Abstract
The weak decays K± → π±a offer a powerful probe of axion-like particles (ALPs). In this work, we provide a comprehensive analysis of these processes within chiral perturbation theory, extending existing calculations by including complete next-to-leading order (NLO) contributions and isospin-breaking corrections at first order in (md – mu). We show that the consistent incorporation of ALPs in the QCD and weak chiral Lagrangians requires a non-trivial extension of the corresponding operator bases, which we describe in detail. Furthermore, we show that in the presence of an ALP the so-called “weak mass term”, which is unobservable in the Standard Model, is non-redundant already at leading order. We find that NLO corrections associated with flavor-violating ALP couplings modify the leading-order result by a few percent, with negligible uncertainties. NLO corrections proportional to flavor-conserving ALP couplings lead to potentially larger corrections, which, however, are accompanied by sizable uncertainties mainly due to the currently limited knowledge of various low-energy constants. We study how these corrections impact bounds on the ALP couplings, first model independently, and then specializing to the case of an ALP with flavor-universal couplings in the UV. Our findings confirm that the decays K± → π±a provide the strongest particle-physics constraints for ma ≲ 300 MeV. In addition, we point out that these bounds have interesting implications for the ALP couplings to nucleons, which were so far only constrained by astrophysical measurements and non-accelerator experiments.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R.D. Peccei and H.R. Quinn, CP Conservation in the Presence of Instantons, Phys. Rev. Lett. 38 (1977) 1440 [INSPIRE].
S. Weinberg, A New Light Boson?, Phys. Rev. Lett. 40 (1978) 223 [INSPIRE].
F. Wilczek, Problem of Strong P and T Invariance in the Presence of Instantons, Phys. Rev. Lett. 40 (1978) 279 [INSPIRE].
W.A. Bardeen and S.-H.H. Tye, Current Algebra Applied to Properties of the Light Higgs Boson, Phys. Lett. B 74 (1978) 229 [INSPIRE].
J.E. Kim, Weak Interaction Singlet and Strong CP Invariance, Phys. Rev. Lett. 43 (1979) 103 [INSPIRE].
M.A. Shifman, A.I. Vainshtein and V.I. Zakharov, Can Confinement Ensure Natural CP Invariance of Strong Interactions?, Nucl. Phys. B 166 (1980) 493 [INSPIRE].
M. Dine, W. Fischler and M. Srednicki, A Simple Solution to the Strong CP Problem with a Harmless Axion, Phys. Lett. B 104 (1981) 199 [INSPIRE].
A.R. Zhitnitsky, On Possible Suppression of the Axion Hadron Interactions (in Russian), Sov. J. Nucl. Phys. 31 (1980) 260 [INSPIRE].
A. Davidson and K.C. Wali, Minimal flavor unification via multigenerational Peccei-Quinn symmetry, Phys. Rev. Lett. 48 (1982) 11 [INSPIRE].
L. Calibbi et al., Minimal axion model from flavor, Phys. Rev. D 95 (2017) 095009 [arXiv:1612.08040] [INSPIRE].
Y. Ema, K. Hamaguchi, T. Moroi and K. Nakayama, Flaxion: a minimal extension to solve puzzles in the standard model, JHEP 01 (2017) 096 [arXiv:1612.05492] [INSPIRE].
D. Cadamuro and J. Redondo, Cosmological bounds on pseudo Nambu-Goldstone bosons, JCAP 02 (2012) 032 [arXiv:1110.2895] [INSPIRE].
M. Millea, L. Knox and B. Fields, New Bounds for Axions and Axion-Like Particles with keV-GeV Masses, Phys. Rev. D 92 (2015) 023010 [arXiv:1501.04097] [INSPIRE].
A. Payez et al., Revisiting the SN1987A gamma-ray limit on ultralight axion-like particles, JCAP 02 (2015) 006 [arXiv:1410.3747] [INSPIRE].
J. Jaeckel, P.C. Malta and J. Redondo, Decay photons from the axionlike particles burst of type II supernovae, Phys. Rev. D 98 (2018) 055032 [arXiv:1702.02964] [INSPIRE].
K. Mimasu and V. Sanz, ALPs at Colliders, JHEP 06 (2015) 173 [arXiv:1409.4792] [INSPIRE].
J. Jaeckel and M. Spannowsky, Probing MeV to 90 GeV axion-like particles with LEP and LHC, Phys. Lett. B 753 (2016) 482 [arXiv:1509.00476] [INSPIRE].
