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Stress tensor distribution around static quarks in hot medium - - PowerPoint PPT Presentation

Feb 26, 2024 95 likes β€’521 views

Stress tensor distribution around static quarks in hot medium Ryosuke Yanagihara (Osaka University) For FlowQCD collaboration : Takumi Iritani, Masakiyo Kitazawa, Masayuki Asakawa, Tetsuo Hatsuda FLQCD 2019 @ YITP (2019/04/18) Confined vs.

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SLIDE 1

Stress tensor distribution around static quarks in hot medium

Ryosuke Yanagihara (Osaka University) For FlowQCD collaboration : Takumi Iritani, Masakiyo Kitazawa, Masayuki Asakawa, Tetsuo Hatsuda

FLQCD 2019 @ YITP (2019/04/18)
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SLIDE 2

Confined vs. Deconfined

π‘ˆ

FLQCD 2019 @ YITP (2019/04/18)

Critical temperature π‘ˆ

𝑑

Confined Deconfined

gluon quark

1

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SLIDE 3

ζΈ©εΊ¦ π‘ˆ

FLQCD 2019 @ YITP (2019/04/18)

ιžι–‰γ˜θΎΌγ‚η›Έ

π‘ˆ

𝑑 Burkert et al.,

Nature 557 (2018) 396. Shanahan et al., PRL 122 (2019) no7, 072003. Exp. Th. Kumano et al., PRD 97 (2018) 014020.

Confined vs. Deconfined

Confined

gluon quark

Pressure distribution inside Hadrons

1

slide-4
SLIDE 4

Pressure distribution inside hadrons vs. Our study

𝑅 ΰ΄€ 𝑅

FLQCD 2019 @ YITP (2019/04/18)

2

Burkert et al., Nature 557 (2018) 396. Shanahan et al., PRL 122 (2019) no7, 072003.

Exp. Th.

Kumano et al., PRD 97 (2018) 014020.

Pressure distribution inside Hadrons Our study

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SLIDE 5

Flux tube

QED QCD

οƒΌ Flux tube, squeezed one-dimensionally οƒΌ Confinement potential οƒΌ Electric field spreads all over the space οƒΌ Coulomb potential

𝑅 ΰ΄€ 𝑅

FLQCD 2019 @ YITP (2019/04/18)

3

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SLIDE 6

Flux tube

QED QCD

οƒΌ Flux tube, squeezed one-dimensionally οƒΌ Confinement potential οƒΌ Electric field spreads all over the space οƒΌ Coulomb potential

𝑅 ΰ΄€ 𝑅 Maxwell stress

Local interaction

FLQCD 2019 @ YITP (2019/04/18)

？

3

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SLIDE 7

Cardoso et al., PRD86 (2013) 054501. Cea et al., PRD88 (2012) 054504.

Action density Color electric field

𝑦 𝑨 𝑧 mid 𝑧𝑨 𝑆

𝑓𝑨 𝑓𝑠 π‘“πœ„

A lot of previous studies

FLQCD 2019 @ YITP (2019/04/18)

4

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SLIDE 8

Cardoso et al., PRD86 (2013) 054501. Cea et al., PRD88 (2012) 054504.

Action density Color electric field

𝑦 𝑨 𝑧 mid 𝑧𝑨 𝑆

𝑓𝑨 𝑓𝑠 π‘“πœ„

A lot of previous studies

FLQCD 2019 @ YITP (2019/04/18)

More direct physical quantity : Stress tensor !!

4

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SLIDE 9

Energy momentum tensor (EMT)

οƒΌ Stress is force per unit area 𝑔

𝑗 = πœπ‘—π‘˜π‘œπ‘˜ ; πœπ‘—π‘˜ = βˆ’π‘ˆπ‘—π‘˜

π‘ˆ

πœˆπœ‰ =

π‘ˆ00 π‘ˆ01 π‘ˆ02 π‘ˆ03 π‘ˆ

10

π‘ˆ

11

π‘ˆ

12

π‘ˆ

13

π‘ˆ20 π‘ˆ30 π‘ˆ21 π‘ˆ31 π‘ˆ22 π‘ˆ23 π‘ˆ32 π‘ˆ33

Energy density

Momentum density Pressure

Stress tensor

Landau and Lifshitz

FLQCD 2019 @ YITP (2019/04/18)

