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Lattice Hadron Physics 123 Editors Alex C Kalloniatis Derek B Leinweber Anthony G Williams University of Adelaide School of Chemistry & Physics Adelaide SA 5005 Australia A Kalloniatis D Leinweber A Williams (Eds.), Lattice Hadron Physics, Lect Notes Phys 663 (Springer, Berlin Heidelberg 2005), DOI 10.1007/b103529 Library of Congress Control Number: 2004115525 ISSN 0075-8450 ISBN-10 3-540-23911-1 Springer Berlin Heidelberg New York ISBN-13 978-3-540-23911-6 Springer Berlin Heidelberg New York This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer Violations are liable to prosecution under the German Copyright Law Springer is a part of Springer Science+Business Media springeronline.com © Springer-Verlag Berlin Heidelberg 2005 Printed in The Netherlands The use of general descriptive names, registered names, trademarks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use Typesetting: Camera-ready by the authors/editor Data conversion by TechBooks Cover design: design & production, Heidelberg Printed on acid-free paper 54/3141/jl - Preface This year marks 30 years since Ken Wilson’s seminal paper of October 1974 formulating non-Abelian gauge theory on a space-time lattice, and proposing its application to the solution of the theory of quark-gluon dynamics, QCD Since then the field has become vast, with several major symposia and workshops per year on the field of lattice gauge theory In particular, the 1990s brought overlap fermions and improved operators which overcame two of the major hurdles of lattice field theory – chirality on the lattice and suppression of discretisation errors It is now a daunting prospect for someone outside the field to quickly become literate and active in the area The present volume in Lecture Notes in Physics attempts to overcome this state of affairs In their earliest form, the various contributions in this volume were first presented by their authors in July 2001 at the international workshop on lattice hadron physics, LHP2001, in Cairns, Australia, under the auspices of the Centre for the Subatomic Structure of Matter based at the University of Adelaide in South Australia Those conference contributions, and those of the other participants at LHP2001 have been presented elsewhere Nevertheless those participants selected to extend their papers for this volume have put considerable effort into shaping the contributions to be accessible both pedagogically, as well as up to date in light of developments since 2001 They represent a broad spectrum of workers in hadronic physics, from graduate students to senior researchers of many years of experience and a solid body of significant work in hadronic physics The hope is that precisely this mix of newcomers and established experts in the field has enhanced the pedagogical value of the volume Thematically, this series of lectures draws upon the developments made in recent years in implementing chirality on the lattice via the overlap formalism, exploiting chiral effective field theory in order to extrapolate lattice results to physical quark masses, new forms of improving operators to remove lattice artefacts, analytical studies of finite volume effects in hadronic observables, studies of quark propagators on the lattice, and state of the art lattice calculations of excited resonances, including the heavy pseudoscalar eta and eta-prime mesons We trust that these contributions will assist graduate students and experienced researchers in other areas of hadronic physics to appreciate, if not become active in, contemporary lattice gauge theory and it’s application to hadronic phenomena We thank the contributing authors for the efforts they put in and VI Preface their patience as this volume was put together, and warmly thank John Hedditch for his assistance in the final stages of compilation Adelaide, January 2005 Alex Kalloniatis Derek Leinweber Tony Williams Contents Quenching Effects in the Hadron Spectrum C Allton 1 The Quenched Approximation Results from the Quenched Approximation Results from Full (Unquenched) Simulations Quantifying Quenching Effects 12 Conclusions 15 References 16 Quark Propagator from LQCD and Its Physical Implications P.O Bowman, U.M Heller, D.B Leinweber, A.G Williams, and