S. Knapen, T. Lin, H.K. Lou and T. Melia, Searching for Axionlike Particles with Ultraperipheral Heavy-Ion Collisions, Phys. Rev. Lett. 118 (2017) 171801 [arXiv:1607.06083] [INSPIRE].
I. Brivio et al., ALPs Effective Field Theory and Collider Signatures, Eur. Phys. J. C 77 (2017) 572 [arXiv:1701.05379] [INSPIRE].
M. Bauer, M. Neubert and A. Thamm, Collider Probes of Axion-Like Particles, JHEP 12 (2017) 044 [arXiv:1708.00443] [INSPIRE].
M. Bauer, M. Heiles, M. Neubert and A. Thamm, Axion-Like Particles at Future Colliders, Eur. Phys. J. C 79 (2019) 74 [arXiv:1808.10323] [INSPIRE].
B. Batell, M. Pospelov and A. Ritz, Multi-lepton Signatures of a Hidden Sector in Rare B Decays, Phys. Rev. D 83 (2011) 054005 [arXiv:0911.4938] [INSPIRE].
M. Freytsis, Z. Ligeti and J. Thaler, Constraining the Axion Portal with B → Kl+l−, Phys. Rev. D 81 (2010) 034001 [arXiv:0911.5355] [INSPIRE].
M.J. Dolan, F. Kahlhoefer, C. McCabe and K. Schmidt-Hoberg, A taste of dark matter: Flavour constraints on pseudoscalar mediators, JHEP 03 (2015) 171 [Erratum ibid. 07 (2015) 103] [arXiv:1412.5174] [INSPIRE].
J. Martin Camalich et al., Quark Flavor Phenomenology of the QCD Axion, Phys. Rev. D 102 (2020) 015023 [arXiv:2002.04623] [INSPIRE].
M. Bauer et al., Axionlike Particles, Lepton-Flavor Violation, and a New Explanation of aμ and ae, Phys. Rev. Lett. 124 (2020) 211803 [arXiv:1908.00008] [INSPIRE].
M. Bauer et al., Flavor probes of axion-like particles, JHEP 09 (2022) 056 [arXiv:2110.10698] [INSPIRE].
W.A. Bardeen, S.-H.H. Tye and J.A.M. Vermaseren, Phenomenology of the New Light Higgs Boson Search, Phys. Lett. B 76 (1978) 580 [INSPIRE].
I. Antoniadis and T.N. Truong, Lower Bound for Branching Ratio of K+ → π+ Axion and Nonexistence of Peccei-Quinn Axion, Phys. Lett. B 109 (1982) 67 [INSPIRE].
L.M. Krauss and M.B. Wise, Constraints on Shortlived Axions From the Decay π+ → e+e−e+ Neutrino, Phys. Lett. B 176 (1986) 483 [INSPIRE].
W.A. Bardeen, R.D. Peccei and T. Yanagida, Constraints on variant axion models, Nucl. Phys. B 279 (1987) 401 [INSPIRE].
B. Döbrich, F. Ertas, F. Kahlhoefer and T. Spadaro, Model-independent bounds on light pseudoscalars from rare B-meson decays, Phys. Lett. B 790 (2019) 537 [arXiv:1810.11336] [INSPIRE].
C. Cornella, P. Paradisi and O. Sumensari, Hunting for ALPs with Lepton Flavor Violation, JHEP 01 (2020) 158 [arXiv:1911.06279] [INSPIRE].
A.W.M. Guerrera and S. Rigolin, Revisiting K → πa decays, Eur. Phys. J. C 82 (2022) 192 [arXiv:2106.05910] [INSPIRE].
H. Georgi, D.B. Kaplan and L. Randall, Manifesting the Invisible Axion at Low-energies, Phys. Lett. B 169 (1986) 73 [INSPIRE].
F. Björkeroth, E.J. Chun and S.F. King, Flavourful Axion Phenomenology, JHEP 08 (2018) 117 [arXiv:1806.00660] [INSPIRE].
F. Ertas and F. Kahlhoefer, On the interplay between astrophysical and laboratory probes of MeV-scale axion-like particles, JHEP 07 (2020) 050 [arXiv:2004.01193] [INSPIRE].
