Letter
Open Access

Theoretical implications for a new measurement of $K_{L} \to π^{0} ℓ \bar{ℓ}$

G. D’Ambrosio ^1,*, A. M. Iyer^2,†, F. Mahmoudi^3,4,5,‡, and S. Neshatpour ^3,§

¹INFN-Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Via Cintia Edificio 6, 80126 Napoli, Italy
²Department of Physics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi-110016, India
³Université Claude Bernard Lyon 1, CNRS/IN2P3, Institut de Physique des 2 Infinis de Lyon, UMR 5822, F-69622, Villeurbanne, France
⁴Theoretical Physics Department, CERN, CH-1211 Geneva 23, Switzerland
⁵Institut Universitaire de France (IUF), 75005 Paris, France

^*Contact author: gdambros@na.infn.it
^†Contact author: iyerabhishek@physics.iitd.ac.in
^‡Contact author: nazila@cern.ch
^§Contact author: s.neshatpour@ip2i.in2p3.fr

Phys. Rev. D 111, L011701 – Published 10 January, 2025

DOI: https://doi.org/10.1103/PhysRevD.111.L011701

Abstract

Kaon physics is at an important experimental juncture with respect to the ongoing measurements of several observables. This work will build on the existing status by formulating different phenomenological analyses corresponding to different paths that may lie ahead. Beginning with the golden channels, $K^{+} \to π^{+} ν \bar{ν}$ and $K_{L} \to π^{0} ν \bar{ν}$ , the paper will eventually cast the spotlight on the importance of a precise measurement of $BR (K_{L} \to π^{0} ℓ \bar{ℓ})$ . The phenomenological analyses involve sequentially adding kaon physics observables at the projected final precision of their respective measurements to the global fit. More specifically, we consider three different scenarios with different sets of observables assumed at their final precisions. Beginning with $BR (K^{+} \to π^{+} ν \bar{ν})$ and $BR (K_{L} \to π^{0} ν \bar{ν})$ , we sequentially add $BR (K_{L} \to π^{0} e \bar{e})$ and $BR (K_{L} \to π^{0} μ \bar{μ})$ to the global fit. The evolution of the result from one scenario to the next makes a strong case for the consideration of future measurement of $BR (K_{L} \to π^{0} ℓ \bar{ℓ})$ .

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References (62)

