cascade baryon spectrum from lattice qcd nilmani mathur tata institute, india

Cascade Baryon Spectrumfrom Lattice QCD

Nilmani MathurTata Institute, India

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)

…PDG Live

(1314)

(1321)

…PDG Live

…V. Zielgler (GlueX meeting)

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.

Octahedral group and lattice operators

Λ J

G1

G2

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

A1

A2

E

T1

T2

0⊕4⊕6⊕8 …3⊕6⊕7⊕9 …2⊕4⊕5⊕6 …1⊕3⊕4⊕5 …2⊕3⊕4⊕5 …

BaryonBaryon

MesonMeson

……R.C. Johnson, Phys. Lett.B 113, 147(1982)R.C. Johnson, Phys. Lett.B 113, 147(1982)

Radial structure : displacements of different lengthsRadial structure : displacements of different lengthsOrbital structure : displacements in different directionsOrbital structure : displacements in different directions

……C. MorningstarC. Morningstar

Lattice operator construction

• Construct operator which transform irreducibly under the symmetries of the lattice

• Classify operators according to the irreps of Oh :

G1g, G1u, G1g, G1u,Hg, Hu

• 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 Oh :

)210(nt displaceme link :)(~~ )( ..,, j nxDAa

nj

CcnkBb

njAa

niabc

FABC

F xDxDxDxB )(~~)(~~)(~~)(

RFiR

OROi UtBURD

gd

tBDh

Dh

F

)()()(

PRD 72,094506 (2005) PRD 72,094506 (2005) A. Lichtl thesis, A. Lichtl thesis, hep-lat/0609019hep-lat/0609019

G1 Total operators : 270• Single site : 4

• Singly displaced : 38

• Doubly displaced-I : 36

• Doubly displaced-L : 96

• Triply displaced T : 96

G2 Total operators : 218• Single site : 0





H Total operators : 487• Single site : 3





• Nf = 2, anisotropic clover lattice– at ~ 5.556 GeV(-1)– Lattice size : 243 X 64– # Configurations : 860

• Quenched anisotropic clover lattice (not analyzed yet)– at = 6.1 GeV(-1)– Lattice size : 163 X 64

• Nf = 2+1, anisotropic clover lattices (cascade calculation will be started soon)

Ground state spectrum (Nf=2)

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.

Effective masses for different channels

Effective masses for positive parity channels

Effective masses for negative parity channels

Effective masses for G1(1/2) channel

Comparison between G1u and regular effective masses

Effective masses for G2 channel

Effective masses for H channel

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.

cascade baryon spectrum from lattice qcd nilmani mathur tata institute, india

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