SU(2)CS and SU(2NF) hidden symmetries L. Ya. Glozman Institut f ur - PowerPoint PPT Presentation

Outline Key questions J = 0 mesons J = 1 mesons Left-right mixing. The chiralspin SU (2) CS and SU (4) groups. J=2 mesons J = 1 / 2 baryons SU (2) CS and SU (4) symmetries of confinement in QCD Conclusions SU(2)CS and SU(2NF) hidden symmetries L. Ya. Glozman Institut f¨ ur Physik, FB Theoretische Physik, Universit¨ at Graz in collaboration with M. Denissenya, C. B. Lang, M. Pak 29th April 2017 L. Ya. Glozman SU(2)CS and SU(2NF) hidden symmetries

Outline Key questions J = 0 mesons J = 1 mesons Left-right mixing. The chiralspin SU (2) CS and SU (4) groups. J=2 mesons J = 1 / 2 baryons SU (2) CS and SU (4) symmetries of confinement in QCD Conclusions Key questions 1 J = 0 mesons 2 J = 1 mesons 3 Left-right mixing. The chiralspin SU (2) CS and SU (4) groups. 4 J=2 mesons 5 J = 1 / 2 baryons 6 SU (2) CS and SU (4) symmetries of confinement in QCD 7 Conclusions 8 L. Ya. Glozman SU(2)CS and SU(2NF) hidden symmetries

Outline Key questions J = 0 mesons J = 1 mesons Left-right mixing. The chiralspin SU (2) CS and SU (4) groups. J=2 mesons J = 1 / 2 baryons SU (2) CS and SU (4) symmetries of confinement in QCD Conclusions What is origin of hadron mass? Are chiral symmetry breaking and confinement uniquely connected? Is it possible to separate confinement and chiral symmetry breaking physics? What physics is responsible for confinement and for chiral symmetry breaking? What is the underlying systematics that drives a genesis of hadrons and hadron spectra? L. Ya. Glozman SU(2)CS and SU(2NF) hidden symmetries

Outline Key questions J = 0 mesons J = 1 mesons Left-right mixing. The chiralspin SU (2) CS and SU (4) groups. J=2 mesons J = 1 / 2 baryons SU (2) CS and SU (4) symmetries of confinement in QCD Conclusions Low mode truncation Banks-Casher: < ¯ qq > = − πρ (0) . What we do: k 1 � S = S Full − λ i | λ i �� λ i | . i =1 What one expects for J = 0 correlators or states, if they survive: SU(2) * SU(2) L R (1/2,1/2) π σ a U(1) U(1) A A (1/2,1/2) a η 0 b SU(2) * SU(2) R L L. Ya. Glozman SU(2)CS and SU(2NF) hidden symmetries

Outline Key questions J = 0 mesons J = 1 mesons Left-right mixing. The chiralspin SU (2) CS and SU (4) groups. J=2 mesons J = 1 / 2 baryons SU (2) CS and SU (4) symmetries of confinement in QCD Conclusions M.Denissenya, L.Ya.G., C.B.Lang, PRD 89(2014)077502; 91(2015)034505 We use JLQCD N f = 2 overlap gauge configurations and quark propagators. σ η 10 -2 a 0 π 10 -3 10 -4 k=30 4 8 12 16 20 24 28 t SU (2) L × SU (2) R × U (1) A is restored in correlators. 1.8 1.8 1.8 1st 1st 1st 1.6 1.6 1.6 2nd 2nd 2nd 1.4 1.4 1.4 1.2 1.2 1.2 1 1 1 0.8 0.8 0.8 0.6 π (k=0) 0.6 π (k=10) 0.6 π (k=60) 0.4 0.4 0.4 0.2 0.2 0.2 0 0 0 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 t t t The ground states do not survive truncation: Without the near-zero modes π , σ , a 0 , η do not exist. These states are not a direct consequence of confinement. L. Ya. Glozman SU(2)CS and SU(2NF) hidden symmetries

