Abstract
We show that the Grossman-Nir (GN) bound, Br(KL → \( {\pi}^0\nu \overline{\nu} \)) ≤ 4.3 Br(K+ → \( {\pi}^{+}\nu \overline{\nu} \)), can be violated in the presence of light new physics with flavor violating couplings. We construct three sample models in which the GN bound can be violated by orders of magnitude, while satisfying all other experimental bounds. In the three models the enhanced branching ratio Br(KL → π0 + inv) is due to KL → π0ϕ1, KL → π0ϕ1ϕ1, KL → \( {\pi}^0{\psi}_1{\overline{\psi}}_1 \) transitions, respectively, where ϕ1(ψ1) is a light scalar (fermion) that escapes the detector. In the three models Br(K+ → π+ + inv) remains very close to the SM value, while Br(KL → π0 + inv) can saturate the present KOTO bound. Besides invisible particles in the final state (which may account for dark matter) the models require additional light mediators around the GeV-scale.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Y. Grossman and Y. Nir, KL → π0νν beyond the standard model, Phys. Lett. B 398 (1997) 163 [hep-ph/9701313] [INSPIRE].
Y. Grossman, G. Isidori and H. Murayama, Lepton flavor mixing and K → \( \pi \nu \overline{\nu} \) decays, Phys. Lett. B 588 (2004) 74 [hep-ph/0311353] [INSPIRE].
X.-G. He, X.-D. Ma, J. Tandean and G. Valencia, Breaking the Grossman-Nir Bound in Kaon Decays, JHEP 04 (2020) 057 [arXiv:2002.05467] [INSPIRE].
T. Li, X.-D. Ma and M.A. Schmidt, Implication of K → \( \pi \nu \overline{\nu} \) for generic neutrino interactions in effective field theories, Phys. Rev. D 101 (2020) 055019 [arXiv:1912.10433] [INSPIRE].
A.J. Buras, M. Gorbahn, U. Haisch and U. Nierste, The Rare decay K+ → \( {\pi}^{+}\nu \overline{\nu} \) at the next-to-next-to-leading order in QCD, Phys. Rev. Lett. 95 (2005) 261805 [hep-ph/0508165] [INSPIRE].
J. Brod, M. Gorbahn and E. Stamou, Two-Loop Electroweak Corrections for the K → \( \pi \nu \overline{\nu} \) Decays, Phys. Rev. D 83 (2011) 034030 [arXiv:1009.0947] [INSPIRE].
A.J. Buras, D. Buttazzo, J. Girrbach-Noe and R. Knegjens, \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu}\ and\ {K}_L\to {\pi}^0\nu \overline{\nu} \) in the Standard Model: status and perspectives, JHEP 11 (2015) 033 [arXiv:1503.02693] [INSPIRE].
R. Volpe, New Result on K+ → \( {\pi}^{+}\nu \overline{\nu} \) from the NA62 Experiment, talk presented at Pheno2020, Pittsburgh U.S.A. (2020).
KOTO collaboration, Search for the KL → \( {\pi}^0\nu \overline{\nu} \) and KL → π0X0 decays at the J-PARC KOTO experiment, Phys. Rev. Lett. 122 (2019) 021802 [arXiv:1810.09655] [INSPIRE].
S. Shinohara, Search for the rare decay KL → \( {\pi}^0\nu \overline{\nu} \) at J-PARC KOTO experiment, talk presented at KAON2019, Perugia Italy (2019).
T. Nomura, E14/KOTO Status, talk given at 29th J-PARC PAC meeting, J-PARC Japan (2020).
T. Kitahara, T. Okui, G. Perez, Y. Soreq and K. Tobioka, New physics implications of recent search for KL → \( {\pi}^0\nu \overline{\nu} \) at KOTO, Phys. Rev. Lett. 124 (2020) 071801 [arXiv:1909.11111] [INSPIRE].
M. Fabbrichesi and E. Gabrielli, Dark-sector physics in the search for the rare decays \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu}\kern0.5em and\ {K}_L\to {\pi}^0\nu \overline{\nu} \), Eur. Phys. J. C 80 (2020) 532 [arXiv:1911.03755] [INSPIRE].
K. Fuyuto, W.-S. Hou and M. Kohda, Loophole in \( K\to \pi \nu \overline{\nu} \) Search and New Weak Leptonic Forces, Phys. Rev. Lett. 114 (2015) 171802 [arXiv:1412.4397] [INSPIRE].
