Glueballs and their decay in holographic QCD

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1 Glueballs and their decay in holographic QCD Anton Rebhan Institute for Theoretical Physics TU Wien, Vienna, Austria March 2, 2015 A. Rebhan Holographic Glueball Decay March 2, / 17

2 Still elusive: Gluonia (Glueballs) Spectrum of bare glueballs (prior to mixing with q q states) more or less known from lattice: m GeV m GeV Morningstar & Peardon hep-lat/ A. Rebhan Holographic Glueball Decay March 2, / 17

3 Still elusive: Gluonia (Glueballs) Spectrum of bare glueballs (prior to mixing with q q states) more or less known from lattice: m GeV m GeV Morningstar & Peardon hep-lat/ Interactions of glueballs still unclear: Are glueballs broad or narrow? (Γ G 1/N 2 c ) Do they mix with q q strongly or weakly? (mixing 1/N c suppressed) no conclusive identification of any glueball in meson spectrum most discussed lowest 0 ++ candidates: narrow f 0(1500) or f 0(1710) vs. broad background ( red dragon ) tensor candidates: broad f 2(1950) or very narrow (unconfirmed) f J(2220) A. Rebhan Holographic Glueball Decay March 2, / 17

4 Still elusive: Gluonia (Glueballs) Spectrum of bare glueballs (prior to mixing with q q states) more or less known from lattice: m GeV m GeV Morningstar & Peardon hep-lat/ Interactions of glueballs still unclear: Are glueballs broad or narrow? (Γ G 1/N 2 c ) Do they mix with q q strongly or weakly? (mixing 1/N c suppressed) no conclusive identification of any glueball in meson spectrum most discussed lowest 0 ++ candidates: narrow f 0(1500) or f 0(1710) vs. broad background ( red dragon ) tensor candidates: broad f 2(1950) or very narrow (unconfirmed) f J(2220) Gauge/gravity duality a new tool to study glueball properties from first principles A. Rebhan Holographic Glueball Decay March 2, / 17

5 Holographic QCD Celebrated AdS/CFT duality relates strongly coupled large-n c supersymmetric Yang-Mills theories to supergravity on anti-de Sitter space in 5 dimensions (AdS 5 S 5 ) Holographic QCD: generalization to nonconformal nonsupersymmetric case Options: Bottom-up: breaking of conformal invariance (necessary for confinement) by hand and matching to QCD with holographic dictionary, e.g. hard-wall model (Erlich-Katz-Son-Stephanov 2005) soft-wall model (Karch-Katz-Son-Stephanov 2006) Top-down: first-principles constructions from superstring theory with nonconformal D-branes here: Witten[1998]-Sakai-Sugimoto[2004] model Both approaches surprisingly successful quantitative description of low-energy QCD with minimal set of parameters WSS model: almost parameter-free (1 coupling at a certain mass scale)! New results on: Glueball decay pattern [arxiv: , with F. Brünner & D. Parganlija] A. Rebhan Holographic Glueball Decay March 2, / 17

6 Witten model: Holographic nonsupersymmetric QCD D4 branes E. Witten, Adv. Theor. Math. Phys. 2, 505 (1998): Nc Type-IIA string theory with N c D4 branes dual to dimensional super-yang-mills theory A. Rebhan Holographic Glueball Decay March 2, / 17

7 Witten model: Holographic nonsupersymmetric QCD D4 branes E. Witten, Adv. Theor. Math. Phys. 2, 505 (1998): Nc Type-IIA string theory with N c D4 branes dual to dimensional super-yang-mills theory supersymmetry completely broken by compactification on thermal-like circle x 4 x 4 + 2π/M KK (Kaluza Klein) antisymmetric b.c. for adjoint fermions: masses M KK adjoint scalars not protected by gauge symmetry: also masses M KK dual to pure-glue YM theory 3+1-dimensional at scales M KK but supergravity approximation needs weak curvature, cannot take limit M KK A. Rebhan Holographic Glueball Decay March 2, / 17

