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Belle II constraints on the nonminimal universal extra dimensional model

Department of Physics, Kalna College, Affiliated to The Burdwan University, Near Old Bus Stand, Kalna, West Bengal 713409, India

^*Contact author: avirup.cu@gmail.com

Phys. Rev. D 113, 095027 – Published 19 May, 2026

DOI: https://doi.org/10.1103/8h4g-rs72

Abstract

Recent measurements by the Belle II Collaboration report a branching ratio for the decay $B^{+} \to K^{+} ν \bar{ν}$ with a $3.5 σ$ significance and deviating by $2.7 σ$ from Standard Model expectation. In this article, we interpret this experimental result through the lens of a nonminimal universal extra dimensional model, where the mass profiles and interactions among various Kaluza-Klein states differ remarkably from those in the minimal scenario. Our analysis indicates that, according to the model’s parameters, the lower limit on the inverse of the compactification radius has been elevated to approximately 900 GeV. In contrast, conducting the same analysis within the model variant in which all boundary terms are nullified does not permit the determination of a lower bound on the inverse compactification radius.

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References (100)

G. Aad et al. (ATLAS Collaboration), Observation of a new particle in the search for the standard model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716, 1 (2012).
S. Chatrchyan et al. (CMS Collaboration), Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716, 30 (2012).
I. Adachi et al. (Belle-II Collaboration), Evidence for $B^{+} \to K^{+} ν \bar{ν}$ decays, Phys. Rev. D 109, 112006 (2024).
L. Allwicher, D. Becirevic, G. Piazza, S. Rosauro-Alcaraz, and O. Sumensari, Understanding the first measurement of $B (B \to K ν \bar{ν})$ , Phys. Lett. B 848, 138411 (2024).
R. Bause, H. Gisbert, and G. Hiller, Implications of an enhanced $B \to K ν \bar{ν}$ branching ratio, Phys. Rev. D 109, 015006 (2024).
W. Altmannshofer, A. Crivellin, H. Haigh, G. Inguglia, and J. Martin Camalich, Light new physics in $B K (*) ν \bar{ν}$ ?, Phys. Rev. D 109, 075008 (2024).
D. McKeen, J. N. Ng, and D. Tuckler, Higgs portal interpretation of the Belle II $B^{+} \to K^{+} ν ν$ measurement, Phys. Rev. D 109, 075006 (2024).
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).
E. Gabrielli, L. Marzola, K. Müürsepp, and M. Raidal, Explaining the $B^{+} \to K^{+} ν \bar{ν}$ excess via a massless dark photon, Eur. Phys. J. C 84, 460 (2024).
T. Felkl, A. Giri, R. Mohanta, and M. A. Schmidt, When energy goes missing: New physics in $b \to s ν ν$ with sterile neutrinos, Eur. Phys. J. C 83, 1135 (2023).
Z. S. Wang, H. K. Dreiner, and J. Y. Günther, The decay $B \to K + ν + \bar{ν}$ at Belle II and a massless bino in R-parity-violating supersymmetry, Eur. Phys. J. C 85, 66 (2025).
X.-G. He, X.-D. Ma, and G. Valencia, Revisiting models that enhance $B^{+} \to K^{+} ν \bar{ν}$ in light of the new Belle II measurement, Phys. Rev. D 109, 075019 (2024).
A. Datta, D. Marfatia, and L. Mukherjee, $B \to K ν \bar{ν}$ , MiniBooNE and muon $g - 2$ anomalies from a dark sector, Phys. Rev. D 109, L031701 (2024).
