DOMAIN WALL NETWORK AS QCD VACUUM: CONFINEMENT, CHIRAL SYMMETRY, - PowerPoint PPT Presentation

S.N. Nedelko Domain wall network as QCD vacuum: confinement, chiral symmetry, hadronization DOMAIN WALL NETWORK AS QCD VACUUM: CONFINEMENT, CHIRAL SYMMETRY, HADRONIZATION Sergei Nedelko Bogoliubov Laboratory of Theoretical Physics Vladimir Voronin Bogoliubov Laboratory of Theoretical Physics & Dubna Uni. BLTP, July 3, 2013 1

S.N. Nedelko Domain wall network as QCD vacuum: confinement, chiral symmetry, hadronization An overall task pursued by most of the approaches to QCD vacuum structure is an identification of the properties of nonperturbative gauge field configurations able to provide a coherent resolution of the confinement, the chiral symmetry breaking, the U A (1) anomaly and the strong CP problems, both in terms of color-charged fields and colorless hadrons. ⇔ Finite classical action, pure gauge singularities Global minima of the effective quantum action ⇔ Instantons, monopoles, vortices, double-layer domain walls Defects in the initally homogeneous background BLTP, July 3, 2013 2

S.N. Nedelko Domain wall network as QCD vacuum: confinement, chiral symmetry, hadronization C dz µ ˆ � → W ( C ) = � Tr P e i A µ � • Confinement of both static and dynamical quarks − S ( x, y ) = � ψ ( y ) ¯ ψ ( x ) � → � ¯ • Dynamical Breaking of chiral SU L ( N f ) × SU R ( N f ) symmetry − ψ ( x ) ψ ( x ) � → η ′ ( χ , Axial Anomaly) • U A (1) Problem − • Strong CP Problem − → Z ( θ ) • Colorless Hadron Formation: − → Effective action for colorless collective modes: hadron masses, formfactors, scattering Light mesons and baryons, Regge spectrum of excited states of light hadrons, heavy-light hadrons, heavy quarkonia What would be a formalism for coherent simultaneous description of all these nonperturbative features of QCD? QCD vacuum as a medium characterized by certain condensates, quarks and gluons - elementary coloured excitations (confined), mesons and baryons - collective colourless excitations (masses, form factors, etc) BLTP, July 3, 2013 3

S.N. Nedelko Domain wall network as QCD vacuum: confinement, chiral symmetry, hadronization ◮ Effective action of SU (3 ) YM theory, global minima of the effective action. ◮ Gluon condensation, Weyl reflections, CP: kink-like gauge field configurations and domain wall network as QCD vacuum ◮ Confinement and the spectrum of charged field fluctuations, color charged quasi-particles ◮ Impact of the strong electromagnetic fields on the QCD vacuum structure ◮ Formulation of the domain model. ◮ Testing the model on the strandard set of problems of pure gluodynamics: σ , χ , � F 2 � . ◮ Chirality of quark modes. Realisation of chiral symmetry and quark condensate: U A (1) and SU L ( N ) × SU R ( N ) . ◮ U A (1) and the strong CP problem. Anomalous Ward Identities. ◮ Nonlocal effective meson Lagrangian: hadronization scheme and meson masses. BLTP, July 3, 2013 4

S.N. Nedelko Domain wall network as QCD vacuum: confinement, chiral symmetry, hadronization P. Minkowski, Nucl. Phys. B 177 , 203 (1981). H. Leutwyler, Phys. Lett. B 96 , 154 (1980); Nucl. Phys. B 179 , 129 (1981). H. Pagels, and E. Tomboulis // Nucl. Phys. B143. 1978. H. D. Trottier and R. M. Woloshyn // Phys. Rev. Lett. 70. 1993. G.V. Efimov, Ja.V. Burdanov, B.V. Galilo, A.C. Kalloniatis, S.N. Nedelko , L. von Smekal, S.A. Solunin, Phys. Rev. D 73 (2006), 71 (2005), 70 (2004), 69 (2004), 66 (2002), 51 (1995), 54 (1996). S.N. Nedelko, V.E. Voronin , in preparation (2013) B. Galilo, S.N. Nedelko, Phys. Rev D 84 (2011) B. Galilo, S.N. Nedelko, PEPAN Lett. 8 (2011) [arXiv:1006.0248v2 ], J. M. Pawlowski, D. F. Litim, S. Nedelko and L. von Smekal , Phys. Rev. Lett. 93 (2004) A. Eichhorn, H. Gies, J. M. Pawlowski, Phys. Rev. D83 (2011) [arXiv:1010.2153 [hep-ph]] BLTP, July 3, 2013 5

S.N. Nedelko Domain wall network as QCD vacuum: confinement, chiral symmetry, hadronization Pure Yang-Mills vacuum (no quarks present): � � : g 2 F 2 : � � = 0 , d 4 x � Q ( x ) Q (0) � � = 0 , � Q ( x ) � = 0 χ = g 2 µν ( x ) ˜ 32 π 2 F a F a Topological charge density Q ( x ) = µν ( x ) BLTP, July 3, 2013 6

S.N. Nedelko Domain wall network as QCD vacuum: confinement, chiral symmetry, hadronization Visualizations of Quantum Chromodynamics (QCD)Buried treasure in the sand of the QCD vacuum P.J. Moran,Derek B. Leinweber, Centre for the Subatomic Structure of Matter (CSSM), University of Adelaide, Australia arXiv:0805.4246v1 [hep-lat], 2008 g 2 µν ( x ) ˜ 32 π 2 F a F a Topological charge density Q ( x ) = µν ( x ) BLTP, July 3, 2013 7

