We present first results for masses of positive and negative parity excited
baryons in lattice QCD using an O(a^2) improved gluon action and a Fat Link
Irrelevant Clover (FLIC) fermion action in which only the irrelevant operators
are constructed with fat links. The results are in agreement with earlier
calculations of N^* resonances using improved actions and exhibit a clear mass
splitting between the nucleon and its chiral partner, even for the Wilson
fermion action. The results also indicate a splitting between the lowest J^P =
1/2^- states for the two standard nucleon interpolating fields.Comment: 5 pages, 3 figures, talk given by W.Melnitchouk at LHP 2001 workshop,
  Cairns, Australi

A.G Williams

Bowler

D.B Leinweber

F.D.R Bonnet

F.X Lee

J.B Zhang

J.M Zanotti

Leinweber

P.D Coddington

Richards

S Bilson-Thompson

Siegel

Veit

W Melnitchouk

English

arXiv

Copyright © 2002 Published by Elsevier Science B.V. All rights reserved. Copyright © 2002. Submitted to Cornell University’s online archive www.arXiv.org in 2002 by James Zanotti. Post-print sourced from www.arxiv.org.We present first results for masses of positive and negative parity excited baryons in lattice QCD using an ∂ (a2) improved gluon action and a Fat Link Irrelevant Clover (FLIC) fermion action in which only the irrelevant operators are constructed with fat links. The results are in agreement with earlier calculations of N* resonances using improved actions and exhibit a clear mass splitting between the nucleon and its chiral partner, even for the Wilson fermion action. The results also indicate a splitting between the lowest JP = ½ − states for the two standard nucleon interpolating fields.W. Melnitchouk, S. Bilson-Thompson, F. D. R. Bonnet, P. D. Coddington, D. B. Leinweber, A. G. Williams, J. M. Zanotti, J. B. Zhang and F. X. Leehttp://www.elsevier.com/wps/find/journaldescription.cws_home/505717/description#descriptio

Melnitchouk, W.

Bilson-Thompson, S.

Bonnet, F.

Coddington, P.

Leinweber, D.

Williams, A.

Zanotti, J.

Zhang, J.

Lee, F.

