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Predictions by string theory?

Predictions by string theory?. f 0 (1500) → 4π 0 : Suppressed. [w/ C.I.Tan and S.Terashima, 0709.2208]. Charge radius of Roper = 0.73[fm]. [w/ T.Sakai and S.Sugimoto, to appear]. ID of QCD glueball ?. → Scalar glueball. （ ex ：　　　　　→　 meson, 　　　　→　 baryon ）.

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Predictions by string theory?

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  1. Predictions by string theory? f0(1500) → 4π0 : Suppressed [w/ C.I.Tan and S.Terashima, 0709.2208] Charge radius of Roper = 0.73[fm] [w/ T.Sakai and S.Sugimoto, to appear]

  2. ID of QCD glueball? →Scalar glueball （ex：　　　　　→　meson,　　　　→　baryon） Lattice prediction of lightest glueball mass: 1600MeV 0++ state We need theoretical description of glueball decay! Chiral perturbation Perturbative QCD Difficult Mixings? Lattice QCD

  3. A Solution : Holographic QCD String theory [Step 1] 10D classical gravity on curved background 4D gauge theory @ large Nc, large λ Gauge/Gravity correspondence [Step 2] 10D classical gravity + “flavor D-brane” on curved background QCD @ large Nc, strong coupling Holographic QCD

  4. Deform [Step 1] D-branes giving the duality Quantizing Strings defined in 10D spacetime Open string → massless gauge field Closed string → massless graviton D-branes = Object on which open strings can end Nc parallel Dp-branes = Source of closed strings = Source of gravity = Extended blackhole “blackbrane” in 10D Open string theory on the Dp-brane is : SU(Nc) gauge theory in p+1 dimensions 2 Nc open strings

  5. Gauge/Gravity correspondence Black brane Nc D-branes Propagation of SU(Nc) gauge theory composite states Propagation of graviton in near-horizon geometry of black p-brane (glueball)

  6. [Step 2] Introducing quarks Nf “flavor D-brane” SU(Nf) gauge fields in higher dim. D-brane on curved background Propagation of meson

  7. We get interacting hadrons from strings [Einstein action + higher dim. YM action] on curved background in 10D Decomposition by fields in 4 dimensions [Glueball + Meson] interacting action No mixing, Coefficients computed explicitly

  8. Power of holography Decay width Experiments f0(1500) [PDG] Decay branch Holographic QCD 0.040 0.025 0.059 0.035 No decay 0.0090 0.0050 not seen No decay f0(1500) can be identified as a pure glueball

  9. Decay width and branching ratios Decay width of each branch ： not produced If we tune the glueball mass and eta mass by hand so that it can fit the experimental data, then Comparison：　In experiments, f0(1500) decays as Our results are consistent

  10. What is the ID of Glueballs? Glueballs　：　Bound state consisting only of Gluons, among many hadrons appearing at low energy of QCD. →Scalar glueball （ex：　　　　　→　meson,　　　　→　baryon） Mystery of Glueballs Which is the glueball, among states observed with ?

  11. Difficulties in identifying the glueball Diff.（１）Perturbative analysis is impossible due to strong coupling at low energy of QCD. This is related to the mass-gap problem in YM, which is a millenium problem! Diff.（２）Lattive QCD predicts that the lightest glueball has and its mass should be around 1600 MeV. But it cannot calculate dynamical decay process, so no more comparison is available. Diff.（３）There are many hadrons having the same quantum number, so the glueball is mixed among mesons. Generally mass eigen states are mixed. Diff.（４）Chiral perturbation cannot be applied to glueball dynamics, since glueballs live not really in low energy.

  12. 27th Nov., 2007 @ KEK Glueball Decay in Holographic QCD Koji Hashimoto (RIKEN) arXiv/0709.2208(hep-th) w/ Seiji Terashima（YITP） and Chung-I Tan（Brown U）

  13. Plan of today’s talk 1. Mystery of Glueballs 2. Holographic QCD： From String Theory to Hadrons 3. Glueball Decay

  14. 1. Mystery of Glueballs What is the ID of Glueballs? Present status of Glueball searches Power of Holographic QCD

  15. What is the ID of Glueballs? Glueballs　：　Bound state consisting only of Gluons, among many hadrons appearing at low energy of QCD. →Scalar glueball （ex：　　　　　→　meson,　　　　→　baryon） Mystery of Glueballs Which is the glueball, among states observed with ?

