Eur. Phys. J. C (2025) 85: 1269
https://doi.org/10.1140/epjc/s10052-025-14881-9

Regular Article - Theoretical Physics

Investigating three body charm hadron decays with missing energy within non-minimal SU(5)

Department of Physics, Faculty of Engineering and Natural Sciences, Süleyman Demirel University, 32260, Isparta, Turkey

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Received: 28 February 2025
Accepted: 1 October 2025
Published online: 8 November 2025

Abstract

In the Standard Model, the $c\to u\nu \overline{\nu }$ transition arises only at the one-loop level, leading to extremely suppressed branching ratios for the corresponding three-body decays of charmed hadrons. This suppression motivates the search for possible enhancements from physics beyond the Standard Model. In this work, we study the contributions to the $c\to u\nu \overline{\nu }$ transition from the $R_2^{a2}$ scalar leptoquark predicted in the Non-Minimal SU(5) GUT framework. We derive constraints on the model parameters using the recent BESIII results on $D^0\to {\pi }^0\nu \overline{\nu }$ and available data on $D^0$–${\overline{D}}^0$ mixing. Additional bounds from direct LHC searches for scalar leptoquarks, lepton flavor violation processes, and the LHCb upper limit on $\mathcal{B}(D^0\to {\mu }^{+}{\mu }^{-})$ are also taken into account. After imposing all constraints, we show that the branching ratios of the three-body charmed hadron decays with missing energy can be enhanced up to $\mathcal{O}({10}^{-6})$.