Adelaide Research & Scholarship

arXiv:hep-lat/0201005v1  4 Jan 2002ADP-01-55/T487JLAB-THY-01-40Baryon resonances from a novel fat-link fermion actionW. Melnitchouka,b, S. Bilson-Thompsona, F. D. R. Bonneta, P. D. Coddingtona, D. B. Leinwebera,A. G. Williamsa, J. M. Zanottia, J. B. Zhanga and F. X. Leeb,caSpecial Research Center for the Subatomic Structure of Matter, andDepartment of Physics and Mathematical Physics, Adelaide University, 5005, AustraliabJefferson Lab, 12000 Jefferson Avenue, Newport News, VA 23606, U.S.A.cCenter for Nuclear Studies, Department of Physics,The George Washington University, Washington, D.C. 20052, U.S.A.We present first results for masses of positive and negative parity excited baryons in lattice QCD using anO(a2) improved gluon action and a Fat Link Irrelevant Clover (FLIC) fermion action in which only the irrelevantoperators are constructed with fat links. The results are in agreement with earlier calculations of N∗ resonancesusing improved actions and exhibit a clear mass splitting between the nucleon and its chiral partner, even forthe Wilson fermion action. The results also indicate a splitting between the lowest JP = 12−states for the twostandard nucleon interpolating fields.1. INTRODUCTIONUnderstanding the dynamics responsible forbaryon excitations provides valuable insight intothe forces which confine quarks inside baryonsand into the nature of QCD in the nonpertur-bative regime. One of the long-standing puzzlesin spectroscopy has been the low mass of thefirst positive parity excitation of the nucleon (theJP = 12+N∗(1440) Roper resonance) comparedwith the lowest lying odd parity excitation. An-other challenge for spectroscopy is presented bythe Λ1/2−(1405), whose anomalously small masshas been interpreted as indicating strong coupledchannel effects involving Σπ, K¯N , · · · [1], anda weak overlap with a three valence constituentquark state.In this paper we present the first results ofexcited octet baryon mass simulations using anO(a2) improved gluon action and an improvedFat Link Irrelevant Clover (FLIC) [2] quark ac-tion in which only the irrelevant operators areconstructed using fat links. Configurations aregenerated on the new Orion computer clusterdedicated to lattice gauge theories at the CSSMat Adelaide University. After reviewing in Sec-tion 2 the main elements of lattice calculationsof excited hadron masses, we describe in Section3 various features of interpolating fields used inthis analysis. In Section 4 we present results forJP = 12±nucleons and hyperons. Finally, in Sec-tion 5 we make concluding remarks and discusssome future extensions of this work.2. BARYONS ON THE LATTICEThe history of excited baryons on the latticeis quite brief, although recently there has beengrowing interest in finding new techniques to iso-late excited baryons, motivated partly by the ex-perimental N∗ program at Jefferson Lab. Previ-ous work on excited baryons on the lattice can befound in Refs. [3–7].Following standard notation, we define a two-point correlation function for a baryon B as:GB(t, ~p) ≡∑~xe−i~p·~x 〈0 |TχB(x) χ¯B(0)| 0〉 , (1)where χB is a (positive parity) baryon interpolat-ing field, and we have suppressed Dirac indices.The choice of interpolating field χB is discussedin Section 3 below. For large Euclidean time, thecorrelation function can be written as a sum of thelowest energy positive and negative parity contri-butions:GB(t, ~p) ≈ λ2B+(γ · p+MB+)2EB+e−EB+ t+ λ2B−(γ · p−MB−)2EB−e−EB− t , (2)2where a fixed boundary condition in the timedirection is used to remove backward propagat-ing states, and where the overlap of the field χBwith positive or negative parity states |B±〉 isparameterized by a coupling strength λB± , withEB± =√M2B± + ~p2 the energy. The energiesof the positive and negative parity states are ob-tained by taking the trace of GB with the opera-tor Γ±, whereΓ± =12(1±MB±EB±γ4). (3)For ~p = 0, EB± = MB± and the operator Γ±projects out the mass, MB± , of the baryon B±.In this case, positive parity states propagate inthe 1, 1 and 2, 2 elements of the Dirac matrix ofEq. (2), while negative parity states propagate inthe 3, 3 and 4, 4 elements.3. INTERPOLATING FIELDSIn this analysis we consider two types of inter-polating fields which have been used in the litera-ture. The notation adopted follows that of Lein-weber et al. [8]. For the positive parity protonwe use as interpolating fields:χp+1 (x) = ǫabc(uTa (x) Cγ5 db(x))uc(x) , (4)andχp+2 (x) = ǫabc(uTa (x) C db(x))γ5 uc(x) , (5)where the fields u, d are evaluated at Euclideanspace-time point x, C is the charge conjugationmatrix, a, b and c are color labels, and the super-script T denotes the transpose. As pointed outby Leinweber [3], because of the Dirac structureof the “diquark” in the parentheses in Eq. (4), thefield χp+1 involves both products of upper × upper× upper and lower × lower × upper componentsof spinors for positive parity baryons, so that inthe nonrelativistic limit χp+1 = O(1). Further-more, since the “diquark” couples to a total spin0, one expects an attractive force between the twoquarks, and hence a lower energy state than fora state in which two quarks do not couple to spin0.The χp+2 interpolating field, on the other hand,is known to have little overlap with the groundstate [3,9]. Inspection of the structure of theDirac matrices in Eq. (5) reveals that it involvesproducts of upper × lower × lower componentsonly for positive parity baryons, so that χp+2 =O(p2/E2) vanishes in the nonrelativistic limit. Asa result of the mixing, the “diquark” term con-tains a factor ~σ · ~p, meaning that the quarks