QCD phase diagram in an extended effective Lagrangian approach J. - - PowerPoint PPT Presentation

▶
qcd phase diagram in an extended effective lagrangian
SMART_READER_LITE
LIVE PREVIEW

QCD phase diagram in an extended effective Lagrangian approach J. - - PowerPoint PPT Presentation

Mar 05, 2024 412 likes •985 views

Outline Introduction and formalism Results Conclusions QCD phase diagram in an extended effective Lagrangian approach J. Moreira 1 , J. Morais 1 , B. Hiller 1 , A. H. Blin 1 ,A. A. Osipov 2 1 Centro de Fsica da Univ. Coimbra, Coimbra,

slide-1
SLIDE 1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

QCD phase diagram in an extended effective Lagrangian approach

  • J. Moreira1, J. Morais1, B. Hiller1, A. H. Blin1,A. A. Osipov2

1Centro de Física da Univ. Coimbra,

Coimbra, Portugal

2Bogoliubov Laboratory of Theoretical Physics, JINR,

Dubna, Moscow region, Russia

SEWM 2018, 28/06/2018

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 1 / 23

slide-2
SLIDE 2

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Outline

1

Introduction and formalism

Motivation Nambu–Jona-Lasinio Model Extended Nambu–Jona-Lasinio Model: multi-quark interactions Extended Nambu–Jona-Lasinio Model: explicit chiral symmetry breaking interactions Thermodynamic potential Polyakov potentials 2

Results

Extended NJL Extended NJL with Log. Polyakov potential Extended NJL with Exp. K-Log. Polyakov potential Correlations in the uds base 3

Conclusions

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 2 / 23

slide-3
SLIDE 3

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Introduction

QCD: the Theory of Strong Interactions Very successfull pQCD at high energy Non-perturbative low energy regime requires the use of other tools for instance: lQCD AdS/QCD Dyson-Schwinger FRG Chiral pertubation theory Effective models

Dynamical/Explicit Chiral Symmetry Breaking plays a big role in low energy phenomenology

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 3 / 23

slide-4
SLIDE 4

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Phase diagram for strongly interacting matter

A clear and present challenge 1:

sQGP uSC dSC CFL 2SC Critical Point

Quarkyonic Matter Quark-Gluon Plasma Hadronic Phase Color Superconductors

?

Temperature T Baryon Chemical Potential mB I n h

  • m
  • g

e n e

  • u

s S c B Liquid-Gas Nuclear Superfluid CFL-K , Crystalline CSC Meson supercurrent Gluonic phase, Mixed phase

  • 1N. Cabbibo, G. Parisi Phys.Lett. 59B (1975) 67-69; Kenji Fukushima, Tetsuo

Hatsuda Rept.Prog.Phys.74:014001,2011; http://nica.jinr.ru/physics.php

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 4 / 23

slide-5
SLIDE 5

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Phase diagram for strongly interacting matter

A clear and present challenge 1:

sQGP uSC dSC CFL 2SC Critical Point

Quarkyonic Matter Quark-Gluon Plasma Hadronic Phase Color Superconductors

?

Temperature T Baryon Chemical Potential mB I n h

  • m
  • g

e n e

  • u

s S c B Liquid-Gas Nuclear Superfluid CFL-K , Crystalline CSC Meson supercurrent Gluonic phase, Mixed phase

  • 1N. Cabbibo, G. Parisi Phys.Lett. 59B (1975) 67-69; Kenji Fukushima, Tetsuo

Hatsuda Rept.Prog.Phys.74:014001,2011; http://nica.jinr.ru/physics.php

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 4 / 23

slide-6
SLIDE 6

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Phase diagram for strongly interacting matter

A clear and present challenge 1:

sQGP uSC dSC CFL 2SC Critical Point

Quarkyonic Matter Quark-Gluon Plasma Hadronic Phase Color Superconductors

?

Temperature T Baryon Chemical Potential mB I n h

  • m
  • g

e n e

  • u

s S c B Liquid-Gas Nuclear Superfluid CFL-K , Crystalline CSC Meson supercurrent Gluonic phase, Mixed phase

  • 1N. Cabbibo, G. Parisi Phys.Lett. 59B (1975) 67-69; Kenji Fukushima, Tetsuo

Hatsuda Rept.Prog.Phys.74:014001,2011; http://nica.jinr.ru/physics.php

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 4 / 23

slide-7
SLIDE 7

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Nambu–Jona-Lasinio Model

NJL: effective model for the non-perturbative low energy regime of QCD with Dynamical Chiral Symmetry Breaking (DχSB) NJL shares the global symmetries with QCD Dynamical generation of the constituent mass Light pseudoscalar as (quasi) Nambu-Goldstone boson Quark condensates as order parameter No gluons (no confinement/deconfinement) Local and non renormalizable

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 5 / 23

slide-8
SLIDE 8

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Multi-quark interations (u, d and s) 2

Leff = qı/ ∂q + Lm

2Σ = (sa − ıpa) 1 2λa, sa = ¯

qλaq, pa = ¯ qλaıγ5q, and a = 0, 1, . . . , 8

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 6 / 23

slide-9
SLIDE 9

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Multi-quark interations (u, d and s) 2

Leff = qı/ ∂q + Lm Explicit Chiral symmetry breaking Lm = q ˆ mq

2Σ = (sa − ıpa) 1 2λa, sa = ¯

qλaq, pa = ¯ qλaıγ5q, and a = 0, 1, . . . , 8

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 6 / 23

slide-10
SLIDE 10

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Multi-quark interations (u, d and s) 2

Leff = qı/ ∂q + Lm + LNJL Lm = q ˆ mq Nambu–Jona-Lasinio (4 q) LNJL = G tr [ Σ†Σ ]

2Σ = (sa − ıpa) 1 2λa, sa = ¯

qλaq, pa = ¯ qλaıγ5q, and a = 0, 1, . . . , 8

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 6 / 23

slide-11
SLIDE 11

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Multi-quark interations (u, d and s) 2