5

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SLIDE 10

οƒΌ Stress is force per unit area 𝑔

𝑗 = πœπ‘—π‘˜π‘œπ‘˜ ; πœπ‘—π‘˜ = βˆ’π‘ˆπ‘—π‘˜

π‘ˆ

πœˆπœ‰ =

π‘ˆ00 π‘ˆ01 π‘ˆ02 π‘ˆ03 π‘ˆ

10

π‘ˆ

11

π‘ˆ

12

π‘ˆ

13

π‘ˆ20 π‘ˆ30 π‘ˆ21 π‘ˆ31 π‘ˆ22 π‘ˆ23 π‘ˆ32 π‘ˆ33

Energy density

Momentum density Pressure

Landau and Lifshitz

FLQCD 2019 @ YITP (2019/04/18)

rubber

Energy momentum tensor (EMT) Stress tensor

5

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SLIDE 11

Maxwell stress

π‘ˆ

π‘—π‘˜ = πœ—0 𝐹𝑗𝐹 π‘˜ βˆ’ πœ€π‘—π‘˜

2 𝐹2 + 1 𝜈0 𝐢𝑗𝐢

π‘˜ βˆ’ πœ€π‘—π‘˜

2 𝐢2 𝐹

οƒΌ Stress tensor

π‘ˆ

π‘—π‘˜π‘œπ‘˜ (𝑙) = πœ‡π‘™π‘œπ‘— (𝑙)

(𝑗, π‘˜ = 1,2,3 ; 𝑙 = 1,2,3) οƒΌ Perpendicular plane: πœ‡π‘™ < 0 οƒΌ Parallel plane: πœ‡π‘™ > 0

Length of arrows= πœ‡π‘™ Τ¦ 𝑔 Τ¦ 𝑔

FLQCD 2019 @ YITP (2019/04/18)

6

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SLIDE 12 FLQCD 2019 @ YITP (2019/04/18)

Measurement on the lattice

β‘ Prepare 𝑅 ΰ΄€ 𝑅 on the lattice β‘‘Measure EMT around 𝑅 ΰ΄€ 𝑅

To do

7

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SLIDE 13 FLQCD 2019 @ YITP (2019/04/18)

Measurement on the lattice

β‘ Prepare 𝑅 ΰ΄€ 𝑅 on the lattice β‘‘Measure EMT around 𝑅 ΰ΄€ 𝑅

To do

7

π‘Š 𝑆 = βˆ’ lim

π‘ˆβ†’βˆž

1 π‘ˆ logβŸ¨π‘‹ 𝑆, π‘ˆ ⟩

Ground state potential

Wilson Loop

Confinement potential βŸ¨π‘‹ 𝑆, π‘ˆ ⟩ = 𝐷0exp βˆ’π‘Š 𝑆 π‘ˆ + 𝐷1exp βˆ’π‘Š

1 𝑆 π‘ˆ + β‹―

οƒΌ quenched SU(3) Yang-Mills οƒΌ 𝛾 = 6.600 (𝑏 = 0.038 fm)

slide-14
SLIDE 14 FLQCD 2019 @ YITP (2019/04/18)

EMT defined via gradient flow

π‘ˆ πœˆπœ‰ 𝑒, 𝑦 = 1 𝛽𝑉 𝑒 π‘‰πœˆπœ‰ 𝑒, 𝑦 + πœ€πœˆπœ‰ 4𝛽𝐹(𝑒) 𝐹 𝑒, 𝑦 βˆ’ 𝐹 𝑒, 𝑦 + 𝑃(𝑒) Suzuki (2013)

Gradient flow

πœ–πΆ 𝜈 𝑒, 𝑦 πœ–π‘’ = βˆ’π‘•0 2 πœ€π‘‡[𝐢] πœ€πΆ 𝜈(𝑒, 𝑦)

Flow eq.

L ሷ uscher (2010)

𝐢

𝜈 : smeared field

Iritani et al. (2018) Entropy density vs. temperature οƒΌ 2-loop coefficient is now available !

