1. Cascade Baryon Spectrum from Lattice QCD Nilmani Mathur Tata Institute, India

2. Collaborators J. Dudek, R. G. Edwards, H. -W. Lin. B. Joo, D. Richards (JLab) A. Lichtl (BNL) J. Bulava, C. Morningstar, J. Foley (CMU) E. Engelson, S. Wallace (UM) G. Fleming (Yale) K. Juge (PU)

3. …PDG Live (1314) (1321)

4. …PDG Live

5. …V. Zielgler (GlueX meeting)

6. Why Cascades?  Except for ground state 1/2 +, 3/2 +, 3/2 -, masses and quantum numbers for other cascade states are not known. Even ground state 1/2 - is not known ( Ξ( 1690)?)  Narrow width reduces potential overlap with neighboring states  Cascades states will be searched in various experiments (e.g., GlueX)  Lattice calculations can predict QCD allowed states before experiments find physical states.  Due to presence of two strange quarks chiral extrapolation will be easier.

7. Octahedral group and lattice operators Λ J G 1 G 2 H 1/2 ⊕ 7/2 ⊕ 9/2 ⊕ 11/2 … 5/2 ⊕ 7/2 ⊕ 11/2 ⊕ 13/2 … 3/2 ⊕ 5/2 ⊕ 7/2 ⊕ 9/2 … Λ J A 1 A 2 E T 1 T 2 0 ⊕ 4 ⊕ 6 ⊕ 8 … 3 ⊕ 6 ⊕ 7 ⊕ 9 … 2 ⊕ 4 ⊕ 5 ⊕ 6 … 1 ⊕ 3 ⊕ 4 ⊕ 5 … 2 ⊕ 3 ⊕ 4 ⊕ 5 … Baryon Meson …R.C. Johnson, Phys. Lett.B 113, 147(1982)

8. Radial structure : displacements of different lengths Orbital structure : displacements in different directions …C. Morningstar

9. Lattice operator construction Construct operator which transform irreducibly under the symmetries of the lattice Classify operators according to the irreps of O h : G 1g, G 1u, G 1g, G 1u,H g, H u Basic building blocks : smeared, coariant displaced quark fields Construct translationaly invariant elemental operators Flavor structure  isospin, color structure  gauge invariance Group theoretical projections onto irreps of O h : PRD 72,094506 (2005) A. Lichtl thesis, hep-lat/0609019

10. G1  Total operators : 270 Single site : 4 Singly displaced : 38 Doubly displaced-I : 36 Doubly displaced-L : 96 Triply displaced T : 96

11. G2  Total operators : 218 Single site : 0 Singly displaced : 14 Doubly displaced-I : 12 Doubly displaced-L : 96 Triply displaced T : 96

12. H  Total operators : 487 Single site : 3 Singly displaced : 52 Doubly displaced-I : 48 Doubly displaced-L : 192 Triply displaced T : 192

13. Nf = 2, anisotropic clover lattice –a t ~ 5.556 GeV( -1 ) –Lattice size : 24 3 X 64 –# Configurations : 860 Quenched anisotropic clover lattice (not analyzed yet) –a t = 6.1 GeV( -1 ) –Lattice size : 16 3 X 64 Nf = 2+1, anisotropic clover lattices (cascade calculation will be started soon)

14. Ground state spectrum (Nf=2)

15. Pruning All operators do not overlap equally and it will be very difficult to use all of them. Need pruning to choose a good operator set for each representation. Error in diagonal effective masses. Construct average correlator matrix in each representation and find condition number. Find a matrix with minimum condition number for each representation.

18. Effective masses for different channels

19. Effective masses for positive parity channels

20. Effective masses for negative parity channels

21. Effective masses for G1(1/2) channel

23. Comparison between G1u and regular effective masses

24. Effective masses for G2 channel

25. Effective masses for H channel

28. Conclusion  Lattice QCD can predict the masses and other quantum numbers of cascade states before experiments (e.g, CLAS12 and GLUEX ) can tell us about those.  First result by using group theoretical operators is quite encouraging.  This calculation will be repeated on anisotropic 2+1 clover lattices at various volumes and lattice spacings.