Copyright © 2003. Elsevier. Printed in U.S.A. Submitted to Cornell University’s online archive www.arXiv.org in 2003 by James Zanotti. Post-print sourced from www.arxiv.org.We present first results for masses of spin-3/2 baryons in lattice QCD, using a novel fat-link clover fermion action in which only the irrelevant operators are constructed using fat links. In the isospin-1/2 sector, we observe, after appropriate spin and parity projection, a strong signal for the J^P=3/2^- state, and find good agreement between the 1/2^+ mass and earlier nucleon mass simulations with a spin-1/2 interpolating field. For the isospin-3/2 Delta states, clear mass splittings are observed between the various 1/2^+/- and 3/2^+/- channels, with the calculated level orderings in good agreement with those observed empirically.J.M. Zanotti, S. Choe, D.B. Leinweber, W. Melnitchouk, A.G. Williams, and J.B. Zhanghttp://www.elsevier.com/wps/find/journaldescription.cws_home/505717/description#descriptio

A.G. Williams

Benmerrouche

Bilson-Thompson

Burkert

Chung

D.B. Leinweber

Go¨ckeler

Ioffe

J.B. Zhang

J.M. Zanotti

Leinweber

Richards

S. Choe

Sasaki

W. Melnitchouk

Zanotti

Nuclear Physics B - Proceedings Supplements

Zanotti, J.

Choe, S.

Leinweber, D.

Melnitchouk, W.

Williams, A.

Zhang, J.

