Meson-Nucleon Coupling. Nobuhito Maru

Transcription

1 Meson-Nucleon Coupling from AdS/QCD Nobuhito Maru (Chuo Univ.) with Motoi Tachibana (Saga Univ.) arxiv: (Accepted in in EPJC) 7/9/9

2 Plan 1: Introduction : Meson sector (review) 3: Meson-Nucleon coupling 4: Summary (review & our results)

3 Introduction AdS/CFT correspondence has opened a new avenue to study strongly coupled gauge theories Application to QCD and hadron physics Top down: String theory QCD Sakai & Sugimoto (5) Bottom up: QCD 5D holographic model Erlich, Kat, Son Son & Stephanov (5) Da Da Lord & Pomarol (5)

4 Introduction AdS/CFT correspondence has opened a new avenue to study strongly coupled gauge theories Application to QCD and hadron physics Top down: String theory QCD Sakai & Sugimoto (5) Bottom up: QCD 5D holographic model Erlich, Kat, Son Son & Stephanov (5) Da Da Lord & Pomarol (5) 5D model of Meson sector (vector, axial-vector meson masses, decay consts, gρππ, )

5 As for baryons, two approaches are known 1: 1: Skyrmion Hashimoto, Sakai & Sugimoto (8) and and many papers : Bulk fermion Hong, Inami & Yee Yee (7)[spin 1/] 1/] Ahn, Hong, Park Park & Siwach (9)[spin3/]

6 As for baryons, two approaches are known 1: 1: Skyrmion Hashimoto, Sakai & Sugimoto (8) and and many papers : Bulk fermion Hong, Inami & Yee Yee (7)[spin 1/] 1/] spin ½ baryon mass spectrum πnn coupling

7 As for baryons, two approaches are known 1: 1: Skyrmion Hashimoto, Sakai & Sugimoto (8) and and many papers : Bulk fermion Hong, Inami & Yee Yee (7)[spin 1/] 1/] spin ½ baryon mass spectrum πnn coupling Our work By extending the model of Hong, Inami & Yee, we calculated (Axial-)Vector Meson-Nucleon couplings using the 5D Holographic QCD

8 Meson sector QCD and a Holographic Model of Hadrons Erlich, Kat, Son and Stephanov PRL (5) Chiral Symmetry Breaking from Five Dimensional Spaces Da Lord and Pomarol NPB71 79 (5)

9 AdS/CFT dictionary 4D 5D Global symmetry Gauge symmetry Operator O 5D field Dimension[ O] 1/Nc Resonance Bulk mass g5^ KK modes Following this dictionary, we guess a holographic model of QCD

10 5D SU(Nf)L x SU(Nf)R gauge theory on a slice of AdS5 1 ds = dx dx d =Λ ( μ ν ), ( η ) μν ε m QCD 1 (Axial-)Vector meson (spin 1) (Axial-)Vector gauge field ( ) ( ) ( ) ( ) x φ x, SU N SU N Δ M = ( Δ p)( Δ+ p 4) 4D: O 5D: p ( ) ( ) μ a a q γ t q L adj,1 1 3 L L μ a a q γ t q R 1, adj 1 3 R R μ μ f L ( ) qq X N, N 3 3 α β 1 αβ R L f f 1 S = d x g ( L R ) meson + + D X M X f 5 Tr MN MN M 5 g5 R 5

11 Bulk scalar field X Source of chiral symmetry breaking Classical solution X ( ) = M+Σ 3 UV B.C. explicit breaking Quark Mass ( ) X = ε = M spontaneous breaking Chiral condensate qq = M exp 4 i d xmqq X= X, M=, = ε cl M = δ = S5 [ X] Σ δ M

12 Defining 1 1 VM LM RM AM LM R ( ), ( ) + M and adding L 1 μ V 1 μ A ξ A gf μv ξv = A μ ξa g5 X P ξvg 5 + ξag 5 L leads to the quadratic Lagrangian in the unitary gauge 1 1 = V η + + η V X = X e a μν μ ν μν a ip quadratic μ 4g ν X A η + + η A + P A 4g Mode equations and boundary conditions 1 ( ε ) ( ) V V V = mn + fn, fn = fn m = ( ) a μν μ ν μν a a a μ ν 3 μ μ 5 1 g5 X A A A = mn + f, n fn ( ε ) = fn ( m) =

13 Meson-Nucleon coupling Baryons in AdS/QCD Hong, Inami and Yee, PLB (7) Meson-Nucleon Coupling from AdS/QCD N.M. and Motoi Tachibana arxiv: (accepted in EPJC)