J.B Zhang Introduction Euclidean Green’s Functions Gauge Fixing Staggered Quark Actions The Lattice Quark Propagator Analysis of Lattice Artefacts for Staggered Quarks Overlap Quark Actions Analysis of Lattice Artefacts for Overlap Quarks The Quark Propagator in Landau Gauge 10 Laplacian Gauge 11 Applications: The Condensate and Running Mass 12 Modelling the Mass Function 13 Conclusions References Generalised Spin Projection for Fermion Actions W Kamleh Introduction Standard Spin-Projection Trick Generalised Spin-Projection Trick The FLIC Fermion Action Conclusion References 17 17 18 23 26 30 32 38 42 47 49 51 56 59 61 65 65 65 66 67 68 69 VIII Contents Baryon Spectroscopy in Lattice QCD D.B Leinweber, W Melnitchouk, D.G Richards, A.G Williams, and J.M Zanotti Introduction and Motivation History of Lattice N ∗ Calculations Lattice Techniques Interpolating Fields Operators for Spin- 12 and Spin- 32 Baryons Survey of Results Conclusions A Appendix − Correlation Matrix Analysis References 71 71 74 75 78 82 92 104 105 110 Hadron Structure and QCD: Effective Field Theory for Lattice Simulations D.B Leinweber, A.W Thomas, and R.D Young Introduction Effective Field Theory for QCD Chiral Expansion of the Nucleon Mass Other Applications Conclusion References 113 113 114 118 123 127 128 Lattice Chiral Fermions from Continuum Defects H Neuberger Introduction Infinite Flavor Space Two Dimensional Flavor Space Compactifications Generalization of the Overlap What Next? References 131 131 131 133 141 143 144 144 The Computation of the η and η Mesons in Lattice QCD K Schilling, H Neff, and T Lippert Introduction Prolegomena: Pseudoscalars in LQCD The Real World with n¯ n s¯ s Mixing The Three Computational Bottlenecks Towards Realistic Physics Results Conclusion References 147 147 149 154 157 165 173 174 Contents IX Strong and Weak Interactions in a Finite Volume M Testa Introduction Summation Theorems The Lă uscher Quantization Condition Matrix Elements of Scalar Operators The Nature of the LL Relation Summation Theorems, Locality and the LL Formula Conclusions References 177 177 179 183 190 191 192 194 197 Hadron Properties with FLIC Fermions J.M Zanotti, D.B Leinweber, W Melnitchouk, A.G Williams, and J.B Zhang Introduction The Lattice Quark Action Fat-Link Irrelevant Fermion Action Lattice Simulations Scaling of FLIC Fermions Search for Exceptional Configurations Octet-Decuplet Mass Splittings Summary References 199 199 200 205 208 210 215 218 223 223 Subject Index 227 Hadron Properties with FLIC Fermions 215 and Wilson fermion action results The fits are constrained to have a common continuum limit and assume errors are O(a2 ) for FLIC and NP-improved clover actions and O(a) for the Wilson action An acceptable χ2 per degree of freedom is obtained for both the nucleon and ρ-meson fits These results indicate that FLIC fermions provide a new form of nonperturbative O(a) improvement The FLIC fermion results display nearly perfect scaling indicating O(a2 ) errors are small for this action Search for Exceptional Configurations Chiral symmetry breaking in the Wilson action allows continuum zero modes of the Dirac operator to be shifted into the negative mass region This problem is accentuated as the gauge fields become rough (a → large) Local lattice artifacts at the scale of the cutoff (often referred to as dislocations) give rise to spurious near zero modes The quark propagator can then encounter singular behaviour as the quark mass becomes light Exceptional configurations are a severe problem in quenched QCD (QQCD) because instantons are low action field configurations which appear readily in QQCD These instanton configurations give rise to approximate zero modes which should be suppressed at light quark masses by det M which is present in the link updates in full QCD This determinant is not present in QQCD and as a result, near-zero modes are overestimated in the ensemble The addition of the clover term to the fermion action broadens the distribution of near-zero modes As a result, the clover action is notorious for revealing the exceptional configuration problem in QQCD The FLIC action is expected to reduce the number of exceptional configurations by smoothing the gauge fields of the irrelevant operator via APE smearing [5, 6] The