Fate of axial U(1) symmetry at two flavor chiral limit of QCD in finite temperature Yasumichi Aoki & XQCD 2018 @ Frankfurt am Main May 21, 2018
Thanks to Those who gave me useful • • for useful discussion information for this talk • Ryuichiro Kitano Phillipe de Forcrand • • Norikazu Yamada Christian Lang • • JLQCD members Gian Carlo Rossi • • Sinya Aoki Peter Petreczky • • Guido Cossu Sayantan Sharma • • Shoji Hasihmoto Vicente Azcoiti • • Hidenori Fukaya Bastian Brandt • • Kei Suzuki ……
U(1) axial 5 = N f ∂ µ J µ 32 π 2 F ˜ F violated by quantum anomaly • 5 ( x ) · O (0) i = N f 32 π 2 h F ˜ h ∂ µ J µ F ( x ) · O (0) i up to contact terms at T=0, responsible for η ’ mass • non-trivial topology of gauge field • at high T, this Ward-Takahashi identity is still valid • however, if configurations that contribute to RHS is suppressed……… • ➡ the symmetry effectively recovers ๏ here N f =2 (including N f =2+1 with “2” driven to chiral limit)
Why bother ? Because it is unsettled problem ! • fate of U(1) A - analytic • Gross-Pisarski-Yaffe (1981) restores in high temperature limit • Dilute instanton gas • Cohen (1996) • measure zero instanton effect → restores • Lee-Hatsuda (1996) • zero mode does contributes → broken • Aoki-Fukaya-Tanigchi (2012) • QCD analysis (overlap) → restores w/ assumption (lattice) • Kanazawa-Yamamoto (2015) • EFT case study how restore / break • Azcoiti (2017) • case study how restore / break •
Why bother ? Because it is unsettled problem ! • fate of U(1) A lattice • HotQCD (DW, 2012) broken • JLQCD (topology fixed overlap, 2013) restores • TWQCD (optimal DW, 2013) restores ? • LLNL/RBC (DW, 2014) broken • HotQCD (DW, 2014) broken • Dick et al. (overlap on HISQ, 2015) broken • Brandt et al. (O(a) improved Wilson 2016) restores • JLQCD (reweighted overlap from DW, 2016) restores • JLQCD (current: see Suzuki et al Lattice 2017) restores • Ishikawa et al (Wilson, 2017) at least Z 4 restores •
Why bother ? it may provide useful information on the phase transition • if the U(1) A continue to be broken • SU(2) L x SU(2) R ≃ O(4) universality class for 2nd order • if the U(1) A recovers • U(2) L x U(2) R / U(2) V for 2nd order • provides crucial information on the universality class • 1st order possible for both cases • though often discussed in context with U(1) A restoration •
Why bother ? it may provide useful information on the phase transition • ➡ Columbia plot ∞ Physical pt : crossover • 1st order Wuppertal 2006 Right upper corner : 1st order • physical pt. pure gauge m s other parts are less known • 1st order crossover ∞ 0 m ud [original Columbia plot: Brown et al 1990]
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
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. • for all N t = 1/ (aT) = 4 or 6 m s WHOT-QCD Lat2016 (O(4) scaling) • problem not settled yet 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
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 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 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] physical ud
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 GL-OV OV-DW 1.5e+08 OV-OV 1st order transition ? 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 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 GL-OV OV-DW 1.5e+08 OV-OV 1st order transition ? 4 ] χ [MeV 1e+08 5e+07 make sense al a Pisarski & Wilczek 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 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 GL-OV OV-DW 1.5e+08 OV-OV 1st order transition ? 4 ] χ [MeV 1e+08 JLQCD: U(1) A restoration 5e+07 make sense al a Pisarski & Wilczek 0 0 5 10 15 20 25 30 m f [MeV] physical ud
if upper left corer is 1st order 0 ≤ m f < m c : 1st oder • might affect the physics around physical point • ∞ ∞ ? physical pt. m s m s ∞ ∞ 0 0 m ud m ud
Columbia plot: direct search of PT / scaling ∞ 1st order physical pt. m s 1st order crossover ∞ 0 m ud
Columbia plot: direct search of PT / scaling ∞ 1st order physical pt. m s 1st order crossover ∞ 0 m ud
Columbia plot: direct search of PT / scaling ∞ 1st order physical pt. m s 1st order crossover ∞ 0 m ud
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)
Why bother ? in relation with “extended symmetry” • spin-chiral symmetry for vector and scalar props. at high T • SU(4) ⊃ SU(2) L x SU(2) R x U(1) A • C. Rohrhofer et al., PRD17 [1707.01881] • C. Lang [1803.08693] • original discussion on this symmetry: Glozman et al • for the T=0 but low-mode subtracted Dirac operator •
Why bother ? axion cosmology scenario may fail for U(1) A restoration • due to vanishing / suppressed topological susceptivility χ t | m=0 = 0 & d n χ t / dm n | m=0 = 0 Aoki-Fukaya-Tanigchi • ➡ χ t = 0 for small non-zero m OR ➡ exponential decay for T>T c � m q Λ 3 QCD , T < T c , χ t ( T ) ∼ QCD e − 2 c ( m q ) T 2 /T 2 c , T > T c , m 2 q Λ 2 h c ( m q ) → ∞ as m q → 0, s χ t = m 2 a f 2 axion mass and decay constant: • a ➡ axion window can possibly be closed Kitano-Yamada JHEP [1506.00370] • see also for θ = π QCD non-standard case with rich implications Di Vecchia et al. JHEP [1709.00731]
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