Critical endpoints of the finite temperature QCD Yoshifumi Nakamura - PowerPoint PPT Presentation

Critical endpoints of the finite temperature QCD Yoshifumi Nakamura RIKEN Center for Computational Science in collaboration with Y. Kuramashi, H. Ohno & S. Takeda International Molecule-type Workshop Frontiers in Lattice QCD and related topics April 15 - April 26 2019 Yukawa Institute for Theoretical Physics, Kyoto University 1 / 34

Contents • introduction • Columbia plot • previous studies for critical endpoint • previous studies for critical endline • preliminary results • New N f = 3 simulations at N t = 12 • New N f = 2 + 1 simulations away from symmetric point • summary 2 / 34

Columbia plot nature of finite temperature phase transition of 2+1 flavor QCD at µ = 0 in the plane of m u , d and m s • 1st order : small m q region [Pisarski, Wilczek, ’84] • 1st order : heavy m q region • crossover : medium m q • 2nd order ( Z 2 ) : boundary between 1st and crossover At small m q region • crossover at the physical point • critical end point at SU(3) flavor symmetric point, m sym , has not been determined yet • critical end line has not been well determined yet 3 / 34

Previous studies for critical endpoint found N f S G S F N t endpoint ref y 3 S W 4 m PS > 1 GeV Iwasaki et al, ’96 y 3 S KS 4 m PS ∼ 290 MeV Karsch et al, ’01 y 3 I p4 4 m PS ∼ 190 MeV Karsch et al, ’01 m PS = 290 ( 20 ) MeV y 3 S KS 4 Karsch et al, ’04 y 3 I p4 4 m PS = 67 ( 17 ) MeV Karsch et al, ’04 y 3 S KS 4 am q ≈ 0 . 033 Karsch et al, ’04 am q = 0 . 0260 ( 5 ) y 3 S KS 4 de Forcrand et al, ’07 y 3 S KS 4 m PS / T = 1 . 680 ( 4 ) de Forcrand et al, ’07 y 3 S KS 6 m PS / T = 0954 ( 12 ) de Forcrand et al, ’07 m q / m phy ≤ 0 . 07 n 2+1 I stout KS 4 Endrodi et al, ’07 m q / m phy ≤ 0 . 12 n 2+1 I stout KS 6 Endrodi et al, ’07 n 3 I HISQ 6 m PS ≲ 50 MeV Bazavov et al, ’17 y 3 I imp. W 4,6,8 m PS ∼ 300 MeV our, ’14 y 3 I imp. W 8,10 m PS ≲ 170 MeV our, ’17 n 2+1 I HISQ 6,8(,12) m π ≤ 80 MeV Ding et al, ’18, ’19 Endrodi et al, ’07 : m l / m s = m phy / m phy s l Ding et al, ’18, ’19 : m s = m phy s 4 / 34

Our study for critical endpoints • Iwasaki gauge + NP O(a) improved Wilson fermions • chiral condensate (10 - 20 noises for Tr D − 1 , − 2 . − 3 , − 4 ) • kurtosis intersection method to determine the critical endpoint • reweighting method to obtain more critical endpoints light heavy 0 x K t V>V>V 1st order K x E K crossover -2 • O(100) zero temperature runs for physical scale setting are covering almost critical endpoints and also transition points of finite temperature simulations 5 / 34

N f = 3 simulation parameters • N t = 4 ( a ≈ 0 . 23 fm) , N l = 6 , 8 , 10 , 12 , 16 • β = 1 . 60 , κ = 0 . 1431 − 0 . 1439 • β = 1 . 65 , κ = 0 . 1410 − 0 . 1415 • β = 1 . 70 , κ = 0 . 1371 − 0 . 1390 • N t = 6 ( a ≈ 0 . 19 fm) , N l = 10 , 12 , 16 , 24 • β = 1 . 715 , κ = 0 . 140900 − 0 . 141100 • β = 1 . 73 , κ = 0 . 140420 − 0 . 140450 • β = 1 . 75 , κ = 0 . 139620 − 0 . 139700 • N t = 8 ( a ≈ 0 . 16 fm) , N l = 16 , 20 , 24 , 28 • β = 1 . 745 , κ = 0 . 140371 − 0 . 140393 • β = 1 . 74995 , κ = 0 . 140240 • β = 1 . 76 , κ = 0 . 139950 • N t = 10 ( a ≈ 0 . 13 fm), N l = 16 , 20 , 24 , 28 • β = 1 . 77 , κ = 0 . 139800 − 0 . 139900 • β = 1 . 78 , κ = 0 . 139550 − 0 . 139650 • β = 1 . 79 , κ = 0 . 139300 − 0 . 139400 6 / 34

