Asymptotic expansion of lattice loop integrals around the continuum limit

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 66, Issue 7, 2002, Pages

  Becher, Thomas ^a   Melnikov, Kirill ^a  

^a SLAC NATIONAL ACCELERATOR LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTIC METHOD; ARTICLE; CALCULATION; MATHEMATICAL ANALYSIS; MOLECULAR INTERACTION; REACTION ANALYSIS; STRUCTURE ANALYSIS;

EID: 0036816495     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.66.074508     Document Type: Article

References (25)

1. For an introduction, see H. J. Rothe, Lattice Gauge Theories: An Introduction, Lecture Notes in Phys. Vol. 59 (World Scientific, Singapore, 1997), p. 1.
2. K. Symanzik, Nucl. Phys. B226, 187 (1983);
3. Nucl. Phys.K. SymanzikB226, 205 (1983).
4. ALPHA Collaboration, S. Sint and P. Weisz, Nucl. Phys. B545, 529 (1999).
5. M. Lüscher and P. Weisz, Phys. Lett. B 349, 165 (1995).
6. M. Lüscher and P. Weisz, Nucl. Phys. B452, 234 (1995).
7. B. Alles, A. Feo, and H. Panagopoulos, Nucl. Phys. B491, 498 (1997).
8. T. Reisz, Commun. Math. Phys. 116, 81 (1988);
9. Commun. Math. Phys.T. Reisz116, 573 (1988).
10. S. Caracciolo, P. Menotti, and A. Pelissetto, Nucl. Phys. B375, 195 (1992).
11. G. Burgio, S. Caracciolo, and A. Pelissetto, Nucl. Phys. B478, 687 (1996).
12. K.G. Wilson, in Quarks: From Paradox To Myth, Erice 1975, Proceedings, New Phenomena In Subnuclear Physics, Part A (Plenum, New York, 1977), pp. 13–32.
13. M. Lüscher and P. Weisz, Nucl. Phys. B445, 429 (1995).
14. For a review, see V. A. Smirnov, Applied Asymptotic Expansions In Momenta And Masses (Springer, Berlin, 2002) p. 262.
15. F.V. Tkachov, Phys. Lett. 100B, 65 (1981);
16. K.G. Chetyrkin and F.V. Tkachov, Nucl. Phys. B192, 159 (1981).
17. The numerators occurring in the evaluation of Feynman diagrams involve powers of (Formula presented) and (Formula presented)
18. S. Laporta, Int. J. Mod. Phys. A 15, 5087 (2000).
19. C. Anastasiou, E.W. Glover, and M.E. Tejeda-Yeomans, Nucl. Phys. B629, 255 (2002).
20. E. Eichten and B. Hill, Phys. Lett. B 234, 511 (1990).
21. E. Eichten and B. Hill, Phys. Lett. B 240, 193 (1990).
22. We note that the hard master integrals in two dimensions can be evaluated analytically: (Formula presented) and (Formula presented)
23. An analytic expression for (Formula presented) can be found in Appendix A of K. Farakos, K. Kajantie, K. Rummukainen, and M.E. Shaposhnikov, Nucl. Phys. B442, 317 (1995). Their Eq. (A.5) contains a typographical error: K has to be replaced by (Formula presented).
24. A. Hasenfratz and P. Hasenfratz, Phys. Lett. 93B, 165 (1980).
25. H. Kawai, R. Nakayama, and K. Seo, Nucl. Phys. B189, 40 (1981).