S. Gori, G. Perez and K. Tobioka, KOTO vs. NA62 Dark Scalar Searches, JHEP 08 (2020) 110 [arXiv:2005.05170] [INSPIRE].
M. Bauer et al., Consistent Treatment of Axions in the Weak Chiral Lagrangian, Phys. Rev. Lett. 127 (2021) 081803 [arXiv:2102.13112] [INSPIRE].
M. Bauer et al., The Low-Energy Effective Theory of Axions and ALPs, JHEP 04 (2021) 063 [arXiv:2012.12272] [INSPIRE].
E. Izaguirre, T. Lin and B. Shuve, Searching for Axionlike Particles in Flavor-Changing Neutral Current Processes, Phys. Rev. Lett. 118 (2017) 111802 [arXiv:1611.09355] [INSPIRE].
M.B. Gavela et al., Flavor constraints on electroweak ALP couplings, Eur. Phys. J. C 79 (2019) 369 [arXiv:1901.02031] [INSPIRE].
M. Srednicki, Axion Couplings to Matter. 1. CP Conserving Parts, Nucl. Phys. B 260 (1985) 689 [INSPIRE].
J. Gasser and H. Leutwyler, Chiral Perturbation Theory: Expansions in the Mass of the Strange Quark, Nucl. Phys. B 250 (1985) 465 [INSPIRE].
P. Herrera-Siklody, J.I. Latorre, P. Pascual and J. Taron, Chiral effective Lagrangian in the large N(c) limit: The Nonet case, Nucl. Phys. B 497 (1997) 345 [hep-ph/9610549] [INSPIRE].
A. Pich, B. Guberina and E. de Rafael, Problem with the Delta I = 1/2 Rule in the Standard Model, Nucl. Phys. B 277 (1986) 197 [INSPIRE].
A. Pich and E. de Rafael, Four quark operators and nonleptonic weak transitions, Nucl. Phys. B 358 (1991) 311 [INSPIRE].
G. Ecker et al., Electromagnetism in nonleptonic weak interactions, Nucl. Phys. B 591 (2000) 419 [hep-ph/0006172] [INSPIRE].
V. Cirigliano, G. Ecker, H. Neufeld and A. Pich, Isospin breaking in K → ππ decays, Eur. Phys. J. C 33 (2004) 369 [hep-ph/0310351] [INSPIRE].
J. Kambor, J.H. Missimer and D. Wyler, The Chiral Loop Expansion of the Nonleptonic Weak Interactions of Mesons, Nucl. Phys. B 346 (1990) 17 [INSPIRE].
J.A. Cronin, Phenomenological model of strong and weak interactions in chiral U (3) × U (3), Phys. Rev. 161 (1967) 1483 [INSPIRE].
C.W. Bernard et al., Application of Chiral Perturbation Theory to K → 2π Decays, Phys. Rev. D 32 (1985) 2343 [INSPIRE].
V. Cirigliano et al., Kaon Decays in the Standard Model, Rev. Mod. Phys. 84 (2012) 399 [arXiv:1107.6001] [INSPIRE].
A. Pich and A. Rodríguez-Sánchez, SU (3) analysis of four-quark operators: K → ππ and vacuum matrix elements, JHEP 06 (2021) 005 [arXiv:2102.09308] [INSPIRE].
G. Grilli di Cortona, E. Hardy, J. Pardo Vega and G. Villadoro, The QCD axion, precisely, JHEP 01 (2016) 034 [arXiv:1511.02867] [INSPIRE].
J. Bijnens and G. Ecker, Mesonic low-energy constants, Ann. Rev. Nucl. Part. Sci. 64 (2014) 149 [arXiv:1405.6488] [INSPIRE].
R.J. Dowdall, C.T.H. Davies, G.P. Lepage and C. McNeile, Vus from pi and K decay constants in full lattice QCD with physical u, d, s and c quarks, Phys. Rev. D 88 (2013) 074504 [arXiv:1303.1670] [INSPIRE].
Flavour Lattice Averaging Group (FLAG) collaboration, FLAG Review 2021, Eur. Phys. J. C 82 (2022) 869 [arXiv:2111.09849] [INSPIRE].
V. Cirigliano, G. Ecker, H. Neufeld and A. Pich, Meson resonances, large N(c) and chiral symmetry, JHEP 06 (2003) 012 [hep-ph/0305311] [INSPIRE].