Leff = qı/ ∂q + Lm + LNJL + LH Lm = q ˆ mq LNJL = G tr [ Σ†Σ ] ’t Hooft determinant (6 q) LH = κ ( det [Σ] + det [ Σ†])

2Σ = (sa − ıpa) 1 2λa, sa = ¯

qλaq, pa = ¯ qλaıγ5q, and a = 0, 1, . . . , 8

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 6 / 23

slide-12
SLIDE 12

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Multi-quark interations (u, d and s) 2

Leff = qı/ ∂q + Lm + LNJL + LH + L8q Lm = q ˆ mq LNJL = G tr [ Σ†Σ ] LH = κ ( det [Σ] + det [ Σ†]) Eight quark interaction term L8q = L(1)

8q + L(2) 8q ,

L(1)

8q = g1

( tr [ Σ†Σ ])2 , L(2)

8q = g2tr

[ Σ†ΣΣ†Σ ]

2Σ = (sa − ıpa) 1 2λa, sa = ¯

qλaq, pa = ¯ qλaıγ5q, and a = 0, 1, . . . , 8

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 6 / 23

slide-13
SLIDE 13

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Multi-quark interations (u, d and s) 2

Leff = qı/ ∂q + Lm + LNJL + LH + L8q Lm = q ˆ mq LNJL = G tr [ Σ†Σ ] LH = κ ( det [Σ] + det [ Σ†]) L8q = L(1)

8q + L(2) 8q ,

L(1)

8q = g1

( tr [ Σ†Σ ])2 , L(2)

8q = g2tr

[ Σ†ΣΣ†Σ ] OZI violation in LH and L(1)

8q .

2Σ = (sa − ıpa) 1 2λa, sa = ¯

qλaq, pa = ¯ qλaıγ5q, and a = 0, 1, . . . , 8

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 6 / 23

slide-14
SLIDE 14

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Multi-quark interations (u, d and s) 2

Leff = qı/ ∂q + Lm + LNJL + LH + L8q + Lχ Lm = q ˆ mq Extended Explicit Chiral symmetry breaking Lχ LNJL = G tr [ Σ†Σ ] LH = κ ( det [Σ] + det [ Σ†]) L8q = L(1)

8q + L(2) 8q ,

L(1)

8q = g1

( tr [ Σ†Σ ])2 , L(2)

8q = g2tr

[ Σ†ΣΣ†Σ ] Non canonical explicit chiral symmetry breaking terms

2Σ = (sa − ıpa) 1 2λa, sa = ¯

qλaq, pa = ¯ qλaıγ5q, and a = 0, 1, . . . , 8

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 6 / 23

slide-15
SLIDE 15

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Inclusion of explicit chiral symmetry breaking terms

Lχ =

10

∑

i=1

Li

χ,

L1

χ = −κ1 eijkemnlΣimχjnχkl + h.c.,

L2

χ = κ2 eijkemnlχimΣjnΣkl + h.c.,

L3

χ = g3 tr

[ Σ†ΣΣ†χ ] + h.c., L4

χ = g4 tr

[ Σ†Σ ] tr [ Σ†χ ] + h.c., L5

χ = g5 tr

[ Σ†χΣ†χ ] + h.c. L6

χ = g6 tr

[ ΣΣ†χχ† + Σ†Σχ†χ ] , L7

χ = g7

( tr [ Σ†χ ] + h.c. )2 L8

χ = g8

( tr [ Σ†χ ] − h.c. )2, L9

χ = −g9 tr

[ Σ†χχ†χ ] + h.c. L10

χ = −g10 tr

[ χ†χ ] tr [ χ†Σ ] + h.c.

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 7 / 23

slide-16
SLIDE 16

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Inclusion of explicit chiral symmetry breaking terms

Lχ =

10

∑

i=1

Li

χ,

L1

χ = −κ1 eijkemnlΣimχjnχkl + h.c.,

L2

χ = κ2 eijkemnlχimΣjnΣkl + h.c.,

L3

χ = g3 tr

[ Σ†ΣΣ†χ ] + h.c., L4

χ = g4 tr

[ Σ†Σ ] tr [ Σ†χ ] + h.c., L5

χ = g5 tr

[ Σ†χΣ†χ ] + h.c. L6

χ = g6 tr

[ ΣΣ†χχ† + Σ†Σχ†χ ] , L7

χ = g7

( tr [ Σ†χ ] + h.c. )2 L8

χ = g8

( tr [ Σ†χ ] − h.c. )2, L9

χ = −g9 tr

[ Σ†χχ†χ ] + h.c. L10

χ = −g10 tr

[ χ†χ ] tr [ χ†Σ ] + h.c. κ1, g9, g10 → 0 without loss of generality

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 7 / 23

slide-17
SLIDE 17

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Inclusion of explicit chiral symmetry breaking terms

Lχ =

10

∑

i=1

Li

χ,

L1

χ = −κ1 eijkemnlΣimχjnχkl + h.c.,

L2

χ = κ2 eijkemnlχimΣjnΣkl + h.c.,

L3

χ = g3 tr

[ Σ†ΣΣ†χ ] + h.c., L4

χ = g4 tr

[ Σ†Σ ] tr [ Σ†χ ] + h.c., L5

χ = g5 tr

[ Σ†χΣ†χ ] + h.c. L6

χ = g6 tr

[ ΣΣ†χχ† + Σ†Σχ†χ ] , L7

χ = g7

( tr [ Σ†χ ] + h.c. )2 L8

χ = g8

( tr [ Σ†χ ] − h.c. )2, L9

χ = −g9 tr

[ Σ†χχ†χ ] + h.c. L10

χ = −g10 tr

[ χ†χ ] tr [ χ†Σ ] + h.c. κ1, g9, g10 → 0 without loss of generality χ → 1

2 ˆ

m

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 7 / 23

slide-18
SLIDE 18

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Inclusion of explicit chiral symmetry breaking terms

