kojo-Suenaga(2022), ハドロン質量: Suenaga-Murakami-Itou-Iida (2023)
トポロジカル感受率: Kawaguchi-Suenaga(2023)

Suenaga-Murakami-Itou-Iida,
PRD 107, 054001 (2023)

2. 有効模型

6/21

・Pauli-Gursey SU(4) 対称性- 2カラーのQCDラグランジアンは、SU(2)cの擬実性より以下に書き換えられる

LQC2 D = ¯i@

gs ¯Aa Tca =<latexit sha1_base64="cVRZtEVpPwvdRMFO3/SGgVw6m9k=">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</latexit><latexit sha1_base64="mHfHDntLCxR4wfljCDh5fQZ3oOk=">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</latexit>

†

i@µ µ

gs

†

Aaµ Tca µ= ( R , ˜L )T = (uR , dR , ũL , d˜L )T with ˜L =<latexit sha1_base64="8unulYZW7w6vCM4esjYFguSL3fY=">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</latexit><latexit sha1_base64="Ky/keRYDhWCsx2A1M3yTLWPEjys=">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</latexit>- 2フレーバーの場合<latexit sha1_base64="os6Hx+8GI7XTH7B0t2K5gPI3NX0=">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</latexit>- 4元パウリ行列- LQC2 D は、
<latexit sha1_base64="EFZalOBQcPi4t5ZpR8v0iXtcgYw=">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</latexit><latexit sha1_base64="iYkEtGLO94+vJ0VL5uCK4EApM/Q=">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</latexit>

µ

!g

= (1,

i

2 2
⌧c

⇤
L

)

(g 2 SU (4)) 変換の下で不変<latexit sha1_base64="uoaxbd0sRrCLfCp76gQmP8RPAxk=">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</latexit>- 2カラーQCDでは、”カイラル対称性は” SU(2)L×SU(2)R 対称性からSU(4)対称性に格上げされる
Pauli-Gursey SU(4) 対称性

Pauli (1957), Gursey (1958)

Suenaga-Murakami-Itou-Iida,
PRD 107, 054001 (2023)

2. 有効模型

7/21

・スピン0のハドロン場- カラー1重項・スピン1重項のクォーク双一次場を以下で定義する
Tj<latexit sha1_base64="sqSykD3127QX3+0v3t9eDfKFxEg=">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</latexit>

⌃ij ⇠

2 2
⌧c

i

with

<latexit sha1_base64="8unulYZW7w6vCM4esjYFguSL3fY=">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</latexit>= ( R , ˜L )T = (uR , dR , ũL , d˜L )T- ハドロン状態は以下で与える<latexit sha1_base64="Ykg027egGThtkuMO77zabiT1NKA=">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</latexit>

B⇠

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Hadron1p2<latexit sha1_base64="Jdl2gPSDLoKM07eB/lPvMoibtQY=">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</latexit>

T<latexit sha1_base64="74Hm2/udGg9+yOabNFoyjVJNwBw=">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</latexit><latexit sha1_base64="NhSodwVziQxO3AK4zB4qwumbuYU=">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</latexit>

T

a0
⌘
⇡
B (B̄)B 0 (B̄ 0 )<latexit sha1_base64="bVHQ9QteBs26XXzEwb0ouoO0ANg=">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</latexit>- 4 ⇥ 4 行列 ⌃ は右のように表現される<latexit sha1_base64="UURf4wFTmTzLWn24jUS1RepqqJc=">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</latexit><latexit sha1_base64="zkX1EYPsfK2UCvb39xmXVrdD+D0=">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</latexit>⌃ ! g⌃g T (g 2 SU (4))<latexit sha1_base64="uoaxbd0sRrCLfCp76gQmP8RPAxk=">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</latexit>⇠ ¯⇡ a ⇠ ¯i 5 ⌧fa<latexit sha1_base64="BdK0GtKGsX7kally/iUjy7DT4og=">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</latexit><latexit sha1_base64="BODNvlirYtqo/bUJQdFUNCrktoc=">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</latexit>C⌧c2 ⌧f2

0

B
1B⌃ = ⇠BB
2B@<latexit sha1_base64="CRu5gkbtgp0PdVoyLTZxQ+DG0KA=">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</latexit>0B 0 piB2 2i⌘+a00 i⇡ 0
4
+
a+
0 pi⇡
2 2

B 0 piB
2 2

0
i⇡
p
2 2
i⌘ a00 +i⇡ 0
4

JP
0+
0+
0
0
0+
0

Quark number0000+2( 2)+2( 2)i⌘+a00 i⇡ 0
4
a0 i⇡
p
2 2

a0

0
B̄ 0 piB̄2 2

cf, 3カラー・2フレーバーQCDでは ⌃ =<latexit sha1_base64="m1iRq9LuRotMFrFR+TVbLoGCyh4=">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</latexit>