Harlander et al. (2018)

Measurement on the lattice

β‘ Prepare 𝑅 ΰ΄€ 𝑅 on the lattice β‘‘Measure EMT around 𝑅 ΰ΄€ 𝑅

To do

7

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SLIDE 15

Set up

FLQCD 2019 @ YITP (2019/04/18)

8

οƒΌ Quenched SU(3) Yang-Mills gauge theory οƒΌ Wilson gauge action οƒΌ Clover operator οƒΌ Continuum limit οƒΌ APE smearing for spatial links οƒΌ Multihit improvement in temporal links οƒΌ Simulation using BlueGene/Q @ KEK 𝜸 Lattice spacing Lattice size # of statistics 6.304 0.057 fm 484 140 6.465 0.046 fm 484 440 6.513 0.043 fm 484 600 6.600 0.038 fm 484 1500 6.819 0.029 fm 644 1000 0.92 fm 0.69 fm 0.46 fm

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SLIDE 16

𝑧 mid-plane 𝑧𝑨-plane

𝑆

𝑨 𝑦 𝑃 𝑃 𝑅 ΰ΄€ 𝑅

FLQCD 2019 @ YITP (2019/04/18)

A lattice study of stress distribution around 𝑅 ΰ΄€ 𝑅 in vacuum

FlowQCD, PLB 789 (2019) 210.

Stress distribution in terms of local interaction

9

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SLIDE 17

Stress distribution around 𝑅 ΰ΄€ 𝑅

𝑦 𝑨 𝑧 mid 𝑧𝑨 𝑆

οƒΌ 𝑏 = 0.029 fm οƒΌ 𝑒/𝑏2 = 2.0 οƒΌ 𝑆 = 0.69 fm οƒΌ Length of arrows = πœ‡π‘™

FLQCD 2019 @ YITP (2019/04/18)

οƒΌ Gauge invariant οƒΌ Local interaction οƒΌ squeezed

FlowQCD, PLB 789 (2019) 210.

10

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SLIDE 18 FLQCD 2019 @ YITP (2019/04/18)

Stress distribution around 𝑅 ΰ΄€ 𝑅 : Cylindrical coordinates

π‘ˆ

πœˆπœ‰ =

π‘ˆ

44

π‘ˆ

𝑨𝑨

π‘ˆ

𝑠𝑠

π‘ˆπœ„πœ„ Diagonalized EMT

(Cylindrical / Parity symmetry)

𝑃 𝑃

Degeneracy (Maxwell Theory) π‘ˆ

44 = π‘ˆ 𝑨𝑨 = π‘ˆ 𝑠𝑠 = |π‘ˆπœ„πœ„|

𝑓𝑨 𝑓𝑠 π‘“πœ„

𝑅 ΰ΄€ 𝑅

11

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SLIDE 19

Stress distribution around 𝑅 ΰ΄€ 𝑅

FLQCD 2019 @ YITP (2019/04/18)

𝑓𝑨 𝑓𝑠 π‘“πœ„

𝑦 𝑨 𝑧 mid 𝑧𝑨 𝑆

οƒΌ π‘ˆ

44 β‰ˆ π‘ˆ 𝑨𝑨, π‘ˆ 𝑠𝑠 β‰ˆ π‘ˆ πœ„πœ„ (Degeneracy)

οƒΌ π‘ˆ

44 β‰  π‘ˆ 𝑠𝑠 (Separation)

οƒΌ Οƒπœˆ π‘ˆ

𝜈𝜈 β‰  0 (Trace anomalyβ‰  0)

Properties in non-Abelian theory

( Note : after double limit )

FlowQCD, PLB 789 (2019) 210.