Outline Key questions J = 0 mesons J = 1 mesons Left-right mixing. The chiralspin SU (2) CS and SU (4) groups. J=2 mesons J = 1 / 2 baryons SU (2) CS and SU (4) symmetries of confinement in QCD Conclusions M.Denissenya, L.Ya.G., C.B.Lang, PRD 89(2014)077502; 91(2015)034505 What one expects for J = 1 mesons: f 1 (0 , 1 ++ ) ! (0 , 1 −− ) (0 , 0) Ψ( 1 F ⊗ γ 5 γ k )Ψ Ψ( 1 F ⊗ γ k )Ψ SU (2) A (1 / 2 , 1 / 2) a b 1 (1 , 1 + − ) ! (0 , 1 −− ) Ψ( τ a ⊗ γ 5 γ 0 γ k )Ψ Ψ( 1 F ⊗ γ 0 γ k )Ψ U (1) A U (1) A SU (2) A (1 / 2 , 1 / 2) b ρ (1 , 1 −− ) h 1 (0 , 1 + − ) Ψ( τ a ⊗ γ 0 γ k )Ψ Ψ( 1 F ⊗ γ 5 γ 0 γ k )Ψ SU (2) A (1 , 0) ⊕ (0 , 1) a 1 (1 , 1 ++ ) ρ (1 , 1 −− ) Ψ( τ a ⊗ γ k )Ψ Ψ( τ a ⊗ γ 5 γ k )Ψ L. Ya. Glozman SU(2)CS and SU(2NF) hidden symmetries

Outline Key questions J = 0 mesons J = 1 mesons Left-right mixing. The chiralspin SU (2) CS and SU (4) groups. J=2 mesons J = 1 / 2 baryons SU (2) CS and SU (4) symmetries of confinement in QCD Conclusions M.Denissenya, L.Ya.G., C.B.Lang, PRD 89(2014)077502; 91(2015)034505 Isovector J = 1 states. 2 1st 5th 1st 10 0 2nd 6th 2nd 1.5 10 -1 3rd 7th 3rd 4th 4th 1 10 -2 10 -3 0.5 ρ (k=10) 10 -4 0 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16 t t 2 1st 4th 1st 10 0 2nd 5th 2nd 1.5 10 -1 3rd 10 -2 1 10 -3 0.5 10 -4 a 1 (k=10) 10 -5 0 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16 t t 2 10 0 1st 4th 1st 2nd 5th 2nd 10 -1 1.5 3rd 6th 10 -2 1 10 -3 0.5 10 -4 b 1 (k=10) 10 -5 0 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16 t t L. Ya. Glozman SU(2)CS and SU(2NF) hidden symmetries

Outline Key questions J = 0 mesons J = 1 mesons Left-right mixing. The chiralspin SU (2) CS and SU (4) groups. J=2 mesons J = 1 / 2 baryons SU (2) CS and SU (4) symmetries of confinement in QCD Conclusions M.Denissenya, L.Ya.G., C.B.Lang, PRD 89(2014)077502; 91(2015)034505 J = 1 0 2 6 10 14 20 30 k mass, MeV a 1 ′ ρ′′ ω′′ 2000 b 1 ′ f 1 1500 ω′ ρ′ a 1 b 1 h 1 1000 ω ρ 500 0 σ , MeV 0 8 40 65 93 125 180 We clearly see a larger degeneracy than the SU (2) L × SU (2) R × U (1) A symmetry of the QCD Lagrangian. What does it mean !? L. Ya. Glozman SU(2)CS and SU(2NF) hidden symmetries

Outline Key questions J = 0 mesons J = 1 mesons Left-right mixing. The chiralspin SU (2) CS and SU (4) groups. J=2 mesons J = 1 / 2 baryons SU (2) CS and SU (4) symmetries of confinement in QCD Conclusions L.Ya.G., EPJA 51(2015)27 (i) (0,0): 1 | ¯ RR ± ¯ | (0 , 0); ± ; J � = √ LL � J . 2 (ii) (1 / 2 , 1 / 2) a and (1 / 2 , 1 / 2) b : 1 | ¯ RL + ¯ | (1 / 2 , 1 / 2) a ; +; I = 0; J � = √ LR � J , 2 1 | ¯ R τ L − ¯ | (1 / 2 , 1 / 2) a ; − ; I = 1; J � = √ L τ R � J , 2 1 | ¯ RL − ¯ | (1 / 2 , 1 / 2) b ; − ; I = 0; J � = √ LR � J , 2 1 | ¯ R τ L + ¯ | (1 / 2 , 1 / 2) b ; +; I = 1; J � = √ L τ R � J . 2 (iii) (0,1) ⊕ (1,0): 1 | ¯ R τ R ± ¯ | (0 , 1) + (1 , 0); ± ; J � = √ L τ L � J , 2 L. Ya. Glozman SU(2)CS and SU(2NF) hidden symmetries