G.W.S. Hou, Loophole in \( K\to \pi \nu \overline{\nu} \) Search & \( {K}_L\to {\pi}^0\nu \overline{\nu} \) Beyond Grossman-Nir Bound, J. Phys. Conf. Ser. 800 (2017) 012024 [arXiv:1611.09673] [INSPIRE].
D. Egana-Ugrinovic, S. Homiller and P. Meade, Light Scalars and the KOTO Anomaly, Phys. Rev. Lett. 124 (2020) 191801 [arXiv:1911.10203] [INSPIRE].
P.S.B. Dev, R.N. Mohapatra and Y. Zhang, Constraints on long-lived light scalars with flavor-changing couplings and the KOTO anomaly, Phys. Rev. D 101 (2020) 075014 [arXiv:1911.12334] [INSPIRE].
Y. Jho, S.M. Lee, S.C. Park, Y. Park and P.-Y. Tseng, Light gauge boson interpretation for (g − 2)μ and the KL → π0 + (invisible) anomaly at the J-PARC KOTO experiment, JHEP 04 (2020) 086 [arXiv:2001.06572] [INSPIRE].
J. Liu, N. McGinnis, C.E.M. Wagner and X.-P. Wang, A light scalar explanation of (g − 2)μ and the KOTO anomaly, JHEP 04 (2020) 197 [arXiv:2001.06522] [INSPIRE].
J.M. Cline, M. Puel and T. Toma, A little theory of everything, with heavy neutral leptons, JHEP 05 (2020) 039 [arXiv:2001.11505] [INSPIRE].
Y. Liao, H.-L. Wang, C.-Y. Yao and J. Zhang, An imprint of a new light particle at KOTO?, arXiv:2005.00753 [INSPIRE].
G. Hiller and R. Zwicky, (A)symmetries of weak decays at and near the kinematic endpoint, JHEP 03 (2014) 042 [arXiv:1312.1923] [INSPIRE].
N.H. Christ, X. Feng, A. Juttner, A. Lawson, A. Portelli and C.T. Sachrajda, First exploratory calculation of the long-distance contributions to the rare kaon decays K → πℓ+ℓ− , Phys. Rev. D 94 (2016) 114516 [arXiv:1608.07585] [INSPIRE].
J. Gasser and H. Leutwyler, Chiral Perturbation Theory: Expansions in the Mass of the Strange Quark, Nucl. Phys. B 250 (1985) 465 [INSPIRE].
A. Pich, Chiral perturbation theory, Rept. Prog. Phys. 58 (1995) 563 [hep-ph/9502366] [INSPIRE].
Flavour Lattice Averaging Group collaboration, FLAG Review 2019: Flavour Lattice Averaging Group (FLAG), Eur. Phys. J. C 80 (2020) 113 [arXiv:1902.08191] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
F. Mescia and C. Smith, Improved estimates of rare K decay matrix-elements from Kl3 decays, Phys. Rev. D 76 (2007) 034017 [arXiv:0705.2025] [INSPIRE].
E949 and E787 collaborations, Measurement of the K+ → π+νν branching ratio, Phys. Rev. D 77 (2008) 052003 [arXiv:0709.1000] [INSPIRE].
A.J. Buras, D. Guadagnoli and G. Isidori, On ϵK Beyond Lowest Order in the Operator Product Expansion, Phys. Lett. B 688 (2010) 309 [arXiv:1002.3612] [INSPIRE].
J. Brod, M. Gorbahn and E. Stamou, Standard-model prediction of ϵK with manifest CKM unitarity, arXiv:1911.06822 [INSPIRE].
UTfit collaboration, Model-independent constraints on ∆F = 2 operators and the scale of new physics, JHEP 03 (2008) 049 [arXiv:0707.0636] [INSPIRE].
UTfit collaboration, http://www.utfit.org/UTfit/, summer 2018 results.
V. Cirigliano, G. Ecker, H. Neufeld, A. Pich and J. Portoles, Kaon Decays in the Standard Model, Rev. Mod. Phys. 84 (2012) 399 [arXiv:1107.6001] [INSPIRE].
G. D’Ambrosio and G. Isidori, CP violation in kaon decays, Int. J. Mod. Phys. A 13 (1998) 1 [hep-ph/9611284] [INSPIRE].
CKMfitter Group collaboration, CP violation and the CKM matrix: Assessing the impact of the asymmetric B factories, Eur. Phys. J. C 41 (2005) 1 [hep-ph/0406184] [INSPIRE].
