Abstract
I review the current status of several lattice QCD results. I concentrate on new analytical developments and on numerical results relevant to phenomenology.
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References
K. Wilson, Phys. Rev.D10 (1974) 2445; K. Wilson, inNew phenomena in subnuclear physics, Erice lectures 1975, ed. A. Zichichi, (Plenum, New York, 1977).
Proceedings of the International Symposium on Lattice Field Theory “LATTICE 90”, Tallahassee, Florida, USA, Nucl. Phys.B (Proc. Suppl.)20 (1991).
Proceedings of the International Symposium on Lattice Field Theory “LATTICE 91”, Tsukuba, Japan,Nucl. Phys. B (Proc. Suppl.)26 (1992).
Proceedings of the International Symposium on Lattice Field Theory “LATTICE 92”, Amsterdam, The Netherlands, to appear in Nucl. Phys.B (Proc. Suppl.) (1993).
G. ’t Hooft, Nucl. Phys.B72 (1974) 461.
See for instance: T. Barczyk, R. Haymaker, V. Singh, E. Laermann and J. Wosiek, in Ref. [3], Proceedings of the International Symposium on Lattice Field Theory “LATTICE 90”, Tsukuba, Japan,Nucl. Phys. B (Proc. Suppl.)26 (1992), p. 462.
J. Polchinski, talk at the Symposium on Black Holes, Wormholes, Membranes and Superstrings, H.A.R.C., Houston, hep-th 9210045 (1992).
F. Gliozzi, Lectures at the XXXII Cracow School of Theoretical Physics, Zakopane, Poland, hep-lat 9210007 (1992).
J. Polchinski and A. Stronminger, Phys. Rev. Lett.67 (1991) 1681.
D. Weingarten, Phys. Lett.B90 (1980) 285.
F. David, Europhys. Lett.9 (1989) 575; F. David and H. Neuberger, Phys. Lett.B269 (1991) 134.
J. Polchinski, Phys. Rev. Lett.68 (1992) 1267.
A. Polyakov, Nucl. Phys.B268 (1986) 406; H. Kleinert, Phys. Lett.B174 (1986) 335.
M. Green, Phys. Lett.B282 (1992) 380.
M. Caselle, F. Gliozzi and S. Vinti, in Ref. [4] Proceedings of the International Symposium on Lattice Field Theory “LATTICE 92”, Amsterdam, The Netherlands, to appear in Nucl. Phys.B (Proc. Suppl.) (1993).
M. Mathur and H. Sharatchandra, “Unified Approach to Duality Transformations: Abelian Symmetries”, IMSc preprint (1992).
R. Anishetty and H. Sharatchandra, Phys. Rev. Lett.65 (1990) 813.
B. Gnanapragasam and H. Sharatchandra, Phys. Rev.D45 (1992) 1010.
G. ’t Hooft, Nucl. Phys.B190 [FS3] (1981) 455.
R. Anishetty, G. Gadiyar, M. Mathur and H. Sharatchandra, Phys. Lett.B271 (1991) 391.
R. Anishetty, S. Cheluvaraja, H. Sharatchandra and M. Mathur, Matscience preprint IMSc-92/41, hep-lat 9211024 (1992).
D. Weingarten, Phys. Rev. Lett.51 (1983) 1830.
C. Vafa and E. Witten, Nucl. Phys.B234 (1984) 173; E. Witten, Phys. Rev. Lett.51 (1983) 2351.
A. Patel, unpublished.
See for instance: R. Gupta, D. Daniel, G. Kilcup, A. Patel and S. Sharpe, Los Alamos preprint LA-UR-91-3522, hep-lat 9210018 (1992).
J. Bijnens and M. Wise, Phys. Lett.B137 (1984) 245.
M. Lüscher, Comm. Math. Phys.104 (1986) 177; Comm. Math. Phys.105 (1986) 153.
Z. Guralnik and A. Manohar, CERN preprint CERN-TH.6766/92, hep-ph 9212289 (1992).
S. Sharpe, Phys. Rev.D46 (1992) 3146; in [4]. Proceedings of the International Symposium on Lattice Field Theory “LATTICE 92”, Amsterdam, The Netherlands, to appear in Nucl. Phys.B (Proc. Suppl.) (1993).