12

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SLIDE 20

EMT and confinement potential

FLQCD 2019 @ YITP (2019/04/18)

confinement potential 𝜍 ≔ βˆ’πΊstress ≔ ΰΆ± mid π‘ˆ

𝑨𝑨 𝑅 ΰ΄€ 𝑅 𝑒2𝑦

From EMT π‘Š 𝑆 = 𝑏 + 𝑐𝑆 + Ξ€ 𝑑 𝑆 ここに数式をε…₯εŠ›γ—γΎγ™γ€‚ 𝐺pot ≔ βˆ’ π‘’π‘Š(𝑆) 𝑒𝑆

13

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SLIDE 21

EMT and confinement potential

FLQCD 2019 @ YITP (2019/04/18)

confinement potential 𝜍 ≔ βˆ’πΊstress ≔ ΰΆ± mid π‘ˆ

𝑨𝑨 𝑅 ΰ΄€ 𝑅 𝑒2𝑦

From EMT π‘Š 𝑆 = 𝑏 + 𝑐𝑆 + Ξ€ 𝑑 𝑆 ここに数式をε…₯εŠ›γ—γΎγ™γ€‚ 𝐺pot ≔ βˆ’ π‘’π‘Š(𝑆) 𝑒𝑆

Good agreement !!

13

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SLIDE 22

Toward analysis at nonzero temperature

π‘ˆ

FLQCD 2019 @ YITP (2019/04/18)

Stress distribution around 𝑅 ΰ΄€ 𝑅/𝑅 at nonzero temperature

？

Critical temperature π‘ˆ

𝑑

14

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SLIDE 23

Measurement on the lattice

β‘ Prepare 𝑅 ΰ΄€ 𝑅 on the lattice β‘‘Measure EMT around 𝑅/ ΰ΄€ 𝑅

To do

FLQCD 2019 @ YITP (2019/04/18)

15

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SLIDE 24 FLQCD 2019 @ YITP (2019/04/18)

π‘“βˆ’πΊ 𝑆 /π‘ˆ = 1 3 Tr Ω† Τ¦ 𝑦 Ξ© ( Τ¦ 𝑧)

Color singlet free energy (We use Coulomb gauge fixing)

Polyakov Loop

Free energy

οƒΌ quenched SU(3) Yang-Mills οƒΌ 𝛾 = 6.600 (𝑏 = 0.038 fm)

𝑦4 Τ¦ 𝑦

𝑅 ΰ΄€ 𝑅 Measurement on the lattice

β‘ Prepare 𝑅 ΰ΄€ 𝑅 on the lattice β‘‘Measure EMT around 𝑅/ ΰ΄€ 𝑅

To do

15

slide-25
SLIDE 25 FLQCD 2019 @ YITP (2019/04/18)

EMT defined via gradient flow

π‘ˆ πœˆπœ‰ 𝑒, 𝑦 = 1 𝛽𝑉 𝑒 π‘‰πœˆπœ‰ 𝑒, 𝑦 + πœ€πœˆπœ‰ 4𝛽𝐹(𝑒) 𝐹 𝑒, 𝑦 βˆ’ 𝐹 𝑒, 𝑦 + 𝑃(𝑒) Suzuki (2013)

Gradient flow

πœ–πΆ 𝜈 𝑒, 𝑦 πœ–π‘’ = βˆ’π‘•0 2 πœ€π‘‡[𝐢] πœ€πΆ 𝜈(𝑒, 𝑦)

Flow eq.

L ሷ uscher (2010)

𝐢

𝜈 : smeared field

Iritani et al. (2018) Entropy density vs. temperature οƒΌ 2-loop coefficient is now available !

Harlander et al. (2018)

Measurement on the lattice

β‘ Prepare 𝑅 ΰ΄€ 𝑅 on the lattice β‘‘Measure EMT around 𝑅/ ΰ΄€ 𝑅

To do

15

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SLIDE 26

Set up (quarkβ€”anti-quark, single quark)

οƒΌ Quenched SU(3) Yang-Mills gauge theory οƒΌ Wilson gauge action οƒΌ Clover operator οƒΌ Fixed 𝑏, 𝑒 οƒΌ Multihit improvement in temporal links οƒΌ Simulation using OCTOPUS, Reedbush

FLQCD 2019 @ YITP (2019/04/18)

𝜸 Lattice spacing Spatial size Temporal size 𝑼/𝑼𝒅 # of statistics 6.600 0.038 fm 483 12 1.44 640

𝑅 ΰ΄€ 𝑅

0.69 fm 0.46 fm

16

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SLIDE 27

Maxwell stress (revisit)

