QCD: axion - PowerPoint PPT Presentation

有限温度 QCD: 相転移、トポロジー、 axion 青木保道 素粒子物理学の進展 2018 @ 基研 Aug. 9, 2018

GL-DW gluonic charge on DW ensemble GL-OV gluonic charge on OV ensemble OV- DW OV index on DW ensemble OV-OV OV index on OV ensemble χ t (m f ) for N f =2 T=220 MeV JLQCD: Lattice 2017 3 x12, β =4.3 32 2e+08 GL-DW 1st order transition ? GL-OV OV-DW 1.5e+08 OV-OV 4 ] χ [MeV 1e+08 5e+07 0 0 5 10 15 20 25 30 m f [MeV]

gluonic charge on DW ensemble GL-OV gluonic charge on OV ensemble OV- DW OV index on DW ensemble OV-OV OV index on OV ensemble GL-DW χ t (m f ) for N f =2 T=220 MeV JLQCD: Lattice 2017 3 x12, β =4.3 32 2e+08 GL-DW 1st order transition ? GL-OV OV-DW 1.5e+08 OV-OV U(1) A restoration suggested from y.a. measurement 4 ] χ [MeV 1e+08 make sense al a Pisarski & Wilczek 5e+07 0 0 5 10 15 20 25 30 m f [MeV]

OV-OV OV index on OV ensemble GL-DW gluonic charge on DW ensemble GL-OV gluonic charge on OV ensemble OV- DW OV index on DW ensemble χ t (m f ) for N f =2 T=220 MeV JLQCD: Lattice 2017 3 x12, β =4.3 32 where is the physical ud mass point ? 2e+08 GL-DW GL-OV OV-DW 1.5e+08 OV-OV ud quark のみの世界の話です 4 ] χ [MeV 1e+08 5e+07 0 0 5 10 15 20 25 30 m f [MeV] physical ud

gluonic charge on DW ensemble GL-OV gluonic charge on OV ensemble OV- DW OV index on DW ensemble OV-OV OV index on OV ensemble 宇宙初期に一次相転移 もし現実世界がこうであったら GL-DW χ t (m f ) for N f =2 T=220 MeV JLQCD: Lattice 2017 3 x12, β =4.3 32 where is the physical ud mass point ? 2e+08 GL-DW GL-OV OV-DW 1.5e+08 OV-OV ud quark のみの世界の話です 4 ] χ [MeV 1e+08 5e+07 axion window が閉じる … 0 0 5 10 15 20 25 30 m f [MeV] physical ud

JLQCD members involved in recent finite temperature study Sinya Aoki YA Guido Cossu Hidenori Fukaya 
 Shoji Hashimoto Takashi Kaneko Kei Suzuki …

もくじ • QCD 相図 : 理解の現状 ( μ =0: zero chemical potential) • 格子作用のいろいろ • axion との関係 • N f =2 JLQCD の結果を中心に • topological susceptibility • fate of the U A (1) symmetry • N f =2+1 • review of topological susceptibility

クロスオーバー 一次転移 二次転移 現在でも : Columbia Plot = 大方の人の理解 || 期待 ∞ m s ∞ 0 m ud [original Columbia plot: Brown et al 1990]

現在でも : Columbia Plot = 大方の人の理解 || 期待 ∞ physical pt. m s ∞ 0 m ud [original Columbia plot: Brown et al 1990]

N f =2+1 相図 • 連続極限で分かっていること ∞ • N f =0: 一次転移 • 右上隅はよく分かっている physical pt. m s • N f =2+1 物理点 : cross-over • staggered (YA, Endrodi, Fodor, Katz, Szabo: Nature 2006) ∞ 0 m ud • 他の正則化でも反証なし • 厳密なカイラル対称性を持つ アプローチでは未踏 • その他の領域は未確定

QCD 有限温度相転移の理論 : N f =2+1 Lattice ∞ • Nf=2+1 相図が完成すれば physical pt. m s • QCD の理解 • 物理点の相転移の存在、次数が分かる。 ∞ • 遠回りだが確実な方法 0 m ud • 相境界 ( μ =0) の μ >0 への伸び方を調べる→ (T, μ ) 臨界終点の研究へつなげる • 大変重要／有用である → ポスト京 重点課題 9 のプロジェクトのひとつ

まずは N f =2 • N f =2+1 physical pt. から遠い？ ∞ • m s ~100 MeV → ∞ • T=0 では s のあるなしは微細効果 physical pt. m s • boundary の情報としては有用 • N f =2 • Wilson, staggered: 未確定 ∞ 0 m ud • 厳密な格子カイラル対称性 ➡ U(1) A 回復を示唆 [JLQCD16] ➡ 一次転移の可能性 → χ t (m) に飛び ? [Pisarski&Wilczek]

一次転移だとどうなるか？ • 0 ≤ m f < m c : 一次転移 • 一つの可能性として : 左下 (N f =3) の一次転移領域と繋がる • 物理点への影響も考えられる • 現状では staggered → 連続極限の結果のみ ∞ ∞ ? physical pt. m s m s ∞ ∞ 0 0 m ud m ud