nolonger couple to spin 0, but are in a relative L = 1state. One expects therefore that two-point corre-lation functions constructed from the interpolat-ing field χp+2 are dominated by larger mass statesthan those arising from χp+1 .Interpolating fields for a negative parity pro-ton can be constructed by multiplying the posi-tive parity fields by γ5, χB− ≡ γ5 χB+, which re-verses the role of the terms in Eq. (2). While themasses of negative parity baryons are obtaineddirectly from the (positive parity) interpolatingfields in (4) and (5) by using the parity projec-tors Γ±, it is instructive nevertheless to exam-ine the general properties of the negative parityinterpolating fields. In contrast to the positiveparity case, both the interpolating fields χp−1 andχp−2 mix upper and lower components, and con-sequently both χp−1 and χp−2 are O(p/E). Phys-ically, two nearby JP = 12−states are observedin the nucleon spectrum. In simple quark mod-els, the splitting of these two orthogonal states islargely attributed to the extent to which scalar di-quark configurations compose the wave function[4]. It is reasonable to expect χp−1 to have betteroverlap with scalar diquark dominated states, andthus provide a lower effective mass in the largeEuclidean time regime explored in lattice simula-tions. If the effective mass associated with the χp2correlator is larger, then this would be evidenceof significant overlap of χp−2 with the higher lyingN12− states. In this event, further analysis di-rected at resolving these two states is warranted.4. RESULTSIn this paper we report results of calculationsof octet excited baryon masses performed on a163 × 32 lattice at β = 4.60 with a lattice spac-ing of a = 0.125(2) fm. The analysis is based ona preliminary sample of 50 configurations gener-ated on the new Orion computer cluster at the30 0.2 0.4 0.6 0.8 1 1.20.81.21.622.4m(GeV)MN(GeV  )N*Fat link cloverpi2 2DWFNP−imp. clover(1/2  )Wilson1535939−+−Figure 1. Masses of the nucleon and the lowestJP = 12−excitation. The FLIC and Wilson re-sults are from the present analysis, with the NPimproved clover [7] and DWF [6] results shownfor comparison. The empirical N and N∗(1535)masses are indicated by the asterisks.CSSM, Adelaide. For the gauge fields, a mean-field improved plaquette plus rectangle action isused, while for the quark fields, the FLIC [2]action is implemented. In the present analysiswe have imposed fixed boundary conditions inthe time direction (Ut(~x, nt) = 0 ∀ ~x), and pe-riodic boundary conditions in spatial directions.Although the simulations were performed withboth n = 4 and 12 fattening sweeps, the im-proved gauge fields were found to be smooth af-ter only 4 sweeps. Since the results with n = 4sweeps exhibit slightly better scaling than thosewith n = 12 [2], we shall focus on the results with4 smearing sweeps. The 12 sweep results lead tothe same conclusions as presented in the follow-ing. Further details of the simulations are givenin Ref. [2].In Fig. 1 we show the N and N∗(12−) massesas a function of the squared pseudoscalar mesonmass, m2π. The results of the new simulationsare indicated by the filled symbols (filled circlesare FLIC; filled diamonds are Wilson). For com-parison, we also show results from earlier sim-ulations with domain wall fermions (DWF) [6](open triangles), and a nonperturbatively (NP)improved clover action at β = 6.2 [7]. The scat-ter of the different NP improved results is due todifferent source smearing and volume effects: theopen squares are obtained by using fuzzed sourcesand local sinks, the open circles use Jacobi smear-ing at both the source and sink, while the opendiamonds, which extend to smaller quark masses,are obtained from a larger lattice (323 × 64) us-ing Jacobi smearing. The empirical masses of thenucleon and the lowest 12−excitation are indi-cated by the asterisks along the ordinate. Thereis excellent agreement between the different im-proved actions for the nucleon mass, in particularbetween the FLIC, NP improved clover [7] andDWF [6] results. On the other hand, the Wil-son results lie systematically low in comparisonto these due to large O(a) errors in this action[2]. A similar pattern is repeated for the N∗(12−)masses. Namely, the FLIC, NP improved cloverand DWF masses are in agreement with eachother, while the Wilson results again lie system-atically low. A mass splitting of around 400 MeVis clearly visible between the N and N∗ for allactions, including the Wilson action, contrary toprevious claims [6].Figure 2 shows the ratio of the masses of theN∗(12−) and the nucleon. Once again, there isgood agreement between the FLIC and DWFactions. However, the results for the Wilsonaction lie above the others, as do those forthe anisotropic D234 action [5]. The D234 ac-tion has been mean-field improved, and uses ananisotropic lattice which is relatively coarse in thespatial direction (a ≈ 0.24 fm). This is an indi-cation of the need for nonperturbative or fat linkimprovement.The mass splitting between the two lightestnearby N∗(12−) states (N∗(1535) and N∗(1650))can be studied by considering the χ1 and χ2 in-terpolating fields in Eqs.