Abstract
The bootstrap approach (demanding consistency conditions to scattering amplitudes) has shown to be quite powerful to tightly constrain gauge theories at large Nc. We extend previous analysis to scattering amplitudes involving pions and external gauge bosons. These amplitudes allow us to access the chiral anomaly and connect low-energy physical quantities to UV properties of the theory. In particular, we are able to obtain an analytic bound on the chiral anomaly coefficient as a function of the pion dipole polarizabilities. This bound can be useful for holographic models whose dual UV completions are not known, and provide a consistency condition to lattice simulations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
G. ’t Hooft, A planar diagram theory for strong interactions, Nucl. Phys. B 72 (1974) 461 [INSPIRE].
E. Witten, Baryons in the 1/n expansion, Nucl. Phys. B 160 (1979) 57 [INSPIRE].
J. Albert and L. Rastelli, Bootstrapping pions at large N, JHEP 08 (2022) 151 [arXiv:2203.11950] [INSPIRE].
C. Fernandez, A. Pomarol, F. Riva and F. Sciotti, Cornering large-Nc QCD with positivity bounds, JHEP 06 (2023) 094 [arXiv:2211.12488] [INSPIRE].
A. Adams et al., Causality, analyticity and an IR obstruction to UV completion, JHEP 10 (2006) 014 [hep-th/0602178] [INSPIRE].
N. Arkani-Hamed, T.-C. Huang and Y.-T. Huang, The EFT-hedron, JHEP 05 (2021) 259 [arXiv:2012.15849] [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].
B. Bellazzini et al., Positive moments for scattering amplitudes, Phys. Rev. D 104 (2021) 036006 [arXiv:2011.00037] [INSPIRE].
A. Sinha and A. Zahed, Crossing symmetric dispersion relations in quantum field theories, Phys. Rev. Lett. 126 (2021) 181601 [arXiv:2012.04877] [INSPIRE].
A.J. Tolley, Z.-Y. Wang and S.-Y. Zhou, New positivity bounds from full crossing symmetry, JHEP 05 (2021) 255 [arXiv:2011.02400] [INSPIRE].
S. Caron-Huot and V. Van Duong, Extremal effective field theories, JHEP 05 (2021) 280 [arXiv:2011.02957] [INSPIRE].
S. Caron-Huot, D. Mazac, L. Rastelli and D. Simmons-Duffin, Sharp boundaries for the swampland, JHEP 07 (2021) 110 [arXiv:2102.08951] [INSPIRE].
J. Henriksson, B. McPeak, F. Russo and A. Vichi, Rigorous bounds on light-by-light scattering, JHEP 06 (2022) 158 [arXiv:2107.13009] [INSPIRE].
M. Gourdin and A. Martin, Pion photon scattering, Nuovo Cim. 17 (1960) 224.
P. Ko, Vector meson contributions to the processes γγ → π0π0, π+π−, KL → π0γγ, and K+ → π+γγ, Phys. Rev. D 41 (1990) 1531 [INSPIRE].
J. Gasser, M.A. Ivanov and M.E. Sainio, Low-energy photon-photon collisions to two loops revisited, Nucl. Phys. B 728 (2005) 31 [hep-ph/0506265] [INSPIRE].
L.V. Fil’kov and V.L. Kashevarov, Determination of π0 meson quadrupole polarizabilities from the process γγ → π0π0, Phys. Rev. C 72 (2005) 035211 [nucl-th/0505058] [INSPIRE].
J. Gasser, M.A. Ivanov and M.E. Sainio, Revisiting γγ → π+π− at low energies, Nucl. Phys. B 745 (2006) 84 [hep-ph/0602234] [INSPIRE].
U. Burgi, Charged pion pair production and pion polarizabilities to two loops, Nucl. Phys. B 479 (1996) 392 [hep-ph/9602429] [INSPIRE].
L.-Y. Dai and M.R. Pennington, Pion polarizabilities from γγ → ππ analysis, Phys. Rev. D 94 (2016) 116021 [arXiv:1611.04441] [INSPIRE].
X.-L. Ren, I. Danilkin and M. Vanderhaeghen, Phenomenological model for the γγ → π+π−π0 reaction, Phys. Rev. D 107 (2023) 054037 [arXiv:2212.03086] [INSPIRE].
F.X. Lee, A. Alexandru, C. Culver and W. Wilcox, Charged pion electric polarizability from four-point functions in lattice QCD, Phys. Rev. D 108 (2023) 014512 [arXiv:2301.05200] [INSPIRE].
D. Karateev, J. Marucha, J. Penedones and B. Sahoo, Bootstrapping the a-anomaly in 4d QFTs, JHEP 12 (2022) 136 [arXiv:2204.01786] [INSPIRE].
J.K. Marucha, Bootstrapping the a-anomaly in 4d QFTs: episode II, arXiv:2307.02305 [INSPIRE].
Particle Data Group collaboration, Review of particle physics, PTEP 2022 (2022) 083C01 [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].
G.S. Bali et al., Mesons in large-N QCD, JHEP 06 (2013) 071 [arXiv:1304.4437] [INSPIRE].
J. Albert and L. Rastelli, Bootstrapping pions at large N. Part II. Background gauge fields and the chiral anomaly, arXiv:2307.01246 [INSPIRE].
I. Guiasu and E.E. Radescu, Higher multipole polarizabilities of hadrons from Compton scattering amplitudes. II, Annals Phys. 122 (1979) 436 [INSPIRE].
M. Moinester, Pion polarizability 2022 status report, arXiv:2205.09954 [INSPIRE].
X. Feng, T. Izubuchi, L. Jin and M. Golterman, Pion electric polarizabilities from lattice QCD, PoS LATTICE2021 (2022) 362 [arXiv:2201.01396] [INSPIRE].
D. Simmons-Duffin, A semidefinite program solver for the conformal bootstrap, JHEP 06 (2015) 174 [arXiv:1502.02033] [INSPIRE].
Acknowledgments
We are very grateful to Francesco Riva and Pyungwon Ko for their valuable insights. We would also like to thank Ziyu Dong for a critical reading of the paper. This work has been partly supported by the research grants 2021-SGR-00649 and PID2020-115845GB-I00/AEI/10.13039/501100011033.
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: 2307.04729
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
Ma, T., Pomarol, A. & Sciotti, F. Bootstrapping the chiral anomaly at large Nc. J. High Energ. Phys. 2023, 176 (2023). https://doi.org/10.1007/JHEP11(2023)176
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2023)176