S.-Y. Ho, J. Kim, and P. Ko, Recent $B^{+} \to K^{+} ν \bar{ν}$ excess and muon $g - 2$ illuminating light dark sector with Higgs portal, Phys. Rev. D 111, 055029 (2025).
F.-Z. Chen, Q. Wen, and F. Xu, Correlating $B \to K^{(*)} ν \bar{ν}$ and flavor anomalies in SMEFT, Eur. Phys. J. C 84, 1012 (2024).
B.-F. Hou, X.-Q. Li, M. Shen, Y.-D. Yang, and X.-B. Yuan, Deciphering the Belle II data on $B \to K ν \bar{ν}$ decay in the (dark) SMEFT with minimal flavour violation, J. High Energy Phys. 06 (2024) 172.
X.-G. He, X.-D. Ma, M. A. Schmidt, G. Valencia, and R. R. Volkas, Scalar dark matter explanation of the excess in the Belle II $B^{+} \to K^{+} +$ invisible measurement, J. High Energy Phys. 07 (2024) 168.
P. D. Bolton, S. Fajfer, J. F. Kamenik, and M. Novoa-Brunet, Signatures of light new particles in $B \to K (*) E_{m i s s}$ , Phys. Rev. D 110, 055001 (2024).
A. J. Buras, J. Harz, and M. A. Mojahed, Disentangling new physics in $K \to π ν \bar{ν}$ and $B \to K (K^{*}) ν \bar{ν}$ observables, J. High Energy Phys. 10 (2024) 087.
W. Altmannshofer and S. Roy, Joint explanation of the $B \to π K$ puzzle and the $B \to K ν \bar{ν}$ excess, Phys. Rev. D 111, 075029 (2025).
D. Marzocca, M. Nardecchia, A. Stanzione, and C. Toni, Implications of $B \to K ν \bar{ν}$ under rank-one flavor violation hypothesis, Eur. Phys. J. C 84, 1217 (2024).
Q.-Y. Hu, Are the new particles heavy or light in $b \to s E_{miss}$ ?, Eur. Phys. J. C 85, 556 (2025).
L. Allwicher, M. Bordone, G. Isidori, G. Piazza, and A. Stanzione, Probing third-generation new physics with $K \to π ν \bar{ν}$ and $B \to K (*) ν \bar{ν}$ , Phys. Lett. B 861, 139295 (2025).
A. Berezhnoy and D. Melikhov, $B \to K^{*} M_{X}$ vs $B \to K M_{X}$ as a probe of a scalar-mediator dark matter scenario, Europhys. Lett. 145, 14001 (2024).
L. Calibbi, T. Li, L. Mukherjee, and M. A. Schmidt, Is dark matter the origin of the $B \to K ν \bar{ν}$ excess at Belle II?, Phys. Rev. D 112, 075020 (2025).
J.-P. Lee, New physics effects in $R (K^{(*)})$ , $B_{s} \to μ^{+} μ^{-}$ , and $B^{+} \to K^{+} ν \bar{ν}$ , arXiv:2502.06370.
P. Athron, R. Martinez, and C. Sierra, B meson anomalies and large $B^{+} \to K^{+} ν \bar{ν}$ in non-universal ${U (1)}^{'}$ models, J. High Energy Phys. 02 (2024) 121.
S. Rosauro-Alcaraz and L. P. S. Leal, Disentangling left and right-handed neutrino effects in $B \to K^{(*)} ν ν$ , Eur. Phys. J. C 84, 795 (2024).
P. D. Bolton, S. Fajfer, J. F. Kamenik, and M. Novoa-Brunet, Impact of new invisible particles on $B \to K (*) Emiss$ observables, Phys. Rev. D 112, 035010 (2025).
T. M. Aliev, A. Elpe, L. Selbuz, and I. Turan, Explaining Belle data on $B \to K (*) ν \bar{ν}$ decays via dark Z resonances, Phys. Rev. D 112, 015025 (2025).
J. Fuentes-Martín, G. Isidori, M. König, and N. Selimović, Vector leptoquarks beyond tree level III: Vector-like fermions and flavor-changing transitions, Phys. Rev. D 102, 115015 (2020).
G. R. Dvali, G. Gabadadze, M. Kolanovic, and F. Nitti, The power of brane induced gravity, Phys. Rev. D 64, 084004 (2001).
M. Carena, T. M. P. Tait, and C. E. M. Wagner, Branes and orbifolds are opaque, Acta Phys. Pol. B 33, 2355 (2002).
F. del Aguila, M. Perez-Victoria, and J. Santiago, Bulk fields with general brane kinetic terms, J. High Energy Phys. 02 (2003) 051.