smoothing procedure has the effect of suppressing the local lattice artifacts and narrowing the distribution of near-zero modes, enabling simulations to be performed at light quark masses not currently accessible with the standard mean-field or non-perturbative improved clover fermion actions In order to access the light quark regime, we would like our preferred action to be efficient when inverting the fermion matrix Figure compares the convergence rates of the different actions on a 163 × 32 lattice at β = 4.60 by plotting the number of stabilised biconjugate gradient [34] iterations required to invert the fermion matrix as a function of mπ /mρ For any particular value of mπ /mρ , the FLIC actions converge faster than both the Wilson and mean-field improved clover fermion actions Also, the slopes of the FLIC lines are smaller in magnitude than those for Wilson and mean-field improved clover actions, which provides great promise for performing cost effective simulations at quark masses closer to the physical values Problems with exceptional configurations have prevented such simulations in the past The ease with which one can invert the fermion matrix using FLIC fermions (also see [36]) leads us to attempt simulations down to light quark masses corresponding to mπ /mρ = 0.35 Previous attempts with Wilson-style fermion 216 J.M Zanotti et al Fig Average number of stabilised biconjugate gradient iterations for the Wilson, FLIC and mean-field improved clover (MFIC) actions plotted against mπ /mρ The fat links are constructed with n = (solid squares) and n = 12 (stars) smearing sweeps at α = 0.7 on a 163 × 32 lattice at β = 4.60 which corresponds to a lattice spacing of 0.122(2) fm set by the string tension actions on configurations with lattice spacing ≥0.1 fm have only succeeded in getting down to mπ /mρ = 0.47 [37] In order to search for exceptional configurations, we follow the technique used by Della Morte et al [37] and note that in the absence of exceptional configurations, the standard deviation of an observable will be independent of the number of configurations considered in the average Exceptional configurations reveal themselves by introducing a significant jump in the standard deviation as the configuration is introduced into the average In severe cases, exceptional configurations can lead to divergences in correlation functions or prevent the matrix inversion process from converging The simulations are on a 203 × 40 lattice with a lattice spacing of 0.134(2) fm set by a string tension analysis incorporating the lattice coulomb term The physical length of the lattice is ∼2.7 fm We have used an initial set of 100 configurations, using n = sweeps of APE-smearing and a five-loop improved lattice field-strength tensor Figure shows the standard deviation of the pion mass for eight quark masses on subsets of 30 (consecutive) configurations with a cyclic property enforced from configuration 100 to configuration At first glance, it is obvious that the error blows up for several quark masses at N = 12 and drops again at N = 42 As configurations 12 through 41 are included in the average at N = 12, this indicates that configuration number 41 is a candidate for an exceptional configuration An inspection of the pion mass in Fig shows that the pion mass for the third lightest quark mass decreases significantly more than the second or fourth lightest quark masses This indicates that κcr for this configuration lies somewhere between κ6 and κ7 A solution to this problem would be to use the the modified quenched approximation (MQM) from [22] and move κcr on this configuration back to the ensemble average for κcr However, since Hadron Properties with FLIC Fermions 217 Fig The standard deviation in the error of the π mass for eight quark masses (with the star symbols being the lightest quark mass) calculated on 30 configurations plotted against the starting configuration number for the FLIC-fermion action on a 203 × 40 lattice with a = 0.134(2) fm Fig The π mass calculated for eight quark masses (with the star symbols being the lightest quark mass) on 30 configurations plotted against the starting configuration number for the FLIC-fermion action on a 203 × 40 lattice with a = 0.134 fm the movement of κcr is largely a quenched artifact and