Open Access

Using $B^{+} \to K^{+} ν \bar{ν}$ to search for the QCD axion

Merna Abumusabh ^1,*, Giulio Dujany ^1,†, Diego Guadagnoli ^2,‡, Axel Iohner ^2,§, and Claudio Toni ^2,∥

¹IPHC, Université de Strasbourg et CNRS, 67200 Strasbourg, France
²LAPTh, Université Savoie Mont-Blanc et CNRS, 74941 Annecy, France

^*Contact author: merna.abumusabh@iphc.cnrs.fr
^†Contact author: giulio.dujany@iphc.cnrs.fr
^‡Contact author: diego.guadagnoli@lapth.cnrs.fr
^§Contact author: axel.iohner@lapth.cnrs.fr
^∥Contact author: claudio.toni@lapth.cnrs.fr

Phys. Rev. Research 8, 023129 – Published 7 May, 2026

DOI: https://doi.org/10.1103/nw6q-6nhz

Abstract

We introduce a model-independent framework to reinterpret Belle II results using only public data, analytically reconstructing the mapping between true and reconstructed kinematic variables within the statistically dominant Inclusive Tagging Analysis. This enables rare-decay measurements to probe light invisible particles—such as the QCD axion or axionlike particles, collectively denoted by $a$ —without relying on internal simulations. Applying the method to $B^{+} \to K^{+} ν \bar{ν}$ yields the strongest bound on the branching fraction for $B^{+} \to K^{+} a$ , improving existing limits by about a factor of 9 and constraining the axion's fundamental flavor-changing coupling to $b$ and $s$ quarks. The approach establishes $B^{+} \to K^{+} ν \bar{ν}$ as a dual probe—simultaneously testing short-distance new physics and light invisible states, the two probes working independently to an excellent approximation—and provides a general strategy for model-independent reinterpretation of collider data.

Physics Subject Headings (PhySH)

Article Text

References (53)