C. Bernard and M. Golterman, Phys. Rev.D46 (1992) 853; in [4]. Proceedings of the International Symposium on Lattice Field Theory “LATTICE 92”, Amsterdam, The Netherlands, to appear in Nucl. Phys.B (Proc. Suppl.) (1993).
R. Gupta, G. Kilcup, A. Patel and S. Sharpe, Phys. Lett.B211 (1988) 132.
S. Sharpe, R. Gupta and G. Kilcup, in Ref. [3], Proceedings of the International Symposium on Lattice Field Theory “LATTICE 91”, Tsukuba, Japan,Nucl. Phys. B (Proc. Suppl.)26 (1992), p. 197.
K. Symanzik, in Proceedings ofTrieste Workshop on Non-perturbative Field Theory and QCD, Dec. 1982, (World Scientific, Singapore), p. 61.
M. Lüscher and P. Weisz, Comm. Math. Phys.97 (1985) 59.
A. Patel and R. Gupta, Phys. Lett.B183 (1986) 193.
M. Bochicchio, L. Maiani, G. Martinelli, G. Rossi and M. Testa, Nucl. Phys.B262 (1985) 331.
See L. Maiani, G. Martinelli, M. Paciello and B. Taglienti, Nucl. Phys.B293 (1987) 420, and references therein.
B. Sheikholeslami and R. Wohlert, Nucl. Phys.B259 (1985) 572.
G. Heatlie, G. Martinelli, C. Pittori, G. Rossi and C. Sachrajda, Nucl. Phys.B352 (1991) 266.
G. Lepage and P. Mackenzie, in [2], Proceedings of the International Symposium on Lattice Field Theory “LATTICE 90”, Tallahassee, Florida, USA, Nucl. Phys.B (Proc. Suppl.)20 (1991), p. 173; Fermilab preprint FERMILAB-PUB-19/355-T, hep-lat 9209022 (1992).
N. Isgur and M. Wise, Phys. Lett.B232 (1989) 113; Phys. Lett.B237 (1990) 527.
An overview of the entire subject can be found in:Heavy Flavours, ed. A. Buras and M. Lindner, Advanced Series on Directions in High Energy Physics, (World Scientific, Singapore, 1992).
See for instance: E. Eichten, in [2], Proceedings of the International Symposium on Lattice Field Theory “LATTICE 90”, Tallahassee, Florida, USA, Nucl. Phys.B (Proc. Suppl.)20 (1991), p. 475.
M. Lüscher, Comm. Math. Phys.54 (1977) 283; G. Lepage, in [3], Proceedings of the International Symposium on Lattice Field Theory “LATTICE 91”, Stukuba, Japan,Nucl. Phys. B (Proc. Suppl.)26 (1992). p. 45; A. Kronfeld, in [4]. Proceedings of the International Symposium on Lattice Field Theory “LATTICE 92”, Amsterdam, The Netherlands, to appear in Nucl. Phys.B (Proc. Suppl.) (1993).
S. Güsken, K. Schilling, R. Sommer, K.-H. Mütter and A. Patel, Phys. Lett.B212 (1988) 216.
G. Lepage and B. Thacker, in Proceedings of the International Symposium on Lattice Field Theory “Field Theory on the Lattice”, Seillac, France, Nucl. Phys.B (Proc. Suppl.)4 (1988), p. 199.; B. Thacker and G. Lepage, Phys. Rev.D43 (1991) 196.
L. Maiani, G. Martinelli and C. Sachrajda, Nucl. Phys.B368 (1992) 281.
G. Lepage, in Ref. [3], p. 45. Proceedings of the International Symposium on Lattice Field Theory “LATTICE 90”, Tsukuba, Japan,Nucl. Phys. B (Proc. Suppl.)26 (1992).
A. Kronfeld, in Ref. [4]; Proceedings of the International Symposium on Lattice Field Theory “LATTICE 92”, Amsterdam, The Netherlands, to appear in Nucl. Phys.B (Proc. Suppl.) (1993). A. Kronfeld and P. Mackenzie, in preparation.