Lχ =

10

∑

i=1

Li

χ,

L1

χ = −κ1 eijkemnlΣimχjnχkl + h.c.,

L2

χ = κ2 eijkemnlχimΣjnΣkl + h.c.,

L3

χ = g3 tr

[ Σ†ΣΣ†χ ] + h.c., L4

χ = g4 tr

[ Σ†Σ ] tr [ Σ†χ ] + h.c., L5

χ = g5 tr

[ Σ†χΣ†χ ] + h.c. L6

χ = g6 tr

[ ΣΣ†χχ† + Σ†Σχ†χ ] , L7

χ = g7

( tr [ Σ†χ ] + h.c. )2 L8

χ = g8

( tr [ Σ†χ ] − h.c. )2, L9

χ = −g9 tr

[ Σ†χχ†χ ] + h.c. L10

χ = −g10 tr

[ χ†χ ] tr [ χ†Σ ] + h.c. κ1, g9, g10 → 0 without loss of generality χ → 1

2 ˆ

m κ1, κ2, g4, g7, g8, g10 OZI violating

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 7 / 23

slide-19
SLIDE 19

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Thermodynamic potential

Ω =Vst [hi] + ∑

i

Nc 8π2 (J−1 [Mi [hi], T, µi] + C [T, µi]) Vst [hi] = 1 16 ( 4G ( h2

i

) + 3g1 ( h2

i

)2 + 3g2 ( h4

i

) + 4g3 ( h3

i mi

) + 4g4 ( h2

i

) ( hjmj ) + 2g5 ( h2

i m2 i

) + 2g6 ( h2

i m2 i

) + 4g7 (himi)2 + 8κhuhdhs + 8κ2 (muhdhs + humdhs + huhdms) )

  • Mi

∆f =Mf − mf = − Ghf − g1 2 hf (h2

i ) − g2

2 (h3

f ) − 3g3

4 h2

f mf − g4

4 ( mf ( h2

i

) + 2hf (mihi) ) − g5 + g6 2 hf m2

f − g7mf (himi) − κ

4 tfijhihj − κ2tfijhimj

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 8 / 23

slide-20
SLIDE 20

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Thermodynamic potential

Ω =Vst [hi] + ∑

i

Nc 8π2 (J−1 [Mi [hi], T, µi] + C [T, µi]) Vst [hi] = 1 16 ( 4G ( h2

i

) + 3g1 ( h2

i

)2 + 3g2 ( h4

i

) + 4g3 ( h3

i mi

) + 4g4 ( h2

i

) ( hjmj ) + 2g5 ( h2

i m2 i

) + 2g6 ( h2

i m2 i

) + 4g7 (himi)2 + 8κhuhdhs + 8κ2 (muhdhs + humdhs + huhdms) )

  • Mi

∆f =Mf − mf = − Ghf − g1 2 hf (h2

i ) − g2

2 (h3

f ) − 3g3

4 h2

f mf − g4

4 ( mf ( h2

i

) + 2hf (mihi) ) − g5 + g6 2 hf m2

f − g7mf (himi) − κ

4 tfijhihj − κ2tfijhimj

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 8 / 23

slide-21
SLIDE 21

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Thermodynamic potential

Ω =Vst [hi] + ∑

i

Nc 8π2 (J−1 [Mi [hi], T, µi] + C [T, µi]) Vst [hi] = 1 16 ( 4G ( h2

i

) + 3g1 ( h2

i

)2 + 3g2 ( h4

i

) + 4g3 ( h3

i mi

) + 4g4 ( h2

i

) ( hjmj ) + 2g5 ( h2

i m2 i

) + 2g6 ( h2

i m2 i

) + 4g7 (himi)2 + 8κhuhdhs + 8κ2 (muhdhs + humdhs + huhdms) )

  • Mi

∆f =Mf − mf = − Ghf − g1 2 hf (h2

i ) − g2

2 (h3

f ) − 3g3

4 h2

f mf − g4

4 ( mf ( h2

i

) + 2hf (mihi) ) − g5 + g6 2 hf m2

f − g7mf (himi) − κ

4 tfijhihj − κ2tfijhimj

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 8 / 23

slide-22
SLIDE 22

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Thermodynamic potential: the fermionic integrals

Ω =Vst [hi] + ∑

i

Nc 8π2 (J−1 [Mi [hi] , T, µi] + C [T, µi]) Jvac

−1 [M, Λ] = −16π2

∫ d4p (2π)4 ∫ E2

M

E2

dE2 ˆ ρ 1 E2 + p2

4

J−1 [M, Λ, µ, T] = −16π2 ∫ d3− → p (2π)3 ∫ E2

M

E2

dE2 T

+∞

∑

n=−∞

ˆ ρ 1 E2 + (π(2n + 1)T − iµ)2 = − ∫ d3− → p (2π)3 ∫ E2

M

E2

dE2 ˆ ρ 8π2 E ( 1 − nq [E, µ, T] − nq [E, µ, T] ) ˆ ρE

PV = 1 − (1 − Λ2

∂ ∂E2 )e

−Λ2

∂ ∂E2

C(T, µ) = ∫ d3p (2π)3 16π2Tlog (( 1 + e− |p|−µ

T

) ( 1 + e− |p|+µ

T

))

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 9 / 23

slide-23
SLIDE 23

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Thermodynamic potential: the fermionic integrals

Ω =Vst [hi] + ∑

i

Nc 8π2 (J−1 [Mi [hi] , T, µi] + C [T, µi]) Jvac

−1 [M, Λ] = −16π2

∫ d4p (2π)4 ∫ E2

M

E2

dE2 ˆ ρ 1 E2 + p2

4

J−1 [M, Λ, µ, T] = −16π2 ∫ d3− → p (2π)3 ∫ E2

M

E2

dE2 T

+∞

∑

n=−∞

ˆ ρ 1 E2 + (π(2n + 1)T − iµ)2 = − ∫ d3− → p (2π)3 ∫ E2

M

E2

dE2 ˆ ρ 8π2 E ( 1 − nq [E, µ, T] − nq [E, µ, T] ) ˆ ρE

PV = 1 − (1 − Λ2

∂ ∂E2 )e

−Λ2

∂ ∂E2

C(T, µ) = ∫ d3p (2π)3 16π2Tlog (( 1 + e− |p|−µ

T

) ( 1 + e− |p|+µ

T

))

