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arxiv: 2605.21908 · v1 · pith:XTXOOPS3new · submitted 2026-05-21 · ✦ hep-ph · hep-ex

Semileptonic sum rules in heavy-to-light charm decays

Motoi Endo , Syuhei Iguro , Satoshi Mishima , Takeru Uchiyama , Ryoutaro Watanabe This is my paper

Pith reviewed 2026-05-22 06:09 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords semileptonic decayscharm quarkslepton flavor universalitysum rulesnew physicsD mesonLambda_c baryon
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The pith

A sum rule relates lepton-flavor universality ratios in charm semileptonic decays to within the percent level under existing new physics bounds.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines a sum rule that connects the ratios R_H^{mu e} across the decays D to pi l nu, D to rho l nu, and Lambda_c to n l nu. These ratios measure how much the muon and electron modes differ from each other. The relation is taken from analogous structures already known in bottom-hadron decays and adapted to the charm sector. Current limits on new physics from low-energy experiments and high transverse-momentum searches keep any violation of the sum rule below one percent. The resulting tight bound turns the relation into a practical cross-check for existing and future charm measurements and supplies a concrete prediction for the still-unmeasured Lambda_c ratio.

Core claim

In the c to d semileptonic transitions the three lepton-flavor universality ratios obey a linear sum rule whose maximum violation is restricted to the sub-percent level once all new-physics operators allowed by low-energy and high-p_T data are taken into account; the relation therefore supplies a consistency test for charm measurements and yields a numerical prediction for the unmeasured R_n^{mu e} in Lambda_c to n l nu.

What carries the argument

The linear sum rule among the three R_H^{mu e} ratios obtained by direct analogy with the b to c and b to u relations and applied to the c to d sector.

If this is right

  • The relation functions as an internal consistency check for charm semileptonic data.
  • Any observed violation exceeding the percent level would require either experimental inconsistency or new physics outside present bounds.
  • The sum rule supplies a definite numerical prediction for the ratio R_n^{mu e} in the Lambda_c to neutron channel.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Future higher-precision measurements of the D and Lambda_c modes could convert the sum rule into a sharper test of lepton-flavor universality.
  • If the relation is confirmed experimentally it would support the assumption that no large additional breaking mechanisms operate in these decays.
  • The same analogy-based construction might be examined in other heavy-to-light transitions where similar data exist.

Load-bearing premise

The algebraic structure that produces the sum rule in bottom decays survives in charm decays once the only sizable corrections are those from new-physics operators already bounded by other data.

What would settle it

Precise measurements of the three ratios that, after standard-model corrections, produce a combined deviation from the sum-rule prediction larger than one percent would show that the claimed bound does not hold.

Figures

Figures reproduced from arXiv: 2605.21908 by Motoi Endo, Ryoutaro Watanabe, Satoshi Mishima, Syuhei Iguro, Takeru Uchiyama.

Figure 1
Figure 1. Figure 1: Sum rule violation coefficients δkl (left) and cancellation measures ϵkl (right) for c → dµν¯ (red), b → cµν¯ (orange), b → cτν¯ (green), b → uµν¯ (cyan), and b → uτν¯ (blue). The superscript of δ, VLSL, indicates that the sum rule coefficient α is determined such that the VLSL term is eliminated. by construction. For all transitions, the coefficient αVLSL , denoted by α in [PITH_FULL_IMAGE:figures/full_f… view at source ↗
Figure 2
Figure 2. Figure 2: The α dependence of δkl (left) and ϵkl (right) for c → dµν¯ with β = 1 − α. The vertical dashed lines show the values αmn obtained from Eq. (3.7), where the corresponding δmn vanishes. are then obtained from Eq. (3.6) [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Allowed range of the residual sum rule violation [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Sum rule prediction for R µe n as a function of α. The blue shaded band shows the 1 σ range from the experimental uncertainties in R µe π and R µe ρ , including the allowed residual violation δ. The dotted contours correspond to the same range with δ = 0, and the dashed line is obtained from the central experimental inputs with δ = 0. The gray region corresponds to the range where at least one of the cance… view at source ↗
Figure 5
Figure 5. Figure 5: The α dependence of δkl and ϵkl for b → cµν (upper) and b → uµν (lower). The left and right panels show δkl and ϵkl, respectively. The vertical dashed lines indicate the values of αmn. C δkl and ϵkl for bottom-hadron decays [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p022_6.png] view at source ↗
read the original 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 $c \to d\overline{\ell}\nu$ decays, $D \to \pi\overline{\ell}\nu$, $D \to \rho\overline{\ell}\nu$, and $\Lambda_c \to n\overline{\ell}\nu$, we examine a relation among their lepton-flavor universality ratios $R_H^{\mu e}$. 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 $R_n^{\mu e}$ in $\Lambda_c \to n\overline{\ell}\nu$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript derives a sum rule relating the lepton-flavor universality ratios R_H^{μe} among the charm semileptonic decays D → π ℓ ν, D → ρ ℓ ν, and Λ_c → n ℓ ν. Motivated by analogous relations in b → c and b → u transitions, it argues that new-physics-induced deviations from the sum rule are bounded below the percent level by existing low-energy and high-p_T constraints, allowing the relation to serve as a consistency check; as an application, a numerical prediction is given for the unmeasured ratio R_n^{μe} in Λ_c → n ℓ ν.