(4) and (5). Recall thatthe “diquarks” in χ1 and χ2 couple differently tospin, so that even though the correlation func-tions built up from the χ1 and χ2 fields will be40 0.2 0.4 0.6 0.8 111.21.41.61.82mDWFDmFat link cloverWilsonN*N1535/939(1/2  )pi ρ/( )/−234Figure 2. Ratio of the N∗(12−) and N masses.The FLIC andWilson results are from the presentanalysis, with results from the DWF [6] and D234[5] actions shown for comparison. The empiricalN∗(1535)/N mass ratio is denoted by the aster-isk.made up of a mixture of many excited states, theywill have dominant overlap with different statesyielding different masses [3]. The results, shownin Fig. 3 for the FLIC action, indicate that in-deed the N∗(12−) corresponding primarily to theχ2 field (labeled “N∗2 ”) lies systematically abovethe N∗(12−) associated primarily with the χ1 field(“N∗1 ”).As has long been known, the positive parity χ2interpolating field (“N2”, which is also sometimesdenoted by “N ′(12+)”) does not have good over-lap with the nucleon ground state [3], and cor-responds to a state which lies around 400 MeVabove the negative parity excitation of χ1. Thereis little evidence that this state is the N∗(1440)Roper resonance (first 12+excitation of the nu-cleon). While it is possible that the Roper res-onance may have a strong nonlinear dependenceon the quark mass at m2π < 0.2 GeV2, arisingfrom pion loop corrections, it is unlikely that thisbehavior would be so dramatically different from0 0.2 0.4 0.6 0.8 10.81.21.622.42.83.2m(GeV)M(GeV  )N*pi2 2NNN*1440939153517101650++−−+1122Figure 3. Masses of the 12+and 12−nucleons, forthe FLIC action. The positive parity (N1 andN2)and negative parity (N∗1 and N∗2 ) states are con-structed from the χp1 and χp2 interpolating fields,respectively. The empirical masses of lowest two12±excitations of the nucleon are indicated by theasterisks.that of the N∗(1535) so as to reverse the levelordering obtained from the lattice. A more likelyexplanation is that the χ2 interpolating field doesnot have good overlap with either the nucleon orthe N∗(1440), but rather a (combination of) ex-cited 12+state(s).Recall that in a constituent quark model in aharmonic oscillator basis the mass of the Roperis higher than the mass of the lowest P -wave ex-citation. The lattice data thus appear to be con-sistent with the naive quark model expectationat large values of mq. Better overlap with theRoper resonance is likely to require more exoticinterpolating fields.5. CONCLUSIONWe have presented the first results for the ex-cited baryon spectrum from lattice QCD usingan O(a2) improved gauge action and an improvedFat Link Irrelevant Clover (FLIC) quark action inwhich only the links of the irrelevant dimension5five operators are smeared. The simulations havebeen performed on a 163 × 32 lattice at β = 4.60,providing a lattice spacing of a = 0.125(2) fm.The analysis is based on a set of 50 configurationsgenerated on the new Orion computer cluster atthe CSSM, Adelaide.Good agreement is obtained between the FLICand other improved actions, such as the nonper-turbatively improved clover [7] and domain wallfermion [6] actions, for the nucleon and its chiralpartner, with a mass splitting of ∼ 400 MeV. Ourresults for the N∗(12−) improve on those using theD234 [5] and Wilson actions. Despite strong chiralsymmetry breaking, the results with the Wilsonaction are still quite reasonable rendering earlierconjectures invalid. Using the two standard nu-cleon interpolating fields, we also confirm earlierobservations [4] of a mass splitting between thetwo nearby 12−states. We find no evidence ofoverlap with the 12+Roper resonance.We have not attempted to extrapolate the lat-tice results to the physical region of light quarks,since the nonanalytic behavior of N∗’s near thechiral limit is not as well understood yet as thatof the nucleon [10,11]. It is vital that future lat-tice N∗ simulations push closer towards the chi-ral limit. On a promising note, our simulationswith the 4 sweep FLIC action are able to reachrelatively low quark masses (mq ∼ 60–70 MeV)already. We have also not addressed the ques-tion of to what extent quenching may affect anyof our results. We naturally expect the effects ofquark loops to be relatively unimportant at thecurrently large quark masses, although quenchingmay well produce some artifacts as one nears thechiral limit.For future work, we intend to use variationaltechniques to better resolve individual excitedstates, for instance, those corresponding to theN∗1 and N∗2 fields (using a 2 × 2 correlator ma-trix). In order to further explore the origin ofthe Roper resonances, more exotic interpolatingfields involving higher Fock states, or other non-local operators should be investigated. Finally,the present N∗ mass analysis will be extended infuture to include N → N∗ transition form factorsthrough the calculation of three-point correlationfunctions.We thank D.G. Richards for providing thedata points from Ref. [7]. This work wassupported by the Australian Research Coun-cil, and the U.S. Department of Energy con-tract DE-AC05-84ER40150, under which theSoutheastern Universities Research Association(SURA) operates the Thomas Jefferson NationalAccelerator Facility (Jefferson Lab).REFERENCES1. R.H. Dalitz and J.G. McGinley, Oxford U.preprint TP-47-80 (1980);E.A. Veit, B.K. Jennings, R.C. Barrett andA.W. Thomas, Phys. Lett. B 137 (1984) 415;P.B. Siegel and W. Weise, Phys. Rev. C 38(1988) 2221.2. J.M. Zanotti et al., hep-lat/0110216; andthese proceedings.3. D.B. Leinweber, Phys. Rev. D 51 (1995)6383.4. F.X. Lee and D.B. Leinweber, Nucl. Phys.Proc. Suppl. 73 (1999) 258.5. F.X. Lee, Nucl. Phys. Proc. Suppl. 94 (2001)251.6. S. Sasaki, T. Blum and S. Ohta, hep-lat/0102010.7. D.G. Richards, Nucl. Phys. Proc. Suppl. 94(2001) 269; Go¨ckeler et al., hep-lat/0106022.8. D.B.Leinweber, R.W.Woloshyn andT.Draper, Phys. Rev. D 43 (1991) 1659.9. K. Bowler et al., Nucl. Phys. B240 (1984)213.10. D.B. Leinweber, A.W. Thomas, K. Tsushimaand S.V. Wright, Phys. Rev. D 61 (2000)074502.11. R.D. Young et al., hep-lat/0111041; and theseproceedings.

