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Pentaquark decay width in QCD sum rules

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

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Pentaquark decay width in QCD sum rules

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

  2. Introduction 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 ! vanishing... may/2005

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

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

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

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

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

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

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

  10. Current contains contribution from the pole (particle) and from the continuum (resonances) S0 =continuum threshold parameter Im  =  =spectral density Combination of 1 and 2 Insert  in the correlation function

  11. Operator product expansion (OPE)

  12. Numerical inputs: (standard) Parameters: s0 ms t What is good sum rule? Borel stability Good OPE convergence Dominance of the pole contribution Reasonable value of S0

  13. M ms=0.1 GeV t=1 s0=2.3 GeV m=1.87 ± 0.22 GeV

  14. OPE perturbative dimension 4 dimension 6

  15. continuum pole

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

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

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

  19. (positive parity) (negative 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 continuum pole pole continuum continuum pole

  24. Continuum and pole-continuum transitions

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

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

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

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

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

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

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

  36. Conclusions We have used QCDSR to study pentaquark properties QCDSR for pentaquarks are not as satisfying as for other hadrons 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

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

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