RBC, UKQCD collaboration, Direct CP-violation and the ∆I = 1/2 rule in K → ππ decay from the Standard Model, arXiv:2004.09440 [INSPIRE].
J. Aebischer, C. Bobeth and A.J. Buras, ε′/ε in the Standard Model at the Dawn of the 2020s, arXiv:2005.05978 [INSPIRE].
BNL-E949 collaboration, Study of the decay K+ → \( {\pi}^{+}\nu \overline{\nu} \) in the momentum region 140 < Pπ < 199 MeV/c, Phys. Rev. D 79 (2009) 092004 [arXiv:0903.0030] [INSPIRE].
G. Ruggiero, Latest measurement of K+ → \( {\pi}^{+}\nu \overline{\nu} \) with the NA62 experiment at CERN, talk presented at KAON2019, Perugia Italy (2019).
E949 collaboration, Upper Limit on the Branching Ratio for the Decay π0 → \( \nu \overline{\nu} \), Phys. Rev. D 72 (2005) 091102 [hep-ex/0506028] [INSPIRE].
W. Altmannshofer, S. Gori and D.J. Robinson, Constraining axionlike particles from rare pion decays, Phys. Rev. D 101 (2020) 075002 [arXiv:1909.00005] [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].
E.E. Jenkins and A.V. Manohar, Baryon chiral perturbation theory using a heavy fermion Lagrangian, Phys. Lett. B 255 (1991) 558 [INSPIRE].
F. Bishara, J. Brod, B. Grinstein and J. Zupan, From quarks to nucleons in dark matter direct detection, JHEP 11 (2017) 059 [arXiv:1707.06998] [INSPIRE].
H. Simma, Equations of motion for effective Lagrangians and penguins in rare B decays, Z. Phys. C 61 (1994) 67 [hep-ph/9307274] [INSPIRE].
J.S. Lee, Revisiting Supernova 1987A Limits on Axion-Like-Particles, arXiv:1808.10136 [INSPIRE].
N. Bar, K. Blum and G. D’amico, Is there a supernova bound on axions?, Phys. Rev. D 101 (2020) 123025 [arXiv:1907.05020] [INSPIRE].
D. Cadamuro and J. Redondo, Cosmological bounds on pseudo Nambu-Goldstone bosons, JCAP 02 (2012) 032 [arXiv:1110.2895] [INSPIRE].
G. Bertone, D. Hooper and J. Silk, Particle dark matter: Evidence, candidates and constraints, Phys. Rept. 405 (2005) 279 [hep-ph/0404175] [INSPIRE].
C.D. Froggatt and H.B. Nielsen, Hierarchy of Quark Masses, Cabibbo Angles and CP-violation, Nucl. Phys. B 147 (1979) 277 [INSPIRE].
A. Smolkovič, M. Tammaro and J. Zupan, Anomaly free Froggatt-Nielsen models of flavor, JHEP 10 (2019) 188 [arXiv:1907.10063] [INSPIRE].
Particle Data Group collaboration, Review of Particle Physics, Chin. Phys. C 40 (2016) 100001 [INSPIRE].
J. Gratrex, M. Hopfer and R. Zwicky, Generalised helicity formalism, higher moments and the \( B\to {KJ}_K\left(\to K\pi \right){\overline{\mathrm{\ell}}}_1{\mathrm{\ell}}_2 \) angular distributions, Phys. Rev. D 93 (2016) 054008 [arXiv:1506.03970] [INSPIRE].
G. Passarino and M.J.G. Veltman, One Loop Corrections for e+e− Annihilation Into μ+μ− in the Weinberg Model, Nucl. Phys. B 160 (1979) 151 [INSPIRE].
T. Hahn and M. Pérez-Victoria, Automatized one loop calculations in four-dimensions and D-dimensions, Comput. Phys. Commun. 118 (1999) 153 [hep-ph/9807565] [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].
R. Mertig, M. Böhm and A. Denner, FEYN CALC: Computer algebraic calculation of Feynman amplitudes, Comput. Phys. Commun. 64 (1991) 345 [INSPIRE].
V. Shtabovenko, R. Mertig and F. Orellana, New Developments in FeynCalc 9.0, Comput. Phys. Commun. 207 (2016) 432 [arXiv:1601.01167] [INSPIRE].
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
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: 2005.00451
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
Ziegler, R., Zupan, J. & Zwicky, R. Three exceptions to the Grossman-Nir bound. J. High Energ. Phys. 2020, 229 (2020). https://doi.org/10.1007/JHEP07(2020)229
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2020)229