Isospin
0
1
0
1
0
0

+
a+
0 pi⇡
2 2
i⌘ a00 +i⇡ 0
4
B̄ 0 piB̄
2 20+ i⇡ a ⌧ a

1
C
C
C
C
C
A

Suenaga-Murakami-Itou-Iida,
PRD 107, 054001 (2023)

2. 有効模型

8/21

・線形シグマ模型<latexit sha1_base64="CFauiCARyreZzwEA/N8kohKKf7w=">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</latexit>- 近似的に SU (4) 不変な線形シグマ模型ラグランジアンは以下で与えられる<latexit sha1_base64="MJl2Q8FLB6Q3hHSMfUoNDEXoAM4=">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</latexit>

L = tr[Dµ ⌃† Dµ ⌃]†2µ̄20 tr[⌃ ⌃]m<latexit sha1_base64="2ATJNyQ5VnPV1xIa41QYcyKflHI=">AAACaHichVG7SgNBFD1Z3/GRVQsVG0mIWIUbERUr0cbSVzTgI+yuYxyyL3Y3AQ3+gI2lipWCiPgZNv6AhZ+glgo2Ft5sFkSDeoeZOXPmnjtnZnTXlH5A9BhTmppbWtvaO+KdXd09CbW3b813yp4hcoZjOl5e13xhSlvkAhmYIu96QrN0U6zrpfna/npFeL507NVg3xVblla05a40tICpnFWg7fGCmqIMhTHSCLIRSCGKRUe9xiZ24MBAGRYEbASMTWjwuW0gC4LL3BaqzHmMZLgvcIg4a8ucJThDY7bEY5FXGxFr87pW0w/VBp9icvdYOYI0PdANvdI93dITffxaqxrWqHnZ51mva4VbSBwNrrz/q7J4DrD3pfrTc4BdTIdeJXt3Q6Z2C6OurxycvK7MLKero3RJL+z/gh7pjm9gV96MqyWxfI44f0D253M3grXxTHYyM7E0kZqdi76iHcNIYozfewqzWMAicnyuxDFOcRZ7VlRlQBmqpyqxSNOPb6EkPwG6gos9</latexit>

1tr[⌃† ⌃]

2

†
2
†
†
†
2 tr[(⌃ ⌃) ] + tr[H ⌃ + ⌃ H] + c(det⌃ + det⌃ )<latexit sha1_base64="53SThk5EOH+igF5pywot083+K7w=">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</latexit>

あらわな破れ<latexit sha1_base64="ls9XmLDjOODkjI+EIok7YK8R6FE=">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</latexit><latexit sha1_base64="5D/Lysxv1xW6CmYAcai4e608H80=">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</latexit>Dµ ⌃ = @µ ⌃iµq µ0 {J, ⌃} with J =<latexit sha1_base64="pxu8g6DeXS8ivO9bOb+TRrsCRUk=">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</latexit>

H = hq E with E =<latexit sha1_base64="BOmwf4MpjEWeJz92/b9vrZoJyvw=">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</latexit>

1cf, ¯ = 2<latexit sha1_base64="fG1GWwJWYmRTHWnNvtoQghhy+54=">AAACz3ichVHPSxtBFH7ZamujrbG9FHpZDIptIcwGqaUgiKXQY6JGBceE2XGynbq/mJlE7JLSa/sP9NBTC1JK/4xePHrx4J8gPVr0IujbzYLY0PYtO/Pme9/35psZN/alNoQcFawbQ8M3b43cLo6O3bk7Xpq4t6qjjuKiwSM/Uusu08KXoWgYaXyxHivBAtcXa+72i7S+1hVKyyhcMbux2AyYF8q25Mwg1Cq9oS5TCY217KWDPW/TtmI8cXpJtUcXpTdDa1o2V6iWXsCaVWpYp8Wb1ZcIYcG2n9gZgW4xzxNqgJYVH6eNHrVKZVIhWdiDiZMnZcijFpW+AYUtiIBDBwIQEILB3AcGGr8NcIBAjNgmJIgpzGRWF9CDImo7yBLIYIhu4+jhaiNHQ1ynPXWm5riLj79CpQ1T5JB8Jydkn/wgx+T8r72SrEfqZRdnt68VcWv844Pls/+qApwNvL5S/dOzgTY8y7xK9B5nSHoK3td33346WX6+NJVMk6/kF/r/Qo7ITzxB2P3N9+pi6TMU8QGcP697MFmtVpynldn6bHlhMX+KEXgIkzCD9z0HC/AKatDAfQ/gFC4KYNWtHeud9b5PtQq55j5cC+vDJb0RsdM=</latexit>

⇣

T

2 2 T
⌧c E

✓

0 1
1 0

◆

+

† 2 2
⌧c E

⇤

✓

1
0

0
1

◆

U (1)A アノマリー← クォーク化学ポテンシャルの導入← カレントクォーク質量の効果⌘

カイラル対称性の破れ方: SU (4) ! Sp(4)<latexit sha1_base64="gbFbaRJDQ69eVzMkrjN48ST2W04=">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</latexit>(hT Eh = E)<latexit sha1_base64="0O9c64rqM7FNF5OKg7S2N2pZehk=">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</latexit>- 線形シグマ模型の有用性→ パリティパートナー間の質量関係の理解が可能