NA62 Collaboration, Measurement of the very rare $K^{+} \to π^{+} ν \bar{ν}$ decay, J. High Energy Phys. 06 (2021) 093.
KOTO Collaboration, Search for the $K_{L} \to π^{0} ν \bar{ν}$ and $K_{L} \to π^{0} X^{0}$ decays at the J-PARC KOTO experiment, Phys. Rev. Lett. 122, 021802 (2019).
KOTO Collaboration, Study of the $K_{L} \to π^{0} ν \bar{ν}$ decay at the J-PARC KOTO experiment, Phys. Rev. Lett. 126, 121801 (2021).
NA62 Collaboration, A measurement of the $K^{+} \to π^{+} μ^{+} μ^{-}$ decay, J. High Energy Phys. 11 (2022) 011.
LHCb Collaboration, Constraints on the $K_{S}^{0} \to μ^{+} μ^{-}$ branching fraction, Phys. Rev. Lett. 125, 231801 (2020).
E787 Collaboration, Search for the decay $K^{+} \to π^{+} ν \bar{ν}$ in the momentum region $P (ϕ)$ less than 195-MeV/c, Phys. Lett. B 537, 211 (2002).
E787 Collaboration, Further search for the decay $K^{+} \to π^{+} ν \bar{ν}$ in the momentum region $P < 195 − MeV / c$ , Phys. Rev. D 70, 037102 (2004).
E949 Collaboration, Improved measurement of the $K^{+} \to π^{+} ν \bar{ν}$ branching ratio, Phys. Rev. Lett. 93, 031801 (2004).
E949 and E787 Collaborations, Measurement of the $K^{+} \to π^{+} ν \bar{ν}$ branching ratio, Phys. Rev. D 77, 052003 (2008).
E949 Collaboration, New measurement of the $K^{+} \to π^{+} ν \bar{ν}$ branching ratio, Phys. Rev. Lett. 101, 191802 (2008).
BNL-E949 Collaboration, Study of the decay $K^{+} \to π^{+} ν \bar{ν}$ in the momentum region $140 < P_{π} < 199 MeV / c$ , Phys. Rev. D 79, 092004 (2009).
E865 Collaboration, A new measurement of the properties of the rare decay $K^{+} \to π^{+} e^{+} e^{-}$ , Phys. Rev. Lett. 83, 4482 (1999).
NA48/2 Collaboration, Precise measurement of the $K^{\pm} \to π^{\pm} e^{+} e^{-}$ decay, Phys. Lett. B 677, 246 (2009).
NA48/2 Collaboration, New measurement of the $K^{\pm} \to π^{\pm} μ^{+} μ^{-}$ decay, Phys. Lett. B 697, 107 (2011).
G. D’Ambrosio, A. M. Iyer, F. Mahmoudi, and S. Neshatpour, Anatomy of kaon decays and prospects for lepton flavour universality violation, J. High Energy Phys. 09 (2022) 148.
G. D’Ambrosio, A. M. Iyer, F. Mahmoudi, and S. Neshatpour, Exploring scalar contributions with $K^{+} \to π^{+} ℓ^{+} ℓ^{-}$ , Phys. Lett. B 855, 138824 (2024).
KTeV Collaboration, Search for the rare decay $K_{L} \to π^{0} e^{+} e^{-}$ , Phys. Rev. Lett. 93, 021805 (2004).
KTEV Collaboration, Search for the decay $K_{L} \to π^{0} μ^{+} μ^{-}$ , Phys. Rev. Lett. 84, 5279 (2000).
KOTO Collaboration, KOTO II at J-PARC: Toward measurement of the branching ratio of $K_{L} \to π^{0} ν \bar{ν}$ , J. Phys. Conf. Ser. 2446, 012037 (2023).
H. Nanjo, KOTO step-2 at J-PARC toward measurement of branching ratio of $K_{L} \to π^{0} ν \bar{ν}$ , J. Phys. Conf. Ser. 2446 012037 (2022).
G. Anzivino et al., Workshop summary: Kaons@CERN 2023, Eur. Phys. J. C 84, 377 (2024).
S. Neshatpour, Short-distance physics with rare kaon decays, Symmetry 16, 946 (2024).
J-PARC, Kaons@J-PARC 2024 Workshop (2024), https://conference-indico.kek.jp/event/273/.
J. C. Swallow, New measurement of the $K^{+} \to π^{+} ν \bar{ν}$ decay by the NA62 experiment, in EP Seminar (CERN, Geneva, 2024).
NA62 Collaboration, 2023 NA62 status report to the CERN SPSC, Report No. CERN-SPSC-2023-013; SPSC-SR-326, 2023, https://cds.cern.ch/record/2856997?ln=en.
G. D’Ambrosio, G. Ecker, G. Isidori, and J. Portoles, The decays $K \to π ℓ^{+} ℓ^{-}$ beyond leading order in the chiral expansion, J. High Energy Phys. 08 (1998) 004.
G. D’Ambrosio, D. Greynat, and M. Knecht, On the amplitudes for the $C P$ -conserving $K^{\pm} (K_{S}) \to π^{\pm} (π^{0}) ℓ^{+} ℓ^{-}$ rare decay modes, J. High Energy Phys. 02 (2019) 049.
G. D’Ambrosio, D. Greynat, and M. Knecht, Matching long and short distances at order $O (α_{s})$ in the form factors for $K \to π ℓ^{+} ℓ^{-}$ , Phys. Lett. B 797, 134891 (2019).
A. Crivellin, G. D’Ambrosio, M. Hoferichter, and L. C. Tunstall, Violation of lepton flavor and lepton flavor universality in rare kaon decays, Phys. Rev. D 93, 074038 (2016).
Particle Data Group, Review of particle physics, Prog. Theor. Exp. Phys. 2020, 083C01 (2020).
G. D’Ambrosio, F. Mahmoudi, and S. Neshatpour, Beyond the standard model prospects for kaon physics at future experiments, J. High Energy Phys. 02 (2024) 166.
G. D’Ambrosio and J. Portoles, Vector meson exchange contributions to $K \to π γ γ$ and $K_{L} \to γ l^{+} l^{-}$ , Nucl. Phys. B492, 417 (1997).
G. D’Ambrosio, G. Isidori, and J. Portoles, Can we extract short distance information from $B (K_{L} \to μ^{+} μ^{-})$ ?, Phys. Lett. B 423, 385 (1998).