I. G. Irastorza and J. Redondo, New experimental approaches in the search for axion-like particles, Prog. Part. Nucl. Phys. 102, 89 (2018).
G. Lanfranchi, M. Pospelov, and P. Schuster, The search for feebly interacting particles, Annu. Rev. Nucl. Part. Sci. 71, 279 (2021).
P. Sikivie, Invisible axion search methods, Rev. Mod. Phys. 93, 015004 (2021).
G. G. Raffelt, Astrophysical methods to constrain axions and other novel particle phenomena, Phys. Rep. 198, 1 (1990).
G. G. Raffelt, Astrophysical axion bounds, Lect. Notes Phys. 741, 51 (2008).
A. Caputo and G. Raffelt, Astrophysical axion bounds: The 2024 edition, in 1st Training School of the COST Action COSMIC WISPers (CA21106) (2024), PoS (COSMICWISPers), 041 (2024).
D. J. E. Marsh, Axion cosmology, Phys. Rep. 643, 1 (2016).
J. E. Kim and G. Carosi, Axions and the strong $CP$ problem, Rev. Mod. Phys. 82, 557 (2010); 91, 049902(E) (2019).
L. Di Luzio, M. Giannotti, E. Nardi, and L. Visinelli, The landscape of QCD axion models, Phys. Rep. 870, 1 (2020).
K. Choi, S. H. Im, and C. Sub Shin, Recent progress in the physics of axions and axion-like particles, Annu. Rev. Nucl. Part. Sci. 71, 225 (2021).
J. E. Kim, Weak interaction singlet and strong $CP$ invariance, Phys. Rev. Lett. 43, 103 (1979).
M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, Can confinement ensure natural $CP$ invariance of strong interactions? Nucl. Phys. B 166, 493 (1980).
M. Dine, W. Fischler, and M. Srednicki, A simple solution to the strong $CP$ problem with a harmless axion, Phys. Lett. B 104, 199 (1981).
A. R. Zhitnitsky, On possible suppression of the axion hadron interactions (in Russian), Sov. J. Nucl. Phys. 31, 260 (1980).
R. D. Peccei and H. R. Quinn, $CP$ conservation in the presence of instantons, Phys. Rev. Lett. 38, 1440 (1977).
R. D. Peccei and H. R. Quinn, Constraints imposed by $CP$ conservation in the presence of instantons, Phys. Rev. D 16, 1791 (1977).
S. Weinberg, A new light boson? Phys. Rev. Lett. 40, 223 (1978).
F. Wilczek, Problem of strong $P$ and $T$ invariance in the presence of instantons, Phys. Rev. Lett. 40, 279 (1978).
L. Ubaldi, Effects of theta on the deuteron binding energy and the triple-alpha process, Phys. Rev. D 81, 025011 (2010).
M. Dine, L. Stephenson Haskins, L. Ubaldi, and D. Xu, Some remarks on anthropic approaches to the strong $CP$ problem, J. High Energy Phys. 05 (2018) 171.
J. Preskill, M. B. Wise, and F. Wilczek, Cosmology of the invisible axion, Phys. Lett. B 120, 127 (1983).
L. F. Abbott and P. Sikivie, A cosmological bound on the invisible axion, Phys. Lett. B 120, 133 (1983).
M. Dine and W. Fischler, The not so harmless axion, Phys. Lett. B 120, 137 (1983).
T. Abe et al. (Belle-II), Belle II technical design report, arXiv:1011.0352.
The spread, or bite, around these momenta is tiny and completely negligible for the purposes of this paper.
The charge-conjugate mode is assumed to be included throughout.
H. Georgi, D. B. Kaplan, and L. Randall, Manifesting the invisible axion at low-energies, Phys. Lett. B 169, 73 (1986).
The sign difference in the $f_{a}$ -defining $a G \tilde{G}$ term in Eq. ( (1) with respect to Ref. [9] arises from our use of opposite $ε$ -tensor conventions.
N. Gubernari, M. Reboud, D. van Dyk, and J. Virto, Dispersive analysis of $B \to K^{(*)}$ and $B_{s} \to ϕ$ form factors, J. High Energy Phys. 12 (2023) 153; 01 (2025) 125.
S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
P. D. Bolton, S. Fajfer, J. F. Kamenik, and M. Novoa-Brunet, Signatures of light new particles in $B \to K^{(*)} E_{miss}$ , Phys. Rev. D 110, 055001 (2024); 111, 039903(E) (2025).
I. Adachi et al. (Belle-II), Evidence for $B^{+} \to K^{+} ν \bar{ν}$ decays, Phys. Rev. D 109, 112006 (2024).
M. T. Prim et al. (Belle), Search for $B^{+} \to μ^{+} ν_{μ}$ and $B^{+} \to μ^{+} N$ with inclusive tagging, Phys. Rev. D 101, 032007 (2020).
F. Abudinén et al. (Belle-II), Search for $B^{+} \to K^{+} ν \bar{ν}$ decays using an inclusive tagging method at Belle II, Phys. Rev. Lett. 127, 181802 (2021).
W. G. Parrott, C. Bouchard, and C. T. H. Davies (HPQCD), Standard Model predictions for $B \to K ℓ + ℓ -, B \to K ℓ 1 - ℓ 2 +$ and $B \to K ν \bar{ν}$ using form factors from $N_{f} = 2 + 1 + 1$ lattice QCD, Phys. Rev. D 107, 014511 (2023); HPQCD), 107, 119903(E) (2023).