パートナー

B(B̄) $ B 0 (B̄ 0 )⌘, ⇡ $ , a0<latexit sha1_base64="5YQlAuIV5LRraGJhfx9+SpRElfA=">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</latexit><latexit sha1_base64="4+t0eERMLJefUh+PEpzRGDJV2pc=">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</latexit>→ カイラル対称性が回復に近づく世界の議論が可能

Suenaga-Murakami-Itou-Iida,
PRD 107, 054001 (2023)

3. 結果

9/21

・平均場
<latexit sha1_base64="SUTbFbiUdHxh/SLVbqzhJVSxA+Y=">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</latexit>-

0 + , B(B̄) ! p + B(B̄) として、 0 と
2!

<latexit sha1_base64="ctJhlkGX9KA8nw7FtOXp5X92Xvo=">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</latexit><latexit sha1_base64="9I6TgHjpMaWsNNE9lKDTDE64YsE=">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</latexit>のギャップ方程式を解く
ダイクォーク凝縮 by lattice<latexit sha1_base64="VOrm0+UbPhQpkBOzgMH+kBOwSow=">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</latexit><latexit sha1_base64="aqKxsjob2ge/eioO/4OxhcumYLA=">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</latexit>

0 ⇠h

⇠

¯ i : カイラル凝縮

i T
h C 5 ⌧c2 ⌧f2 i + h.c. : ダイクォーク凝縮
2Iida-Itou-Lee (2019)<latexit sha1_base64="9I6TgHjpMaWsNNE9lKDTDE64YsE=">AAACaXichVFNLwNBGH66vuujLRfhIjYVp2YqDeIkODi26EfSNrK7BqP7ld1pExp/wMlNcCIRET/DxR9w8BPEkcTFwdvtJoLgnczMM8+8zzvPzOiuKXzJ2GNE6ejs6u7p7Yv2DwwOxeKJ4YLv1D2D5w3HdLySrvncFDbPSyFNXnI9rlm6yYt6bbm1X2xwzxeOvSH3XV61tB1bbAtDk0QVKivclNpmXGUpFsTET5AOgYowsk78GhVswYGBOixw2JCETWjwqZWRBoNLXBVN4jxCItjnOESUtHXK4pShEVujcYdW5ZC1ad2q6Qdqg04xqXuknECSPbAb9sLu2S17Yu+/1moGNVpe9mnW21rubsaORtff/lVZNEvsfqr+9CyxjfnAqyDvbsC0bmG09Y2Dk5f1hbVkc4pdsmfyf8Ee2R3dwG68Glc5vnaOKH1A+vtz/wSFmVR6NpXJZdTFpfArejGOSUzTe89hEavIIk/n7uEYpziLPCsJZVQZa6cqkVAzgi+hqB9V0IwB</latexit>-

0と<latexit sha1_base64="ctJhlkGX9KA8nw7FtOXp5X92Xvo=">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</latexit>とクォーク密度 ⇢ の µq 依存性<latexit sha1_base64="E2nmX2q/5mdp86ZxUWZAO8kSqB4=">AAACaHichVG7SgNBFD1Z3/GRqIWKjSRErMJEgoqVaGOZhzGBJITddaJD9uXuJqDBH7CxVLFSEBE/w8YfsMgnqKWCjYU3mwXRoN5hZs6cuefOmRnF0oTjMtYKSD29ff0Dg0PB4ZHRsVB4fGLbMeu2ynOqqZl2QZEdrgmD51zharxg2VzWFY3nldpGez/f4LYjTGPLPbB4WZd3DVEVquwSlSvp9cp+JRxlcebFXDdI+CAKP1Jm+AYl7MCEijp0cBhwCWuQ4VArIgEGi7gymsTZhIS3z3GEIGnrlMUpQya2RuMurYo+a9C6XdPx1CqdolG3STmHGHtkt+yVPbA79sQ+fq3V9Gq0vRzQrHS03KqEjqez7/+qdJpd7H2p/vTsoooVz6sg75bHtG+hdvSNw9PX7Gom1pxnV+yF/F+yFrunGxiNN/U6zTMXCNIHJH4+dzfYXownluLJdDK6tu5/xSBmEcECvfcy1rCJFHJ0rsAJznAeeJbC0pQ000mVAr5mEt9CinwCvwKLvw==</latexit><latexit sha1_base64="WfJmpo1FR6pKAvVlvAQXDBA3Uxg=">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</latexit>

mvac
⇡ /2
<latexit sha1_base64="jCgdZH7Gygn11Qj1yWMmklnGgzM=">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</latexit>