Columbia plot: direct search of PT / scaling ∞ 1st order 2nd order • improved Wilson physical pt. • m s WHOT-QCD Lat2016 (O(4) scaling) • Ejiri et al PRD 2016 [heavy many flavor] • 1st oder • imaginary μ → 0 • 1st order crossover staggered Bonati et al PRD 2014 • ∞ 0 Wilson Phillipsen et al PRD 2016 m ud • external parameter → phase boundary → point of interest ➡ detour the demanding region

Columbia plot: direct search of PT / scaling ∞ 1st order 2nd order • improved Wilson physical pt. • m s WHOT-QCD Lat2016 (O(4) scaling) • Ejiri et al PRD 2016 [heavy many flavor] • 1st oder • imaginary μ → 0 • 1st order crossover staggered Bonati et al PRD 2014 • ∞ 0 Wilson Phillipsen et al PRD 2016 m ud • B 0 Bonati et al -0.25 external parameter second order region → phase boundary -0.5 2 ( µ /T) → point of interest first order -0.75 region ➡ detour the demanding region -1 0 0.05 0.1 0.15 0.2 0.25 (am u,d ) 2/5

Columbia plot: direct search of PT / scaling ∞ 1st order 2nd order • improved Wilson physical pt. • m s WHOT-QCD Lat2016 (O(4) scaling) • N t = 1/ (aT) = 4 or 6 so far Ejiri et al PRD 2016 [heavy many flavor] • 1st oder • imaginary μ → 0 • → far from continuum limit 1st order crossover staggered Bonati et al PRD 2014 • ∞ 0 Wilson Phillipsen et al PRD 2016 m ud • B 0 problem not settled yet Bonati et al -0.25 external parameter second order region → phase boundary -0.5 2 ( µ /T) → point of interest first order -0.75 region ➡ detour the demanding region -1 0 0.05 0.1 0.15 0.2 0.25 (am u,d ) 2/5

Columbia plot: direct search of PT / scaling ∞ 1st order N f =2+1 or 3 physical pt. either • m s no PT found • 1st order region • shrinks as a → 0 • 1st order crossover with both staggered and Wilson ∞ 0 m ud or even disappear ? • for more information see eg • Meyer Lattice 2015 • Ding Lattice 2016 • de Forcrand • “Surprises in the Columbia plot” (Lapland talk 2018)

Columbia plot: direct search of PT / scaling ∞ 1st order N f =2+1 or 3 physical pt. either • m s no PT found • 1st order region • shrinks as a → 0 • 1st order crossover with both staggered and Wilson ∞ 0 m ud or even disappear ? • for more information see eg • Understanding of the diagram being changed a lot Meyer Lattice 2015 • Ding Lattice 2016 • de Forcrand • “Surprises in the Columbia plot” (Lapland talk 2018)

格子作用いろいろ almost × U(1) cheep domain wall ✓ ✓ exact staggered expensive overlap ✓ ✓ ✓ almost ✓ moderate impossible simulation U(1) B × SU(N f ) A SU(N f ) V cost Wilson ✓ ✓ 現状良く行われる改良 Wilson → improved version • staggered → improved version • domain wall fermion → “reweighting” to overlap [JLQCD] •

QCD and Lattice QCD Lattice QCD = QCD defined on discretized Euclidian space-time • discreteness: lattice spacing = a ( ~0.1 fm ~ (2 GeV) -1 ) • eventually continuum limit : a → 0 needed • put the system in finite 4d box : V = L s3 x L t • eventually: V → ∞ needed • able to put on the computer as a statistical system • Z = Σ exp( − S ) → Monte Carlo simulation • some symmetry is lost • infinitesimal translation and rotation • a chiral: partially or completely lost • ψ ( n + ψ ( n ) expected to recover in the continuum lim. a → 0 • U µ ( n ) exact symmetry • gauge ! • “chiral” for special discretization • (close to) exact chiral symmetry crucial for some applications •

a ψ ( n + ˆ µ ) ψ ( n ) QCD and Lattice QCD U µ ( n ) Lattice QCD = QCD defined on discretized Euclidian space-time • discreteness: lattice spacing = a ( ~0.1 fm ~ (2 GeV) -1 ) • continuum limit is needed: a → 0 • near the continuum limit • lattice operators can be expanded in powers of a • O| LQCD = O| QCD + ac 1 O 1 + a 2 c 2 O 2 . . . for some operators in some lattice discretizations • c 1 = 0 automatically → effectively close to cont. lim. • c 1 = 0 by engineering = “improvements” • most of the lattice actions used now → c 1 = 0 or c 1 ≃ 0 • • However, the size of c 2 term wildly varies among different actions

T=0 HISQ N f =4: stout improved staggered [LatKMI collab.] • t 0 from Symanzik flow: β =3.8 β =3.7 1.6 • a 2 ( β =3.7)/a 2 ( β =3.8) ≃ 1.3 1.4 2 t 0 a 2 ~30% difference in a 1.2 1 • taste symmetry violation 0 0.01 0.02 0.03 0.04 m f a 0.3 N f =4, β =3.7 0.2 ξ I ξ i π 5 ξ 4 π 05 0.2 2 2 π i5 M π M π ξ i ξ j π i0 0.1 ξ i ξ 4 π ij ξ 4 ξ 5 0.1 π 0 ξ i ξ 5 π i π I ξ 5 0 0 0 0.02 0.04 0.06 0 0.02 0.04 0.06 m f m f 改良した作用でも SU(4) V の破れが大きい