8 Deconfinement phase transition Thermal circle in Euclidean time τ in addition to compactified x 4 Hawking-Page transition when 2πT = M KK (thus 1 GeV?) Confined phase Deconfined phase ds 2 = ( ) u 3/2 [dτ 2 + dx 2 + f(u)dx 2 4 R ] ( ) [ ] R 3/2 du 2 + u f(u) + u2 dω 2 4 ds 2 = ( ) u 3/2 [ f(u)dτ 2 + δ ijdx 2 + dx 2 4 R ] ( ) [ ] R 3/2 du 2 + u f(u) + u2 dω 2 4 τ 1/(2 πt) x 4 1/M KK u= 8 u τ 1/(2 πt) x 4 1/M KK u= 8 u M KK = 3 u 1/2 KK 2 R 3/2 u= u KK f(u) 1 u3 KK u 3 Cigar topology in x 4 -u subspace u= u T = 3 u 1/2 T u f(u) 3 1 T 4π R 3/2 u 3 Cigar in τ-u = Euclidean black hole T A. Rebhan Holographic Glueball Decay March 2, / 17

9 Glueballs in confined phase scalar and tensor glueballs corresponding to 5D dilaton Φ and graviton G ij Csaki, Ooguri, Oz & Terning 1999 A. Rebhan Holographic Glueball Decay March 2, / 17

10 Glueballs in confined phase scalar and tensor glueballs corresponding to 5D dilaton Φ and graviton G ij Csaki, Ooguri, Oz & Terning 1999 Type-IIA supergravity compactified on x 4-circle many more modes: Constable & Myers 1999; Brower, Mathur & Tan 2000 Mode S 4 T 4 V 4 N 4 M 4 L 4 Sugra fields G 44 Φ, G ij C 1 B ij C ij4 G α α J P C / n= n= n= n= n= Lowest mode not from dilaton, but from exotic polarization in 11D notation: δg 44 = r2 L 2 f H(r)G(x), [ ( ) ] r2 1 1 δgµν = L 2 4 H(r)ηµν 4 + 3R 6 H(r) µ ν G(x) 5r 6 2R 6 M 2 δg 11,11 = r2 1 L2 H(r)G(x), L 2 δgrr = 4 r f 1 3R 6 H(r)G(r), δg 2 5r 6 2R 6 rµ = 90r7 R 6 H(r) µg(x) M 2 L 2 (5r 6 2R 6 ) 2 A. Rebhan Holographic Glueball Decay March 2, / 17

11 Lattice glueballs vs. supergravity glueballs Morningstar & Peardon hep-lat/ : Brower, Mathur & Tan 2000: (mass scales matched on 2 ++ ) seemingly good qualitative agreement! A. Rebhan Holographic Glueball Decay March 2, / 17

12 Sakai-Sugimoto model: Adding chiral quarks T. Sakai, S. Sugimoto, Prog. Theor. Phys. 113, 843 (2005) add N f D8- and D8-branes, separated in x 4, N f N c (probe branes) D4 x x x x x D8/D8 x x x x x x x x x D4 D8 L D8 x 5 9 x 0 3 x 4 4-8, 4-8 strings fundamental, massless chiral fermions flavor symmetry U(N f ) L U(N f ) R A. Rebhan Holographic Glueball Decay March 2, / 17

13 Sakai-Sugimoto model: Adding chiral quarks T. Sakai, S. Sugimoto, Prog. Theor. Phys. 113, 843 (2005) add N f D8- and D8-branes, separated in x 4, N f N c (probe branes) D4 x x x x x D8/D8 x x x x x x x x x 4-8, 4-8 strings fundamental, massless chiral fermions flavor symmetry U(N f ) L U(N f ) R spontaneously broken because D8-D8 have to join in cigar-shaped topology for now: maximal separation in x 4 (antipodal on x 4 circle): L = π/m KK A. Rebhan Holographic Glueball Decay March 2, / 17