例えばインプットを以下に取る<latexit sha1_base64="7rmReOfFGgZmamfQTZezGsUKcAE=">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</latexit><latexit sha1_base64="yR0aZCvkCch9jFSLLKWIWm301U0=">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</latexit>

vac= 250 MeV0

1 = c = 0 (large Nc)

mvac⇡ = 738 MeV<latexit sha1_base64="wxN9X+QoGC33zLl8jF0TbgblWTM=">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</latexit>

vac
mvac
a0 /m⇡ = 2.18

lattice<latexit sha1_base64="apPzZOw2gu1qRFPaTMSQp7LeiH8=">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</latexit>

Murakami et alcf, 非線形表現 by Kogut et al (2000)

Suenaga-Murakami-Itou-Iida,
PRD 107, 054001 (2023)

3. 結果

10/21

・ハドロン質量の結果- 右の三通りのパラメーターでlarge Nc !
結果を示す
w/ anomaly !
<latexit sha1_base64="Kc73MffiJblVZhXGp8J7tB7q4OM=">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</latexit><latexit sha1_base64="9u5bcNR01pt7MqiNPvmVR/g65b4=">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</latexit>

Suenaga-Murakami-Itou-Iida,
PRD 107, 054001 (2023)

3. 結果

11/21

・ハドロン質量の結果- 右の三通りのパラメーターでlarge Nc !
結果を示す
w/ anomaly !
<latexit sha1_base64="Kc73MffiJblVZhXGp8J7tB7q4OM=">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</latexit><latexit sha1_base64="9u5bcNR01pt7MqiNPvmVR/g65b4=">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</latexit>

Set (I) の結果- 超流動相ではバリオン数が破れる$ B $ B̄ mixing (0+系)⌘ $ B 0 $ B̄ 0 mixing (0-系)<latexit sha1_base64="+aJa/km1sWnMdhswxR9Moivjc5E=">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</latexit><latexit sha1_base64="JGHgmacT5T2uTNay8MUsGWF/X7Q=">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</latexit>

Suenaga-Murakami-Itou-Iida,
PRD 107, 054001 (2023)

3. 結果

12/21

・ハドロン質量の結果- 右の三通りのパラメーターでlarge Nc !
結果を示す
w/ anomaly !
<latexit sha1_base64="Kc73MffiJblVZhXGp8J7tB7q4OM=">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</latexit><latexit sha1_base64="9u5bcNR01pt7MqiNPvmVR/g65b4=">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</latexit>

Set (I) の結果① ゼロ質量- 超流動相ではバリオン数が破れる② 押し下げられる① ゼロ質量粒子 ( U (1)B 破れのNGモード)<latexit sha1_base64="qD9FOeGNO+DzBpK4R49Sg2r9Hi4=">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</latexit><latexit sha1_base64="+aJa/km1sWnMdhswxR9Moivjc5E=">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</latexit>$ B $ B̄ mixing (0+系)⌘ $ B 0 $ B̄ 0 mixing (0-系)<latexit sha1_base64="JGHgmacT5T2uTNay8MUsGWF/X7Q=">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</latexit>② ⌘ 質量が押し下げられる (準位反発)<latexit sha1_base64="E6PLDeg0FvmNn+hmUMkd7R5aTZg=">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</latexit>

Suenaga-Murakami-Itou-Iida,
PRD 107, 054001 (2023)

3. 結果

13/21

・ハドロン質量の結果- 右の三通りのパラメーターでlarge Nc !
結果を示す
w/ anomaly !
<latexit sha1_base64="Kc73MffiJblVZhXGp8J7tB7q4OM=">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</latexit><latexit sha1_base64="9u5bcNR01pt7MqiNPvmVR/g65b4=">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</latexit>

Set (II) の結果① 縮退が解ける- 超流動相ではバリオン数が破れる<latexit sha1_base64="+aJa/km1sWnMdhswxR9Moivjc5E=">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</latexit>

mixing (0+系)$ B $ B̄
⌘ $ B 0 $ B̄ 0 mixing (0-系)<latexit sha1_base64="JGHgmacT5T2uTNay8MUsGWF/X7Q=">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</latexit>①<latexit sha1_base64="C2WO/PBxkVtwQi7FiUNomTcqzjw=">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</latexit>

1 項により , a0 の縮退が解ける<latexit sha1_base64="k/C3AlEsng+MtsdKd+A9ho0Yx0s=">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</latexit>

Suenaga-Murakami-Itou-Iida,
PRD 107, 054001 (2023)

3. 結果

14/21

・ハドロン質量の結果- 右の三通りのパラメーターでlarge Nc !
結果を示す
w/ anomaly !
<latexit sha1_base64="Kc73MffiJblVZhXGp8J7tB7q4OM=">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</latexit><latexit sha1_base64="9u5bcNR01pt7MqiNPvmVR/g65b4=">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</latexit>