N f = 3 susceptibility and kurtosis (example 1) 450 N t =8, β =1.745 400 350 300 susceptibility 250 200 150 100 50 0 1.0 0.5 0.0 kurtosis -0.5 -1.0 N s =16 N s =20 -1.5 N s =24 N s =28 -2.0 0.14037 0.14038 0.14038 0.14039 0.14039 0.14040 0.14040 κ 7 / 34

N f = 3 susceptibility and kurtosis (example 2) 90 N t =10, β =1.78 80 70 60 susceptibility 50 40 30 20 10 0 1.0 0.5 kurtosis 0.0 N s =16 -0.5 N s =20 N s =24 N s =28 -1.0 0.13956 0.13958 0.13960 0.13962 0.13964 0.13966 κ 8 / 34

N f = 3 kurtosis intersection ( N t = 4 ) 0.0 N s =10 N t =4 N s =12 N s =16 CEP 3-dim Z 2 -0.5 kurtosis -1.0 -1.5 -2.0 1.59 1.60 1.61 1.62 1.63 1.64 1.65 1.66 β 9 / 34

N f = 3 kurtosis intersection ( N t = 6 ) 0.0 N s =10 N t =6 N s =12 N s =16 N s =24 CEP -0.5 3-dim Z 2 kurtosis -1.0 -1.5 -2.0 1.71 1.72 1.73 1.74 1.75 1.76 β 10 / 34

N f = 3 kurtosis intersection ( N t = 8 ) 0.0 N s =16 N t =8 N s =20 N s =24 N s =28 CEP -0.5 3-dim Z 2 kurtosis -1.0 -1.5 -2.0 1.740 1.745 1.750 1.755 1.760 1.765 1.770 β 11 / 34

N f = 3 kurtosis intersection ( N t = 10 ) 0.0 N s =16 N t =10 N s =20 N s =24 N s =28 CEP -0.5 3-dim Z 2 kurtosis -1.0 -1.5 -2.0 1.75 1.76 1.77 1.78 1.79 1.80 1.81 β 12 / 34

N f = 3 kurtosis intersection fitting [ ] K E + AN 1 /ν ( 1 + BN y t − y h K = ( β − β E ) ) l l χ 2 / dof N t Fit β E K E ν A B y t − y h 1 . 6115 ( 26 ) − 1 . 383 ( 48 ) 0 . 84 ( 13 ) 0 . 88 ( 42 ) 4 1 × × 1 . 75 1 . 61065 ( 61 ) 0 . 313 ( 12 ) 2 − 1 . 396 0 . 63 × × 3 . 05 1 . 6099 ( 17 ) 0 . 311 ( 14 ) 0 . 10 ( 21 ) 3 − 1 . 396 0 . 63 − 0 . 894 3 . 77 6 1 1 . 72518 ( 71 ) − 1 . 373 ( 17 ) 0 . 683 ( 54 ) 0 . 58 ( 17 ) 0 . 68 × × 2 1 . 72431 ( 24 ) − 1 . 396 0 . 63 0 . 418 ( 11 ) 0 . 70 × × 3 1 . 72462 ( 40 ) − 1 . 396 0 . 63 0 . 422 ( 12 ) − 0 . 052 ( 52 ) − 0 . 894 0 . 70 8 1 1 . 75049 ( 57 ) − 1 . 219 ( 25 ) 0 . 527 ( 55 ) 0 . 146 ( 88 ) 0 . 73 × × 2 1 . 74721 ( 42 ) − 1 . 396 0 . 63 0 . 404 ( 36 ) 5 . 99 × × 3 1 . 74953 ( 33 ) − 1 . 396 0 . 63 0 . 414 ( 13 ) − 1 . 33 ( 15 ) − 0 . 894 0 . 73 1 . 77796 ( 48 ) − 0 . 974 ( 25 ) 0 . 466 ( 45 ) 0 . 084 ( 52 ) 10 1 × × 0 . 22 1 . 7694 ( 16 ) 0 . 421 ( 95 ) 2 − 1 . 396 0 . 63 × × 10 . 03 1 . 77545 ( 53 ) 0 . 559 ( 29 ) − 2 . 97 ( 25 ) 3 − 1 . 396 0 . 63 − 0 . 894 0 . 43 Fit-1: no correction term ( B = y t − y h = 0 ) and all other parameters are used as fit parameter. Fit-2: no correction term and assuming the 3D Z 2 universality class for K E and ν . Fit-3: including correction term and assuming the 3D Z 2 universality class for K E , ν and y t − y h . 13 / 34