14 Quantitative predictions Matching 1 m ρ 776 MeV fixes M KK = 949 MeV ( T deconf = 151 MeV) 2 matching f 2 π = λnc 54π 4 M 2 KK gives λ = g 2 YMN c [Sakai&Sugimoto ] (matching instead large-n c lattice result [Bali et al. 2013] for m ρ/ σ gives λ 12.55) A. Rebhan Holographic Glueball Decay March 2, / 17

15 Quantitative predictions Matching 1 m ρ 776 MeV fixes M KK = 949 MeV ( T deconf = 151 MeV) 2 matching f 2 π = λnc 54π 4 M 2 KK gives λ = g 2 YMN c [Sakai&Sugimoto ] (matching instead large-n c lattice result [Bali et al. 2013] for m ρ/ σ gives λ 12.55) yields (for N c = 3 and λ = ): m 2 a 1 /m 2 ρ 2.4 (versus 2.5 from experiment!) nonzero η mass from anomaly inflow: Witten-Veneziano formula with Nf /N c m η = 3 3π λmkk MeV for N f = 3 (exp.: 958 MeV!) decay rate of ρ meson Γ ρ 2π/m ρ = (exp.: 0.191(1)) decay rate for ω 3π (from Chern-Simons part of D8 action) Γ ω 3π/m ω = (exp.: (1)) gluon condensate [Kanitscheider, Skenderis & Taylor JHEP 0809] C 4 αs π F µν 2 = π 4 Ncλ2 MKK GeV 4 classical SVZ value: GeV 4 (lattice higher but with large subtraction ambiguities) A. Rebhan Holographic Glueball Decay March 2, / 17

16 Lattice vs. supergravity glueballs seemingly good qualitative agreement by matchup up 2 ++ (but AdS spectrum somewhat stretched... ) Morningstar & Peardon hep-lat/ : Brower, Mathur & Tan 2000: A. Rebhan Holographic Glueball Decay March 2, / 17

17 Lattice vs. supergravity glueballs in Sakai-Sugimoto model Sakai-Sugimoto model: glueball masses M KK = 949 MeV fixed by m ρ A. Rebhan Holographic Glueball Decay March 2, / 17

18 Lattice vs. supergravity glueballs in Sakai-Sugimoto model Sakai-Sugimoto model: glueball masses M KK = 949 MeV fixed by m ρ dilaton & tensor 1487 MeV exotic polarization 855 MeV A. Rebhan Holographic Glueball Decay March 2, / 17

19 Lattice vs. supergravity glueballs in Sakai-Sugimoto model Sakai-Sugimoto model: glueball masses M KK = 949 MeV fixed by m ρ now good match lowest 0 ++ dilaton dilaton & tensor 1487 MeV exotic polarization 855 MeV A. Rebhan Holographic Glueball Decay March 2, / 17

20 Lattice vs. supergravity glueballs in Sakai-Sugimoto model Should exotic polarization (δg 44 with x 4 the compactified direction of SYM 4+1) be excluded as lowest glueball mode? possibly not part of spectrum of holographic QCD in limit M KK, λ 0 (already asked by Constable & Myers) simpler bottom-up AdS/QCD have dilaton mode as dual for lowest glueball A. Rebhan Holographic Glueball Decay March 2, / 17

21 Lattice vs. supergravity glueballs in Sakai-Sugimoto model Should exotic polarization (δg 44 with x 4 the compactified direction of SYM 4+1) be excluded as lowest glueball mode? possibly not part of spectrum of holographic QCD in limit M KK, λ 0 (already asked by Constable & Myers) simpler bottom-up AdS/QCD have dilaton mode as dual for lowest glueball next lowest scalar mode 1487 MeV is (predominantly) dilaton mode (induces metric perturbations other than δg 44) A. Rebhan Holographic Glueball Decay March 2, / 17