Outline Key questions J = 0 mesons J = 1 mesons Left-right mixing. The chiralspin SU (2) CS and SU (4) groups. J=2 mesons J = 1 / 2 baryons SU (2) CS and SU (4) symmetries of confinement in QCD Conclusions L.Ya.G., EPJA 51(2015)27 Consider rotations in an imaginary 3-dim space of doublets constructed from the Weyl spinors � u L � � d L � U = D = u R d R U → U ′ = e i ε · σ D → D ′ = e i ε · σ 2 U , 2 D , where σ are the standard Pauli matrices: [ σ i , σ j ] = 2 i ǫ ijk σ k . We refer to this imaginary three-dimensional space as the chiralspin space and denote this symmetry group as SU (2) cs A group that contains at the same time SU (2) L × SU (2) R and SU (2) CS is SU (4) with the fundamental vector   u L u R   Ψ =   d L   d R L. Ya. Glozman SU(2)CS and SU(2NF) hidden symmetries

Outline Key questions J = 0 mesons J = 1 mesons Left-right mixing. The chiralspin SU (2) CS and SU (4) groups. J=2 mesons J = 1 / 2 baryons SU (2) CS and SU (4) symmetries of confinement in QCD Conclusions L.Ya.G., M. Pak, PRD 92(2015)016001 Instead of the states constructed with Weyl spinors we can consider the left- and right-handed Dirac bispinors and bilinear operators. Then the SU (2) cs chiralspin rotations are generated through [Σ i , Σ j ] = 2 i ǫ ijk Σ k . Σ = { γ 0 , i γ 5 γ 0 , − γ 5 } , The SU (4) group contains at the same time SU (2) L × SU (2) R and SU (2) CS ⊃ U (1) A with the fundamental vector   u L u R   Ψ =   d L   d R and has the following set of generators: { ( τ a ⊗ 1 D ) , ( 1 F ⊗ Σ i ) , ( τ a ⊗ Σ i ) } L. Ya. Glozman SU(2)CS and SU(2NF) hidden symmetries

Outline Key questions J = 0 mesons J = 1 mesons Left-right mixing. The chiralspin SU (2) CS and SU (4) groups. J=2 mesons J = 1 / 2 baryons SU (2) CS and SU (4) symmetries of confinement in QCD Conclusions L.Ya.G., M. Pak, PRD 92(2015)016001 f 1 (0 , 1 ++ ) ! (0 , 1 −− ) (0 , 0) Ψ( 1 F ⊗ γ 5 γ k )Ψ Ψ( 1 F ⊗ γ k )Ψ SU (4) SU (2) CS b 1 (1 , 1 + − ) (1 / 2 , 1 / 2) a ! (0 , 1 −− ) Ψ( τ a ⊗ γ 5 γ 0 γ k )Ψ Ψ( 1 F ⊗ γ 0 γ k )Ψ SU (2) CS h 1 (0 , 1 + − ) (1 / 2 , 1 / 2) b ρ (1 , 1 −− ) Ψ( τ a ⊗ γ 0 γ k )Ψ Ψ( 1 F ⊗ γ 5 γ 0 γ k )Ψ (1 , 0) ⊕ (0 , 1) a 1 (1 , 1 ++ ) ρ (1 , 1 −− ) Ψ( τ a ⊗ γ k )Ψ Ψ( τ a ⊗ γ 5 γ k )Ψ L. Ya. Glozman SU(2)CS and SU(2NF) hidden symmetries