π‘ˆ

π‘—π‘˜ = πœ—0 𝐹𝑗𝐹 π‘˜ βˆ’ πœ€π‘—π‘˜

2 𝐹2 + 1 𝜈0 𝐢𝑗𝐢

π‘˜ βˆ’ πœ€π‘—π‘˜

2 𝐢2 𝐹

οƒΌ Stress tensor

π‘ˆ

π‘—π‘˜π‘œπ‘˜ (𝑙) = πœ‡π‘™π‘œπ‘— (𝑙)

(𝑗, π‘˜ = 1,2,3 ; 𝑙 = 1,2,3) οƒΌ Perpendicular plane: πœ‡π‘™ < 0 οƒΌ Parallel plane: πœ‡π‘™ > 0

Length of arrows= πœ‡π‘™ Τ¦ 𝑔 Τ¦ 𝑔

FLQCD 2019 @ YITP (2019/04/18)

6’

slide-28
SLIDE 28 FLQCD 2019 @ YITP (2019/04/18) 𝑦 𝑨 𝑧 mid 𝑧𝑨 𝑆

Preliminary

οƒΌ singlet οƒΌ 𝑏 = 0.038 fm (fixed) οƒΌ 𝑒/𝑏2 = 2.0 (fixed) οƒΌ 𝑆 = 0.69 fm οƒΌ Length of arrows = πœ‡π‘™

Stress distribution around 𝑅 ΰ΄€ 𝑅

17

slide-29
SLIDE 29 FLQCD 2019 @ YITP (2019/04/18) 𝑦 𝑨 𝑧 mid 𝑧𝑨 𝑆

π‘ˆ Preliminary Critical temperature π‘ˆ

𝑑

Stress distribution around 𝑅 ΰ΄€ 𝑅

18

slide-30
SLIDE 30 FLQCD 2019 @ YITP (2019/04/18)

Stress distribution around 𝑅 ΰ΄€ 𝑅 : Cylindrical coordinates

π‘ˆ

πœˆπœ‰ =

π‘ˆ

44

π‘ˆ

𝑨𝑨

π‘ˆ

𝑠𝑠

π‘ˆπœ„πœ„ Diagonalized EMT

(Cylindrical / Parity symmetry)

𝑃 𝑃

Degeneracy (Maxwell Theory) π‘ˆ

44 = π‘ˆ 𝑨𝑨 = π‘ˆ 𝑠𝑠 = |π‘ˆπœ„πœ„|

𝑓𝑨 𝑓𝑠 π‘“πœ„

𝑅 ΰ΄€ 𝑅

19

slide-31
SLIDE 31 FLQCD 2019 @ YITP (2019/04/18) 𝑦 𝑨 𝑧 mid 𝑧𝑨 𝑆

𝑓𝑨 𝑓𝑠 π‘“πœ„

Preliminary

( Note : singlet )

Stress distribution around 𝑅 ΰ΄€ 𝑅

20

slide-32
SLIDE 32 FLQCD 2019 @ YITP (2019/04/18) 𝑦 𝑨 𝑧 mid 𝑧𝑨 𝑆

𝑓𝑨 𝑓𝑠 π‘“πœ„ Preliminary Preliminary

οƒΌ π‘ˆ

𝑠𝑠 β‰ˆ π‘ˆ πœ„πœ„ (Degeneracy)

οƒΌ π‘ˆ

44 β‰  π‘ˆ 𝑠𝑠 (Separation)

οƒΌ Οƒπœˆ π‘ˆ

𝜈𝜈 β‰  0 (Trace anomalyβ‰  0)

οƒΌ Damping ↔ Debye mass οƒΌ 𝑒𝐺/𝑒𝑆 ↔ Χ¬ π‘ˆ

𝑨𝑨 𝑒2𝑦

Stress distribution around 𝑅 ΰ΄€ 𝑅

20

slide-33
SLIDE 33 FLQCD 2019 @ YITP (2019/04/18) 𝑦 𝑨 𝑧 mid 𝑧𝑨 𝑆

Preliminary 𝑓𝑨 𝑓𝑠 π‘“πœ„

Stress distribution around 𝑅 ΰ΄€ 𝑅

οƒΌ π‘ˆ

𝑠𝑠 β‰ˆ π‘ˆ πœ„πœ„ (Degeneracy)

