1. Hadrons from a hard wall AdS/QCD model Ulugbek Yakhshiev (Inha University & National University of Uzbekistan) Collaboration Hyun-Chul Kim (Inha University) Youngman Kim (APCTP) QNP09, Beijing, 24.09.2009

2. Content 1.AdS/QCD models 2.Hard-Wall model 3.Mesonic Sector 4.Baryonic Sector 5.Parameter restriction 6.Results and Summary Beijing, 24.09.2009QNP09, Beijing, 24.09.2009

3. AdS/QCD models Beijing, 24.09.2009 Top-Down (From String Theory IIA) AdS/CFT duality is well understood [Sakai-Sugumoto, PTP113] Bottom-Up (From Phenomenology) More freedom to build in properties of QCD One constructs 5D dual model of QCD, taking into account the general futures of QCD (chiral symmetry breaking, VMD, Large N, solitons, …): KK modes are identified with towers of radial excitations of QCD states; It has some free input parameters which are fitted to experimental data; There is a hope that one can get the model from more general theory. [Erlich et al.,PRL95; Rold and Pomarol, NPB721] QNP09, Beijing, 24.09.2009

4. Bottom-Up approach Beijing, 24.09.2009 Hard-Wall Compactification via Sharp IR Cut-off Soft-Wall Conformal Invariance is broken smoothly via Background Dilaton Field [Batell&Gherghetta,PRD78; Colangelo et al. PRD78] I.Mesonic sector – Input parameters are fixed according to mesonic data. II.Baryonic sector – Input parameters are fixed according to baryonic data. III.Unified approach – Input parameters should be fixed in unique way. In opposite case the integrals and wave functions will not be well defined. QNP09, Beijing, 24.09.2009

5. The Model (Mesonic Sector) Beijing, 24.09.2009QNP09, Beijing, 24.09.2009

7. The Model (Mesonic Sector) Beijing, 24.09.2009 One can find the expectation value of X defined as the classical solutions of field equations, using UV boundary conditions M is quark mass matrix Σ is chiral condensate While QCD is not conformal theory the values of M and Σ, in general, are free parameters of the model. QNP09, Beijing, 24.09.2009

8. The Model (Mesonic Sector) Beijing, 24.09.2009 Erlich et al., PRL95 QNP09, Beijing, 24.09.2009 M and Σ values are consistent with phenomenological values

9. The Model (Baryonic Sector) Effective Action where g is mass coupling. Using the expression for the scalar field one solves equations for fermionic fields Beijing, 24.09.2009 X QNP09, Beijing, 24.09.2009

10. The Model (Baryonic Sector) Decomposing 5d Nucleons in terms of KK modes one gets equations where Φ(z) is expressed by expectation value of scalar field and mass coupling g and Δ‘s related to the five dimensional fermion mass. One also can introduce relation between different parity states and get the decoupled equation Beijing, 24.09.2009QNP09, Beijing, 24.09.2009

11. The Model (Baryonic Sector) Introducing the new functions and looking for solutions of the type one can simplify the problem. Beijing, 24.09.2009QNP09, Beijing, 24.09.2009

12. The problem It is a one dimensional potential well problem with the effective potential Beijing, 24.09.2009QNP09, Beijing, 24.09.2009

13. Parameter fixing Mass coupling parameter is not fully free it is bounded in some region where Beijing, 24.09.2009QNP09, Beijing, 24.09.2009

14. Parameter fixing Mass coupling parameter is not fully free it is bounded in some region Critical value of the parameter Beijing, 24.09.2009QNP09, Beijing, 24.09.2009

15. Small mass coupling At the small mass coupling limit can be ignored and problem can be solved analytically. The solution has the form and baryon spectra presented by solutions of algebraic equations In this approximation the correct order of positive and negative parity state masses reproduced naturally Beijing, 24.09.2009QNP09, Beijing, 24.09.2009

16. Hadron Spectra Beijing, 24.09.2009 Input data fixed from mesonic sector and five dimensional mass also fixed QNP09, Beijing, 24.09.2009

17. Hadron Spectra Beijing, 24.09.2009 Input data from mesonic sector and five dimensional mass is free (due to the nonzero possible anomalous dimension coming from renormalization flow) to change Two different parameter sets are used to fix mesonic sector [Erlich et al. PRL 95 (2005)] A) Rho meson mass fixedB) General fit to experimental data QNP09, Beijing, 24.09.2009 g from minimization

18. Hadron Spectra Beijing, 24.09.2009 Global fit to mesonic and nucleonic sectors in chiral limit. The five dimensional mass is set to zero due to the large possible anomalous dimension. The static properties are predicted within 10 to 20 % deviations from experiment. Couplings are underestimated! QNP09, Beijing, 24.09.2009

19. Summary Beijing, 24.09.2009 To improve results:  one can include higher dimensional operators  or consider finite UV cutoff  … Hard wall model is not good approximation… QNP09, Beijing, 24.09.2009 Index is 3 for baryons and 0 for mesons