Set (III) の結果① 縮退が解ける② 押し下げが緩和① 縮退が解ける- 超流動相ではバリオン数が破れる$ B $ B̄ mixing (0+系)⌘ $ B 0 $ B̄ 0 mixing (0-系)<latexit sha1_base64="+aJa/km1sWnMdhswxR9Moivjc5E=">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</latexit><latexit sha1_base64="JGHgmacT5T2uTNay8MUsGWF/X7Q=">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</latexit>① アノマリーにより , a0 や ⇡, ⌘ の縮退が解ける② アノマリーにより「押し下げ」が緩和される<latexit sha1_base64="zPYs4YpFD0tN2Xd2S1tFJ9axn/0=">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</latexit><latexit sha1_base64="k/C3AlEsng+MtsdKd+A9ho0Yx0s=">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</latexit>

Suenaga-Murakami-Itou-Iida,
PRD 107, 054001 (2023)

3. 結果

15/21

有効模型

・格子QCDとの比較 -Set (I) での比較-<latexit sha1_base64="ixeT2vGx0wfCucgnk3MWAiKZaSQ=">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</latexit>① ゼロ質量mixingによる縮退の観測<latexit sha1_base64="ixeT2vGx0wfCucgnk3MWAiKZaSQ=">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</latexit>

j 6= 0 の効果→(近似的に)ゼロ質量

j 6= 0 により相転移点が少し早い② 押し下げられる② 押し下げられる→

格子QCD (Murakami et al)① ゼロ質量mixingによる縮退の観測

押し下げられている

Suenaga-Murakami-Itou-Iida,
PRD 107, 054001 (2023)

3. 結果

16/21

・格子QCDとの比較 ‒アノマリーに着目有効模型

格子QCD (Murakami et al)

アノマリー効果無し

弱い押し下げ⇡ と ⌘ の縮退
<latexit sha1_base64="E6PLDeg0FvmNn+hmUMkd7R5aTZg=">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</latexit><latexit sha1_base64="OXwHuTtSz3FhPOQXwfNLPe9vWA0=">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</latexit>- ⇡ と ⌘ が縮退 (※ 非連結グラフが入っていない)<latexit sha1_base64="E6PLDeg0FvmNn+hmUMkd7R5aTZg=">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</latexit><latexit sha1_base64="OXwHuTtSz3FhPOQXwfNLPe9vWA0=">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</latexit>

大きなアノマリー効果あり- 非連結グラフを入れてもほぼ縮退のまま
弱い押し下げSuenaga-Murakami-Itou-Iida,
PRD 107, 054001 (2023)

3. 結果

17/21

・格子QCDとの比較 ‒アノマリーに着目有効模型

格子QCD (Murakami et al)

アノマリー効果無し

弱い押し下げconsistent⇡ と ⌘ の縮退
<latexit sha1_base64="E6PLDeg0FvmNn+hmUMkd7R5aTZg=">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</latexit><latexit sha1_base64="OXwHuTtSz3FhPOQXwfNLPe9vWA0=">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</latexit>- ⇡ と ⌘ が縮退 (※ 非連結グラフが入っていない)<latexit sha1_base64="E6PLDeg0FvmNn+hmUMkd7R5aTZg=">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</latexit><latexit sha1_base64="OXwHuTtSz3FhPOQXwfNLPe9vWA0=">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</latexit>

大きなアノマリー効果あり- 非連結グラフを入れてもほぼ縮退のまま
弱い押し下げ- ゼロ密度ではアノマリー効果は小さいが有限密度ではアノマリー効果が増幅される可能性

consistentSuenaga-Murakami-Itou-Iida,
PRD 107, 054001 (2023)

最新の研究(宣伝)18/21

・スピン1粒子を含む線形シグマ模型<latexit sha1_base64="2xSdoKNd64BcppkIhZH7heCy+7I=">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</latexit>

-

† µ
j

µ
ij ⇠

i で表されるスピン1粒子のフレーバー 4 ⇥ 4 行列を導入する<latexit sha1_base64="zkX1EYPsfK2UCvb39xmXVrdD+D0=">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</latexit>

スピン1 メソン

スピン1 ダイクォーク
cf, 3カラーのSHBとの対応

BS $ ⌃c (2455) [⌃c (2520)]<latexit sha1_base64="EtO4wR0CKbyYF/MfyvcjHjTrubA=">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</latexit>