M. Lüscher, Nucl. Phys.B364 (1991) 237.
A. Duncan, E. Eichten and H. Thacker, in Ref. [4]. Proceedings of the International Symposium on Lattice Field Theory “LATTICE 92”, Amsterdam, The Netherlands, to appear in Nucl. Phys.B (Proc. Suppl.) (1993).
M. Hecht and T. DeGrand, Phys. Rev.D46 (1992) 2155, and references therein.
F. Butler, H. Chen, A. Vaccarino, J. Sexton and D. Weingarten, in Ref. [4]. Proceedings of the International Symposium on Lattice Field Theory “LATTICE 92”, Amsterdam, The Netherlands, to appear in Nucl. Phys.B (Proc. Suppl.) (1993).
S. Cabasinoet al. (APE collaboration), Phys. Lett.B258 (1991) 195.
M. Guagnelliet al. (APE collaboration), Nucl. Phys.B378 (1992) 616.
P. Geiger and N. Isgur, Phys. Rev.D41 (1990) 1595.
Y. Iwasaki, K. Kanaya, S. Sakai, T. Yoshié, T. Hoshino, T. Shirakawa and Y. Oyanagi, in Ref. [4]. Proceedings of the International Symposium on Lattice Field Theory “LATTICE 92”, Amsterdam, The Netherlands, to appear in Nucl. Phys.B (Proc. Suppl.) (1993).
D. Daniel, R. Gupta, G. Kilcup, A. Patel and S. Sharpe, Phys. Rev.D 46 (1992) 3130.
S. Cabasinoet al. (APE collaboration), Phys. Lett.B258 (1991) 202.
R. Gupta, G. Guralnik, G. Kilcup and S. Sharpe, Phys. Rev.D43 (1991) 2003.
M.-P. Lombardo, G. Parisi and A. Vladikas, Rome preprint ROM2F-92-46, hep-lat 9206023 (1992).
C. Alltonet al., Phys. Lett.B284 (1992) 377.
M. Fukugita, H. Mino, M. Okawa and A. Ukawa, Phys. Rev. Lett.68 (1992) 761; M. Fukugita, H. Mino, M. Okawa, G. Parisi and A. Ukawa, Phys. Lett.B294 (1992) 380.
M. Lüscher, Comm. Math. Phys.104 (1986) 177; J. Gasser and H. Leutwyler, Phys. Lett.B184 (1987) 83; Phys. Lett.B188 (1987) 477.
C. Bernard, T. DeGrand, C. DeTar, S. Gottlieb, A. Krasnitz, R. Sugar and D. Toussaint, in Ref. [4]. Proceedings of the International Symposium on Lattice Field Theory “LATTICE 92”, Amsterdam, The Netherlands, to appear in Nucl. Phys.B (Proc. Suppl.) (1993).
A. Hasenfratz and P. Hasenfratz, Phys. Lett.B93 (1980) 165; R. Dashen and D. Gross, Phys. Rev.D23 (1981) 2340.
G. Bali and K. Schilling, in Ref. [4]. Proceedings of the Internationational Symposium on Lattice Field Theory “LATTICE 92”, Amsterdam, The Netherlands, to appear in Nucl. Phys.B (Proc. Suppl.) (1993).
S. Boothet al. (UKQCD collaboration), Phys. Lett.B294 (1992) 385.
A. El-Khadra, G. Hockney, A. Kronfeld and P. Mackenzie, Phys. Rev. Lett.69 (1992) 729.
K. Hikasaet al. (Particle Data Group), Phys. Rev.D45 (1992) S1.
S. Banerjee, these proceedings.
M. Lüscher, R. Narayanan, P. Weisz and U. Wolff, Nucl. Phys.B384 (1992) 168; M. Lüscher, R. Sommer, U. Wolff and P. Weisz, DESY preprint DESY 92-096, hep-lat 9207010 (1992).