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 9 / 23

slide-24
SLIDE 24

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Thermodynamic potential: the fermionic integrals

Ω =Vst [hi] + ∑

i

Nc 8π2 (J−1 [Mi [hi] , T, µi] + C [T, µi]) Jvac

−1 [M, Λ] = −16π2

∫ d4p (2π)4 ∫ E2

M

E2

dE2 ˆ ρ 1 E2 + p2

4

J−1 [M, Λ, µ, T] = −16π2 ∫ d3− → p (2π)3 ∫ E2

M

E2

dE2 T

+∞

∑

n=−∞

ˆ ρ 1 E2 + (π(2n + 1)T − iµ)2 = − ∫ d3− → p (2π)3 ∫ E2

M

E2

dE2 ˆ ρ 8π2 E ( 1 − nq [E, µ, T] − nq [E, µ, T] ) ˆ ρE

PV = 1 − (1 − Λ2

∂ ∂E2 )e

−Λ2

∂ ∂E2

C(T, µ) = ∫ d3p (2π)3 16π2Tlog (( 1 + e− |p|−µ

T

) ( 1 + e− |p|+µ

T

))

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 9 / 23

slide-25
SLIDE 25

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Inclusion of the Polyakov loop.

Introduce homogeneous background A4 gluonic field ∂µ →Dµ = ∂µ + ıAµ, Aµ = δµ

0 gA0 a

λa 2 , L = Pe

∫ β

0 dx4ıA4,

ϕ = 1 Nc TrL, ϕ = 1 Nc TrL†

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 10 / 23

slide-26
SLIDE 26

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Inclusion of the Polyakov loop.

Introduce homogeneous background A4 gluonic field ∂µ →Dµ = ∂µ + ıAµ, Aµ = δµ

0 gA0 a

λa 2 , L = Pe

∫ β

0 dx4ıA4,

ϕ = 1 Nc TrL, ϕ = 1 Nc TrL† Polyakov loop: ∼order parameter (exact in the quenched limit) for (de)confinement (ϕ = 0 ↔ confined)

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 10 / 23

slide-27
SLIDE 27

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Inclusion of the Polyakov loop.

Introduce homogeneous background A4 gluonic field ∂µ →Dµ = ∂µ + ıAµ, Aµ = δµ

0 gA0 a

λa 2 , L = Pe

∫ β

0 dx4ıA4,

ϕ = 1 Nc TrL, ϕ = 1 Nc TrL† Polyakov loop: ∼order parameter (exact in the quenched limit) for (de)confinement (ϕ = 0 ↔ confined) enters the action as an imaginary µ nq(M, p, µ, T) = ( 1 + e

(√ M2+p2−µ ) /T

)−1 nq(M, p, µ, T) = ( 1 + e

(√ M2+p2+µ ) /T

)−1 ˜ nq(M, p, µ, T, ϕ, ϕ) ≡ 1 Nc

Nc

∑

i=1

nq( √ M2 + p2, µ + ı (A4)ii , T) ˜ nq(M, p, µ, T, ϕ, ϕ) ≡ 1 Nc

Nc

∑

i=1

nq( √ M2 + p2, µ + ı (A4)ii , T)

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 10 / 23

slide-28
SLIDE 28

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Inclusion of the Polyakov loop.

Introduce homogeneous background A4 gluonic field ∂µ →Dµ = ∂µ + ıAµ, Aµ = δµ

0 gA0 a

λa 2 , L = Pe

∫ β

0 dx4ıA4,

ϕ = 1 Nc TrL, ϕ = 1 Nc TrL† Polyakov loop: ∼order parameter (exact in the quenched limit) for (de)confinement (ϕ = 0 ↔ confined) enters the action as an imaginary µ nq(M, p, µ, T) = ( 1 + e

(√ M2+p2−µ ) /T

)−1 nq(M, p, µ, T) = ( 1 + e

(√ M2+p2+µ ) /T

)−1 ˜ nq(M, p, µ, T, ϕ, ϕ) ≡ 1 Nc

Nc

∑

i=1

nq( √ M2 + p2, µ + ı (A4)ii , T) ˜ nq(M, p, µ, T, ϕ, ϕ) ≡ 1 Nc

Nc

∑

i=1

nq( √ M2 + p2, µ + ı (A4)ii , T) Ω [ Mi, T, µ, ϕ, ϕ ] = Vst [hi] +

Nc 8π2

∑

f=u,d,s

( J−1 [ Mf , T, µ, ϕ, ϕ ] + C(T, µ) ) + U [ ϕ, ϕ, T ]

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 10 / 23

slide-29
SLIDE 29

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Polyakov potentials

Logarithmic form 3 (a0 = 3.51, a1 = −2.47, a2 = 15.2, b3 = −1.75, T0 = 200 MeV) : UI T 4 = − 1 2 a [T] ¯ φφ + b [T] ln [ 1 − 6 ¯ φφ + 4 ( ¯ φ3 + φ3) − 3 ( ¯ φφ )2] a [T] = a0 + a1 T0 T + a2 ( T0 T )2 ; b [T] = b3 ( T0 T )3 Exponential K-Log form 4 (a0 = 6.75, a1 = −9.8, a2 = 0.26, b3 = 0.805, b4 = 7.555, K = 0.1, T0 = 175 MeV): UII T 4 = − 1 2 a [T] ¯ φφ − b3 6 ( ¯ φ3 + φ3) + b4 4 ( ¯ φφ )2 + Kln [ 27 24π2 ( 1 − 6 ¯ φφ + 4 ( ¯ φ3 + φ3) − 3 ( ¯ φφ )2)] a [T] = a0 + a1 ( T0 T ) e−a2

