Abstract
The conditions for the absence of gauge anomalies in effective field theories (EFT) are rivisited. General results from the cohomology of the BRST operator do not prevent potential anomalies arising from the non-renormalizable sector, when the gauge group is not semi-simple, like in the Standard Model EFT (SMEFT). By considering a simple explicit model that mimics the SMEFT properties, we compute the anomaly in the regularized theory, including a complete set of dimension six operators. We show that the dependence of the anomaly on the non-renormalizable part can be removed by adding a local counterterm to the theory. As a result the condition for gauge anomaly cancellation is completely controlled by the charge assignment of the fermion sector, as in the renormalizable theory.
Article PDF
Similar content being viewed by others
References
A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi, Causality, analyticity and an IR obstruction to UV completion, JHEP 10 (2006) 014 [hep-th/0602178] [INSPIRE].
L. Vecchi, Causal versus analytic constraints on anomalous quartic gauge couplings, JHEP 11 (2007) 054 [arXiv:0704.1900] [INSPIRE].
A. Nicolis, R. Rattazzi and E. Trincherini, Energy’s and amplitudes’ positivity, JHEP 05 (2010) 095 [Erratum ibid. 11 (2011) 128] [arXiv:0912.4258] [INSPIRE].
B. Bellazzini, Softness and amplitudes’ positivity for spinning particles, JHEP 02 (2017) 034 [arXiv:1605.06111] [INSPIRE].
C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou, Positivity bounds for scalar field theories, Phys. Rev. D 96 (2017) 081702 [arXiv:1702.06134] [INSPIRE].
C. de Rham, S. Melville, A.J. Tolley and S.-Y. Zhou, UV complete me: positivity bounds for particles with spin, JHEP 03 (2018) 011 [arXiv:1706.02712] [INSPIRE].
C. Zhang and S.-Y. Zhou, Positivity bounds on vector boson scattering at the LHC, Phys. Rev. D 100 (2019) 095003 [arXiv:1808.00010] [INSPIRE].
Q. Bi, C. Zhang and S.-Y. Zhou, Positivity constraints on aQGC: carving out the physical parameter space, JHEP 06 (2019) 137 [arXiv:1902.08977] [INSPIRE].
B. Bellazzini, J. Elias Miró, R. Rattazzi, M. Riembau and F. Riva, Positive moments for scattering amplitudes, arXiv:2011.00037 [INSPIRE].
G.N. Remmen and N.L. Rodd, Consistency of the Standard Model effective field theory, JHEP 12 (2019) 032 [arXiv:1908.09845] [INSPIRE].
G.N. Remmen and N.L. Rodd, Signs, spin, SMEFT: positivity at dimension six, arXiv:2010.04723 [INSPIRE].
C. Zhang and S.-Y. Zhou, Convex geometry perspective on the (Standard Model) effective field theory space, Phys. Rev. Lett. 125 (2020) 201601 [arXiv:2005.03047] [INSPIRE].
S.L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev. 177 (1969) 2426 [INSPIRE].
J.S. Bell and R. Jackiw, A PCAC puzzle: π0 → γγ in the σ model, Nuovo Cim. A 60 (1969) 47 [INSPIRE].
H. Georgi and S.L. Glashow, Gauge theories without anomalies, Phys. Rev. D 6 (1972) 429 [INSPIRE].
G. Barnich and M. Henneaux, Renormalization of gauge invariant operators and anomalies in Yang-Mills theory, Phys. Rev. Lett. 72 (1994) 1588 [hep-th/9312206] [INSPIRE].
G. Barnich, F. Brandt and M. Henneaux, Local BRST cohomology in gauge theories, Phys. Rept. 338 (2000) 439 [hep-th/0002245] [INSPIRE].
J.A. Dixon and M. Ramon Medrano, Anomalies in the operator product expansion, Phys. Rev. D 22 (1980) 429 [INSPIRE].
J.A. Dixon, Anomalies, BRS cohomology and effective theories, Phys. Rev. Lett. 67 (1991) 797 [INSPIRE].
S. Marculescu and L. Mezincescu, Axial anomaly in nonrenormalizable theories, preprint IFIN-FT-162-1978, Bucarest, Romania (1978).
Y. Kim, P.Y. Pac and H.K. Shin, Spinor loop anomalies in higher derivative theories, Phys. Rev. D 39 (1989) 1251 [INSPIRE].
J. Minn, J. Kim and C.-K. Lee, Spinor loop anomalies with very general local fermion Lagrangians, Phys. Rev. D 35 (1987) 1872 [INSPIRE].
L. Álvarez-Gaumé and E. Witten, Gravitational anomalies, Nucl. Phys. B 234 (1984) 269 [INSPIRE].
J. Soto, Anomaly cancellation at finite cutoff, Phys. Rev. D 45 (1992) 4621 [INSPIRE].
O. Catà, W. Kilian and N. Kreher, Gauge anomalies in the Standard-Model effective field theory, arXiv:2011.09976 [INSPIRE].
Q. Bonnefoy, L. Di Luzio, C. Grojean, A. Paul and A.N. Rossia, Comments on gauge anomalies at dimension-six in the Standard Model effective field theory, arXiv:2012.07740 [INSPIRE].
S.L. Adler and W.A. Bardeen, Absence of higher order corrections in the anomalous axial vector divergence equation, Phys. Rev. 182 (1969) 1517 [INSPIRE].
D. Anselmi, Adler-Bardeen theorem and cancellation of gauge anomalies to all orders in nonrenormalizable theories, Phys. Rev. D 91 (2015) 105016 [arXiv:1501.07014] [INSPIRE].
J. Wess and B. Zumino, Consequences of anomalous Ward identities, Phys. Lett. B 37 (1971) 95 [INSPIRE].
B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, Dimension-six terms in the Standard Model Lagrangian, JHEP 10 (2010) 085 [arXiv:1008.4884] [INSPIRE].
W.A. Bardeen, Anomalous Ward identities in spinor field theories, Phys. Rev. 184 (1969) 1848 [INSPIRE].
T.E. Clark and S.T. Love, The axial anomaly and antisymmetric tensor fields, Nucl. Phys. B 223 (1983) 135 [INSPIRE].
W.A. Bardeen and N. Deo, Comment on spinor anomalies, Nucl. Phys. B 264 (1986) 364 [INSPIRE].
G. ’t Hooft and M.J.G. Veltman, Regularization and renormalization of gauge fields, Nucl. Phys. B 44 (1972) 189 [INSPIRE].
T. Marinucci and M. Tonin, Dimensional regularization and anomalies, Nuovo Cim. A 31 (1976) 381 [INSPIRE].
P. Breitenlohner and D. Maison, Dimensional renormalization and the action principle, Commun. Math. Phys. 52 (1977) 11 [INSPIRE].
A. Bilal, Lectures on anomalies, arXiv:0802.0634 [INSPIRE].
G. Durieux, J. Gu, E. Vryonidou and C. Zhang, Probing top-quark couplings indirectly at Higgs factories, Chin. Phys. C 42 (2018) 123107 [arXiv:1809.03520] [INSPIRE].
C. Degrande, G. Durieux, F. Maltoni, K. Mimasu, E. Vryonidou and C. Zhang, Automated one-loop computations in the SMEFT, arXiv:2008.11743 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2012.13989
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Feruglio, F. A note on gauge anomaly cancellation in effective field theories. J. High Energ. Phys. 2021, 128 (2021). https://doi.org/10.1007/JHEP03(2021)128
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2021)128