1. Pentaquark decay width in QCD sum rules F.S. Navarra, M. Nielsen and R.R da Silva University of São Paulo, USP Brazil (  decay width) hep-ph/0503193 (  mass) Phys. Lett. B578 (2004) 323 (  mass) Phys. Lett. B602 (2004) 185 LC 2005 CAIRNS Introduction Pentaquark mass  decay width Conclusions

2. Something new in Hadron Physics:  + (1540 MeV) july/2003  -- (1860 MeV) september/2003  c (3099 MeV) april/2004 Exotic baryons: can not be three-quark states contain an antiquark ! Introduction may/2005 vanishing...

3. No peak ! Resonance in the s channel  peak in the cross section K + d scattering: Sibirtsev et al., PLB 599 (2004) 230  decay width MeV Extremely narrow !

4. Meson-baryon molecules? n K+K+ Pentaquark structure Five-quark bags? Strottman, PRD 20 (1979) 748

5. Topological solitons? Diakonov, Petrov, Poliakov ZP A359 (1997) 305 “Diamonds”? (non-planar flux tubes) Song and Zhu, MPL A 19(2004)2791

6. Triquark-Diquark? Karliner and Lipkin PLB 575 (2003) 249 Diquark-Diquark-Antiquark? Jaffe and Wilczek, PRL 91 (2003) 232003

7. Identities between correlation functions written with hadron and quark – gluon degrees of freedom Method for calculations in the non - perturbative regime of QCD Two - point function: hadron masses Results are functions of the quark masses and vacuum expectation values of QCD operators : condensates QCD Sum Rules Three - point function: form factors and decay width

8.  mass  = current (interpolating field) How to combine quark fields in a DDA arrange ? hadronic fields composite quark fields   -- :  + :

9. 2 scalar diquarks 2 pseudoscalar diquarks pseudoscalar diquark scalar diquark Matheus, Navarra, Nielsen, Rodrigues da Silva, PLB 578 (2004) 323 Sugiyama, Doi, Oka PLB 581 (2004) 167

10. Combination of  1 and  2 Insert  in the correlation function Current contains contribution from the pole (particle) and from the continuum (resonances) Im  =  = spectral density S 0 = continuum threshold parameter

11. Operator product expansion (OPE)

12. Numerical inputs: (standard) Parameters: t s0s0 msms What is good sum rule? Borel stability Good OPE convergence Dominance of the pole contribution Reasonable value of S 0

13. m s =0.1 GeV t=1  s 0 =2.3 GeV MM m  =1.87 ± 0.22 GeV

14. OPE perturbative dimension 4 dimension 6

15. pole continuum

16. Extremely narrow width: < 10 MeV or even < 1 MeV Mass excess of 100 MeV (no problem with phase space)  decay width Possible reasons for a narrow width: Spatial configuration Color configuration Non-trivial string rearrangement Destructive interference between almost degenerate states Chiral symmetry...

17. K n Θ  decay in QCDSR: Three-point function: (p) (p´) (q)

18. Phenomenological side L = (negative parity) L = (positive parity) (negative parity) (positive parity)

19. (negative parity) (positive parity) from QCD sum rules + continuum

20. Theoretical side (OPE side): currents correlator

21. OPE

22. color disconnected color connected

23. Continuum and pole-continuum transitions pole continuum

24. Continuum and pole-continuum transitions

25. (quark-hadron duality) Continuum and pole-continuum transitions

26. A B

27. Borel transform schemes I) II) III) (unstable sum rule)

28. Sum rules I A I B II A II B

29. Numerical evaluation of the sum rules From each sum rule and its derivative determine G and A ´s are known from the mass sum rules : G 

30. I A Sum rules with color connected diagrams  N = 0.5 GeV  N = 0.4 GeV  N = 0.6 GeV

31. II A  N = 0.5 GeV  N = 0.4 GeV  N = 0.6 GeV

32. I B  N = 0.5 GeV  N = 0.4 GeV  N = 0.6 GeV M´ = 1.0 GeV M = 1.5 GeV

33. II B  N = 0.5 GeV  N = 0.4 GeV  N = 0.6 GeV M´ = 1.0 GeV M = 1.5 GeV

34. Results IA IIA IB IIB 0.7 0.8 1.0 2.6 3.6 3.2 4.5 color connected all diagrams (negative parity)   = 8.6 MeV implies that g  nK = 0.4

35. Decay width Negative parity:   = 650 MeV Color connected:   = 37 MeV All diagrams:

36. Conclusions We have used QCDSR to study pentaquark properties It is possible to obtain reasonable values for the  and  masses However: the continuum contribution is large ! the OPE has irregular behavior ! The  narrow width is more difficult to understand : With all diagrams we can not obtain a narrow width! With only the color connected diagrams we obtain a smaller width Negative parity  strongly disfavored QCDSR for pentaquarks are not as satisfying as for other hadrons

37. Pentaquarks properties One unit of angular momentum  mass Constituent quark mass: MeV  mq = 340 + 510 = 860 MeV Adition of two quarks MeV Non-trivial atraction mechanism