T0 T

  • 3S. RöSSner, C. Ratti, and W. Weise, Phys. Rev. D 75, 034007 (2007)
  • 4A. Bhattacharyya, S. K. Ghosh, S. Maity, S. Raha, R. Ray, K. Saha, and S. Upadhaya, Phys. Rev. D 95, 054005 (2017)
  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 11 / 23

slide-30
SLIDE 30

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

NJL: C2

s and Θµµ |µ=0 vs lQCD 5

C2

s ≡ ∂P ∂ϵ = − ∂Ω

∂T

T ∂2Ω

∂T2

0.10 0.15 0.20 0.25 0.30

T

0.05 0.10 0.15 0.20 0.25 0.30

Cs

2

NJLH8qA NJLH8qB NJLH8qmA NJLH8qmB WBEoS HotQCDEoS

Θμ

μ

5WB: S. Borsanyi, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, and K. K. Szabo, Phys. Lett. B730, 99 (2014), arXiv:1309.5258 [hep-lat] HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D90, 094503 (2014), arXiv:1407.6387 [hep-lat]

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 12 / 23

slide-31
SLIDE 31

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

NJL: C2

s and Θµµ |µ=0 vs lQCD 5

C2

s ≡ ∂P ∂ϵ = − ∂Ω

∂T

T ∂2Ω

∂T2

0.10 0.15 0.20 0.25 0.30

T

0.05 0.10 0.15 0.20 0.25 0.30

Cs

2

NJLH8qA NJLH8qB NJLH8qmA NJLH8qmB WBEoS HotQCDEoS

Θµµ = ϵ − 3P

0.05 0.10 0.15 0.20 0.25 0.30

T

2 4 6 8

Θμ

μ/T4

NJLH8qA NJLH8qB NJLH8qmA NJLH8qmB WBEoS HotQCDEoS

5WB: S. Borsanyi, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, and K. K. Szabo, Phys. Lett. B730, 99 (2014), arXiv:1309.5258 [hep-lat] HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D90, 094503 (2014), arXiv:1407.6387 [hep-lat]

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 12 / 23

slide-32
SLIDE 32

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

NJL: χB

2, χB 2, χS 2 |µ=0 vs lQCD 6

χB

2 = 1 2 ∂2Ω/T 4 ∂(

µB T ) 2

0.05 0.10 0.15 0.20 0.25 0.30

T

0.05 0.10 0.15

χ2

B

NJLH8qA NJLH8qB NJLH8qmA NJLH8qmB WBEoS HotQCDEoS

χB 2 = 1 9 (χu 2+χd 2 +χs 2+2χus 11+2χds 11+ 2χud 11 ) χ χ

6WB: S. Borsanyi, Z. Fodor, S. D. Katz, S. Krieg, C. Ratti, and K. Szabo, JHEP 01, 138 (2012), arXiv:1112.4416 [hep-lat]. HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D86, 034509 (2012), arXiv:1203.0784 [hep-lat].

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 13 / 23

slide-33
SLIDE 33

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

NJL: χB

2, χB 2, χS 2 |µ=0 vs lQCD 6

χB

2 = 1 2 ∂2Ω/T 4 ∂(

µB T ) 2

0.05 0.10 0.15 0.20 0.25 0.30

T

0.05 0.10 0.15

χ2

B

NJLH8qA NJLH8qB NJLH8qmA NJLH8qmB WBEoS HotQCDEoS

χB 2 = 1 9 (χu 2+χd 2 +χs 2+2χus 11+2χds 11+ 2χud 11 )

χQ

2 = 1 2 ∂2Ω/T 4 ∂(

µQ T ) 2

0.05 0.10 0.15 0.20 0.25 0.30

T

0.1 0.2 0.3 0.4

χ2

Q

NJLH8qA NJLH8qB NJLH8qmA NJLH8qmB WBEoS HotQCDEoS

χQ 2 = 1 9 (4χu 2+χd 2 +χs 2−4χus 11+ 2χds 11−4χud 11 ) χ

6WB: S. Borsanyi, Z. Fodor, S. D. Katz, S. Krieg, C. Ratti, and K. Szabo, JHEP 01, 138 (2012), arXiv:1112.4416 [hep-lat]. HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D86, 034509 (2012), arXiv:1203.0784 [hep-lat].

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 13 / 23

slide-34
SLIDE 34

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

NJL: χB

2, χB 2, χS 2 |µ=0 vs lQCD 6

χB

2 = 1 2 ∂2Ω/T 4 ∂(

µB T ) 2

0.05 0.10 0.15 0.20 0.25 0.30

T

0.05 0.10 0.15

χ2

B

NJLH8qA NJLH8qB NJLH8qmA NJLH8qmB WBEoS HotQCDEoS

χB 2 = 1 9 (χu 2+χd 2 +χs 2+2χus 11+2χds 11+ 2χud 11 )

χQ

2 = 1 2 ∂2Ω/T 4 ∂(

µQ T ) 2

0.05 0.10 0.15 0.20 0.25 0.30

T

0.1 0.2 0.3 0.4

χ2

Q

NJLH8qA NJLH8qB NJLH8qmA NJLH8qmB WBEoS HotQCDEoS

χQ 2 = 1 9 (4χu 2+χd 2 +χs 2−4χus 11+ 2χds 11−4χud 11 )

χS

2 = 1 2 ∂2Ω/T 4 ∂(

µS T ) 2

0.05 0.10 0.15 0.20 0.25 0.30

T

0.1 0.2 0.3 0.4 0.5

χ2

S

NJLH8qA NJLH8qB NJLH8qmA NJLH8qmB WBEoS HotQCDEoS

χS 2 =χs 2

6WB: S. Borsanyi, Z. Fodor, S. D. Katz, S. Krieg, C. Ratti, and K. Szabo, JHEP 01, 138 (2012), arXiv:1112.4416 [hep-lat]. HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D86, 034509 (2012), arXiv:1203.0784 [hep-lat].

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 13 / 23

slide-35
SLIDE 35

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

NJL: χB Q

1 1 , χB S 1 1 , χQ S 1 1 |µ=0 vs lQCD 7

χBQ

11 = ∂2Ω/T 4 ∂(

µB T )∂( µQ T )

0.05 0.10 0.15 0.20 0.25 0.30

T

0.01 0.02 0.03 0.04 0.05 0.06

χ1 1

B Q

NJLH8qA NJLH8qB NJLH8qmA NJLH8qmB HotQCDEoS

χBQ 11 = 1 9 (2χu 2−χd 2 −χs 2+χud 11 + χus 11−2χds 11) χ χ

7HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D86, 034509 (2012), arXiv:1203.0784 [hep-lat].

