Higher covariant derivative Pauli-Villars regularization does not lead to A consistent QCD

Thumbnail Image
Full text at PDC
Publication Date
Advisors (or tutors)
Journal Title
Journal ISSN
Volume Title
Elsevier Science Bv
Google Scholar
Research Projects
Organizational Units
Journal Issue
We compute the beta function at one loop for Yang-Mills theory using as regulator the combination of higher covariant derivatives and Pauli-Villars determinants proposed by Faddeev and Slavnov. This regularization prescription has the appealing feature that it is manifestly gauge invariant and essentially four dimensional. It happens however that the one-loop coefficient in the beta function that it yields is not 11/3, as it should be, but -23/6. The difference is due to unphysical logarithmic radiative corrections generated by the Pauli-Villars determinants on which the regularization method is based. This no-go result discards the prescription as a viable gauge invariant regularization, thus solving a long-standing open question in the literature. We also observe that the prescription can be modified so as to not generate unphysical logarithmic corrections, but at the expense of losing manifest gauge invariance,
© 1995 Elsevier Science B.V. All fights reserved. The authors are grateful to G. 't Hooft, J.C. Taylor and M. Veltman for discussions. FRR was supported by FOM, The Netherlands. Partial support from CICyT, Spain is also acknowledged.
Unesco subjects
[1] G. 't Hooft and M. Veltman, Nucl Phys. B 44 (1972) 189. [2l A.A. Slavnov, Theor. Math. Phys. 33 (1977) 977. [3] L.D. Faddeev and A.A. Slavnov, Gauge fields, introduction to quantum theory, second edition (Benjamin, Reading, 1990). C.P. Martin, E Ruiz Ruiz/Nuclear Physics B 436 (1995) 545-581 581 [4] Z. Bern, M.B. Halpern, L. Sadun and C. Taubes, Nucl. Phys. B 284 (1987) 35. [5] M. Asorey and E Falceto, Nucl. Phys. B 327 (1989) 427. [6] A.A. Slavnov, Symmetry preserving mguladzation for gauge and supergauge theories, in Superspace and supergravity, ed. S.W. Hawking and M. Rocek (Cambridge Univ. Press, Cambridge, 1981 ) p. 177. [7] B.J. Wart, Ann. Phys. 183 (1988) 1. [8] R. Srnror, Some remarks for the construction of Yang MUis theories, in Renormalization of quantum field theories with non-linear field transformations, ed. P. Breitenlohner, D. Maison and K. Sibold (Springer-Verlag, Berlin, 1988). [9] M. Day, Nncl. Phys. B 213 (1983) 591. [10] REDUCE 3.4.1 and 3.5 (The Brand Corporation, Santa Moniea, 1991 and 1993). [11] O. Piguet and A. Ronet, Phys. Rep. 76 (1981) 1. [12] C.P. Martin and E Ruiz Ruiz, Higher covariant derivative regulators and non-multiplicative renormalization, NIKHEF-H preprint, to appear in Phys. Lett. B. [13] G. 't Hooft and M. Veltman, Diagrammar, in Particle interactions at very high energies, ed. D. Speiser, E Halzen and J. Weyers (Plenum Press, London, 1974). [14] E.H. Lifshitz and L.P. Pitaevskii, Relativistic quantum theory, Part 2, Chapters XI and XII (Pergamon Press, New York, 1973). [15] H. van Dam and M. Veltman, Nuci. Phys. B 22 (1970) 397. [16] G. Giavarini, C.P. Martin and E Rniz Ruiz, Nucl. Phys. B 381 (1992) 222. [17] J.C. Collins, Renormalization (Cambridge Univ. Press, Cambridge, 1987