Adelaide Research &amp; Scholarship

arXiv:hep-lat/0210043v1  24 Oct 2002ADP-02-87/T526JLAB-THY-02-46Spin-3/2 baryons in lattice QCDJ. M. Zanottia, S. Choeb, D. B. Leinwebera, W. Melnitchoukc, A. G. Williamsa∗ and J. B. ZhangaaSpecial Research Center for the Subatomic Structure of Matter, and Department of Physics andMathematical Physics, University of Adelaide, 5005, AustraliabHiroshima Univ., Dept. of Physics, 1-3-1 Kagamiyama, Higashi-Hiroshima 739-8526, JapancJefferson Lab, 12000 Jefferson Avenue, Newport News, VA 23606, U.S.A.We present first results for masses of spin-3/2 baryons in lattice QCD, using a novel fat-link clover fermionaction in which only the irrelevant operators are constructed using fat links. In the isospin-1/2 sector, we observe,after appropriate spin and parity projection, a strong signal for the JP = 32−state, and find good agreementbetween the 12+mass and earlier nucleon mass simulations with a spin-1/2 interpolating field. For the isospin-3/2∆ states, clear mass splittings are observed between the various 12±and 32±channels, with the calculated levelorderings in good agreement with those observed empirically.1. INTRODUCTIONRecent advances in computing power and thedevelopment of improved actions have enabledsimulations of the spectrum of excited states ofthe nucleon in lattice QCD [1,2,3]. The latticestudies complement the high precision measure-ments of the N∗ spectrum under way at Jef-ferson Lab [4]. In a recent paper [5], resultswere presented for the excited nucleon and spin-1/2 hyperon spectra using the Fat-Link IrrelevantClover (FLIC) fermion action [6] with an O(a2)improved gluon action. Here we extend the anal-ysis of Ref. [5] to the spin-3/2 sector, and presentresults in both the isospin-1/2 and 3/2 channels.In the isospin-3/2 sector, our results for the∆(32+) state agree well with earlier simulations[7] using Wilson fermions. We find a clear sig-nal for the P -wave ∆(32−) parity partner of the∆ ground state, and a discernible signal for the∆(12±) states. In particular, the ∆(12−) state isfound to have a mass ∼ 350–400 MeV above the∆(32+), with the ∆(32−) slightly heavier. The∆(12+) state is found to lie ∼ 200–300 MeV abovethese. This level ordering is consistent with ex-periment.∗Presented by A. G. WilliamsIn the spin-3/2 nucleon sector, there is goodagreement for the projected 12+state with earliernucleon mass calculations [5] using standard spin-1/2 nucleon interpolating fields. Furthermore, wefind a good signal for the N(32−) state, with amass splitting of ∼ 700–1000 MeV with the nu-cleon ground state.2. SPIN-32BARYONS ON THE LATTICEThe standard isospin-1/2, spin-3/2, charge+1 interpolating field is given by χN+µ (x) =ǫabc(uTa(x) Cγ5γµ db(x))γ5uc(x), which trans-forms as a pseudovector under parity, in accordwith a positive parity Rarita-Schwinger spinor.The quark field operators u and d act at Eu-clidean space-time point x, C is the charge conju-gation matrix, a, b and c are color labels, and thesuperscript T denotes the transpose. The chargeneutral interpolating field is obtained by inter-changing u↔ d.The commonly used interpolating field forthe ∆++ resonance is given by [8] χ∆++µ (x) =ǫabc(uTa(x) Cγµ ub(x))uc(x). Since the spin-3/2 Rarita-Schwinger spinor-vector is a tensorproduct of a spin-1 vector and a spinor, the spin-3/2 interpolating field contains spin-1/2 contri-butions. To project a spin-3/2 state one needs2to use a spin-3/2 projection operator [9]. Follow-ing spin projection, the correlation function for agiven spin s, Gsµν , still contains positive and neg-ative parity states. In an analogous procedure tothat used in Ref. [5], where a fixed boundary con-dition is used in the time direction, positive andnegative parity states are obtained by taking thetrace of Gsµν with the operators Γ± =12(1± γ4),respectively.3. RESULTSLattice simulations are performed on a 163×32lattice at β = 4.60, corresponding to a latticespacing of a = 0.122(2) fm set by the stringtension [10] with√σ = 440 MeV. We consider392 configurations generated on the Orion clus-ter at the CSSM, U. Adelaide. A mean-field im-proved plaquette plus rectangle gauge action isused. For the quark fields, a Fat-Link IrrelevantClover (FLIC) [6] action is implemented. We em-ploy a highly improved definition of Fµν [6,11]leaving errors of O(a6). Mean-field improvementof the tree-level clover coefficient with fat linksrepresents a small correction and proves to bequite adequate [6]. A fixed boundary conditionin the time direction is used for the fermions bysetting Ut(~x,Nt) = 0 ∀ ~x in the hopping terms ofthe fermion action, with periodic boundary con-ditions imposed in the spatial directions. Gauge-invariant gaussian smearing in the spatial dimen-sions is applied at the fermion source (placed attime slice t = 3) to increase the overlap of theinterpolating operators with the ground states.In Fig. 1 the results for the spin-projected∆(32+) (triangles) and ∆(32−) (diamonds) massesare shown as a function of the pseudoscalar mesonmass, m2pi. The trend of the ∆(32+) data pointswith decreasing mq is consistent with the physi-cal mass of the ∆(1232), with some nonlinearityin m2pi expected near the chiral limit. The massof the ∆(32−) lies some 500 MeV above that of itsparity partner.When performing a spin projection to extractthe ∆(12±) states, a discernible, although noisy,signal is detected. The χ∆++µ interpolating fieldhas small overlap with spin-1/2 states, however,Figure 1. Masses of the spin-projected ∆(32±) and∆(12±) states. The empirical masses are indicatedalong the ordinate.with ∼ 400 configurations we are able to extractmasses for the spin-1/2 states at sufficiently earlytimes. The ∆(12+) (squares) and ∆(12−) (opencircles) are also displayed in Fig. 1. The lowestexcitation of the ground state, namely the ∆(12−),has a mass ∼ 350–400 MeV above the ∆(32+),with the ∆(32−) slightly heavier. The ∆(12+) stateis found to lie ∼ 200–300 MeV above these, al-though the signal becomes weak at smaller quarkmasses. This level ordering is consistent with thatobserved in the empirical mass spectrum.In the isospin-1/2 sector, large statistical fluc-tuations make it difficult to obtain a clear sig-nal, even with 392 configurations. A reason-able value of χ2/NDF is obtained for time slicest = 7–8. These results are shown as a functionof m2pi in Fig. 2. Parity projecting to extract theN(32+) state, we find that the correlation func-tion changes sign and has a large negative con-tribution in the range t = 7–11. This behavioris an artifact associated with the quenched decayof the excited state into N + η′, and is furtherexplored in Ref. [12].The N(12+) channel displays the interplay ofa quenched decay channel and the ground statecontribution. A strong P -wave coupling of theN(12+) to Nη′ forces the correlation function tobe negative at small times, which then turns posi-tive at larger times when the ground state contri-3Figure 2. Masses of the spin-projected N(32−)and N(12+) states, compared with the nucleonand N(12−) masses from Ref. [5].bution begins to dominate the correlation func-tion. A good χ2/NDF value is obtained for a fitto time slices t = 10–14. This suggests that thefirst excited state has strong coupling to the η′,which implies a gluon-rich structure for the Roperresonance [13].The extracted masses of the N(32−) and N(12+)states are displayed in Fig. 2 as a function of m2pi.Earlier results using the standard spin-1/2 inter-polating field [5,6] are also shown in Fig. 2 for ref-erence. There is excellent agreement between thespin-projected 12+state obtained from the spin-3/2 interpolating field and the earlier 12+results.A clear mass splitting is also seen between theN(32−) and N(12+) states obtained from the spin-3/2 interpolating field, with a mass difference of700–1000 MeV.4. CONCLUSIONFirst results for the spectrum of spin-3/2baryons in the isospin-1/2 and 3/2 channels arereported, using a FLIC fermion action and anO(a2) mean-field improved gauge action. Goodagreement is found with earlier calculations forthe ∆ ground state, and clear mass splittings be-tween the ground state and its parity partner areobserved. A signal is also obtained for the ∆(12±)states, with the level ordering consistent with theobserved empirical mass spectrum.For isospin-1/2 baryons, clear signals are ob-tained for both the N(32−) and spin-projectedN(12+) states from a spin-3/2 interpolating field.The 12+state in particular is in good agreementwith earlier simulations of the nucleon mass usingstandard spin-1/2 interpolating fields.We thank R.G. Edwards and D.G. Richardsfor helpful discussions. This work was supportedby the Australian Research Council. W.M. issupported by the U.S. Department of Energycontract DE-AC05-84ER40150 under which theSoutheastern Universities Research Association(SURA) operates the Thomas Jefferson NationalAccelerator Facility (Jefferson Lab).REFERENCES1. D. B. Leinweber, Phys. Rev. D 51, 6383(1995); F. X. Lee and D. B. Leinweber, Nucl.Phys. Proc. Suppl. 73, 258 (1999); F. X. Lee,Nucl. Phys. Proc. Suppl. 94, 251 (2001).2. D. G. Richards, Nucl. Phys. Proc. Suppl.94, 269 (2001); D. G. Richards et al., hep-lat/0112031.3. M. Go¨ckeler et al., hep-lat/0106022; S. Sasakiet al., hep-lat/0102010; S. Sasaki, hep-lat/0110052.4. V. Burkert et al., Few Body Syst. Suppl. 11,1 (1999).5. W. Melnitchouk et al., submitted to Phys.Rev. D, hep-lat/0202022.6. J. M. Zanotti et al., Phys. Rev. D 60, 074507(2002); Nucl. Phys. Proc. Suppl. 109, 101(2002); these proceedings.7. D. B. Leinweber et al., Phys. Rev. D 46, 3067(1992); Phys. Rev. D 43, 1659 (1991).8. Y. Chung et al., Nucl. Phys. B197, 55 (1982).9. M. Benmerrouche et al., Phys. Rev. C 39,2339 (1989).10. R. G. Edwards et al., Nucl. Phys. B 517, 377(1998) [hep-lat/9711003].11. S. Bilson-Thompson et al., Nucl. Phys. Proc.Suppl. 109, 116 (2002); hep-lat/0203008.12. J. M. Zanotti et al., in preparation.13. Z.-P. Li, V. Burkert and Z.-J. Li, Phys. Rev.D 46

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Spin-3/2 baryons in lattice QCD

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