BAS $ ⇤c (2595) [⇤c (2625)]<latexit sha1_base64="Zn1VaMI9reIBx5Os9AczuOFDhZQ=">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</latexit><latexit sha1_base64="zwqK7L7/ub2jMX4PdjkYpdci1Bk=">AAACa3ichVG7SgNBFD1ZXzE+Ek0jaiGGiFWYSFCxCtpY5mE0YFR21zEZsi92N4EY/AFLG4vYKIiIn2HjD1jkE0SsIthYeLNZEBX1LrNz5sw9d87cUSxNOC5j7YDU1z8wOBQcDo2Mjo2HIxOT245Zs1VeUE3NtIuK7HBNGLzgClfjRcvmsq5ofEepbnT3d+rcdoRpbLkNi+/pctkQR0KVXaKKpUxF7Jf02kEkxhLMi7mfIOmDGPzImJEblHAIEypq0MFhwCWsQYZD3y6SYLCI20OTOJuQ8PY5ThAibY2yOGXIxFbpX6bVrs8atO7WdDy1SqdoNGxSziHOHtkt67AHdsee2PuvtZpeja6XBs1KT8utg/DpVP7tX5VOs4vKp+pPzy6OsOp5FeTd8pjuLdSevn583smv5eLNBXbFnsn/JWuze7qBUX9Vr7M810KIHiD5vd0/wfZSIrmcSGVTsfS6/xRBzGAei9TvFaSxiQwKXp/P0MJF4EWKStPSbC9VCviaKL6EFP8AS7yM6A==</latexit>-µ<latexit sha1_base64="6p7t434hriX8eYejBngi5uxiXk8=">AAACknichVG7TuNAFD0YlkdYIDwKJBqLCAQF0QRFgKh4NBQUgRBAikNkO4MZ4ZfsSSSI+AFaCgoqVlohxBfQQsMPUPAJiBIkGoq9cbxaLQi4lmfOPXPPnTMzhm+LUDL20KK0tv1o7+jsSnT/7OntS/YPbIZeNTB5wfRsL9g29JDbwuUFKaTNt/2A645h8y1jf7mxvlXjQSg8d0Me+Lzk6JYrdoWpS6LKySkttyd2NKeqSU+1/iaqtaNVdMvigaYWLU24ar4wkZ0slZMplmZRqB9BJgYpxJHzkhfQUIEHE1U44HAhCdvQEdJXRAYMPnEl1IkLCIloneMICdJWqYpThU7sPo0WZcWYdSlv9AwjtUm72PQHpFQxxu7ZJXtmd+yKPbK3T3vVox4NLwc0G00t98t9x8P5129VDs0Se/9UX3qW2MVc5FWQdz9iGqcwm/ra4elzfn59rD7OfrEn8n/OHtgtncCtvZi/1/j6GRL0AJn31/0RbE6nMzPp7Fo2tbAUP0UnRjCKCbrvWSxgBTkUaN8TXOMGt8qQMq8sKsvNUqUl1gziv1BW/wDLsJox</latexit><latexit sha1_base64="CFauiCARyreZzwEA/N8kohKKf7w=">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</latexit>の SU (4) 変換則は(matter field method)

µ

!g

µ †

g [g 2 SU (4)]cf, HLS; Harada-Nonaka-Yamaoka (2010)

カイラル模型
Harada-Liu-Oka-Suzuki (2020)
Suenaga-Hosaka (2021,2022)
etc.

最新の研究(宣伝)19/21

・スピン1粒子を含む線形シグマ模型

Suenaga et at, in preparation<latexit sha1_base64="CFauiCARyreZzwEA/N8kohKKf7w=">AAACaHichVFNLwNBGH66vuujiwPi0mhIXZpZaRAn4eKI2pIgsrtGTexXdqdNaPwBF0fEiURE/AwXf8DBT8CRxMXB2+0mQoN3MjPPPPM+7zwzY/q2CCVjjwmlqbmlta29I9nZ1d2TUnv7iqFXDiyuW57tBWumEXJbuFyXQtp8zQ+44Zg2XzX35mv7qxUehMJzV+S+zzcdo+SKHWEZkii9oGfz41tqhuVYFOlGoMUggzgWPfUaG9iGBwtlOOBwIQnbMBBSW4cGBp+4TVSJCwiJaJ/jEEnSlimLU4ZB7B6NJVqtx6xL61rNMFJbdIpNPSBlGqPsgd2wV3bPbtkT+/i1VjWqUfOyT7NZ13J/K3U0WHj/V+XQLLH7pfrTs8QOpiOvgrz7EVO7hVXXVw5OXgszy6PVMXbJXsj/BXtkd3QDt/JmXS3x5XMk6QO0n8/dCIoTOW0yl1/KZ2bn4q9oxzBGkKX3nsIsFrAInc4VOMYpzhLPiqoMKEP1VCURa/rxLZSRT/uzit4=</latexit>- SU (4) 不変なラグランジアンの構築

cf, extended LSM from Frankfurt group

and

1+ ハドロン質量の結果の例<latexit sha1_base64="uX6dtaBYUaU7ulbrxblWQH6A9Y0=">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</latexit>

平均場の µq 依存性の例

1 ハドロン質量の結果の例<latexit sha1_base64="Q+hm01pxEjjgOgdIx5l0kqUgnm8=">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</latexit><latexit sha1_base64="E2nmX2q/5mdp86ZxUWZAO8kSqB4=">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</latexit>

q

1.5
1.0

2
0 +

2

<latexit sha1_base64="9I6TgHjpMaWsNNE9lKDTDE64YsE=">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</latexit>

0.5

4

preliminary<latexit sha1_base64="5fXv/d6vkAivkeOZLSLb37AgfJY=">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</latexit><latexit sha1_base64="ctJhlkGX9KA8nw7FtOXp5X92Xvo=">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</latexit>