M. Lüscher, Comm. Math. Phys.105 (1986) 153; Nucl. Phys.B354 (1991) 531.
S. Sharpe, R. Gupta and G. Kilcup, Nucl. Phys.B383 (1992) 309.
R. Gupta, D. Daniel, G. Kilcup, A. Patel and S. Sharpe, Los Alamos preprint LA-UR-92-3641, hep-lat 9301016 (1993).
S. Weinberg, Phys. Rev. Lett.17 (1966) 616.
M. Voloshin and M. Shifman, Sov. J. Nucl. Phys.45 (1987) 292.
C. Bernard, J. Labrenz and A. Soni, in Ref. [4]. Proceedings of the International Symposium on Lattice Field Theory “LATTICE 92”, Amsterdam, The Netherlands, to appear in Nucl. Phys.B (Proc. Suppl.) (1993).
T. Aliev and V. Eletskiî, Sov. J. Nucl. Phys.38 (1983) 936.
C. Alltonet al., Nucl. Phys.B349 (1991) 598; S. Abadaet al., Nucl. Phys.B376 (1992) 172.
D. Richardset al., (UKQCD collaboration), in Ref. [4]. Proceedings of the International Symposium on Lattice Field Theory “LATTICE 92”, Amsterdam, The Netherlands, to appear in Nucl. Phys.B (Proc. Suppl.) (1993).
See for instance: M. Lusignoli, L. Maiani, G. Martinelli and L. Reina, Nucl. Phys.B369 (1992) 139.
G. Kilcup, S. Sharpe, R. Gupta and A. Patel, Phys. Rev. Lett.64 (1990) 25.
S. Sharpe, R. Gupta and G. Kilcup, in Ref. [3]. Proceedings of the International Symposium on Lattice Field Theory “LATTICE 91”, Tsukuba, Japan,Nucl. Phys. B (Proc. Suppl.)26 (1992). p. 197.
G. Martinelli, C. Sachrajda, G. Salina and A. Vladikas, Nucl. Phys.B378 (1992) 591.
G. Buchalla, A. Buras and M. Harlander, Nucl. Phys.B337 (1990) 313.
S. Sharpe, in Ref. [2], Proceedings of the International Symposium on Lattice Field Theory “LATTICE 90”, Tallahassee, Florida, USA, Nucl. Phys.B (Proc. Suppl.)20 (1991). p. 429.
J. Gasser, H. Leutwyler and M. Sainio, Phys. Lett.B253 (1991) 252.
R. Gupta, C. Baillie, R. Brickner, G. Kilcup, A. Patel and S. Sharpe, Phys. Rev.D44 (1991) 3272.
F. Brownet al., Phys. Rev. Lett.67 (1991) 1062.
A. Patel, in Ref. [3], Proceedings of the International Symposium on Lattice Field Theory “LATTICE 91”, Tsukuba, Japan,Nucl. Phys. B (Proc. Suppl.)26 (1992). p. 350.
A. Patel, Phys. Lett.B236 (1990) 102.
J. Mandula, in Ref. [3], Proceedings of the International Symposium on Lattice Field Theory “LATTICE 91”, Tsukuba, Japan,Nucl. Phys. B (Proc. Suppl.)26 (1992). p. 356.
R. Altmeyer, M. Göckeler, R. Horsley, E. Laermann and G. Schierholz, in Ref. [4]. Proceedings of the International Symposium on Lattice Field Theory “LATTICE 92”, Amsterdam, The Netherlands, to appear in Nucl. Phys.B (Proc. Suppl.) (1993).
Contrary to their claims, both Refs. [93,94] extract only the sea quark contribution to the singlet axial current matrix element and not the full singlet axial current matrix element.
J. Mandula and M. Ogilvie, PRINT-92-0341 (DOE), hep-lat 920809 (1992).
R. Gupta, A. Patel and S. Sharpe, in progress.
See for instance: Ref. [89] and references therein R. Gupta, C. Baillie, R. Brickner, G. Kilcup, A. Patel and S. Sharpe, Phys. Rev.D44 (1991) 3272.
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Patel, A. Recent developments in lattice QCD. Pramana - J. Phys. 41 (Suppl 1), 139–165 (1993). https://doi.org/10.1007/BF02908081
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DOI: https://doi.org/10.1007/BF02908081