Nuclear Physics B - Proceedings Supplements

Baryon resonances from a novel fat-link fermion action

Crossref

We present first results for masses of positive and negative parity excited baryons in lattice QCD using an O(a{sup 2}) improved gluon action and a Fat Link Irrelevant Clover (FLIC) fermion action in which only the irrelevant operators are constructed with fat links. The results are in agreement with earlier calculations of N* resonances using improved actions and exhibit a clear mass splitting between the nucleon and its chiral partner, even for the Wilson fermion action. The results also indicate a splitting between the lowest J{sup P}=1/2{sup -} states for the standard nucleon interpolating fields

Bonnet, F. D. R.

Coddington, P. D.

Lee, F. X.

Leinweber, D. B.

Williams, A. G.

Zanotti, J. M.

Zhang, J. B.

UNT (University of North Texas) Digital Library

PROCEEDINGS SUPPLEMENTS ELSEVIER Nuclear Physics B (Proc. Suppl.) 109A (2002) 96-100 www.elsevier.com/locate/npc: Baryon resonances from a novel fat-link fermion action W. Melnitchoukaa b, S. Bilson-Thompson”, F. D. R. Bonneta, P. D. Coddingtona, D. B. Leinwebera, A. G. Williams”, J. M. Zanottia, J. B. Zhang” and F. X. Leeb,c aSpecial Research Center for the Subatomic Structure of Matter, and Department of Physics and Mathematical Physics, Adelaide University, 5005, Australia bJefferson Lab, 12000 Jefferson Avenue, Newport News, VA 23606, U.S.A. ‘Center for Nuclear Studies, Department of Physics, The George Washington University, Washington, D.C. 20052, U.S.A. We present first results for masses of positive and negative parity excited baryons in lattice QCD using an O(a’) improved gluon action and a Fat Link Irrelevant Clover (FLIC) f ermion action in which only the irrelevant operators are constructed with fat links. The results are in agreement with earlier calculations of N’ resonances using improved actions and exhibit a clear mass. splitting between the nucleon and its chiral partner, even for the Wilson fermion action. The results also indicate a splitting between the lowest Jp = $- states for the two standard nucleon interpolating fields. 1. INTRODUCTION Understanding the dynamics responsible for baryon excitations provides valuable insight into the forces which confine quarks inside baryons and into the nature of QCD in the nonpertur- bative regime. One of the long-standing puzzles in spectroscopy has been the low mass of the first positive parity excitation of the nucleon (the Jp = f’ N’ (1440) Roper resonance) compared with the lowest lying odd parity excitation. An- other challenge for spectroscopy is presented by the A1i2-( 1405), whose anomalously small mass has been interpreted as indicating strong coupled channel effects involving CT, h’N, ... [l], and a weak overlap with a three valence constituent quark state. In this paper we present the first results of ex- cited octet mass simulations using an 0(a2) im- proved gluon action and an improved Fat Link Ir- relevant Clover (FLIC) [2] quark action in which only the irrelevant operators are constructed us- ing fat links. Configurations are generated on the new Orion computer cluster dedicated to lattice gauge theories at the CSSM at Adelaide Univer- sity. After reviewing in Section 2 the main el- ements of lattice calculations of excited hadron masses, we describe in Section 3 various features of interpolating fields used in this analysis. In Section 4 we present results for Jp = a’ nucle- ons and hyperons. Finally, in Section 5 we make concluding remarks and discuss some future ex- tensions of this work. 2. BARYONS ON THE LATTICE The history of excited baryons on the lattice is quite brief, although recently there has been growing interest in finding new techniques to iso- late excited baryons, motivated partly by the ex- perimental N’ program at Jefferson Lab. Previ- ous work on excited baryons on the lattice can be found in Refs. [3-71. Following standard notation, we define a two- point correlation function for a baryon B as: GB(t,j7) E c e+’ (OITXB(Z) XB(O)lO) 7 (1) 3 where XB is a baryon interpolating field trans- forming positively under parity operation, and we have suppressed Dirac indices. The choice of interpolating field XB is discussed in Section III below. For large Euclidean time, the correlation function can be written as a sum of the lowest en- 0920-5632/02/$ - see front matter Q 2002 Elsevier Science B.V: All rights reserved. PI1 SO920-5632(02)01396-8 K Melnitchouk et al. /Nuclear Physics B (Pmt. Suppl.) 