0

0.0

V̄4

-0.5

ベクターダイクォーク平均場<latexit sha1_base64="0c4zju94Ihb8LpFXDAJOz/LFe+A=">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</latexit><latexit sha1_base64="KmtYgqs8sea214gLaiT+WO+C9iM=">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</latexit>

-1.0
-1.5
0.0

!
¯

ベクターメソン平均場
0.5

1.0
μq /mvacπ3<latexit sha1_base64="+F2AepzFwD4Lgi1ZFwbGt/Cwudo=">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</latexit><latexit sha1_base64="Y7OvuOA8g+ZPMVbl7Hy6EnLQeW8=">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</latexit>! BAS B̄AS mix

B̄AS<latexit sha1_base64="+F2AepzFwD4Lgi1ZFwbGt/Cwudo=">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</latexit>

2! BAS B̄AS mix

BAS<latexit sha1_base64="QCGf7zeugFlH8Gkl3IKEyph0yDQ=">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</latexit>⇢<latexit sha1_base64="WfJmpo1FR6pKAvVlvAQXDBA3Uxg=">AAACZ3ichVHLSsNAFD2Nr1ofrQpScKOWiqtyK0XFVdGNy1atFqqUJE5taJqEJC3U4g+4cFvBlYKI+Blu/AEXfoK4VHDjwps0IFrUO8zMmTP33Dkzo1i65rhETyGpr39gcCg8HBkZHRuPxiYmdx2zYauioJq6aRcV2RG6ZoiCq7m6KFq2kOuKLvaU2oa3v9cUtqOZxo7bssRBXT4ytIqmyq5H7dtVsxxLUIr8mO0F6QAkEETOjN1gH4cwoaKBOgQMuIx1yHC4lZAGwWLuAG3mbEaavy9wgghrG5wlOENmtsbjEa9KAWvw2qvp+GqVT9G526ycRZIe6ZZe6YHu6Jk+fq3V9mt4Xlo8K12tsMrR0/j2+7+qOs8uql+qPz27qGDV96qxd8tnvFuoXX3zuPO6vbaVbC/QFb2w/0t6onu+gdF8U6/zYusCEf6A9M/n7gW7S6n0ciqTzySy68FXhDGDeSzye68gi03kUOBzqzhDB+ehZykqTUvxbqoUCjRT+BbS3CfF7YtM</latexit>

1

4

preliminary!, ⇢<latexit sha1_base64="8T1qwxijE+VG4pOOB6h5pzhtZt4=">AAACbnichVG7SgNBFD1Z3/EVFUQQMRgUCwkTCSpWoo2lRvOARGR3HZMh+2J3EojBH7AXC0FREBE/w8YfsMgniI2gYGPhzWZBVNS7zM6ZM/fcOXNHcwzhScYaIaWtvaOzq7sn3NvXPzAYGRrOeHbF1Xlatw3bzWmqxw1h8bQU0uA5x+WqqRk8q5XXmvvZKnc9YVvbsubwHVMtWmJf6KokKl+wTV5U5wpuyd6NxFic+RH9CRIBiCGIDTtyjQL2YENHBSY4LEjCBlR49OWRAIND3A7qxLmEhL/PcYgwaSuUxSlDJbZM/yKt8gFr0bpZ0/PVOp1i0HBJGcU0e2A37IXds1v2yN5/rVX3azS91GjWWlru7A4ejW29/asyaZYofar+9CyxjyXfqyDvjs80b6G39NWDk5et5dR0fYZdsifyf8Ea7I5uYFVf9atNnjpFmB4g8b3dP0FmPp5YiCc3k7GV1eApujGOKcxSvxexgnVsIO137BhnOA89K6PKhDLZSlVCgWYEX0KZ/QAA844j</latexit><latexit sha1_base64="+F2AepzFwD4Lgi1ZFwbGt/Cwudo=">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</latexit>! BAS B̄AS mix

1+ hadron masses

2.0

1- hadron masses

Mean fields

Suenaga-Murakami-Itou-Iida,
PRD 107, 054001 (2023)

2.0

0.0

3
<latexit sha1_base64="5linKOurq6cjkpkDhmXF4VdaTRw=">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</latexit>

a1 BS B̄S mix

f 1 , a1<latexit sha1_base64="DZeHCRHuCTBfAPcS1W+FBDW35t8=">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</latexit>

f1<latexit sha1_base64="yElV39273GDvCfz5CN+40q69joE=">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</latexit>

2<latexit sha1_base64="5linKOurq6cjkpkDhmXF4VdaTRw=">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</latexit><latexit sha1_base64="canBBODg0eSal9pWNyaQgfINfGc=">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</latexit>

a1 BS B̄S mix

B̄S

1<latexit sha1_base64="5linKOurq6cjkpkDhmXF4VdaTRw=">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</latexit>

a1 BS B̄S mix

BS<latexit sha1_base64="8mb4ZrlwhEt5oRZO2jp2bLazt5I=">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</latexit>

0

0
1.5

preliminary

0.5

1.0
μq /mvac
π

1.5

2.0

0.0

0.5

1.0
μq /mvac
π

1.5

2.0

Suenaga-Murakami-Itou-Iida,
PRD 107, 054001 (2023)