would be suppressed in a full QCD simulation we prefer to simply identify and remove such configurations from the ensemble Obviously, if we find that a significant percentage of our configurations are having trouble at a particular quark mass, then it would make no sense to proceed with the simulation We would then have to conclude 218 J.M Zanotti et al that we have reached the light quark mass limit of our action and simply step back to the next lightest mass Now let us return to Fig In addition to the highly exceptional configuration number 41, we also notice a large increase in error in the lightest quark mass for configuration numbers 2, 13, 30, 34 and 53 Upon removal of these configurations, we see in Fig a near-constant behaviour of the standard deviation for the remaining configurations This means that our elimination rate for our FLIC6 action on a lattice with a spacing 0.134 fm is about 6% So for the 100 configurations used in this analysis, we are able to use 94 of them to extract hadron masses Fig The standard deviation in the error of the π mass for eight quark masses (with the star symbols being the lightest quark mass) calculated on 30 configurations plotted against the starting configuration number for the FLIC-fermion action on a 203 × 40 lattice with a = 0.134 fm Configuration numbers 2, 13, 30, 34, 41 and 53 have been omitted A similar analysis on a 163 × 32 lattice at β = 4.60 providing a finer lattice spacing of 0.122(2) fm reveals a much smaller exceptional configuration rate In a sample of 200 configurations, were identified as exceptional The increase from 2% to 6% in going from a 0.125 to 0.135 fm suggests that the coarser lattice spacing is near the limit of applicability for FLIC fermions in the light quark mass regime Octet-Decuplet Mass Splittings The results presented in this section are based on an initial sample of 94 gaugefield configurations of an anticipated 400 configurations Table reports simulation results for non-strange low-lying hadrons Figure 10 shows the N and ∆ Hadron Properties with FLIC Fermions 219 Table Values of κ and the corresponding π, ρ, N and ∆ masses on a 203 × 40 lattice for the FLIC action with sweeps of smearing at α = 0.7 A string tension analysis √ incorporating the lattice coulomb term provides a = 0.134(2) fm for σ = 440 MeV κ 0.1278 0.1283 0.12885 0.1294 0.1299 0.13025 0.1306 0.1308 mπ a mρ a mN a m∆ a 0.5400(30) 0.4998(31) 0.4521(34) 0.3990(38) 0.3434(43) 0.2978(47) 0.2419(54) 0.1972(69) 0.7304(55) 0.7053(58) 0.6774(63) 0.6491(72) 0.6228(87) 0.6040(107) 0.5845(143) 0.5812(213) 1.0971(80) 1.0522(84) 1,0006(91) 0.9465(101) 0.8944(116) 0.8562(134) 0.8172(171) 0.7950(215) 1.2238(98) 1.1899(102) 1.1528(108) 1.1162(115) 1.0841(125) 1.0630(135) 1.0443(154) 1.0380(189) masses as a function of m2π for the FLIC-fermion action on 203 ×√40 lattices with a = 0.132 fm (which corresponds to a string tension scale with σ = 450 MeV) such that the nucleon extrapolation passes through the physical value for clarity An upward curvature in the ∆ mass for decreasing quark mass is observed in the FLIC fermion results This behaviour, increasing the quenched N − ∆ mass spitting, was predicted by Young et al [38, 39] using quenched chiral perturbation theory (QχPT) formulated with a finite-range regulator A fit to the Fig 10 Nucleon and ∆ masses for the FLIC-fermion action on a 203 × 40 lattice Here √ we select a = 0.132 fm (which corresponds to the string tension with σ = 450 MeV) such that the nucleon extrapolation passes through the physical value for clarity The solid curves illustrate fits of finite-range regularised quenched chiral perturbation theory [38, 39] to the lattice QCD results The dashed curves estimate the correction that will arise in unquenching the lattice QCD simulations [38, 39] Stars at the physical pion mass denote experimentally measured values 220 J.M Zanotti et al FLIC-fermion results is illustrated by the solid curves The dashed curves estimate the correction that will arise in unquenching the lattice QCD simulations [38, 39] We note that after we have corrected for the absence of sea quark loops, our results agree simultaneously with the physical values for both the nucleon and ∆ We also calculate the light quark mass behaviour of the octet and decuplet hyperons