109A (2002) 96100 97 ergy positive and negative parity contributions: G~(trP3 ia A;+ (7 ‘P + MB+) e-E,+ t DEB+ + p_ (Y’P-“B-)e-E,_t , (44 2EB- where a fixed boundary condition in the time direction is used to remove backward propagat- ing states, and where the overlap of the field XB with positive or negative parity states ]B*) is parameterized by a coupling strength XBf, with Egf = dm the energy. The energies of the positive and negative parity states are ob- tained by taking the trace of GB with the opera- tor rk, where For p’ = 0, Egk = MB* and the operator rk projects out the mass, n/3,*, of the baryon B*. In this case, positive parity states propagate in the 1, 1 and 2, 2 elements of the Dirac matrix of Eq. (2), while negative parity states propagate in the 3, 3 and 4, 4 elements. 3. INTERPOLATING FIELDS In this analysis we consider two types of inter- polating fields which have been used in the litera- ture. The notation adopted follows that of Lein- weber et al. [S]. For the positive parity proton we use as interpolating fields: x:+(z) = hbc (u:(x) @5 db(z)) UC(~) > (4) and X;+(z) = fobc (u:(x) c db(z)) -7’5 UC(~) , (5) where the fields U, d are evaluated at Euclidean space-time point x, C is the charge conjugation matrix, a, b and c are color labels, and the super- script T denotes the transpose. As pointed out by Leinweber [3], because of the Dirac structure of the “diquark” in the parentheses in Eq. (4), the field x{’ involves both products of upper x upper x upper and lower x lower x upper components of spinors for positive parity baryons, so that in the nonrelativistic limit $ = O(1). Further- more, since the “diquark” couples to a total spin 0, one expects an attractive force between the two quarks, and hence a lower energy state than for a state in which two quarks do not couple to spin 0. The & interpolating field, on the other hand, is known to have little overlap with the ground state [3,9]. Inspection of the structure of the Dirac matrices in Eq. (5) reveals that it involves products of upper x lower x lower components only for positive parity baryons, so that x;+ = S(p2/E2) vanishes in the nonrelativistic limit. As a result of the mixing, the “diquark” term con- tains a factor ii . p’, meaning that the quarks no longer couple to spin 0, but are in a relative L = 1 state. One expects therefore that two-point corre- lation functions constructed from the interpolat- ing field x$+ are dominated by larger mass states than those arising from XT+. Interpolating fields for a negative parity pro- ton can be constructed by multiplying the posi- tive parity fields by y5, xB- 5 75 xBf , which re- verses the role of the terms in Eq. (2). While the masses of negative parity baryons are obtained directly from the (positive parity) interpolating fields in (4) and (5) by using the parity projec- tors I’&, it is instructive nevertheless to exam- ine the general properties of the negative parity interpolating fields. In contrast to the positive parity case, both the interpolating fields x’;- and x;- mix upper and lower components, and con- sequently both x7- and &- are O(p/E). Phys- ically, two nearby .Jp = $- states are observed in the nucleon spectrum. In simple quark mod- els, the splitting of these two orthogonal states is largely attributed to the extent to which scalar diquark configurations compose the wavefunction [4]. It is reasonable to expect x{- to have better overlap with scalar diquark dominated states, and thus provide a lower effective mass in the large Euclidean time regime explored in lattice simula- tions. If the effective mass associated with the x; correlator is larger, then this would be evidence of significant overlap of xg- with the higher lying N *- states. In this event, further analysis di- rected at resolving these two states is warranted. 98 Ff! Melnitchouk et al. /Nuclear Physics B (Pmt. Suppl.) 109A (2002) 96-100 4. RESULTS In this paper we report results of calculations of octet excited baryon masses performed on a 163 x 32 lattice at p = 4.60 with a lattice spac- ing of a = 0.125(2) fm. The analysis is based on a preliminary sample of 50 configurations gener- ated on the new Orion computer cluster at the CSSM, Adelaide. For the gauge fields, a mean- field improved plaquette plus rectangle action is used, while for the quark fields, the FLIC [2] action is implemented. In the present analysis we have imposed fixed boundary conditions in the time direction (Ut(Z, nt) = 0 V s), and pe- riodic boundary conditions in spatial directions. Although the simulations were performed with both n = 4 and 12 fattening sweeps, the im- proved gauge fields were found to be smooth af- ter only 4 sweeps. Since the results with n = 4 sweeps exhibit slightly better scaling than those with n = 12 [2], we shall focus on the results with 4 smearing sweeps. The 12 sweep results lead to the same conclusions as presented in the follow- ing. Further details of the simulations are given in Ref.