  16. Ref：PDG data of decay of glueball candidates

  17. Difficulties in identifying the glueball Diff.（１）Perturbative analysis is impossible due to strong coupling at low energy of QCD. This is related to the mass-gap problem in YM, which is a millenium problem! Diff.（２）Lattive QCD predicts that the lightest glueball has and its mass should be around 1600 MeV. But it cannot calculate dynamical decay process, so no more comparison is available. Diff.（３）There are many hadrons having the same quantum number, so the glueball is mixed among mesons. Generally mass eigen states are mixed. Diff.（４）Chiral perturbation cannot be applied to glueball dynamics, since glueballs live not really in low energy.

  18. Present status of glueball ID proposal PDG prediction is f0(1500)＝glueball Reason： f0(1370) can be produced by 2γ and thus composed by charged quarks. f0(1710) decays mainly to ２K, thus strangeness should be the main component. But, no one could compute these…. Not decisive! Our motivation, and Result Holographic QCD＝Application of AdS/CFT to QCD Holographic QCD enables us to compute spectra and couplings of/among composite states of stronly coupled QCD! Decay products, width, branching ratios : Computable! （but at large Nc） Conclusion: f0(1500) is the glueball

  19. 2. Holographic QCD AdS/CFT From AdS/CFT to QCD Sakai-Sugimoto model The model and experimental data

  20. Very brief history of string theory and AdS/CFT 1960’s～70’s： String theory was born in hadron physics Regge trajectory, s-t channel duality, ’tHooft large N, …. ？ 1970’s～80’s：String as quantum gravity and unification Standard model and superstrings, supergravity Late in 1990’s～：Revolution by D-branes and duality Toward non-perturbative definition AdS/CFT (gauge/string duality）

  21. AdS/CFT：　Equivalence of two ways to describe D-branes [Maldacena(97)] Open string （gauge theory） Closed string （gravity） Closed string in blackbrane background of N D3-branes Low energy effective action of open strings on N D3-branes 10 dim. supergravity in curved backgrounds 4dim. gauge theory Corresp.

  22. Theories in correspondence super Yang-Mills Open string side: with the low energy limit Supergravity on Closed string side: Near horizon geometry of BPS black 3-brane solution in 10 dimensions : This classical geometry is valid when is required

  23. Black brane D-branes Closed string Closed string Open string Closed string Closed string Physical quantities in correspondence ＝ Correlation functions in gauge theory can be computed by gravity theory. [Gubser-Klebanov-Polyakov] [Witten] Bulk fields in supergravity Gauge invariant composite operators in YM theory

  24. Holographic QCD (“AdS/QCD”) Philosophy AdS/CFT deals with strongly coupled gauge theories; Then why not QCD? Present status： It reproduces various characteristics of low energy hadron physics and provides a new viewpoint (paradigm), though with some difficulties Difficulties： ・　Large N ・　Decoupling of higher dimensional DoF

  25. Sakai-Sugimoto model(hep-th/0412141) Open string side (D-branes) ・　Nc D4-branes wrap , and gauginos satisfy anti-periodic boundary condition 　　　→ 4d pure Yang-Mills at low energy ・　Nf D8-branes intersect with the D4s → Nf left-handed massless quarks ・　Nf anti-D8-branes intersect with the D4s → Nf right-handed massless quarks [Witten] Massless QCD is brane-engineered at low energy

  26. Closed string side (gravity) D8s are put there as probes (probe approximation, valid at ) Near horizon geometry of black 4-brane solution on which fermions satisfy the anti-periodic b.c. is [Witten] Once the correspondence is applied ・・・ ・ gravity → bound states of gluons（Glueballs） ・ D8 → bound states of quarks（Mesons, Baryons） KK modes of gauge fields on the D8 → Meson D8-brane action → Chiral lagrangian