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 14 / 23

slide-36
SLIDE 36

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

NJL: χB Q

1 1 , χB S 1 1 , χQ S 1 1 |µ=0 vs lQCD 7

χBQ

11 = ∂2Ω/T 4 ∂(

µB T )∂( µQ T )

0.05 0.10 0.15 0.20 0.25 0.30

T

0.01 0.02 0.03 0.04 0.05 0.06

χ1 1

B Q

NJLH8qA NJLH8qB NJLH8qmA NJLH8qmB HotQCDEoS

χBQ 11 = 1 9 (2χu 2−χd 2 −χs 2+χud 11 + χus 11−2χds 11)

χBS

11 = ∂2Ω/T 4 ∂(

µB T )∂( µS T )

0.05 0.10 0.15 0.20 0.25 0.30

T

0.1 0.2 0.3 0.4

  • χ1 1

B S

NJLH8qA NJLH8qB NJLH8qmA NJLH8qmB HotQCDEoS

χBS 11 =− 1 3 (χs 2+χus 11+χds 11) χ

7HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D86, 034509 (2012), arXiv:1203.0784 [hep-lat].

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 14 / 23

slide-37
SLIDE 37

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

NJL: χB Q

1 1 , χB S 1 1 , χQ S 1 1 |µ=0 vs lQCD 7

χBQ

11 = ∂2Ω/T 4 ∂(

µB T )∂( µQ T )

0.05 0.10 0.15 0.20 0.25 0.30

T

0.01 0.02 0.03 0.04 0.05 0.06

χ1 1

B Q

NJLH8qA NJLH8qB NJLH8qmA NJLH8qmB HotQCDEoS

χBQ 11 = 1 9 (2χu 2−χd 2 −χs 2+χud 11 + χus 11−2χds 11)

χBS

11 = ∂2Ω/T 4 ∂(

µB T )∂( µS T )

0.05 0.10 0.15 0.20 0.25 0.30

T

0.1 0.2 0.3 0.4

  • χ1 1

B S

NJLH8qA NJLH8qB NJLH8qmA NJLH8qmB HotQCDEoS

χBS 11 =− 1 3 (χs 2+χus 11+χds 11)

χQS

11 = ∂2Ω/T 4 ∂(

µQ T )∂( µS T )

0.05 0.10 0.15 0.20 0.25 0.30

T

0.1 0.2 0.3 0.4

χ1 1

Q S

NJLH8qA NJLH8qB NJLH8qmA NJLH8qmB HotQCDEoS

χQS 11 = 1 3 (χs 2−2χus 11+χds 11)

7HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D86, 034509 (2012), arXiv:1203.0784 [hep-lat].

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 14 / 23

slide-38
SLIDE 38

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

PNJL (Log): C2

s and Θµµ |µ=0 vs lQCD 8

C2

s ≡ ∂P ∂ϵ = − ∂Ω

∂T

T ∂2Ω

∂T2

0.10 0.15 0.20 0.25 0.30

T

0.05 0.10 0.15 0.20 0.25 0.30

Cs

2

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB WBEoS HotQCDEoS

Θμ

μ

8WB: S. Borsanyi, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, and K. K. Szabo, Phys. Lett. B730, 99 (2014), arXiv:1309.5258 [hep-lat] HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D90, 094503 (2014), arXiv:1407.6387 [hep-lat]

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 15 / 23

slide-39
SLIDE 39

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

PNJL (Log): C2

s and Θµµ |µ=0 vs lQCD 8

C2

s ≡ ∂P ∂ϵ = − ∂Ω

∂T

T ∂2Ω

∂T2

0.10 0.15 0.20 0.25 0.30

T

0.05 0.10 0.15 0.20 0.25 0.30

Cs

2

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB WBEoS HotQCDEoS

Θµµ = ϵ − 3P

0.05 0.10 0.15 0.20 0.25 0.30

T

2 4 6 8

Θμ

μ/T4

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB WBEoS HotQCDEoS

8WB: S. Borsanyi, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, and K. K. Szabo, Phys. Lett. B730, 99 (2014), arXiv:1309.5258 [hep-lat] HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D90, 094503 (2014), arXiv:1407.6387 [hep-lat]

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 15 / 23

slide-40
SLIDE 40

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

PNJL (Log): χB

2, χB 2, χS 2 |µ=0 vs lQCD 9

χB

2 = 1 2 ∂2Ω/T 4 ∂(

µB T ) 2

0.05 0.10 0.15 0.20 0.25 0.30

T

0.05 0.10 0.15

χ2

B

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB WBEoS HotQCDEoS

χ χ

9WB: S. Borsanyi, Z. Fodor, S. D. Katz, S. Krieg, C. Ratti, and K. Szabo, JHEP 01, 138 (2012), arXiv:1112.4416 [hep-lat]. HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D86, 034509 (2012), arXiv:1203.0784 [hep-lat].

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 16 / 23

slide-41
SLIDE 41

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

PNJL (Log): χB

2, χB 2, χS 2 |µ=0 vs lQCD 9

χB

2 = 1 2 ∂2Ω/T 4 ∂(

µB T ) 2

0.05 0.10 0.15 0.20 0.25 0.30

T

0.05 0.10 0.15

χ2

B

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB WBEoS HotQCDEoS

χQ

2 = 1 2 ∂2Ω/T 4 ∂(

µQ T ) 2

0.05 0.10 0.15 0.20 0.25 0.30

T

0.1 0.2 0.3 0.4

χ2

Q

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB WBEoS HotQCDEoS

χ

9WB: S. Borsanyi, Z. Fodor, S. D. Katz, S. Krieg, C. Ratti, and K. Szabo, JHEP 01, 138 (2012), arXiv:1112.4416 [hep-lat]. HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D86, 034509 (2012), arXiv:1203.0784 [hep-lat].