N f = 3 , b = γ/ν of χ max ∝ N b l 3.0 2.5 2.0 1.5 b 1.0 N t =4 N t =6 0.5 N t =8 N t =10 3-dim Z 2 0.0 1.60 1.62 1.64 1.66 1.68 1.70 1.72 1.74 1.76 1.78 1.80 β critical endpoints determined by kurtosis intersection and critical exponent are consistent 14 / 34

𝑢 0.04 SU(3) symmetric point 1st order crossover 𝑢 𝑢 0 0.07 0.06 0.05 0.03 𝑢 0.02 0.01 0 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Critical endpoint ( m PS ) 󰠌𝑢 0 𝑛 PS, E fit: 𝑏 0 + 𝑏 1 ⁄𝑂 2 𝑢 + 𝑏 2 ⁄𝑂 3 solve: 𝑏 0 + 𝑏 1 ⁄𝑂 2 solve: 𝑏 0 + 𝑏 1 ⁄𝑂 2 𝑢 + 𝑏 2 ⁄𝑂 3 1⁄𝑂 2 Continuum extrapolation for √ t 0 m PS , E is still uncertain 15 / 34

0.02 0 0.07 0.06 0.05 0.04 0.03 0.09 0.01 0.17 𝑢 0.16 0.15 0.14 0.13 0.12 0.11 0.1 𝑢 Critical endpoint ( T ) 󰠌𝑢 0 𝑈 E fit: 𝑏 0 + 𝑏 1 ⁄𝑂 2 1⁄𝑂 2 16 / 34

Critical endpoint In the continuum limit m PS , E ≲ 170 MeV T E = 134 ( 3 ) MeV m PS , E / T E ≲ 1 . 3 We shall extend our study at N t = 12 17 / 34

Previous study for critical end line 0.35 [de Forcrand, Philipsen, ’07] Nf=2+1 0.3 physical point 0.25 tric - C m ud 2/5 m s 0.2 am s 0.15 0.1 0.05 0 0 0.01 0.02 0.03 0.04 am u,d • staggered fermions • N t = 4 , a ≈ 0 . 3 fm • data exhibits that slope at m sym is not - 2 ≈ 0 . 7 (roughly 5 times larger than m phy • am crit ) s s 18 / 34

0.35 (󰠌𝑢 0 𝑛 𝜌 ) 2 -2.0 -2.2 -2.4 0.45 0.40 slope 0.30 0.25 0.20 3rd degree poly. fit -1.6 2nd degree poly. fit endpoints (󰠌𝑢 0 𝑛 𝜃 𝑡 ) 2 0.45 0.40 0.35 0.30 0.25 0.20 -1.8 Our study for critical end line(1/2) around m sym • Wilson-clover fermion 𝑂 𝑔 = 3 • N t = 6 • a ≈ 0 . 19 fm • we confirmed that slope at m sym is - 2 19 / 34

Our study for critical end line(2/2) We shall extend our study for critical end line away form m sym 20 / 34

Preliminary results • New N f = 3 simulation at N t = 12 • New N f = 2 + 1 simulation away from symmetric point 21 / 34

New N f = 3 simulation at N t = 12 • N t = 12 ( a ≈ 0 . 1 fm ? ), N l = 16 , 20 , 24 , 28 , 32 • β = 1 . 78 , κ = 0 . 1396 − 0 . 1397 • β = 1 . 79 , κ = 0 . 1393 − 0 . 1395 • β = 1 . 80 , κ = 0 . 1390 − 0 . 1394 • β = 1 . 81 , κ = 0 . 13895 − 0 . 13910 • β = 1 . 82 , κ = 0 . 13875 − 0 . 13895 • β = 1 . 83 , κ = 0 . 13855 − 0 . 13880 • β = 1 . 84 , κ = 0 . 13835 − 0 . 13870 • β = 1 . 85 , κ = 0 . 13815 − 0 . 13860 22 / 34

N f = 3 susceptibility ( N t = 12 ) 120 β =1.80 N s =16 β =1.80 N s =20 β =1.80 N s =24 100 80 pbpz sus 60 40 20 0 0.1391 0.13915 0.1392 0.13925 0.1393 0.13935 κ 23 / 34

N f = 3 kurtosis ( N t = 12 ) 2 Z 2 β =1.80 N s =16 β =1.80 N s =20 1.5 β =1.80 N s =24 1 0.5 pbpz krt 0 -0.5 -1 -1.5 -2 0.1391 0.13915 0.1392 0.13925 0.1393 0.13935 κ 24 / 34

N f = 3 kurtosis intersection ( N t = 12 ) N t =12 (Fit 3) 0 N s =24 N s =28 N s =32 CEP 3-dim Z 2 -0.5 kurtosis -1 -1.5 -2 1.79 1.795 1.8 1.805 1.81 1.815 1.82 1.825 1.83 β 25 / 34