  27. The role of the D8-branes ＝ D4 D8

  28. Spontaneous chiral symmetry breaking Chiral symmetry Gauge symmetries on the D8 and anti D8 ＝ Massless QCD (weak coupling description) Replacing the D4by its gravity solution Spontaneous chiral SB at strong coupling D8s are connected, and gauge symmetry is

  29. Meson sector in the SS model D8-brane action on the curved background Metric induced on the D8 by the D4-brane graviy solution is Redefinition of coordinates： KK decomposition of this YM theory on the curved background is the meson lagrangian AdS/CFT : KK modes of 　　　　 → Vector mesons A KK mode of → Pion

  30. Action is evaluated as ・　KK modes of gauge field : Eigen equation for the modes : ・　Pion is given by the zeroth mode of the decomposition : ・　Higher modes are absorbed by field redefinition :

  31. Final lagrangian quadratic in KK modes is Eigenvalues correpond to masses of vector mesons. Comparison with observed data Meson interactions can be computed from YM interactions.

  32. 3. Glueball Decay Summary We describe decay of lightest glueball in QCD by using AdS/CFT. The computed decay products and width are consistent with a hadron f0(1500) which is a glueball candidate. arXiv/0709.2208(hep-th) Seiji Terashima（YITP） and Chung-I Tan（Brown）

  33. Our strategy Using holographic QCD, we compute analytically interactions between Glueballs and Mesons / photons, calculate the decay products and widths, and compare them with experimental data. Gauge （QCD） side Gravity side Our work Gravity fluctuations around near horizon geometry of non -BPS black 4-brane（Witten） We compute couplings between the two sectors in the gravity side, and describe the glueball decay Gluon sector （Glueballs） Csaki,Ooguri,Oz,Terning(98) Brower,Mathur,Tan(00) Gauge fluctuation on the probe D8 （Sakai-Sugimoto） Quark sector （Mesons） Sakai,Sugimoto(04,05)

  34. Review: Computing Glueball spectrum via AdS/CFT Gravity background dual to 4d pure YM（Witten） Wrap a D4-brane around a circle, and impose anti-periodic boundary condition for the fermions to break the SUSY Supergravity fluctuation ocrresponding to the lightest glueball （Constable・Myers, Brower・Mathur・Tan） ：eigenfunction in higher dim ：Glueball field

  35. Glueball spectrum obtained in AdS/CFT Lattice calculation (SU(3) pure YM) （Morningstar・Peardon,1999） （Brower・Mathur・Tan,2003）

  36. Computing the coupling between glueballs and mesons Glueball　→　Gravity Meson →Gauge (on D8) ①correspondence: ②In string theory, all the interactions between gravity and D8 gauge fields are encoded in D8-brane action We substitute gravity and D8 gauge fluctuations representing the mesons and glueballs, and perform the integration of higher dimensional space We obtain interacting lagrangian of glueball / meson fields

  37. Result Glueball , Pion ,ρmeson Kinetic terms No mixing between mesons and lightest glueball Interaction terms （This expression is for a single flavor, for simplicity）

  38. Possible decay process of the lightest glueball Interaction terms obtained via AdS/CFT : YM ←CS Among these, （ii）（iii） includes more than 5 pions after the decay and so are negligible. Possible decay processes are These reproduces decay products of f0(1500)

  39. Decay width and branching ratios Decay width of each branch ： not produced If we tune the glueball mass and eta mass by hand so that it can fit the experimental data, then Comparison：　In experiments, f0(1500) decays as Our results are consistent

  40. 4. Summary and Prediction

  41. Summary Holographic QCD can really help computing interactions among hadrons. It enables us to compute glueball interactions analytically, and f0(1500) can be identified as a scalar glueball. Other results ・Other decay process： No decay to ２γ →f0(1370) is not a glueball Small decay width to ２K→f0(1710) is not a glueball ・Prediction：　No decay of f0(1500) to 4 π０ Many more can be computed similarly Interactions of heavier glueballs (with different spins etc) Glueball-glueball interactions Glueballs in finite temperature, finite baryon density,・・・・

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