22 Glueball- qq couplings in Sakai-Sugimoto model Gravitational modes stable in confined background, but can calculate effective action for glueball- qq interactions done for lowest (exotic) mode by Hashimoto, Tan & Terashima, Phys.Rev. D77 (2008) , arxiv: revisited, corrected, and extended to other modes by Brünner, Parganlija & AR, arxiv: For example: Vertices of one glueball and two (massless) pions for exotic mode: S GE ππ = Tr for predominantly dilatonic mode: S GD ππ = Tr d 4 x 1 2 µπ νπ ( c 1η µν c 1 µ ν M 2 E d 4 x 1 2 µπ νπ c1 ( η µν µ ν with {c 1, c 1, c 1} = {62.66, 16.39, 17.23} λ 1/2 Nc 1 M 1 KK and many more: S Gρρ λ 1/2 N 1 c, S Gρππ λ 1 N 3/2 c,... M 2 D ) G E ) G D A. Rebhan Holographic Glueball Decay March 2, / 17

23 Glueball decay rates in Sakai-Sugimoto model Results for decay into two pions: Exotic mode: Γ GE ππ/m E λnc 2 Dilaton mode: Γ D ππ/m D λnc 2 (M E 855MeV) (M D 1487MeV) A. Rebhan Holographic Glueball Decay March 2, / 17

24 Glueball decay rates in Sakai-Sugimoto model Results for decay into two pions: Exotic mode: Γ GE ππ/m E (M λnc 2 E 855MeV) Dilaton mode: Γ D ππ/m D (M λnc 2 D 1487MeV) Most likely experimental candidates for meson with dominant scalar glueball content: f 0(1500) or f 0(1710) (the latter favored by Janowski et al. arxiv: ) Γ (ex) (f 0(1500) ππ)/(1505mev) = { 0.025(3) Γ (ex) 0.017(4) (BES) (f 0(1710) ππ)/(1722mev) = 0.009(2) (WA102) A. Rebhan Holographic Glueball Decay March 2, / 17

25 Glueball decay rates in Sakai-Sugimoto model Results for decay into two pions: Exotic mode: Γ GE ππ/m E (M λnc 2 E 855MeV) Dilaton mode: Γ D ππ/m D (M λnc 2 D 1487MeV) Most likely experimental candidates for meson with dominant scalar glueball content: f 0(1500) or f 0(1710) (the latter favored by Janowski et al. arxiv: ) Γ (ex) (f 0(1500) ππ)/(1505mev) = { 0.025(3) Γ (ex) 0.017(4) (BES) (f 0(1710) ππ)/(1722mev) = 0.009(2) (WA102) NB: relative width of lowest (exotic) scalar mode much larger than next ones!? another hint that G E should be discarded? A. Rebhan Holographic Glueball Decay March 2, / 17

26 Glueball decay rates in Sakai-Sugimoto model Results for decay into two pions: Exotic mode: Γ GE ππ/m E (M λnc 2 E 855MeV) Dilaton mode: Γ D ππ/m D (M λnc 2 D 1487MeV) Most likely experimental candidates for meson with dominant scalar glueball content: f 0(1500) or f 0(1710) (the latter favored by Janowski et al. arxiv: ) Γ (ex) (f 0(1500) ππ)/(1505mev) = { 0.025(3) Γ (ex) 0.017(4) (BES) (f 0(1710) ππ)/(1722mev) = 0.009(2) (WA102) NB: relative width of lowest (exotic) scalar mode much larger than next ones!? another hint that G E should be discarded? or could it perhaps correspond to broad glueball component of σ-meson à la Narison 1998: QCD sum rules need very broad glueball around 1 GeV plus narrow glueball around 1.5 GeV (cp.: Janowski et al : elsm fit of f 0(1710) as predominantly glue, but only with extremely large gluon condensate) A. Rebhan Holographic Glueball Decay March 2, / 17