G. Isidori and R. Unterdorfer, On the short distance constraints from $K_{L, S} \to μ^{+} μ^{-}$ , J. High Energy Phys. 01 (2004) 009.
J.-M. Gerard, C. Smith, and S. Trine, Radiative kaon decays and the penguin contribution to the delta $I = 1 / 2$ rule, Nucl. Phys. B730, 1 (2005).
M. Hoferichter, B.-L. Hoid, and J. R. de Elvira, Improved standard-model prediction for $K_{L} \to ℓ^{+} ℓ^{-}$ , J. High Energy Phys. 04 (2024) 071.
G. D’Ambrosio and T. Kitahara, Direct $C P$ violation in $K \to μ^{+} μ^{-}$ , Phys. Rev. Lett. 119, 201802 (2017).
V. Chobanova, G. D’Ambrosio, T. Kitahara, M. Lucio Martinez, D. Martinez Santos, I. S. Fernandez, and K. Yamamoto, Probing SUSY effects in $K_{S}^{0} \to μ^{+} μ^{-}$ , J. High Energy Phys. 05 (2018) 024.
A. Dery and M. Ghosh, $K \to μ^{+} μ^{-}$ beyond the standard model, J. High Energy Phys. 03 (2022) 048.
A. Dery, M. Ghosh, Y. Grossman, and S. Schacht, $K \to μ^{+} μ^{-}$ as a clean probe of short-distance physics, J. High Energy Phys. 07 (2021) 103.
V. Chobanova, D. M. Santos, C. Prouve, and M. Romero Lamas, Fast simulation of a forward detector at 50 and 100 TeV proton-proton colliders, arXiv:2012.02692.
LHCb Collaboration, Physics case for an LHCb Upgrade II—Opportunities in flavour physics, and beyond, in the HL-LHC era, arXiv:1808.08865.
D. M. Santos (private communication).
G. Buchalla, G. D’Ambrosio, and G. Isidori, Extracting short distance physics from $K_{L, S} \to π^{0} e^{+} e^{-}$ decays, Nucl. Phys. B672, 387 (2003).
F. J. Gilman and M. B. Wise, $K \to π e^{+} e^{-}$ in the six quark model, Phys. Rev. D 21, 3150 (1980).
G. Ecker, A. Pich, and E. de Rafael, Radiative kaon decays and $C P$ violation in chiral perturbation theory, Nucl. Phys. B303, 665 (1988).
J. Flynn and L. Randall, The $C P$ conserving long distance contribution to the decay $K_{L} \to π^{0} e^{+} e^{-}$ , Phys. Lett. B 216, 221 (1989).
G. Isidori, C. Smith, and R. Unterdorfer, The rare decay $K_{L} \to π^{0} μ^{+} μ^{-}$ within the SM, Eur. Phys. J. C 36, 57 (2004).
F. Mescia, C. Smith, and S. Trine, $K_{L} \to π^{0} e^{+} e^{-}$ and $K_{L} \to π^{0} μ^{+} μ^{-}$ : A binary star on the stage of flavor physics, J. High Energy Phys. 08 (2006) 088.
F. Mescia and C. Smith, Improved estimates of rare K decay matrix-elements from Kl3 decays, Phys. Rev. D 76, 034017 (2007).
G. Ecker, A. Pich, and E. de Rafael, $K^{0} \to π^{0} γ γ$ decays in chiral perturbation theory, Phys. Lett. B 189, 363 (1987).
L. Cappiello and G. D’Ambrosio, $K_{L} \to π^{0} γ γ$ decay in the chiral effective Lagrangian, Nuovo Cimento Soc. Ital. Fis. 99A, 155 (1988).
L. Cappiello, G. D’Ambrosio, and M. Miragliuolo, Corrections to $K \to π γ γ$ from $K \to 3 π$ , Phys. Lett. B 298, 423 (1993).
A. G. Cohen, G. Ecker, and A. Pich, Unitarity and $K_{L} \to π^{0} γ γ$ , Phys. Lett. B 304, 347 (1993).
T. Morozumi and H. Iwasaki, The $C P$ conserving contribution in the decays $K_{L} \to π^{0} γ γ$ and $K_{L} \to π^{0} e^{+} e^{-}$ , Prog. Theor. Phys. 82, 371 (1989).
J. Redeker, The search for $K_{L} \to π^{0} ν \bar{ν}$ in the KOTO experiment, in ICHEP (2024), arXiv:2411.11237.
Particle Data Group, Review of particle physics, Phys. Rev. D 110, 030001 (2024).
F. Mahmoudi, superiso: A program for calculating the isospin asymmetry of $B \to K^{*} γ$ in the MSSM, Comput. Phys. Commun. 178, 745 (2008).
F. Mahmoudi, superiso v2.3: A program for calculating flavor physics observables in Supersymmetry, Comput. Phys. Commun. 180, 1579 (2009).
F. Mahmoudi, superiso v3.0, flavor physics observables calculations: Extension to NMSSM, Comput. Phys. Commun. 180, 1718 (2009).
S. Neshatpour and F. Mahmoudi, Flavour physics with superiso, Proc. Sci. TOOLS2020 (2021) 036 [arXiv:2105.03428].
S. Neshatpour and F. Mahmoudi, Flavour physics phenomenology with superiso, Proc. Sci. CompTools2021 (2022) 010 [arXiv:2207.04956].

Phys. Rev. D 111, L011701– Published 10 January, 2025

Vol. 111, Iss. 1 — 1 January 2025

Received 18 September 2024
Accepted 8 November 2024

DOI: https://doi.org/10.1103/PhysRevD.111.L011701

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Theoretical implications for a new measurement of $K_{L} \to π^{0} ℓ \bar{ℓ}$

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Theoretical implications for a new measurement of KL→π0ℓℓ¯

Abstract

Physics Subject Headings (PhySH)

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References (62)

Theoretical implications for a new measurement of $K_{L} \to π^{0} ℓ \bar{ℓ}$