~0 QCD phase diagram (for , , quarks) Phase transition - PowerPoint PPT Presentation

Frontiers in Lattice QCD and related topics Kei Suzuki (JAEA) from JLQCD Collaboration: Sinya Aoki (YITP) , Yasumichi Aoki (RIKEN R-CCS) , Guido Cossu (Edinburgh) , Hidenori Fukaya (Osaka U.) , Shoji Hashimoto (KEK)

𝑟𝑟 ~0 ത QCD phase diagram (for 𝑣, 𝑒, 𝑡 quarks) Phase transition （ crossover ） 𝑟 𝑟 ത 𝑟𝑟 ≠ 0 ത Chiral condensate （ chiral symmetry breaking ）

U(1) A symmetry （ in vacuum, broken by anomaly ） is restored above Tc ？ • Above Tc, chiral symmetry breaking by ത 𝑟𝑟 is restored ⇒ How about U(1) A symmetry? ∞ 𝑒 4 𝑦 𝜌 𝑏 (𝑦)𝜌 𝑏 (𝑦) − 𝜀 𝑏 (𝑦)𝜀 𝑏 (𝑦) ∆ 𝜌−𝜀 = න 0 U(1) A breaking ？ 𝑟 𝑟 ത 𝑟𝑟 ത 𝑈 𝑑 3

Cf.) S. Aoki, H. Fukaya, and Y. Taniguchi, PRD86 If U(1) A is restored… Colombia plot is modified? 𝑛 𝑑𝑠𝑗 (?) 𝑂 𝑔 = 2 world 𝑛 𝑡 → ∞ 𝑛 𝑣,𝑒,𝑡 → ∞ (Pure gauge) Conventionally, at 𝑛 𝑣,𝑒 → 0 , 2 nd with 𝑃(4) 1st 𝑔 = 1 world Critical line is shifted? 1 st order? crossover 2 nd order, not 𝑃(4) ? 𝑂 1st 𝑛 𝑣,𝑒,𝑡 → 0 𝑛 𝑣,𝑒 → ∞

U(1) A symmetry above Tc ⇒ Long-standing problem in QCD • Gross-Pisarski-Yaffe (Dilute instanton gas model, 1981) restored at enough high T • Cohen (1996) w/o zero mode (or instanton) ⇒ restored • Aoki-Fukaya-Taniguchi (theory, 2012) zero mode suppressed, restored in chiral limit at 𝑂 𝑔 = 2 • HotQCD (DW, 2012) broken • JLQCD (topology fixed overlap, 2013) restored • TWQCD (optimal DW, 2013) restored • LLNL/RBC (DW, 2014) broken (restored at higher T?) • Dick et al. (overlap on HISQ, 2015) broken • Sharma et al. (overlap on DW, 2015,2016,2018) broken • Brandt et al. (Wilson, 2016) restored • Ishikawa et al. (Wilson, 2017) restored • JLQCD (reweighted overlap on DW, 2016) restored • Gomez Nicola-Ruiz de Elvira (theory, 2017) restored • Rohrhofer et al. (DW, 2017) restored ⇒ Many suggestions from lattice QCD (and models)… 5

U(1) A symmetry restoration by JLQCD Collaboration ⇒ overlap fermion (exact chiral symmetry on the lattice) valence/sea quark Setup G. Cossu et al. PRD87 OV on OV (2013) (Topology fixed sector) DW on DW A. Tomiya et al. PRD96 1/a=1.7GeV OV on DW (2017) (a=0.11fm) OV on (reweighted) OV 1/a=2.6GeV OV on DW In progress (a=0.076fm) OV on (reweighted) OV (Finer lattice) 18/Apr/2019 YITP workshop 6

Outline １． Introduction ２． U(1) A and topology from Dirac spectra ３． Results 3-1: U(1) A susceptibility at finite T 3-2: Topological susceptibility at finite T 3-3: Mesonic correlators at finite T 4. Summary 𝑟𝑟 ത 𝑟𝑟 ത 𝑟𝑟 ത U(1) A 𝑟𝑟 ത 𝑅 𝑢 = 1 𝜇 ov

Chiral condensate and Dirac spectra Banks-Casher relation: ∞ 2𝑛 𝑟𝑟 = lim ത 𝑛→0 න 𝑒𝜇 𝜍 𝜇 𝜇 2 + 𝑛 2 0 1 𝑊 Σ 𝜇 ′ < 𝜀 𝜇 − 𝜇 ′ > 𝜍 𝜇 ≡ lim 𝑊→∞ 𝜍 𝜇 with interaction 𝑟𝑟 ത 𝑟𝑟 ത 𝑟𝑟 ത 𝑟𝑟 ത Chiral condensate induced by low modes 𝜍 𝜇 ~𝜇 3 𝜇 w/o interaction 𝜍 0 = − ത 𝑟𝑟 /𝜌 18/Apr/2019 YITP workshop 8