4. まとめ20/21- 2カラーQCDの線形シグマ模型を構築し、ハドロン質量 (B, B̄, ⇡, ⌘ とそのパリティ
パートナー B 0 , B̄ 0 , a0 , ) の µq 依存性を調べた<latexit sha1_base64="7VLiV+SyTqv1wUnImpwoYS6vQ+I=">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</latexit><latexit sha1_base64="e/RVvInm6n3ca7zpzuS72EQmTjA=">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</latexit><latexit sha1_base64="E2nmX2q/5mdp86ZxUWZAO8kSqB4=">AAACaHichVG7SgNBFD1Z3/GRqIWKjSRErMJEgoqVaGOZhzGBJITddaJD9uXuJqDBH7CxVLFSEBE/w8YfsMgnqKWCjYU3mwXRoN5hZs6cuefOmRnF0oTjMtYKSD29ff0Dg0PB4ZHRsVB4fGLbMeu2ynOqqZl2QZEdrgmD51zharxg2VzWFY3nldpGez/f4LYjTGPLPbB4WZd3DVEVquwSlSvp9cp+JRxlcebFXDdI+CAKP1Jm+AYl7MCEijp0cBhwCWuQ4VArIgEGi7gymsTZhIS3z3GEIGnrlMUpQya2RuMurYo+a9C6XdPx1CqdolG3STmHGHtkt+yVPbA79sQ+fq3V9Gq0vRzQrHS03KqEjqez7/+qdJpd7H2p/vTsoooVz6sg75bHtG+hdvSNw9PX7Gom1pxnV+yF/F+yFrunGxiNN/U6zTMXCNIHJH4+dzfYXownluLJdDK6tu5/xSBmEcECvfcy1rCJFHJ0rsAJznAeeJbC0pQ000mVAr5mEt9CinwCvwKLvw==</latexit>

格子QCDとconsistent！
Murakami et al, in preparation
ゼロ質量

押し下げられる- 格子QCDとの比較により、有限密度系でアノマリー効果の増大の可能性を発見
cf, 3カラーでFRGによる解析とconsistenteg, Fejos-Hosaka (2017, 2018)

Suenaga-Murakami-Itou-Iida,
PRD 107, 054001 (2023)

4. まとめ21/21- 2カラーQCDの線形シグマ模型を構築し、ハドロン質量 (B, B̄, ⇡, ⌘ とそのパリティ
パートナー B 0 , B̄ 0 , a0 , ) の µq 依存性を調べた<latexit sha1_base64="7VLiV+SyTqv1wUnImpwoYS6vQ+I=">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</latexit><latexit sha1_base64="e/RVvInm6n3ca7zpzuS72EQmTjA=">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</latexit><latexit sha1_base64="E2nmX2q/5mdp86ZxUWZAO8kSqB4=">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</latexit>

格子QCDとconsistent！
Murakami et al, in preparation
ゼロ質量

押し下げられる- 格子QCDとの比較により、有限密度系でアノマリー効果の増大の可能性を発見
cf, 3カラーでFRGによる解析とconsistenteg, Fejos-Hosaka (2017, 2018)- 線形シグマ模型によるトポロジカル感受率も調べた<latexit sha1_base64="tYp3BUxA7fMx0LnrlZrgA5kZTQQ=">AAACbXichVHLLgRBFD3TXmO8BpFIiIiJx8akejJBrISNJcYgBpPuVujol35MMjp+wFpiISQkIuIzbPyAxXyCWFiQ2Fi43dOJMMGtVNWpU/fcOlUlW5rquIxVYkJdfUNjU7w50dLa1t6R7OxacUzPVnheMTXTXpMlh2uqwfOu6mp8zbK5pMsaX5X354L91RK3HdU0lt2yxTd1addQd1RFcola39C94sGWP545KiZTLM3CGKwFYgRSiGLBTN5gA9swocCDDg4DLmENEhxqBYhgsIjbhE+cTUgN9zmOkCCtR1mcMiRi92ncpVUhYg1aBzWdUK3QKRp1m5SDGGaP7Ja9sgd2x57Yx6+1/LBG4KVMs1zVcqvYcdybe/9XpdPsYu9L9adnFzuYCr2q5N0KmeAWSlVfOjx9zU0vDfsj7Io9k/9LVmH3dAOj9KZcL/KlMyToA8Sfz10LVjJpcSKdXcymZmajr4ijD0MYo/eexAzmsYA8nWvgBOe4iL0IPUK/MFBNFWKRphvfQhj9BPIVjaY=</latexit>

2→ 漸近系はカイラルの回復と共に µq で抑制される(アノマリー効果の強さに依存しない)
Kawagchi-Suenaga, to appear in JHEP (2023)<latexit sha1_base64="XuSC6SpjGBJqnItSXyje/pdr2lk=">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</latexit>(f⇡vac )2 2
top
⇠
µq
4
(mvac
12
⇡ )