The strange quark mass is chosen in order to reproduce the physical strange quark mass according to the phenomenological value of an s¯ s pseudoscalar meson, (41) m2ss = 2m2K − m2π Upon substitution of the physical masses for the π and K mesons, this corresponds to an s¯ s pseudoscalar meson mass of ∼ 0.470 GeV2 which occurs at our third heaviest quark mass in the 203 × 40 lattice analysis The results from this calculation are given in Table and are illustrated in Fig 11 The results show the correct ordering and in particular, we notice a mass splitting between the strangeness = −1 (I = 1) Σ and (I = 0) Λ baryons becoming evident in the light quark mass regime Table Values of κ, the octet Λ, Σ, Ξ and decuplet Σ ∗ , Ξ ∗ masses on a 203 × 40 lattice for the FLIC action with sweeps of smearing at α = 0.7 A string tension √ analysis provides a = 0.134(2) fm for σ = 440 MeV κ mΛ a mΣ a mΞ a mΣ∗ a mΞ∗ a 0.1278 0.1283 0.12885 0.1294 0.1299 0.13025 0.1306 0.1308 1.0696(84) 1.0376(86) 1.0006(91) 0.9615(97) 0.9235(106) 0.8955(117) 0.8667(137) 0.8544(154) 1.0616(83) 1.0328(86) 1.0006(91) 0.9680(97) 0.9383(106) 0.9178(116) 0.8980(132) 0.8919(152) 1.0381(87) 1.0206(88) 1,0006(91) 0.9799(94) 0.9603(98) 0.9462(102) 0.9323(109) 0.9254(114) 1.2002(101) 1.1776(104) 1.1528(108) 1.1284(113) 1.1070(118) 1.0930(124) 1.0806(132) 1.0772(142) 1.1765(104) 1.1652(106) 1.1528(108) 1.1406(110) 1.1299(113) 1.1229(115) 1.1166(118) 1.1145(120) Just as we saw the non-analytic behaviour of quenched chiral perturbation theory in the ∆-baryon mass in Fig 10 leading to an enhancement of the quenched N − ∆ mass spitting, Fig 12 shows a similar enhancement for the decuplet-octet mass splittings in Σ and Ξ baryons respectively The quark model predicts that the hyperfine splittings should approximately satisfy [40] Ξs∗ − Ξs = µs µq = Σs∗ − Σs , (42) Hadron Properties with FLIC Fermions 221 Fig 11 Octet (top) and decuplet (bottom) baryon masses for the FLIC-fermion action on a 203 × 40 lattice with a = 0.134 fm where the baryon label denotes the hyperon mass and µs (µq ) denotes the magnetic moment of the strange (light) constituent quark Figure 13 shows that even though the quenched approximation enhances the splitting between octet and decuplet baryons, the splittings for the Σ and Ξ baryons still satisfy (42) Agreement of the quenched QCD results with the quark model prediction is not surprising since both have a suppressed meson cloud Similarly, one expects further suppression of the meson cloud when two (heavy) strange quarks are present in a baryon 222 J.M Zanotti et al Fig 12 Octet and decuplet baryon masses for Σ (top) and Ξ (bottom) for the FLICfermion action on a 203 × 40 lattice with a = 0.134 fm Fig 13 Decuplet (MD ) – octet (MO ) baryon mass splittings for the FLIC-fermion action on a 203 × 40 lattice with a = 0.132 fm Hadron Properties with FLIC Fermions 223 Summary We have calculated hadron masses to test the scaling of the Fat-Link Irrelevant Clover (FLIC) fermion action, in which only the irrelevant, higher-dimension operators involve smeared links One of the main conclusions of this work is that the use of fat links in the irrelevant operators provides a new form of nonperturbative O(a) improvement This technique competes well with O(a) nonperturbative improvement on mean field-improved gluon configurations, with the advantage of a reduced exceptional configuration problem Quenched simulations at quark masses down to mπ /mρ = 0.35 have been successfully performed on a 203 × 40 lattice with a lattice spacing of 0.134(2) fm on 94 out of 100 configurations Simulations at such light quark masses reveal the non-analytic behaviour of quenched chiral perturbation theory and provide for an interesting analysis of the hyperfine splittings between octet and decuplet baryons Acknowledgements We thank Ross Young for contributing the fits of finite-range regularized quenched chiral perturbation theory to the FLIC fermion results illustrated in Fig 10 Generous grants of supercomputer time from the Australian Partnership for Advanced Computing (APAC) and the Australian National Computing Facility for Lattice Gauge Theory are gratefully acknowledged This work was supported in part by the Australian Research Council and by DOE contract DE-AC05-84ER40150 under