F. del Aguila, M. Perez-Victoria, and J. Santiago, Some consequences of brane kinetic terms for bulk fermions, in 38th Rencontres De Moriond on Electroweak Interactions and Unified Theories (2003), arXiv:hep-ph/0305119.
F. del Aguila, M. Perez-Victoria, and J. Santiago, Physics of brane kinetic terms, Acta Phys. Pol. B 34, 5511 (2003).
C. Schwinn, Higgsless fermion masses and unitarity, Phys. Rev. D 69, 116005 (2004).
T. Flacke, A. Menon, and D. J. Phalen, Non-minimal universal extra dimensions, Phys. Rev. D 79, 056009 (2009).
A. Datta, U. K. Dey, A. Shaw, and A. Raychaudhuri, Universal extra-dimensional models with boundary localized kinetic terms: Probing at the LHC, Phys. Rev. D 87, 076002 (2013).
T. Flacke, K. Kong, and S. C. Park, Phenomenology of universal extra dimensions with bulk-masses and brane-localized terms, J. High Energy Phys. 05 (2013) 111.
T. Appelquist, H.-C. Cheng, and B. A. Dobrescu, Bounds on universal extra dimensions, Phys. Rev. D 64, 035002 (2001).
G. Servant and T. M. P. Tait, Elastic scattering and direct detection of Kaluza-Klein dark matter, New J. Phys. 4, 99 (2002).
G. Servant and T. M. P. Tait, Is the lightest Kaluza-Klein particle a viable dark matter candidate?, Nucl. Phys. B650, 391 (2003).
H.-C. Cheng, J. L. Feng, and K. T. Matchev, Kaluza-Klein dark matter, Phys. Rev. Lett. 89, 211301 (2002).
D. Majumdar, Detection rates for Kaluza-Klein dark matter, Phys. Rev. D 67, 095010 (2003).
F. Burnell and G. D. Kribs, The abundance of Kaluza-Klein dark matter with coannihilation, Phys. Rev. D 73, 015001 (2006).
K. Kong and K. T. Matchev, Precise calculation of the relic density of Kaluza-Klein dark matter in universal extra dimensions, J. High Energy Phys. 01 (2006) 038.
M. Kakizaki, S. Matsumoto, and M. Senami, Relic abundance of dark matter in the minimal universal extra dimension model, Phys. Rev. D 74, 023504 (2006).
G. Belanger, M. Kakizaki, and A. Pukhov, Dark matter in UED: The role of the second KK level, J. Cosmol. Astropart. Phys. 02 (2011) 009.
K. R. Dienes, E. Dudas, and T. Gherghetta, Extra space-time dimensions and unification, Phys. Lett. B 436, 55 (1998).
K. R. Dienes, E. Dudas, and T. Gherghetta, Grand unification at intermediate mass scales through extra dimensions, Nucl. Phys. B537, 47 (1999).
G. Bhattacharyya, A. Datta, S. K. Majee, and A. Raychaudhuri, Power law blitzkrieg in universal extra dimension scenarios, Nucl. Phys. B760, 117 (2007).
K. Hsieh, R. N. Mohapatra, and S. Nasri, Dark matter in universal extra dimension models: Kaluza-Klein photon and right-handed neutrino admixture, Phys. Rev. D 74, 066004 (2006).
Y. Fujimoto, K. Nishiwaki, M. Sakamoto, and R. Takahashi, Realization of lepton masses and mixing angles from point interactions in an extra dimension, J. High Energy Phys. 10 (2014) 191.
G.-Y. Huang, K. Kong, and S. C. Park, Bounds on the fermion-bulk masses in models with universal extra dimensions, J. High Energy Phys. 06 (2012) 099.
H.-C. Cheng, K. T. Matchev, and M. Schmaltz, Radiative corrections to Kaluza-Klein masses, Phys. Rev. D 66, 036005 (2002).
T. Flacke, K. Kong, and S. C. Park, 126 GeV Higgs in next-to-minimal universal extra dimensions, Phys. Lett. B 728, 262 (2014).
