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Semileptonic sum rules in heavy-to-light charm decays

Motoi Endo ^1,2, Syuhei Iguro ^3,4, Satoshi Mishima ⁵, Takeru Uchiyama ⁶, and Ryoutaro Watanabe ⁷

¹KEK Theory Center, IPNS, KEK, Tsukuba 305–0801, Japan
²Graduate Institute for Advanced Studies, SOKENDAI, Tsukuba, Ibaraki 305–0801, Japan
³Institute for Advanced Research (IAR), Nagoya University, Nagoya 464–8601, Japan
⁴Kobayashi-Maskawa Institute (KMI) for the Origin of Particles and the Universe, Nagoya University, Nagoya 464–8602, Japan
⁵Department of Liberal Arts, Saitama Medical University, Moroyama, Saitama 350-0495, Japan
⁶Department of Physics, Nagoya University, Nagoya 464-8602, Japan
⁷Institute of Particle Physics and Key Laboratory of Quark and Lepton Physics (MOE), Central China Normal University, Wuhan, Hubei 430079, China

Phys. Rev. D 114, 095004 – Published 2 November, 2026

DOI: https://doi.org/10.1103/vdtw-k6fb

Abstract

We investigate semileptonic sum rules in heavy-to-light charm decays, motivated by analogous relations in $b \to c$ and $b \to u$ transitions. Focusing on the $c \to d \bar{ℓ} ν$ decays, $D \to π \bar{ℓ} ν$ , $D \to ρ \bar{ℓ} ν$ , and $Λ_{c} \to n \bar{ℓ} ν$ , we examine a relation among their lepton-flavor universality ratios $R_{H}^{μ e}$ . Although the charm sum rule is less precise than the relations in bottom-hadron decays, current low-energy and high- $p_{T}$ constraints on new physics restrict the actual deviation from the relation to below the percent level. The relation can therefore provide a useful consistency check of charm semileptonic measurements. As an application, we derive a prediction for the yet-unmeasured ratio $R_{n}^{μ e}$ in $Λ_{c} \to n \bar{ℓ} ν$ .

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References (58)

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Phys. Rev. D 114, 095004– Published 2 November, 2026

Vol. 114, Iss. 9 — 1 November 2026

Received 27 May 2026
Accepted 24 September 2026

DOI: https://doi.org/10.1103/vdtw-k6fb

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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Semileptonic sum rules in heavy-to-light charm decays

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