which the Southeastern Universities Research Association (SURA) operates the Thomas Jefferson National Accelerator Facility References J M Zanotti et al [CSSM Lattice Collaboration], Phys Rev D 65, 074507 (2002) hep-lat/0110216 199 J M Zanotti et al., Nucl Phys Proc Suppl 109, 101 (2002) hep-lat/0201004 199 J M Zanotti, D B Leinweber, W Melnitchouk, A G Williams and J B Zhang, hep-lat/0210041 199 D B Leinweber et al., nucl-th/0211014 199 M Falcioni, M L Paciello, G Parisi and B Taglienti, Nucl Phys B 251, 624 (1985) 199, 206, 215 M Albanese et al [APE Collaboration], Phys Lett B 192, 163 (1987) 199, 206, 215 H Neuberger, Phys Rev D 61, 085015 (2000) hep-lat/9911004 199 K G Wilson, CLNS-321 New Phenomena In Subnuclear Physics Part A Proceedings of the First Half of the 1975 International School of Subnuclear Physics, Erice, Sicily, July 11 – August 1, 1975, ed A Zichichi, Plenum Press, New York, 1977, p 69, CLNS-321 199, 200, 201, 202 B Sheikholeslami and R Wohlert, Nucl Phys B 259, 572 (1985) 199, 203, 204 224 J.M Zanotti et al 10 J J Sakurai, “Advanced Quantum Mechanics”, Addison-Wesley, Redwood City, CA, 1982 200 11 K Symanzik, Nucl Phys B 226, 187 (1983) 201, 202, 203 12 H J Rothe, World Sci Lect Notes Phys 59, (1997) 201, 205 13 R Gupta, hep-lat/9807028 201, 205 14 M G Alford, T R Klassen, and G P Lepage, Nucl Phys B 496, 377 (1997) [arXiv:hep-lat/9611010] 202 15 H W Hamber and C M Wu, Phys Lett B 133, 351 (1983) 203 16 F X Lee and D B Leinweber, Phys Rev D 59, 074504 (1999) [hep-lat/9711044] 203 17 C Dawson, G Martinelli, G C Rossi, C T Sachrajda, S R Sharpe, M Talevi and M Testa, Nucl Phys Proc Suppl 63 (1998) 877 [hep-lat/9710027] 204 18 G Heatlie, G Martinelli, C Pittori, G C Rossi, and C T Sachrajda, Nucl Phys B 352 (1991) 266 204 19 M Luscher, S Sint, R Sommer and P Weisz, Nucl Phys B 478, 365 (1996), hep-lat/9605038 204, 205 20 S O Bilson-Thompson, D B Leinweber, and A G Williams, Annals Phys 304, (2003) [hep-lat/0203008] 205, 207, 208 21 T DeGrand [MILC collaboration], Phys Rev D 60, 094501 (1999) heplat/9903006 206, 208 22 W Bardeen, A Duncan, E Eichten, G Hockney, and H Thacker, Phys Rev D 57, 1633 (1998) hep-lat/9705008 206, 216 23 F D Bonnet, P Fitzhenry, D B Leinweber, M R Stanford and A G Williams, Phys Rev D 62, 094509 (2000) hep-lat/0001018 206, 208 24 M C Chu, J M Grandy, S Huang, and J W Negele, Phys Rev D 49, 6039 (1994) hep-lat/9312071 206 25 T DeGrand, A Hasenfratz, and T G Kovacs [MILC Collaboration], heplat/9807002 206, 208 26 M Stephenson, C DeTar, T DeGrand, and A Hasenfratz, Phys Rev D 63, 034501 (2001) hep-lat/9910023 206 27 C W Bernard and T DeGrand, Nucl Phys Proc Suppl 83, 845 (2000) heplat/9909083 206 28 C Bernard et al [MILC Collaboration], Phys Rev D 66, 094501 (2002) heplat/0206016 206 29 P de Forcrand, M Garcia Perez, and I O Stamatescu, Nucl Phys B 499, 409 (1997) hep-lat/9701012 208 30 F D Bonnet, D B Leinweber, A G Williams, and J M Zanotti, Phys Rev D 65, 114510 (2002) hep-lat/0106023 208 31 M Luscher and P Weisz, Commun Math Phys 97, 59 (1985) [Erratum-ibid 98, 433 (1985)] 208 32 F D Bonnet, D B Leinweber, and A G Williams, J Comput Phys 170, (2001) hep-lat/0001017 209 33 S Gusken, Nucl Phys Proc Suppl 17, 361 (1990) 209 34 A Frommer, V Hannemann, B Nockel, T Lippert and K Schilling, Int J Mod Phys C 5, 1073 (1994) hep-lat/9404013 210, 215 35 R G Edwards, U M Heller, and T R Klassen, Phys Rev Lett 80, 3448 (1998) hep-lat/9711052 212 36 W Kamleh, D H Adams, D B Leinweber, and A G Williams, Phys Rev D 66, 014501 (2002) hep-lat/0112041 215 37 M Della Morte, R Frezzotti, and J Heitger [ALPHA collaboration], heplat/0111048 216 Hadron Properties with FLIC Fermions 225 38 R D Young, D B Leinweber, A W Thomas and S V Wright, Phys Rev D 66, 094507 (2002) hep-lat/0205017 219, 220 39 R D Young, D B Leinweber, and A W Thomas, arXiv:hep-lat/0311038 219, 220 40 F E Close, “An Introduction To Quarks And Partons”, Academic Press, London, 1979, 481p 220 Subject Index algorithm 30, 49, 81, 157, 209, 210 angular momentum 72, 80, 135, 136, 183, 184, 186 anisotropic 74, 94, 95 anomaly 147, 171 APE-smearing 67, 68, 214, 216 Asqtad 49 Asqtad action 29, 30, 32–35, 37, 43, 44, 49, 50, 53, 56 asymptotic behaviour 18, 32, 34, 55, 57 axial vector 147, 149 bag 141, 142 baryons 10–12, 15, 71–75, 82, 84, 88, 89, 