14 Spin ½ Baryon Spin ½ Dirac fermion Hong, Inami & Yee (7) 5 5 S = d x g in e Γ D N + in e Γ D N N N + N N 5 M A M A Baryon 1 A M 1 A M μ μ μ μ μ 5 ( ) D = + Γ Γ il, D = il, m = Δ = To incorporate chiral symmetry breaking, the following Yukawa coupling is introduced S = d x g g NXN g NXN 5 Yukawa Y 1 1 Y Δ gy X 4 Δ gy X n n n n f 1L f 1R f 1R f 1L m, n = n m n n = n n gy X 4 Δ fl fr g f Y X Δ R fl ( ) ( ) ( ε) ( ε) f = f = f = f =, Other B.C. from EOM n n n n 1R m L m 1L R

15 πnn coupling L m i L i L π NN m ( ) ( ) (,1 ) = d g N Γ ia N ia N Γ N + L R + d g gyn XN g N X N πnn coupling is generated from 1: Gauge coupling (5 th component) : Yukawa coupling 3: Pauli term (through Goldberger-Treiman relation) 1 1 Y m 1 g f g l l = d f NN ( f f f f ) f f f f π v g ( ) l* l l* l Y π l* l l* l 4 π 1L 1R L R 1L R L 1R ( ) 5

16 L gauge Vector & Axial-vector Meson-Nucleon coupling Vector & Axial-vector meson-nucleon couplings come from m i ( ) i = d g N e ia N ( ia N ) Γ e Γ N 1: Gauge coupling : Pauli term M A L L M A 1 A M 1 M 1 A 1 i ( ) i + Ne Γ ia N ( ia N ) e Γ N M A R R M A A M M A m 1 d N γ V N + N γ V N + N γ A N N γ A N 4 μ μ μ μ 1 μ 1 μ 1 μ 1 μ

17 L Pauli m = c d g in Γ F N in Γ F N MN L MN R 1 MN 1 MN m 1 μ 5 5 c d N 3 1Lγ γ V V N1L + N1R V V N1R μ ( μ μ) γ γ ( μ μ) ( 1 ) m 1 μ 5 5 c d N 3 1Lγ γ A A N1L + N1R A A N1R + μ ( μ μ) γ γ ( μ μ) ( 1 ) m 1 V V l l g n l l d f v N N 4 n + c f n f1l + f 1R m 1 A A l l g n l l d f a N N 4 n + c f n f1l + f 1R m 1 l l mπ l l π NN 3 π 1L 1R πnn πnn + = m N g c d f f f g g (GT)

18 Numerical Results Data: gρnn = 4.~6.5, gπnn ~ 13.6 ( GeV ) ρ 1 g g g g 1 m Y NN a NN πnn fitted prediction 5% dev. Parameters: m, gy (free parameters), mn=.94gev M=.34MeV, Σ=(311MeV)^3 mπ,fπ g5=π Matching to pqcd Erlich et al (5) c Nucleon g- Hong, Kim, Siwach & Yee (7)

19 Numerical Results Data: gρnn = 4.~6.5, gπnn ~ 13.6 ( GeV ) ρ 1 g g g g 1 m Y NN a NN πnn fitted prediction 5% dev. Comparison to Skyrmion approach for baryons Similar results: gρnn = 5.8, gπnn ~ 7.46 Hashimoto, Sakai & Sugimoto (8)

20 Summary We have formulated meson-baryon couplings in in 5D holographic QCD Spin ½ baryon 5D Dirac fermion πnn, ρnn, a1nn couplings were computed In particular, a1nn coupling is is a prediction, our model can be tested by measuring this coupling

21 Summary We have formulated meson-baryon couplings in in 5D holographic QCD Spin ½ baryon 5D Dirac fermion πnn, ρnn, a1nn couplings were computed In particular, a1nn coupling is is a prediction our model can be tested by measuring this coupling Ways out to improve the results in our simplified model Deformation of the metric Anomalous dimension Bulk mass correction Quantum gravity, Stringy effects

22 Backup Slides

23 ρmeson mass & its its mode function 3 m f ρ ( m ) 1 ρ π, ( ) m 4 m a1 a1meson mass & its its mode function J 1 d J 1 ρ ( m ) Mode equation cannot be solved analytically due to a -dependent mass Approximation: brane localied mass@ IR brane 3 g5σ J 4 a 1 1 tan ma, ( ) 1 m π m f 4 m m a1 d J ρ ( m ) a 1 1 ( m ) a 1

24 L Pion mode function Note that in the unitary gauge, if A vg5 P= its orthogonal combination of A & P are massless Pion μ A v A, = g5 8g5v 8g5 v A P A g A ( ) ( μ ) Pion mode function is defined from A = fπ()π(x) and obtained by 3 3 m fπ 1 fπ 4 g5 fπ =, 1= d f π + 4 v g 5 8v g5