D. Bečirević, G. Piazza, and O. Sumensari, Revisiting $B \to K^{(*)} ν \bar{ν}$ decays in the Standard Model and beyond, Eur. Phys. J. C 83, 252 (2023).
A. J. Buras, J. Girrbach-Noe, C. Niehoff, and D. M. Straub, $B \to K^{(*)} ν \bar{ν}$ decays in the Standard Model and beyond, J. High Energy Phys. 02 (2015) 184.
J. Brod, M. Gorbahn, and E. Stamou, Two-loop electroweak corrections for the $K \to π ν \bar{ν}$ decays, Phys. Rev. D 83, 034030 (2011).
V. Bertacchi et al. (Belle II Tracking Group), Track finding at Belle II, Comput. Phys. Commun. 259, 107610 (2021).
The below-2% $N_{B}$ error has a negligible impact on our analysis, because $n_{ν \bar{ν}, bkg}^{i}$ have an error approaching 10%.
K. Fridell, M. Ghosh, T. Okui, and K. Tobioka, Decoding the $B \to K ν ν$ excess at Belle II: Kinematics, operators, and masses, Phys. Rev. D 109, 115006 (2024).
P. D. Bolton, S. Fajfer, J. F. Kamenik, and M. Novoa-Brunet, Impact of new invisible particles on $B \to K^{(*)} E_{miss}$ observables, Phys. Rev. D 112, 035010 (2025).
C. Praz, Search for B → $K v v$ decays with a machine learning method at the Belle II experiment, Ph.D. thesis, Department of Mathematics, University of Hamburg, Hamburg, 2022.
A. J. Buras, J. Girrbach, D. Guadagnoli, and G. Isidori, On the Standard Model prediction for $B (B_{s, d} \to μ^{+} μ^{-})$ , Eur. Phys. J. C 72, 2172 (2012).
The suppression arises because the lightest charged emitter is the $K^{+}$ , which makes the exponent $b$ in $\begin{matrix} B (B \to K ν \bar{ν} (+ n γ)) = {(\frac{2 Δ E}{m_{B}})}^{\frac{α}{4 π} b} B (B \to K ν \bar{ν}), \end{matrix}$ parametrically small. Here, $Δ E$ denotes the minimal photon energy in the $B$ rest frame required for detectability—a “theoretical” scale usually proxied by the $\sqrt{q^{2}}$ resolution.
T. Keck et al., The full event interpretation: An exclusive tagging algorithm for the Belle II experiment, Comput. Softw. Big Sci. 3, 6 (2019).
The dominant effect is that a few events with small positive $q^{2}$ migrate to slightly negative reconstructed values, thus shifting between adjacent bins of the Belle II spectrum.
Reference [53] obtains a bound slightly above $1 \times 10^{- 6}$ for the branching ratio in the low- $m_{a}$ regime, based on a projected dataset of 0.5 ${ab}^{- 1}$ . Since Ref. [53] predates Ref. [32], a detailed numerical comparison of the limits is not straightforward. We note, however, that we achieve a very similar sensitivity—see results in Table 1—using $0.362 {ab}^{- 1}$ of actual data, dominated by the ITA selection.
W. Altmannshofer, A. Crivellin, H. Haigh, G. Inguglia, and J. Martin Camalich, Light new physics in $B \to K^{(} *) ν \bar{ν}$ ? Phys. Rev. D 109, 075008 (2024).
J. Alda, M. Fuentes Zamoro, L. Merlo, X. Ponce Díaz, and S. Rigolin, Comprehensive ALP searches in meson decays, arXiv:2507.19578.
M. Cavan-Piton, D. Guadagnoli, A. Iohner, D. Martinez Santos, and L. Vittorio, Probing QCD axions or axion-like particles in three-body $K$ decays, J. High Energy Phys. 06 (2025) 039.
J. M. Camalich, M. Pospelov, P. N. H. Vuong, R. Ziegler, and J. Zupan, Quark flavor phenomenology of the QCD axion, Phys. Rev. D 102, 015023 (2020).
T. Ferber, A. Filimonova, R. Schäfer, and S. Westhoff, Displaced or invisible? ALPs from B decays at Belle II, J. High Energy Phys. 04 (2023) 131.

Phys. Rev. Research 8, 023129– Published 7 May, 2026

Vol. 8, Iss. 2 — May - July 2026

Received 14 November 2025
Accepted 6 April 2026

DOI: https://doi.org/10.1103/nw6q-6nhz

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.

Published by the American Physical Society

Physical Review Research

Reuse & Permissions

Export citation

Export citation

Using $B^{+} \to K^{+} ν \bar{ν}$ to search for the QCD axion

Abstract

Physics Subject Headings (PhySH)

Article Text

References (53)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation

Using B+→K+νν¯ to search for the QCD axion

Abstract

Physics Subject Headings (PhySH)

Article Text

References (53)

Using $B^{+} \to K^{+} ν \bar{ν}$ to search for the QCD axion