96, 99, 100, 109, 113, 114, 117, 125, 199, 210, 221, 223 Bayesian prior 75 Bayesian techniques 75 Bethe-Salpeter (BS) 187 BGR collaboration 74, 97 boundary condition 80–82, 91, 94, 141–143, 184–186, 209 branch cut 115 Callan-Harvey 134, 139, 140 CEBAF 71 chiral condensate 18, 53 chiral expansion 105, 114, 115, 118, 121, 123 chiral extrapolation 10–12, 16, 45, 59, 95, 101, 113, 114, 117, 123, 124, 126, 166 chiral Lagrangian 171 chiral limit 5, 18, 45, 47–49, 52–54, 56–61, 103, 114, 115, 119, 126, 200 chiral perturbation theory 5, 55, 114, 117, 127, 219, 223 chiral symmetry breaking 17, 27, 47, 55, 60, 114, 215 chirally improved 74, 94, 95, 97 CLEO 71 clover action 3, 5, 60, 95, 199, 204–206, 212 coarse lattice 203 condensate 17, 18, 52–55 confinement 47, 60, 104 connected diagrams 172 constituent quark 57, 72, 99, 221 continuum extrapolation 167 continuum limit 27, 40, 51, 80, 177, 201–204, 207, 213–215 convergence 2, 33, 114, 116, 118, 119, 121, 123, 163, 179, 189, 215 cooling 208 correlation function 15, 76, 82, 83, 85–89, 91, 97, 105, 107, 109, 110 correlation matrix 73, 75, 85, 95, 97–101, 105, 110 coupling 2–4, 14, 18, 20, 21, 29, 30, 42, 72, 73, 82, 89, 99, 102, 105, 108, 114, 126, 127, 149, 153, 154, 166, 167, 200, 203, 204, 210 covariance matrix 94, 209 CP-PACS collaboration 5, 6, 8, 10, 12, 118, 128 CSSM Lattice Collaboration 112 cut-off 14, 116, 117, 119, 120, 183, 184 decay constants 15, 154, 155, 204, 206 decuplet 6, 10, 74, 75, 88, 220, 221, 223 DeGrand-Rossi representation 92 determinant 1, 14, 22, 25, 133, 143, 168, 215 dimensional regularization 117 diquark 72, 84 Dirac operator 21, 39, 66, 141, 150, 151, 157–160, 206, 215 disconnected diagrams 148, 152 228 Subject Index domain wall fermion 74 dynamical fermions 11, 63, 169 Dyson–Schwinger equation 18, 33, 49 Edinburgh plot 11 Effective Field Theory 114, 116 effective field theory 4, 73, 114, 116–119, 123, 139 elastic states 179, 190, 192 Elitzur’s theorem 159 η mesons η mesons 5, 147 exceptional configurations 200, 215, 216 excited baryon 71, 73, 74, 92, 104, 125, 126 excited nucleon 73, 84, 92, 93, 97, 105 exotic 72, 75, 97, 102, 126 expectation value 1, 22, 138, 149, 150, 159 fat links 68, 199, 206–208, 210, 211, 213, 214, 216, 223 fermion doubling fifth dimension 74, 139 finite range regularization (FRR) 117, 127 finite volume 11, 15, 33, 36, 47, 60, 74, 97, 124, 177–179, 181, 183, 185, 186, 188, 192, 213, 214 Fixed Point 95 fixed point 74, 94 flavour 2, 7, 29, 30, 78, 79, 86, 91, 101, 147–150, 152–154, 157, 158, 173 flavour structure 79 flavour symmetry breaking 30, 86 FLIC 65–69, 74, 75, 93–96, 98, 99, 101, 104, 105, 199, 206, 208–216, 218, 219, 223 Fourier transform 28, 39, 169, 179–181, 183, 186, 189, 201 gap 132, 138, 141, 147, 153, 154, 164–166, 170–173 Gauge Dependence 50 gauge fixing 18 Gell-Mann-Oakes-Renner (GOR) relation 114 generating functional 19, 21, 22 Ginsparg-Wilson relation 132, 144 gluon propagator 18, 32, 50 Goldstone boson 28, 72, 102, 147, 199 Gribov copies 17, 24, 25 Gribov copy 25 GSI 71 Haar measure 21 Hadron Spectrum 1, 12 hadron spectrum 4, 6, 7, 15, 17, 80, 147 heavy-hadron heavy-mesons 5, 15 Higgs field 139 hybrid 150, 157, 160 hyperfine 5, 6, 72, 220, 223 hyperon 72, 85, 221 inelastic threshold 179, 187–190, 192 instanton 58–60 interpolating fields 71, 73, 75, 78, 82–86, 88, 91, 97–99, 101, 102, 105, 107, 108, 110, 126, 210 irreducible representations 80, 91 irrelevant operators 67, 68, 199, 203, 206, 208, 212, 223 J-parameter 9, 12 jackknife 55, 94, 209 Jacobi smearing 95 Jefferson Lab 71, 74 JLQCD Collaboration 118 K-mesons 3, 12, 220 kaon-decay 177 kappa 202 kernel 39, 42 Kogut–Susskind 17, 27, 30, 32 Kogut–Susskind action 32 Landau gauge 18, 23, 24, 33, 34, 47 Laplacian gauge 18, 24, 25, 49, 51 lattice 1–3, 5–15, 17–24, 26–28, 30–36, 38–40, 42–47, 49, 53–56, 58–61, 65, 71–76, 78–82, 84, 87, 91–95, 97, 98, 104, 105, 107, 113–119, 123–127, 131, 132, 140, 142–144, 147, 149–151, 155–167, 169, 172, 174, 177, 199–201, 203–220, 222, 223 lattice artefacts 18, 33 Lellouch-Lă uescher (LL) 177, 195 Lepage term 30 light-baryons 10 Subject Index link 2, 20, 21, 23, 65–68, 74, 83, 108, 109, 144, 200, 202, 203, 205, 206, 209, 215 LNA 125 logarithms 5, 109, 115 low energy 139 magnetic moment 114, 221 mass function 18, 33–37, 43, 45, 