οƒΌ π‘ˆ

44 β‰  π‘ˆ 𝑠𝑠 (Separation)

οƒΌ Οƒπœˆ π‘ˆ

𝜈𝜈 β‰  0 (Trace anomalyβ‰  0)

οƒΌ Damping ↔ Debye mass οƒΌ 𝑒𝐺/𝑒𝑆 ↔ Χ¬ π‘ˆ

𝑨𝑨 𝑒2𝑦

20

slide-34
SLIDE 34 FLQCD 2019 @ YITP (2019/04/18) 𝑦 𝑨 𝑧 mid 𝑧𝑨 𝑆

Preliminary

𝐺stress β‰ˆ 0.30 GeV/fm 𝐺Free β‰ˆ 0.41 GeV/fm

𝑓𝑨 𝑓𝑠 π‘“πœ„

Stress distribution around 𝑅 ΰ΄€ 𝑅

οƒΌ π‘ˆ

𝑠𝑠 β‰ˆ π‘ˆ πœ„πœ„ (Degeneracy)

οƒΌ π‘ˆ

44 β‰  π‘ˆ 𝑠𝑠 (Separation)

οƒΌ Οƒπœˆ π‘ˆ

𝜈𝜈 β‰  0 (Trace anomalyβ‰  0)

οƒΌ Damping ↔ Debye mass οƒΌ 𝑒𝐺/𝑒𝑆 ↔ Χ¬ π‘ˆ

𝑨𝑨 𝑒2𝑦

20

slide-35
SLIDE 35 FLQCD 2019 @ YITP (2019/04/18)

Stress distribution around 𝑅 : Spherical coordinates

𝑅 𝑠 πœ„, 𝜚 πœ„, 𝜚

π‘ˆ

πœˆπœ‰ =

π‘ˆ

44

π‘ˆ

𝑠𝑠

π‘ˆπ‘’π‘’ π‘ˆπ‘’π‘’

𝑃 𝑃

Diagonalized EMT

(Spherical symmetry)

Degeneracy (Maxwell Theory) π‘ˆ

44 = π‘ˆ 𝑠𝑠 = |π‘ˆπ‘’π‘’|

21

(𝑒: πœ„, 𝜚)

slide-36
SLIDE 36 FLQCD 2019 @ YITP (2019/04/18)

Stress distribution around 𝑅

𝑠 πœ„, 𝜚 πœ„, 𝜚

οƒΌ Overlap : 𝑠 ≲ 2𝑒 οƒΌ Separation οƒΌ Around origin∼ 𝛽𝑑(𝑠)/𝑠4 οƒΌ Damping∼ π‘“βˆ’π‘›πΈπ‘  οƒΌ Conservation law： πœ–π‘  𝑠2π‘ˆ

𝑠𝑠 = π‘ π‘ˆ 𝑒𝑒

Preliminary 22

slide-37
SLIDE 37

Pressure distribution inside hadrons vs. Our study

FLQCD 2019 @ YITP (2019/04/18)

23

Burkert et al., Nature 557 (2018) 396. Shanahan et al., PRL 122 (2019) no7, 072003.

Exp. Th.

Kumano et al., PRD 97 (2018) 014020.

Pressure distribution inside Hadrons Our study

slide-38
SLIDE 38 FLQCD 2019 @ YITP (2019/04/18)

24

Summary and Outlook

Summary οƒΌ We first measure stress distribution around 𝑅 ΰ΄€ 𝑅/𝑅 at zero/nonzero temperature on the lattice Outlook οƒΌ 𝑏, 𝑒 β†’ 0 (double limit) οƒΌ Temperature dependence οƒΌ ApplicationοΌšπ‘…π‘…γ€π‘…π‘…π‘…γ€excited state、hadron (full QCD)…

Single quark Quarkβ€”Anti-Quark Preliminary Preliminary Preliminary

slide-39
SLIDE 39

Back up

FLQCD 2019 @ YITP (2019/04/18)
slide-40
SLIDE 40 FLQCD 2019 @ YITP (2019/04/18)

Flow time dependence (single quark system)

slide-41
SLIDE 41

Interference b/w singlet and octet state

FLQCD 2019 @ YITP (2019/04/18)

Preliminary Preliminary