J. Bonnevier, H. Melbeus, A. Merle, and T. Ohlsson, Monoenergetic gamma-rays from non-minimal Kaluza-Klein dark matter annihilations, Phys. Rev. D 85, 043524 (2012).
A. Datta, U. K. Dey, A. Raychaudhuri, and A. Shaw, Boundary localized terms in universal extra-dimensional models through a dark matter perspective, Phys. Rev. D 88, 016011 (2013).
U. K. Dey and T. S. Ray, Constraining minimal and nonminimal universal extra dimension models with Higgs couplings, Phys. Rev. D 88, 056016 (2013).
A. Datta, K. Nishiwaki, and S. Niyogi, Non-minimal universal extra dimensions: The strongly interacting sector at the Large Hadron Collider, J. High Energy Phys. 11 (2012) 154.
A. Datta, K. Nishiwaki, and S. Niyogi, Non-minimal universal extra dimensions with brane local terms: The top quark sector, J. High Energy Phys. 01 (2014) 104.
A. Datta, A. Raychaudhuri, and A. Shaw, LHC limits on KK-parity non-conservation in the strong sector of universal extra-dimension models, Phys. Lett. B 730, 42 (2014).
A. Shaw, KK-parity non-conservation in UED confronts LHC data, Eur. Phys. J. C 75, 33 (2015).
A. Shaw, Status of exclusion limits of the KK-parity non-conserving resonance production with updated 13 TeV LHC, Acta Phys. Pol. B 49, 1421 (2018).
N. Ganguly and A. Datta, Exploring non minimal universal extra dimensional model at the LHC, J. High Energy Phys. 10 (2018) 072.
T. Jha and A. Datta, $Z \to b \bar{b}$ in non-minimal universal extra dimensional model, J. High Energy Phys. 03 (2015) 012.
A. Datta and A. Shaw, Nonminimal universal extra dimensional model confronts $B_{s} \to μ^{+} μ^{-}$ , Phys. Rev. D 93, 055048 (2016).
A. Datta and A. Shaw, Effects of non-minimal universal extra dimension on $B \to X_{s} γ$ , Phys. Rev. D 95, 015033 (2017).
A. Shaw, Looking for $B \to X_{s} ℓ^{+} ℓ^{-}$ in a nonminimal universal extra dimensional model, Phys. Rev. D 99, 115030 (2019).
A. Biswas, A. Shaw, and S. K. Patra, $R (D^{(*)})$ anomalies in light of a nonminimal universal extra dimension, Phys. Rev. D 97, 035019 (2018).
S. Dasgupta, U. K. Dey, T. Jha, and T. S. Ray, Status of a flavor-maximal nonminimal universal extra dimension model, Phys. Rev. D 98, 055006 (2018).
J.-P. Lee, $B$ anomalies in the nonminimal universal extra dimension model, Phys. Rev. D 100, 075005 (2019).
U. K. Dey and T. Jha, Rare top decays in minimal and nonminimal universal extra dimension models, Phys. Rev. D 94, 056011 (2016).
C.-W. Chiang, U. K. Dey, and T. Jha, $t \to c g$ and $t \to c Z$ in universal extra-dimensional models, Eur. Phys. J. Plus 134, 210 (2019).
A. Shaw, The impact of nonminimal universal extra dimensional model on $Δ B = 2$ transitions, Eur. Phys. J. C 81, 137 (2021).
T. Jha, Unitarity constraints on non-minimal universal extra dimensional model, J. Phys. G 45, 115002 (2018).
A. Datta and A. Shaw, A note on gauge-fixing in the electroweak sector of non-minimal UED, Mod. Phys. Lett. A 31, 1650181 (2016).
P. Colangelo, F. De Fazio, P. Santorelli, and E. Scrimieri, Rare $B \to K^{(*)}$ neutrino anti-neutrino decays at $B$ factories, Phys. Lett. B 395, 339 (1997).
W. Altmannshofer, A. J. Buras, D. M. Straub, and M. Wick, New strategies for new physics search in $B \to K^{*} ν \bar{ν}$ , $B \to K ν \bar{ν}$ and $B \to X_{s} ν \bar{ν}$ decays, J. High Energy Phys. 04 (2009) 022.