47–49, 51–53, 55, 56, 58–60 mass generation 47 mass splittings 5, 6, 11, 72, 99, 200, 206, 220, 222 matrix elements 15, 154, 155, 157, 177, 179, 190, 191, 193, 194, 204 maximum entropy method 74, 75, 97 mean-field improvement 40, 68, 207 MILC 93, 123 mixing 8, 72, 84, 86, 147, 154–157 molecule 72 MOM 53 Monte Carlo 2, 21, 22, 150, 157, 160, 206 Naik term 29 naive lattice action NLNA 115 noisy sources 159 nonanalytic behaviour 73, 199 nonperturbatively (NP) improved 95 nonrelativistic limit 84 nucleon 10, 71, 73–76, 84, 87, 91, 93–95, 97, 99, 104, 105, 114, 115, 117–121, 123–126, 210–212, 215, 219, 220 octahedral group 79, 80 octet 10, 74, 75, 85, 86, 101, 125, 149, 153, 154, 172, 220, 221, 223 Overlap action 44, 46, 48 overlap actions 17, 61 overlap fermions 75, 97 OZI 162, 168 parallel transport 20 parity 71–75, 78–84, 87–89, 91, 92, 95, 98–101, 103, 109, 110, 125, 126, 149 partially quenched 157, 167–171, 173 path integral 1, 18 path ordering 20 PCAC relation 155 pentaquark 73, 75, 92, 104 π-mesons 3, 12, 147, 149–151, 220 229 pion decay constant 5, 149 plaquette 2, 20, 68, 93, 118, 206, 208, 209, 211 point group 80 precision 50, 71, 147, 166, 180, 181, 190, 192, 193 projection 25, 50, 65, 67, 68, 74, 79, 83, 87–89, 92, 98, 103, 107, 125, 158, 163, 182, 184, 188, 191, 206 pseudoscalar meson 3, 8, 10, 94, 147, 150, 152, 166, 169, 220 quantization 177–179, 183, 188, 190, 194 quantum field theory 1, 2, 19, 121, 179, 194 quark model 14, 72, 79, 97, 104, 124, 220, 221 quark propagator 17, 18, 20, 22, 23, 30–32, 35, 36, 41–45, 47, 49, 51, 56, 57, 59, 60, 215 quenched 3–8, 10, 12–17, 22, 30, 55, 59–61, 71, 73, 75, 92, 95, 102–105, 125, 127, 147, 149, 153, 167, 169, 200, 204, 215–217, 219–221, 223 quenched approximation 22, 30, 59 Rarita-Schwinger 87, 89 renormalization 117, 143, 147, 148 resonances 71, 72, 93, 103, 104, 110, 126, 127 ρ-mesons 124, 166, 171, 212, 213, 215 RIKEN-BNL group 74 Roper 71, 75, 93, 95–97, 100 rotational symmetry 29, 33, 35, 43–45, 49, 59, 79 running coupling constant 63 running mass 18, 32, 34, 42, 48, 53, 55 running quark mass 17, 53, 55, 60 sea quark 7–10, 13, 151, 153, 157, 158, 160, 161, 165–170, 172, 173, 220 SESAM 160–162, 164–170 Sheikholeslami-Wohlert (SW) action 74, 204 short-distance physics 68 Σ baryons 99, 220, 221 sign function 40, 42, 65 singlet 85, 86, 101, 147–149, 152–155, 158, 164–169, 172–174 smoothing 208, 215 230 Subject Index source-smearing 81, 209 spectroscopy 71–73, 75, 78, 104, 105, 126, 157 spin-projection 65, 68 split-link 65, 67, 68 spontaneous symmetry breaking 113 spurious states 184 Staggered action 27–29 staggered actions 17 staggered fermions 113, 201 staples 30, 68, 206 static quark potential 13, 14, 32 stochastic estimate 158 string model 13, 14 string tension 93, 207, 208, 210–212, 216, 219, 220 sum-rule 72, 91 summation 154, 158, 160, 178, 179, 181, 186, 192, 195 Symanzik improved action 35, 202 tadpole-improvement 30, 31, 68, 74, 204, 209 taste 28 topological charge 39, 147, 149, 206–208 topological susceptibility 147, 149 transfer matrix 77, 131, 143 tree-level correction 32, 42, 45 truncated eigenmode approximation (TEA) 161 UKQCD collaboration 8, 13, 74, 129 vacuum 3, 15, 108, 113, 147, 149–151, 153–159, 163, 166, 179, 191, 193, 204, 210 valence quark 5, 8, 10, 71–73, 79, 150, 158, 169, 170, 172, 173 vector-meson 63, 212–214 Ward identities 133 Ward-Takahashi identity 155 Weyl fermion 132, 140 Wilson action 5, 7, 65–67, 69, 94, 95, 202, 203, 207, 211, 212, 215 Wilson doublers 39 Wilson loop 20 Wilson mass parameter 40 Wilson-Dirac operator 39, 40, 42 Witten-Veneziano relation 147 Z function 46 zero mode 132, 135, 136, 138–140 zero momentum 108, 151, 178 Zolotarev 42 ... Leinweber A.G Williams (Eds.) Lattice Hadron Physics 123 Editors Alex C Kalloniatis Derek B Leinweber Anthony G Williams University of Adelaide School of Chemistry & Physics Adelaide SA 5005 Australia... 5005 Australia A Kalloniatis D Leinweber A Williams (Eds.), Lattice Hadron Physics, Lect Notes Phys 663 (Springer, Berlin Heidelberg 2005) , DOI 10.1007/b103529 Library of Congress Control Number:... broad spectrum of workers in hadronic physics, from graduate students to senior researchers of many years of experience and a solid body of significant work in hadronic physics The hope is that precisely