Staggered Diquarks for Singly Heavy Baryons

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Presentation transcript:

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:0707.3537 [hep-lat] LATTICE 2007 @ Regensburg

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) 014502. 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) 054505. 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/0610009) 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 . LATTICE 2007 @ Regensburg

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 LATTICE 2007 @ Regensburg

Diquarks in Singly Heavy Baryons (Single Taste) SU(6) Non-relativistic Quark Model suggests : Spin Flavor In 2+1 flavor LATTICE 2007 @ Regensburg

Staggered Diquarks in S.H.B. (Four Tastes) Taste Symm. Flavor-Taste Symm. Up & Down Strange In 2+1 Flavor Unphysical LATTICE 2007 @ Regensburg

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. LATTICE 2007 @ Regensburg

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 LATTICE 2007 @ Regensburg

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) 094505 … 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. LATTICE 2007 @ Regensburg

Spin-Taste basis : mesons : Irreps c.f.) mesons : Contributions in Non-relativistic limit Irreps LATTICE 2007 @ Regensburg

Only the states contribute in the non-relativistic limit Spin x Taste into GTS Irreps LATTICE 2007 @ Regensburg

LATTICE 2007 @ Regensburg

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 (Tomorrow @ H3 : 14:20–14:40) LATTICE 2007 @ Regensburg

LATTICE 2007 @ Regensburg