We study whether higher-dimensional operators in effective field theories, in particular in the Standard Model Effective Field Theory (SMEFT), can source gauge anomalies via the modification of the interactions involved in triangle diagrams. We find no evidence of such gauge anomalies at the level of dimension-6 operators that can therefore be chosen independently to each others without spoiling the consistency of SMEFT, at variance with recent claims. The underlying reason is that gauge-invariant combinations of Goldstone bosons and massive gauge fields are allowed to couple to matter currents which are not conserved. We show this in a toy model by computing the relevant triangle diagrams, as well as by working out Wess-Zumino terms in the bosonic EFT below all fermion masses. The same approach applies directly to the Standard Model both at the renormalisable level, providing a convenient and unusual way to check that the SM is anomaly free, as well as at the non-renormalisable level in SMEFT.
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].
A. Bilal, Lectures on Anomalies, arXiv:0802.0634 [INSPIRE].
O. Catà, W. Kilian and N. Kreher, Gauge anomalies in the Standard-Model Effective Field Theory, arXiv:2011.09976 [INSPIRE].
J. de Blas, J. C. Criado, M. Pérez-Victoria and J. Santiago, Effective description of general extensions of the Standard Model: the complete tree-level dictionary, JHEP 03 (2018) 109 [arXiv:1711.10391] [INSPIRE].
J. D. Wells and Z. Zhang, Effective theories of universal theories, JHEP 01 (2016) 123 [arXiv:1510.08462] [INSPIRE].
C. Grojean, M. Montull and M. Riembau, Diboson at the LHC vs LEP, JHEP 03 (2019) 020 [arXiv:1810.05149] [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].
J. Wess and B. Zumino, Consequences of anomalous Ward identities, Phys. Lett. B 37 (1971) 95 [INSPIRE].
E. Witten, Global Aspects of Current Algebra, Nucl. Phys. B 223 (1983) 422 [INSPIRE].
J. Preskill, Gauge anomalies in an effective field theory, Annals Phys. 210 (1991) 323 [INSPIRE].
D. J. Gross and R. Jackiw, Effect of anomalies on quasirenormalizable theories, Phys. Rev. D 6 (1972) 477 [INSPIRE].
C. Bouchiat, J. Iliopoulos and P. Meyer, An Anomaly Free Version of Weinberg’s Model, Phys. Lett. B 38 (1972) 519 [INSPIRE].
P. Anastasopoulos, M. Bianchi, E. Dudas and E. Kiritsis, Anomalies, anomalous U(1)′s and generalized Chern-Simons terms, JHEP 11 (2006) 057 [hep-th/0605225] [INSPIRE].
Q. Bonnefoy, L. Di Luzio, C. Grojean, A. Paul and A. N. Rossia, The Anomalous Case of Axion EFTs and Massive Chiral Gauge Fields, arXiv:2011.10025 [INSPIRE].
F. Feruglio, A Note on Gauge Anomaly Cancellation in Effective Field Theories, JHEP 03 (2021) 128 [arXiv:2012.13989] [INSPIRE].
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ArXiv ePrint: 2012.07740
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Bonnefoy, Q., Di Luzio, L., Grojean, C. et al. Comments on gauge anomalies at dimension-six in the Standard Model Effective Field Theory. J. High Energ. Phys. 2021, 153 (2021). https://doi.org/10.1007/JHEP05(2021)153
- Anomalies in Field and String Theories
- Beyond Standard Model
- Effective Field Theories
- Gauge Symmetry