S.N. Nedelko Domain wall network as QCD vacuum: confinement, chiral symmetry, hadronization In Euclidean functional integral for YM theory one has to allow the gluon condensate to be nonzero : � Z = N DA exp {− S [ A ] } F B 1 � µν ( x ) = B 2 } , B 2 � = 0 . d 4 xg 2 F a µν ( x ) F a F B = { A : lim V V →∞ V Separation of the long range modes B a µ and local fluctuations Q a µ in the background B a µ , background gauge fixing condition ( D ( B ) Q = 0 ): A a µ = B a µ + Q a µ � � � Dωδ [ A ω − Q ω − B ω ] δ [ D ( B ω ) Q ω ] 1 = DB Φ[ A, B ] DQ B Q Ω Q a µ – local (perturbative) fluctuations of gluon field with zero gluon condensate: Q ∈ Q ; B a µ are long range field configurations with nonzero condensate: B ∈ B . � � Z = N ′ DQ det[ D ( B ) D ( B + Q )] δ [ D ( B ) Q ] exp {− S [ B + Q ] } DB B Q Self-consistency: the character of long range fields has yet to be identified by the dynamics of fluctuations: � Z = N ′ DB exp {− S eff [ B ] } . B Global minima of S eff [ B ] – field configurations that are dominant in the thermodynamic limit V → ∞ . L. D. Faddeev,“Mass in Quantum Yang-Mills Theory”, arcxiv:0911.1013v1[math-ph] BLTP, July 3, 2013 8

S.N. Nedelko Domain wall network as QCD vacuum: confinement, chiral symmetry, hadronization The Abelian ˆ B µ ( x ) part of the gauge fields A µ ( x ) = ˆ ˆ B µ ( x ) + ˆ [ ˆ B µ ( x ) , ˆ X µ ( x ) , B ν ( x )] = 0 L. D. Faddeev, A. J. Niemi (2007); Kei-Ichi Kondo, Toru Shinohara, Takeharu Murakami ( 2008); Y.M. Cho (1980, 1981); S.V. Shabanov (1989,1999) Covariantly constant Abelian (anti-)self-dual fields µ = − 1 ˜ B a 2 n a B µν x ν , B µν = ± B µν are stable against local fluctuations Q . Explicit one-loop effective action: � 11 24 π 2 ln λB � S 1 − loop = B 2 Λ 2 + ε 0 . (1) eff H. Leutwyler (1980,1981); P. Minkowski (1981); H. Pagels, and E. Tomboulis (1978); H. D. Trottier and R. M. Woloshyn (1993). Effective action for covariantly constant Abelian (anti-)self-dual field within the Functional RG: A. Eichhorn, H. Gies, J. M. Pawlowski, Phys. Rev. D83 (2011) [arXiv:1010.2153 [hep-ph]] BLTP, July 3, 2013 9

S.N. Nedelko Domain wall network as QCD vacuum: confinement, chiral symmetry, hadronization Effective Lagrangian Consider the following Ginsburg-Landau effective Lagrangian for the soft gauge fields satisfying the re- quirements of invariance under the gauge group SU (3) and space-time transformations, L eff = − 1 D ab ν F b ρµ D ac ν F c ρµ + D ab µ F b µν D ac ρ F c � � − U eff ρν 4 � � U eff = 1 F 2 + 4 F 4 − 16 C 1 ˆ 3 C 2 ˆ 9 C 3 ˆ F 6 12Tr , where µ = δ ab ∂ µ − i ˆ D ab A ab µ = ∂ µ − iA c µ ( T c ) ab , F a µν = ∂ µ A a ν − ∂ ν A a µ − if abc A b µ A c ν , � F 2 � ˆ ˆ = ˆ µν ˆ F µν = F a µν T a , T a bc = − if abc F ab F ba νµ = − 3 F a µν F a Tr µν ≤ 0 , gA µ → A µ . � V →∞ V − 1 d 4 x � F 2 � � = 0 − → C 1 > 0 , C 2 > 0 , C 3 > 0 . lim V �� � vac Λ 4 > 0 , b 2 F a µν F a µν = 4 b 2 C 2 2 + 3 C 1 C 3 − C 2 vac = / 3 C 3 . BLTP, July 3, 2013 10

S.N. Nedelko Domain wall network as QCD vacuum: confinement, chiral symmetry, hadronization Consider A µ fields with the Abelian field strength ˆ F µν = ˆ nB µν , where matrix ˆ n can be put into Cartan subalgebra n = T 3 cos ξ + T 8 sin ξ, 0 ≤ ξ < 2 π. ˆ It is convenient to introduce the following notation: nB µν / Λ 2 = ˆ ˆ nb µν , b µν b µν = 4 b 2 b µν = ˆ vac , e i = b 4 i , h i = 1 2 ε ijk b jk , e 2 + h 2 = 2 b 2 vac . ( eh ) = | e | | h | cos ω, ( eh ) 2 = h 2 � 2 b 2 − h 2 � cos 2 ω. Hence the effective potential takes the form � vac − 3 ( eh ) 2 �� + 1 9 C 3 b 2 (10 + cos 6 ξ ) � vac − ( eh ) 2 � � U eff = Λ 4 − C 1 b 2 2 b 4 4 b 4 vac + C 2 . There are twelve discrete global degenerated minima at the following values of the variables h , ω and ξ vac > 0 , ω = πk ( k = 0 , 1) , ξ = π h 2 = b 2 6 (2 n + 1) ( n = 0 , . . . , 5) . BLTP, July 3, 2013 11