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 16 / 23

slide-42
SLIDE 42

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

PNJL (Log): χB

2, χB 2, χS 2 |µ=0 vs lQCD 9

χB

2 = 1 2 ∂2Ω/T 4 ∂(

µB T ) 2

0.05 0.10 0.15 0.20 0.25 0.30

T

0.05 0.10 0.15

χ2

B

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB WBEoS HotQCDEoS

χQ

2 = 1 2 ∂2Ω/T 4 ∂(

µQ T ) 2

0.05 0.10 0.15 0.20 0.25 0.30

T

0.1 0.2 0.3 0.4

χ2

Q

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB WBEoS HotQCDEoS

χS

2 = 1 2 ∂2Ω/T 4 ∂(

µS T ) 2

0.05 0.10 0.15 0.20 0.25 0.30

T

0.1 0.2 0.3 0.4 0.5

χ2

S

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB WBEoS HotQCDEoS

9WB: S. Borsanyi, Z. Fodor, S. D. Katz, S. Krieg, C. Ratti, and K. Szabo, JHEP 01, 138 (2012), arXiv:1112.4416 [hep-lat]. HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D86, 034509 (2012), arXiv:1203.0784 [hep-lat].

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 16 / 23

slide-43
SLIDE 43

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

PNJL (Log): χB Q

1 1 , χB S 1 1 , χQ S 1 1 |µ=0 vs lQCD 10

χBQ

11 = ∂2Ω/T 4 ∂(

µB T )∂( µQ T )

0.05 0.10 0.15 0.20 0.25 0.30

T

0.01 0.02 0.03 0.04 0.05 0.06

χ1 1

B Q

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB HotQCDEoS

χ χ

10HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D86, 034509 (2012), arXiv:1203.0784 [hep-lat].

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 17 / 23

slide-44
SLIDE 44

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

PNJL (Log): χB Q

1 1 , χB S 1 1 , χQ S 1 1 |µ=0 vs lQCD 10

χBQ

11 = ∂2Ω/T 4 ∂(

µB T )∂( µQ T )

0.05 0.10 0.15 0.20 0.25 0.30

T

0.01 0.02 0.03 0.04 0.05 0.06

χ1 1

B Q

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB HotQCDEoS

χBS

11 = ∂2Ω/T 4 ∂(

µB T )∂( µS T )

0.05 0.10 0.15 0.20 0.25 0.30

T

0.1 0.2 0.3 0.4

  • χ1 1

B S

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB HotQCDEoS

χ

10HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D86, 034509 (2012), arXiv:1203.0784 [hep-lat].

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 17 / 23

slide-45
SLIDE 45

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

PNJL (Log): χB Q

1 1 , χB S 1 1 , χQ S 1 1 |µ=0 vs lQCD 10

χBQ

11 = ∂2Ω/T 4 ∂(

µB T )∂( µQ T )

0.05 0.10 0.15 0.20 0.25 0.30

T

0.01 0.02 0.03 0.04 0.05 0.06

χ1 1

B Q

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB HotQCDEoS

χBS

11 = ∂2Ω/T 4 ∂(

µB T )∂( µS T )

0.05 0.10 0.15 0.20 0.25 0.30

T

0.1 0.2 0.3 0.4

  • χ1 1

B S

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB HotQCDEoS

χQS

11 = ∂2Ω/T 4 ∂(

µQ T )∂( µS T )

0.05 0.10 0.15 0.20 0.25 0.30

T

0.1 0.2 0.3 0.4

χ1 1

Q S

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB HotQCDEoS

10HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D86, 034509 (2012), arXiv:1203.0784 [hep-lat].

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 17 / 23

slide-46
SLIDE 46

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

PNJL (Exp K-Log): C2

s and Θµµ |µ=0 vs lQCD 11

C2

s ≡ ∂P ∂ϵ = − ∂Ω

∂T

T ∂2Ω

∂T2

0.10 0.15 0.20 0.25 0.30

T

0.05 0.10 0.15 0.20 0.25 0.30

Cs

2

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB WBEoS HotQCDEoS

Θμ

μ

11WB: S. Borsanyi, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, and K. K. Szabo, Phys. Lett. B730, 99 (2014), arXiv:1309.5258 [hep-lat] HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D90, 094503 (2014), arXiv:1407.6387 [hep-lat]

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 18 / 23

slide-47
SLIDE 47

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

PNJL (Exp K-Log): C2

s and Θµµ |µ=0 vs lQCD 11

C2

s ≡ ∂P ∂ϵ = − ∂Ω

∂T

T ∂2Ω

∂T2

0.10 0.15 0.20 0.25 0.30

T

0.05 0.10 0.15 0.20 0.25 0.30

Cs

2

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB WBEoS HotQCDEoS

Θµµ = ϵ − 3P

0.05 0.10 0.15 0.20 0.25 0.30

T

2 4 6 8

Θμ

μ/T4

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB WBEoS HotQCDEoS

11WB: S. Borsanyi, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, and K. K. Szabo, Phys. Lett. B730, 99 (2014), arXiv:1309.5258 [hep-lat] HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D90, 094503 (2014), arXiv:1407.6387 [hep-lat]

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 18 / 23

slide-48
SLIDE 48

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

PNJL (Exp K-Log): χB

2, χB 2, χS 2 |µ=0 vs lQCD 12

χB

2 = 1 2 ∂2Ω/T 4 ∂(

µB T ) 2

0.05 0.10 0.15 0.20 0.25 0.30

T

0.05 0.10 0.15

χ2

B

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB WBEoS HotQCDEoS

χ χ

12WB: S. Borsanyi, Z. Fodor, S. D. Katz, S. Krieg, C. Ratti, and K. Szabo, JHEP 01, 138 (2012), arXiv:1112.4416 [hep-lat]. HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D86, 034509 (2012), arXiv:1203.0784 [hep-lat].