27 Glueball decay rates in Sakai-Sugimoto model (cont d) Full decay pattern: decay G D 4π suppressed (below 2ρ threshold): Γ G 4π/Γ G 2pi λ 1 N 1 c, while f 0(1500) 4π dominant: decay Γ/M (PDG) Γ/M[G D] f 0(1500) (total) 0.072(5) f 0(1500) 4π 0.036(3) f 0(1500) 2π 0.025(2) f 0(1500) 2K 0.006(1) f 0(1500) 2η 0.004(1) : f 0(1500) seemingly disfavored A. Rebhan Holographic Glueball Decay March 2, / 17

28 Glueball decay rates in Sakai-Sugimoto model (cont d) Full decay pattern: decay G D 4π suppressed (below 2ρ threshold): Γ G 4π/Γ G 2pi λ 1 N 1 c, while f 0(1500) 4π dominant: decay Γ/M (PDG) Γ/M[G D] f 0(1500) (total) 0.072(5) f 0(1500) 4π 0.036(3) f 0(1500) 2π 0.025(2) f 0(1500) 2K 0.006(1) f 0(1500) 2η 0.004(1) : f 0(1500) seemingly disfavored f 0(1710) ππ OK, but f 0(1710) decays predominantly into 2K! not reproduced by (chiral) WSS model, but might be different in mass-deformed WSS (under investigation) cf. mechanism of chiral suppression of scalar glueball decay (Chanowitz 2005) A. Rebhan Holographic Glueball Decay March 2, / 17

29 Glueball decay rates in Sakai-Sugimoto model (cont d) Tensor glueball in WSS and extrapolated to higher mass: decay M Γ/M[T (M)] T 2π T 2K T 2η T (total) T 2ρ 4π T 2ω 6π T 2π T 2K T 2η T (total) With a mass of 2 GeV, the relative width turns out to be comparable with that of the comparatively broad tensor meson f 2(1950), which has Γ/M = 0.24(1). Very narrow (unconfirmed) candidate f J(2220) not compatible with WSS A. Rebhan Holographic Glueball Decay March 2, / 17

30 Summary Glueballs in Witten-Sakai-Sugimoto model After fitting just m ρ to fix M KK = 949 MeV good prediction of higher vector and axial vector mesons masses, good prediction of deconfinement/chiral transition temperature, good prediction of glueball masses if exotic mode discarded (or identified with Narison s σ B) after fitting f π or m ρ/ σ to also fix t Hooft coupling at λ = good prediction of ρ and ω decay rates good prediction of anomalous m η N 1 2 c λm KK narrow partial width G D ππ, quite compatible with experimental data for f 0(1710) Warrants further studies! A. Rebhan Holographic Glueball Decay March 2, / 17

31 Summary Glueballs in Witten-Sakai-Sugimoto model After fitting just m ρ to fix M KK = 949 MeV good prediction of higher vector and axial vector mesons masses, good prediction of deconfinement/chiral transition temperature, good prediction of glueball masses if exotic mode discarded (or identified with Narison s σ B) after fitting f π or m ρ/ σ to also fix t Hooft coupling at λ = good prediction of ρ and ω decay rates good prediction of anomalous m η N 1 2 c λm KK narrow partial width G D ππ, quite compatible with experimental data for f 0(1710) Warrants further studies! Plans: inclusion of nonzero mass for strange quark mixing with quarkonia (suppressed by N 1 2 c ) A. Rebhan Holographic Glueball Decay March 2, / 17

1/N Expansions in String and Gauge Field Theories. Adi Armoni Swansea University

1/N Expansions in String and Gauge Field Theories Adi Armoni Swansea University Oberwoelz, September 2010 1 Motivation It is extremely difficult to carry out reliable calculations in the strongly coupled