1. Staggered Diquarks for Singly Heavy Baryons
Kazuhiro NAGATA
Dept. of Phys., Indiana Univ.
Based on the collaboration with
S. Gottlieb Dept. of Phys., Indiana Univ.
H. Na Dept. of Phys., Indiana Univ.
arXiv: [hep-lat]
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2. Introduction & Motivation Heavy Baryon Spectroscopy on Lattice
K.C. Bowler et al. (UKQCD), Phys. Rev. D54 (1996) 3619.
N. Mathur et al., Phys. Rev. D66 (2002)
R.M. Woloshyn, Phys. Lett. B476 (2000) 309.
S. Gottlieb and S. Tamhankar, Nucl. Phys. Proc. 119 (2003) 644.
A. Ali Khan et al., Phys. Rev. D62 (2000)
T.W. Chiu and T.H. Hsieh, Nucl. Phys. A755 (2005) 471c.
Introduction
& Motivation …
Heavy Baryon Spectroscopy on Lattice
Several quenched Wilson quark calculations
giving fair agreement with experiments
Study of singly heavy baryons using a pair of
2+1 flavor dynamical staggered light quarks
(Gottlieb & Na, hep-lat/ )
Should be studied extensively by using finer lattices.
Staggered Quarks
Having Taste d.o.f. besides Color and Flavor
Non-trivially embedded in (Spacetime x Taste) Lattice
Needs to establish Group Theoretical Connection between
Continuum and Lattice Irreps of Staggered Diquarks
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3. Contents 1. Diquarks in SU(6) quark model
2. Staggered Diquarks in SU(24) symmetry
3. Review of Lattice Staggered Symmetries
4. Lattice Diquark Classifications
5. Summary
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4. Diquarks in Singly Heavy Baryons (Single Taste)
SU(6) Non-relativistic Quark Model suggests :
Spin
Flavor
In 2+1 flavor
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5. Staggered Diquarks in S.H.B. (Four Tastes)
Taste Symm.
Flavor-Taste Symm.
Up & Down
Strange
In 2+1 Flavor
Unphysical
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6. Staggered Diquarks in S.H.B. (Four Tastes)
We further decompose :
Lattice Symm. Group
The main goal is to construct Lattice Diquarks categorized into these Irreps.
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7. Symmetries on the Lattice
M.F.L. Golterman, Nucl. Phys. B273 (1986) 663
M.F.L. Golterman & J. Smit, Nucl. Phys. B255 (1985) 328
M.F.L. Golterman & J. Smit, Nucl. Phys. B245 (1984)61
C.P. van den Doel and J. Smit, Nucl. Phys. B228 (1983)122 …
Symmetries on the Lattice
Symmetries (momentum space)
Pure translation
Twisted Lorentz group
Parity
Non-local in time
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8. Symmetry Group & Diquark Irreps
M.F.L. Golterman, Nucl. Phys. B273 (1986) 663
M.F.L. Golterman & J. Smit, Nucl. Phys. B255 (1985) 328
M.F.L. Golterman, Nucl. Phys. B278 (1986) 417
S. Gupta, Phys. Rev. D60 (1999) …
Symm. Group
for Spectroscopy
Static
Commute with
Local in Time
Fund. Irrep :
Diquark rep :
: Meson rep (Golterman 1986)
: eigenvalue of
Lattice Staggered Diquark classifications
1. Categorize them w.r.t. GTS
2. Pick up the
structures
3. Take into account the 2+1 flavor
Cont. Irreps w.r.t.
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9. Spin-Taste basis : mesons : Irreps
c.f.)
mesons :
Contributions in Non-relativistic limit
Irreps
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10. Only the states contribute in the non-relativistic limit
Spin x Taste into GTS Irreps
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11. LATTICE Regensburg

12. Staggered diquark classifications through :
Summary & Prospects
Staggered diquark classifications through :
: Physical Irreps
Flavor-taste
c.f.) Staggered Baryons (J. Bailey 2006)
GTS equivalence of Staggered Diquarks and Mesons :
Diquarks :
: Mesons (Golterman 1986)
Only the positive parity state survives in Non-rela. limit.
Numerical results of Staggered Heavy Baryons
Talk by H. Na H3 : 14:20–14:40)
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13. LATTICE Regensburg