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 19 / 23

slide-49
SLIDE 49

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

PNJL (Exp K-Log): χB

2, χB 2, χS 2 |µ=0 vs lQCD 12

χB

2 = 1 2 ∂2Ω/T 4 ∂(

µB T ) 2

0.05 0.10 0.15 0.20 0.25 0.30

T

0.05 0.10 0.15

χ2

B

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB WBEoS HotQCDEoS

χQ

2 = 1 2 ∂2Ω/T 4 ∂(

µQ T ) 2

0.05 0.10 0.15 0.20 0.25 0.30

T

0.1 0.2 0.3 0.4

χ2

Q

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB WBEoS HotQCDEoS

χ

12WB: S. Borsanyi, Z. Fodor, S. D. Katz, S. Krieg, C. Ratti, and K. Szabo, JHEP 01, 138 (2012), arXiv:1112.4416 [hep-lat]. HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D86, 034509 (2012), arXiv:1203.0784 [hep-lat].

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 19 / 23

slide-50
SLIDE 50

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

PNJL (Exp K-Log): χB

2, χB 2, χS 2 |µ=0 vs lQCD 12

χB

2 = 1 2 ∂2Ω/T 4 ∂(

µB T ) 2

0.05 0.10 0.15 0.20 0.25 0.30

T

0.05 0.10 0.15

χ2

B

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB WBEoS HotQCDEoS

χQ

2 = 1 2 ∂2Ω/T 4 ∂(

µQ T ) 2

0.05 0.10 0.15 0.20 0.25 0.30

T

0.1 0.2 0.3 0.4

χ2

Q

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB WBEoS HotQCDEoS

χS

2 = 1 2 ∂2Ω/T 4 ∂(

µS T ) 2

0.05 0.10 0.15 0.20 0.25 0.30

T

0.1 0.2 0.3 0.4 0.5

χ2

S

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB WBEoS HotQCDEoS

12WB: S. Borsanyi, Z. Fodor, S. D. Katz, S. Krieg, C. Ratti, and K. Szabo, JHEP 01, 138 (2012), arXiv:1112.4416 [hep-lat]. HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D86, 034509 (2012), arXiv:1203.0784 [hep-lat].

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 19 / 23

slide-51
SLIDE 51

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

PNJL (Exp K-Log): χB Q

1 1 , χB S 1 1 , χQ S 1 1 |µ=0 vs lQCD 13

χBQ

11 = ∂2Ω/T 4 ∂(

µB T )∂( µQ T )

0.05 0.10 0.15 0.20 0.25 0.30

T

0.01 0.02 0.03 0.04 0.05 0.06

χ1 1

B Q

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB HotQCDEoS

χ χ

13HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D86, 034509 (2012), arXiv:1203.0784 [hep-lat].

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 20 / 23

slide-52
SLIDE 52

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

PNJL (Exp K-Log): χB Q

1 1 , χB S 1 1 , χQ S 1 1 |µ=0 vs lQCD 13

χBQ

11 = ∂2Ω/T 4 ∂(

µB T )∂( µQ T )

0.05 0.10 0.15 0.20 0.25 0.30

T

0.01 0.02 0.03 0.04 0.05 0.06

χ1 1

B Q

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB HotQCDEoS

χBS

11 = ∂2Ω/T 4 ∂(

µB T )∂( µS T )

0.05 0.10 0.15 0.20 0.25 0.30

T

0.1 0.2 0.3 0.4

  • χ1 1

B S

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB HotQCDEoS

χ

13HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D86, 034509 (2012), arXiv:1203.0784 [hep-lat].

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 20 / 23

slide-53
SLIDE 53

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

PNJL (Exp K-Log): χB Q

1 1 , χB S 1 1 , χQ S 1 1 |µ=0 vs lQCD 13

χBQ

11 = ∂2Ω/T 4 ∂(

µB T )∂( µQ T )

0.05 0.10 0.15 0.20 0.25 0.30

T

0.01 0.02 0.03 0.04 0.05 0.06

χ1 1

B Q

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB HotQCDEoS

χBS

11 = ∂2Ω/T 4 ∂(

µB T )∂( µS T )

0.05 0.10 0.15 0.20 0.25 0.30

T

0.1 0.2 0.3 0.4

  • χ1 1

B S

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB HotQCDEoS

χQS

11 = ∂2Ω/T 4 ∂(

µQ T )∂( µS T )

0.05 0.10 0.15 0.20 0.25 0.30

T

0.1 0.2 0.3 0.4

χ1 1

Q S

PNJLH8qA PNJLH8qB PNJLH8qmA PNJLH8qmB HotQCDEoS

13HotQCD: A. Bazavov et al. (HotQCD), Phys. Rev. D86, 034509 (2012), arXiv:1203.0784 [hep-lat].

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 20 / 23

slide-54
SLIDE 54

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

PNJL: χus

11 |µ=0 vs lQCD 14 : gluonic signature?

χu s

1 1 = ∂2Ω/T 4 ∂( µu

T )∂( µs T )

0.1 0.2 0.3 0.4 T

  • 0.05
  • 0.04
  • 0.03
  • 0.02
  • 0.01

0.00

χ1 1

u s

LogTc200 ExpKLogTc175 WBEoS

14WB: S. Borsanyi, Z. Fodor, S. D. Katz, S. Krieg, C. Ratti, and K. Szabo, JHEP 01, 138 (2012), arXiv:1112.4416 [hep-lat].

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 21 / 23

slide-55
SLIDE 55

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Conclusions

Multiquark interaction and full pattern of explicit chiral symmetry breaking play a key role in the reproduction of several key lQCD results Perfect fit across the board is not achieved with this Polykov potential but very promising results PNJL can however shift several results in temperature towards lQCD data Correlations in the uds base dissapear without Polyakov loop

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 22 / 23

slide-56
SLIDE 56

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Outline Introduction and formalism Results Conclusions

Additional information:

“Thermodynamical properties of strongly interacting matter in a model with explicit chiral symmetry breaking interactions” J. Moreira, J. Morais, B. Hiller, A.A. Osipov, A.H. Blin, e-Print: arXiv:1806.00327 I would like to thank the support:

FCT through grant SFRH/BPD/110421/2015. Networking support by the COST Action CA15213 THOR. AFIF-Associação de Física de Interacções Fortes.

  • J. Moreira (CFisUC,BLTP)

QCD PD in an extended ELA SEWM 2018, 28/06/2018 23 / 23