G. Cossu et al. (JLQCD) PRD87 (2013), 114514 T-dependence of Dirac spectra Low T ： ρ(0)≠ 0 ⇒ Spontaneous chiral symmetry breaking 𝑟𝑟 ത 𝑟𝑟 ത 𝑟𝑟 ത 𝑟𝑟 ത Critical Temp. High T ： ρ(0)=0 ⇒ Chiral symmetry restoration Low energy High energy

U(1) A susceptibility and low modes of Dirac spectra ∞ 2𝑛 2 ∆ 𝜌−𝜀 = න 𝑒𝜇 𝜍 𝜇 (𝜇 2 + 𝑛 2 ) 2 0 𝜍 𝜇 Low mode contribution is enhanced by the factor of 1/𝜇 4 𝜇 ∞ 2𝑛 𝑟𝑟 = lim ത 𝑛→0 න 𝑒𝜇 𝜍 𝜇 Cf.) Banks-Casher relation: 𝜇 2 + 𝑛 2 0 10

S. Aoki, H. Fukaya, and Y. Taniguchi PRD86 (2012), 114512 A. Tomiya et al. (JLQCD) PRD96 (2017), 034509 Note ： U(1) A susc. ＝ Low modes ＋ Zero mode ？ ∞ 2𝑛 2 (𝑗)2 ) 2 2𝑛 2 (1 − 𝜇 ov 1 ∆ 𝜌−𝜀 = න 𝑒𝜇 𝜍 𝜇 ov ∆ 𝜌−𝜀 ≡ 𝑊(1 − 𝑛 2 ) 2 ෍ (𝜇 2 + 𝑛 2 ) 2 (𝑗)4 0 𝜇 ov 𝑗 𝜍 𝜇 ov integrated up to λ ＝ 0 The factor of 1/𝜇 4 enhances zero-mode contribution? subtracted zero mode In 𝑊 → ∞ limit, we know zero- 𝜇 ov mode contribution is suppressed: = 2𝑂 0 ov Δ 0−𝑛𝑝𝑒𝑓 𝑊𝑛 2 (∝ 1/ 𝑊) − 2𝑂 0 New order parameter: ov ov ഥ Δ 𝜌−𝜀 ≡ ∆ 𝜌−𝜀 𝑊𝑛 2 we subtract zero mode 11

JLQCD, preliminary (2019) Overlap Dirac spectra at T = 220MeV 𝑛 𝑟 =2.6MeV Low modes suppressed 𝑛 𝑟 =26MeV Low modes enhanced

JLQCD, preliminary (2019) U(1) A susceptibility at T = 220MeV ഥ Δ 𝜌−𝜀 is almost zero ⇒ In the chiral limit, U(1) A will be restored ⇒ At 𝑛 𝑟 = 2.6MeV, we found suppression of 10 -4 GeV 2 13

Large mass region ⇒ large ഥ Δ 𝜌−𝜀 by low mode enhancement Small mass region ⇒ small ഥ Δ 𝜌−𝜀 by low mode suppression

JLQCD, preliminary (2019) U(1) A susceptibility (Volume dependence) Finite V effect enhanced? 48 32 24 ⇒ For small 𝑛 𝑟 , V-dependence seems to be small 15

JLQCD, preliminary (2019) U(1) A susceptibility (T=220, 330MeV) Low T High T ⇒ With increasing T, U(1) A is more resotored 16

Topological susceptibility and zero mode of Dirac spectra 𝑟 𝑟 2 𝜓 𝑢 ≡ 𝑅 𝑢 L-hand R-hand , 𝑅 𝑢 = 𝑜 + − 𝑜 − 𝑊 𝑅 𝑢 = 0 Topological charge 𝑅 𝑢 is related to 𝜍 𝜇 #of Dirac zero mode （ Index theorem ） 𝑅 𝑢 = 1 Nontrivial sector Trivial sector 𝑅 𝑢 = ±1, ±2, … 𝑅 𝑢 = 0 𝑅 𝑢 = −1 𝜇 𝜇 𝑅 𝑢 = +1 − 1 = 0 𝑕 2 𝑏 ෨ 32𝜌 2 ׬ 𝑒 4 𝑦 𝐻 𝜈𝜉 𝑏 Cf.) Gluonic definition: 𝑅 𝑢 ≡ 𝐻 𝜈𝜉

JLQCD, preliminary (2019) Top. susceptibility at T = 220MeV Critical mass? ⇒ For small 𝑛 𝑟 , 𝜓 𝑢 = 0 ⇒ Around 𝑛 𝑟 ~10MeV, we found a jump (critical mass? ） Cf.) S. Aoki, H. Fukaya, and Y. Taniguchi PRD86 (2012), 114512

JLQCD, preliminary (2019) Top. susceptibility (Volume depend.) 48 32 24 ⇒ For small 𝑛 𝑟 , no volume dependence 18/Apr/2019 19