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.
A. J. Buras, M. Spranger, and A. Weiler, The impact of universal extra dimensions on the unitarity triangle and rare K and B decays, Nucl. Phys. B660, 225 (2003).
G. Buchalla and A. J. Buras, QCD corrections to rare K and B decays for arbitrary top quark mass, Nucl. Phys. B400, 225 (1993).
G. Buchalla and A. J. Buras, The rare decays $K \to π ν \bar{ν}$ , $B \to X ν \bar{ν}$ and $B \to l^{+} l^{-}$ : An update, Nucl. Phys. B548, 309 (1999).
M. Misiak and J. Urban, QCD corrections to FCNC decays mediated by Z penguins and W boxes, Phys. Lett. B 451, 161 (1999).
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).
S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
G. Buchalla, A. J. Buras, and M. E. Lautenbacher, Weak decays beyond leading logarithms, Rev. Mod. Phys. 68, 1125 (1996).
J. Grygier et al. (Belle Collaboration), Search for $B \to h ν \bar{ν}$ decays with semileptonic tagging at Belle, Phys. Rev. D 96, 091101 (2017).
A. Datta and S. Raychaudhuri, Vacuum stability constraints and LHC searches for a model with a universal extra dimension, Phys. Rev. D 87, 035018 (2013).
P. Dey and G. Bhattacharyya, A comparison of ultraviolet sensitivities in universal, nonuniversal, and split extra dimensional models, Phys. Rev. D 70, 116012 (2004).
D. M. Straub, flavio: A python package for flavour and precision phenomenology in the standard model and beyond, arXiv:1810.08132.
Y. S. Amhis et al. (HFLAV Collaboration), Averages of b-hadron, c-hadron, and $τ$ -lepton properties as of 2021, Phys. Rev. D 107, 052008 (2023).
J. P. Lees et al. (BABAR Collaboration), Measurement of the $B \to X_{s} l^{+} l^{-}$ branching fraction and search for direct $C P$ violation from a sum of exclusive final states, Phys. Rev. Lett. 112, 211802 (2014).
N. Deutschmann, T. Flacke, and J. S. Kim, Current LHC constraints on minimal universal extra dimensions, Phys. Lett. B 771, 515 (2017).
P. Ball and R. Zwicky, New results on $B \to π, K, η$ decay formfactors from light-cone sum rules, Phys. Rev. D 71, 014015 (2005).
M. Bartsch, M. Beylich, G. Buchalla, and D. N. Gao, Precision flavour physics with $B \to K ν \bar{ν}$ and $B \to K l^{+} l^{-}$ , J. High Energy Phys. 11 (2009) 011.
Y. Aoki et al. (Flavour Lattice Averaging Group (FLAG) Collaboration), FLAG review 2021, Eur. Phys. J. C 82, 869 (2022).
W. Altmannshofer, P. Ball, A. Bharucha, A. J. Buras, D. M. Straub, and M. Wick, Symmetries and asymmetries of $B \to K^{*} μ^{+} μ^{-}$ decays in the standard model and beyond, J. High Energy Phys. 01 (2009) 019.
A. Bharucha, D. M. Straub, and R. Zwicky, $B \to V ℓ^{+} ℓ^{-}$ in the standard model from light-cone sum rules, J. High Energy Phys. 08 (2016) 098.

Phys. Rev. D 113, 095027– Published 19 May, 2026

Vol. 113, Iss. 9 — 1 May 2026

Received 13 October 2025
Accepted 8 May 2026

DOI: https://doi.org/10.1103/8h4g-rs72

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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Belle II constraints on the nonminimal universal extra dimensional model

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