[2]. In Fig. 1 we show the N and N*( $-) masses as a function of the squared pseudoscalar meson mass, rng. The results of the new simulations are indicated by the filled symbols (filled circles are FLIC; filled diamonds are Wilson). For com- parison, we also show results from earlier sim- ulations with domain wall fermions (DWF) [6] (open triangles), and a nonperturbatively (NP) improved clover action at /3 = 6.2 [7]. The scat- ter of the different NP improved results is due to different source smearing and volume effects: the open squares are obtained by using fuzzed sources and local sinks, the open circles use Jacobi smear- ing at both the source and sink, while the open diamonds, which extend to smaller quark masses, are obtained from a larger lattice (323 x 64) US- ing Jacobi smearing. The empirical masses of the nucleon and the lowest L- excitation are indi- 2 cated by the asterisks along the ordinate. There is excellent agreement between the different im- proved actions for the nucleon mass, in particular between the FLIC, NP improved clover [7] and DWF [6] results. On the other hand, the Wilson 2.4) . . . . - . . . , 1.2 l Fat link clover 00” NP-imp. clover N l Wilson A DWF 0.8 I 0 0.2 0.4 0.6 0.8 1 1.2 m2, (GeV2) Figure 1. Masses of the nucleon and the lowest JP = i- excitation. The FLIC and Wilson re- sults are from the present analysis, with the NP improved clover [7] and DWF [S] results shown for comparison. The empirical N and N’(1535) masses are indicated by the asterisks. results for the nucleon mass lie systematically low in comparison to these due to large O(a) errors in this action [2]. A similar pattern is repeated for the N*(i-) masses. Namely, the FLIC, NP improved clover and DWF masses are in agree- ment with each other, while the Wilson results again lie systematically low. A mass splitting of around 400 MeV is clearly visible between the N and N* for all actions, including the Wilson ac- tion, contrary to previous claims [6]. Fig. 2 shows the ratio of the masses of the N*(g-) and the nucleon. Once again, there is good agreement between the FLIC and DWF actions. However, the results for the Wilson action lie above the others, as do those for the anisotropic D234 action [5]. The D234 a~- tion has been mean-field improved, and uses an anisotropic lattice which is relatively coarse in the spatial direction (a M 0.24 fm). This is an indi- cation of the need for nonperturbative or fat link improvement. K Melnitchouk et al. /Nuclear Physics B (proc. Suppl.) 109A (2002) 96100 99 1.8 l Fat link clover c * 1535,939 1.6 * \ I I- q 1*4- c s 1.2. l Wilson * DWF o 9% 1’ m . ’ m . * ’ 0 0.2 0.4 0.6 0.8 1 (m,lmp)2 Figure 2. Ratio of the N*(&-) and N masses. The FLIC and Wilson results are from the present analysis, with results from the DWF [6] and Dzs4 [5] actions shown for comparison. The empirical N*(1535)/N mass ratio is denoted by the aster- isk. The mass splitting between the two lightest nearby N*(h-) states (N*(1535) and N*(1650)) can be studied by considering the x1 and x2 in- terpolating fields in Eqs. (4) and (5). Recall that the “diquarks” in x1 and x2 couple differently to spin, so that even though the correlation func- tions built up from the x1 and x2 fields will be made up of a mixture of many excited states, they will have dominant overlap with different states yielding different masses [3]. The results, shown in Fig. 3 for the FLIC action, indicate that in- deed the N*($-) corresponding primarily to the x2 field (labeled “N,*“) lies systematically above the N*( $-) associated primarily with the x1 field ( “NT”). As has long been known, the positive parity x2 interpolating field ( “Nz”, which is also sometimes denoted by “N/(4+)“) does not have good over- lap with the nucleon ground state [3], and cor- responds to a state which lies around 400 MeV above the negative parity excitation of ~1. There 3.2 2.8 - o Y 0 t *939+ 0.8 0 0.2 0.4 0.6 0.8 1 m,c2 (GeV2) Figure 3. Masses of the 3’ and +- nucleons, for the FLIC action. The positive parity (Nl and N2) and negative parity (N,* and N;) states are con- structed from the ~7 and x; interpolating fields, respectively. The empirical masses of lowest two f” excitations of the nucleon are indicated by the asterisks. is little evidence that this state is the N’(1440) Roper resonance (first $’ excitation of the nu- cleon). While it is possible that the Roper res- onance may have a strong nonlinear dependence on the quark msss