G. Ecker, J. Kambor and D. Wyler, Resonances in the weak chiral Lagrangian, Nucl. Phys. B 394 (1993) 101 [INSPIRE].
J. Bijnens and F. Borg, Isospin breaking in K → 3π decays III: Bremsstrahlung and fit to experiment, Eur. Phys. J. C 40 (2005) 383 [hep-ph/0501163] [INSPIRE].
J. Bijnens, P. Dhonte and F. Borg, K → 3π decays in chiral perturbation theory, Nucl. Phys. B 648 (2003) 317 [hep-ph/0205341] [INSPIRE].
J. Kambor, J.H. Missimer and D. Wyler, K → 2π and K → 3π decays in next-to-leading order chiral perturbation theory, Phys. Lett. B 261 (1991) 496 [INSPIRE].
R.J. Crewther, Chiral Reduction of K → 2π Amplitudes, Nucl. Phys. B 264 (1986) 277 [INSPIRE].
M. Leurer, The tadpole in the Chiral Lagrangian of K Decays, Phys. Lett. B 201 (1988) 128 [INSPIRE].
A.J. Buras and J.-M. Gerard, Final state interactions in K → ππ decays: ∆I = 1/2 rule vs. ε′/ε, Eur. Phys. J. C 77 (2017) 10 [arXiv:1603.05686] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, PTEP 2022 (2022) 083C01 [INSPIRE].
H. Leutwyler and M. Roos, Determination of the Elements V(us) and V(ud) of the Kobayashi-Maskawa Matrix, Z. Phys. C 25 (1984) 91 [INSPIRE].
NA62 collaboration, Measurement of the very rare \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) decay, JHEP 06 (2021) 093 [arXiv:2103.15389] [INSPIRE].
M. Gorghetto, E. Hardy and G. Villadoro, More axions from strings, SciPost Phys. 10 (2021) 050 [arXiv:2007.04990] [INSPIRE].
M. Chala, G. Guedes, M. Ramos and J. Santiago, Running in the ALPs, Eur. Phys. J. C 81 (2021) 181 [arXiv:2012.09017] [INSPIRE].
C. O’Hare, cajohare/axionlimits: Axionlimits, https://cajohare.github.io/AxionLimits/.
Particle Data Group collaboration, Review of Particle Physics, PTEP 2020 (2020) 083C01 [INSPIRE].
J. Ellis, TikZ-Feynman: Feynman diagrams with TikZ, Comput. Phys. Commun. 210 (2017) 103 [arXiv:1601.05437] [INSPIRE].
H.H. Patel, Package-X: a Mathematica package for the analytic calculation of one-loop integrals, Comput. Phys. Commun. 197 (2015) 276 [arXiv:1503.01469] [INSPIRE].
H.H. Patel, Package-X 2.0: a Mathematica package for the analytic calculation of one-loop integrals, Comput. Phys. Commun. 218 (2017) 66 [arXiv:1612.00009] [INSPIRE].
G. Ecker, Geometrical aspects of the nonleptonic weak interactions of mesons, in the proceedings of the 9th International Conference on the Problems of Quantum Field Theory, Dubna, USSR, Union of Soviet Socialist Republics, April 24–28 (1990) [INSPIRE].
Acknowledgments
It is a pleasure to thank Gerhard Ecker, Gino Isidori, Stefan Scherer, and Marvin Schnubel for valuable discussion. The research of C.C., A.M.G. and M.N. was supported by the Cluster of Excellence Precision Physics, Fundamental Interactions, and Structure of Matter (PRISMA+, EXC 2118/1) within the German Excellence Strategy (Project-ID 390831469). C.C. would also like to thank Perimeter Institute for hospitality during the completion of this work. This research was supported in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Research, Innovation and Science. The Feynman diagrams in this paper have been drawn with the Latex package TikZ-Feynman [74]. Results for the loop graphs have been cross-checked with Package-X [75, 76].
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: 2308.16903
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
Cornella, C., Galda, A.M., Neubert, M. et al. K± → π±a at next-to-leading order in chiral perturbation theory and updated bounds on ALP couplings. J. High Energ. Phys. 2024, 29 (2024). https://doi.org/10.1007/JHEP06(2024)029
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2024)029