JLQCD, preliminary (2019) Top. susceptibility (T=220, 260, 330MeV) Low T High T ⇒ With increasing T, 𝜓 𝑢 is more suppressed 18/Apr/2019 YITP workshop 20

ҧ ҧ Mesonic correlators (PS for 𝑶 𝒈 = 𝟑 ) 𝜌 𝑦 𝜌(0) 𝜏 𝑦 𝜏(0) SU(2) L × SU(2) R ? ? 𝑣 ത 𝑒 𝛿 5 𝜐 𝑏 1 𝑣 𝑣 Also, Only connected disconnected U(1) A U(1) A diagram diagram 𝜃 𝑦 𝜃(0) 𝜀 𝑦 𝜀(0) SU(2) L × SU(2) R ? ? 𝑣 ത 𝑒 𝜐 𝑏 𝛿 5 𝑣 𝑣 21

JLQCD, preliminary (2019) PS-S (Connected) Correlators: U(1) A partners 24 32 ⇒ Small 𝑛 𝑟 ： U(1) A restoration, Large 𝑛 𝑟 ： U(1) A breaking 22

JLQCD, preliminary (2019) PS-S (Connected) Correlators: U(1) A partners 24 32 ⇒ Small 𝑛 𝑟 ： U(1) A restoration, Large 𝑛 𝑟 ： U(1) A breaking 23

JLQCD, preliminary (2019) V-AV Correlators ： Chiral partners 24 32 ⇒ Small 𝑛 𝑟 ： Chiral restoration, Large 𝑛 𝑟 ： Chiral breaking 24

JLQCD, preliminary (2019) V-AV Correlators ： Chiral partners 24 32 ⇒ Small 𝑛 𝑟 ： Chiral restoration, Large 𝑛 𝑟 ： Chiral breaking 25

JLQCD, preliminary (2019) Correlator ratios(C S /C PS , C AV /C V ) Small 𝑛 𝑟 : Chiral restored Small 𝑛 𝑟 : U(1) A restored (breaking<3%) Large 𝑛 𝑟 : Large 𝑛 𝑟 : U(1) A breaking Chiral breaking 18/Apr/2019

JLQCD, preliminary (2019) PS (Disconnected) correlator 𝛿 5 𝛿 5 from Dirac modes Large 𝑛 𝑟 : strong correlation? Small 𝑛 𝑟 : weak correlation ⇒ Large 𝑛 𝑟 : Correlation becomes strong ⇒ screening masses? 27

JLQCD, preliminary (2019) PS (Disconnected) screening mass Small 𝑛 𝑟 : heavy screening 𝑒𝑗𝑡 ~700MeV mass ⇒ 𝑛 𝑄𝑇 Large 𝑛 𝑟 : Light screening 𝑒𝑗𝑡 ~420MeV mass ⇒ 𝑛 𝑄𝑇 𝑒𝑗𝑡 ~ 𝑛 𝑄𝑇 𝑑𝑝𝑜 ⇒ Small 𝑛 𝑟 : 𝑛 𝑄𝑇 𝑒𝑗𝑡 [~420MeV] ＜ 𝑛 𝑄𝑇 𝑑𝑝𝑜 [~700MeV] ⇒ Large 𝑛 𝑟 : 𝑛 𝑄𝑇 28

JLQCD, preliminary (2019) Scalar (Disconnected) correlator 1 1 from Dirac modes Small 𝑛 𝑟 ： Large 𝑛 𝑟 ： Large 𝑛 𝑟 ： light screening Small 𝑛 𝑟 : heavy screening 𝑛 𝑟 が重いとき遮蔽質量 𝑒𝑗𝑡 ~300MeV mass ⇒ 𝑛 𝑇 𝑒𝑗𝑡 ~750MeV mass ⇒ 𝑛 𝑇 𝑒𝑗𝑡 ~300MeV は軽い： 𝑛 𝑇 ⇒ Large 𝑛 𝑟 : 𝑒𝑗𝑡 ~300MeV < 𝑛 𝑄𝑇 𝑒𝑗𝑡 ~420MeV !? 𝑛 𝑇 ⇒ Long-distance correlations by scalar particle? （ Finite volume effect between L=24 [~1.8fm] and L=32 [~2.4fm] ? ） 29

PS Conn. (π) － PS Disc. ＝ η’ correlation Strong Disc. Small 𝒏 𝒓 ： Large 𝒏 𝒓 ： (~150MeV) Strong Conn. = Light π (~150MeV) Low T Cancelation: Heavy η’ Cancelation: Strong Disc. High T Heavy η’ (~420MeV) Heavy π (~700MeV) Weak Disc. Heavy π (~700MeV) (~700MeV) NOT cancelation: 𝛿 5 𝛿 5 𝛿 5 𝛿 5 Light η’