at rn$ < 0.2 GeV2, arising from pion loop corrections, it is unlikely that this behavior would be so dramatically different from that of the N*(1535) so as to reverse the level ordering obtained from the lattice. A more likely explanation is that the x2 interpolating field does not have good overlap with either the nucleon or the N*(1440), but rather a (combination of) ex- cited i’ state(s). Recall that in a constituent quark model in a harmonic oscillator basis the mass of the Roper is higher than the mass of the lowest P-wave ex- citation. The lattice data thus appear to be con- sistent with the naive quark model expectation at large values of m,. Better overlap with the Roper resonance is likely to require more exotic interpolating fields. 100 K Melnitchouk et al. /Nuclear Physics B (Proc. Suppl.) 109A (2002) 96100 5. CONCLUSION We have presented the first results for the ex- cited baryon spectrum from lattice QCD using an O(a’) improved gauge action and an improved Fat Link Irrelevant Clover (FLIC) quark action in which only the links of the irrelevant dimension five operators are smeared. The simulations have been performed on a 163 x 32 lattice at p = 4.60, providing a lattice spacing of a = 0.125(2) fm. The analysis is baaed on a set of 50 configurations generated on the new Orion computer cluster at the CSSM, Adelaide. Good agreement is obtained between the FLIC and other improved actions, such as the nonper- turbatively improved clover [7] and domain wall fermion [6] actions, for the nucleon and its chiral partner, with a mass splitting of - 400 MeV. Our results for the N*( i-) improve on those using the D234 [5] and Wilson actions. Despite strong chiral symmetry breaking, the results with the Wilson action are still quite reasonable rendering earlier conjectures invalid. Using the two standard nu- cleon interpolating fields, we also confirm earlier observations [4] of a mass splitting between the two nearby I- states. 2 We find no evidence of overlap with the f’ Roper resonance. We have not attempted to extrapolate the lat- tice results to the physical region of light quarks, since the nonanalytic behavior of N*‘s near the chiral limit is not as well understood yet as that of the nucleon [lO,ll]. It is vital that future lat- tice N* simulations push closer towards the chi- ral limit. On a promising note, our simulations with the 4 sweep FLIC action are able to reach relatively low quark masses (m. - 60-70 MeV) already. We have also not addressed the question of the extent to which quenching may affect any of our results. We naturally expect the effects of quark loops to be relatively unimportant at the currently large quark masses, although quenching may well produce some artifacts as one nears the chiral limit. For future work, we intend to use variational techniques to better resolve individual excited states, for instance, those corresponding to the Ni” and Nz fields (using a 2 x 2 correlator ma- We thank D.G. Richards for providing the data points from Ref.[7]. This work was supported by the Australian Research Coun- cil, and the U.S. Department of Energy con- tract DEAC05-84ER40150, under which the Southeastern Universities Research Association (SURA) operates the Thomas Jefferson National Accelerator Facility (Jefferson Lab). REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10 11 E.A. Veit, B.K. Jennings, R.C. Barrett and A.W. Thomas, Phys. Lett. B 137 (1984) 415; P.B. Siegel and W. Weise, Phys. Rev. C 38 (1988) 2221. J.M. Zanotti et al., heplat/0110216; and these proceedings. D.B. Leinweber, Phys. Rev. D 51 (1995) 6383. F.X. Lee and D.B. Leinweber, Nucl. Phys. B (Proc.Suppl.) 73 (1999) 258. F.X. Lee, Nucl. Phys. B (Proc.Suppl.) 94 (2001) 251. S. Sasaki, T. Blum and S. Ohta, hep lat/0102010. D.G. Richards, Nucl. Phys. Proc. Suppl. 94 (2001) 269; M. Gijckeler et al., hep- lat/0106022. D.B.Leinweber, R.W.Woloshyn and T.Draper, Phys. Rev. D 43 (1991) 1659. K. Bowler et al., Nucl. Phys. B240 (1984) 213. D.B. Leinweber, A.W. Thomas, K. Tsushima and S.V. Wright, Phys. Rev. D 61 (2000) 074502. R.D. Young et al., hep-lat/0111041; and these proceedings. trix). In order to further explore the origin of the Roper resonances, more exotic interpolating fields involving higher Fock states, or other non- local operators should be investigated. Finally, the present N’ mass analysis will be extended in future to include N + N* transition form factors through the calculation of three-point correlation functions. 

Baryon Resonances from a Novel Fat-Link Fermion Action

Baryon resonances from a novel fat-link fermion action

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