Significance. If the central claim holds, the work supplies a modest but useful phenomenological consistency test for emerging charm semileptonic data. The explicit use of external NP bounds to limit deviations, together with the falsifiable prediction for an unmeasured observable, constitutes a clear strength; the relation is acknowledged to be less precise than its bottom-sector counterparts.

major comments (2)
  1. [§3] §3 (sum-rule derivation): the claim that the c → d sum rule inherits a structure comparable to the b → c/u relations requires an explicit operator matching or form-factor argument showing that SU(3)-breaking and 1/m_c corrections do not spoil the relation at the claimed level; without this step the percent-level NP bound cannot be directly transferred.
  2. [§4] §4 (NP constraints): the statement that low-energy and high-p_T data restrict deviations below one percent is load-bearing for the consistency-check claim, yet the manuscript provides neither the explicit list of operators considered nor the numerical inputs and error propagation that produce the <1 % figure; this must be supplied with a table or equation.
minor comments (2)
  1. [Introduction] Define R_H^{μe} explicitly at first appearance and state the kinematic range over which the sum rule is asserted to hold.
  2. [§2] Add a brief comparison table of the precision achieved in the b-sector sum rules versus the charm case to quantify the statement that the charm relation is 'less precise'.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the positive recommendation for minor revision. The comments are constructive and will improve the clarity of the presentation. We respond to each major comment below.

read point-by-point responses

  1. Referee: [§3] §3 (sum-rule derivation): the claim that the c → d sum rule inherits a structure comparable to the b → c/u relations requires an explicit operator matching or form-factor argument showing that SU(3)-breaking and 1/m_c corrections do not spoil the relation at the claimed level; without this step the percent-level NP bound cannot be directly transferred.

    Authors: We agree that an explicit discussion strengthens the argument. Although the manuscript already notes that the charm sum rule is less precise than its bottom-sector counterparts, we will revise §3 to include a concise operator-matching argument in the effective theory together with order-of-magnitude estimates of SU(3)-breaking and 1/m_c corrections. These corrections remain at the few-percent level and do not prevent transferring the existing NP bounds at the percent level for the purpose of a consistency check. revision: yes

  2. Referee: [§4] §4 (NP constraints): the statement that low-energy and high-p_T data restrict deviations below one percent is load-bearing for the consistency-check claim, yet the manuscript provides neither the explicit list of operators considered nor the numerical inputs and error propagation that produce the <1 % figure; this must be supplied with a table or equation.

    Authors: We acknowledge that the supporting details for the <1% bound should be presented more transparently. In the revised version we will add a table in §4 that enumerates the relevant operators, cites the low-energy and high-p_T experimental inputs, and shows the error propagation leading to the quoted bound. This will make the numerical claim fully reproducible while preserving the overall conclusion. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses external NP bounds and analogous relations

full rationale

The paper motivates a sum rule relating R_H^{μe} ratios in D→π, D→ρ, and Λ_c→n decays from b→c/u analogs, then invokes external low-energy and high-p_T constraints to bound NP-induced deviations below the percent level. The prediction for the unmeasured R_n^{μe} follows directly from applying this externally bounded relation as a consistency check. No self-definitional equations, fitted parameters renamed as predictions, or load-bearing self-citations appear in the abstract or summary; the central claim remains independent and falsifiable against external data.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The claim rests on the transferability of sum-rule relations from bottom to charm decays and on the sufficiency of existing low-energy and collider constraints to bound new-physics contributions; no free parameters or new entities are introduced in the abstract.

axioms (2)
  • domain assumption Sum rules derived for b to c and b to u transitions retain analogous structure when applied to c to d transitions.
    The abstract motivates the charm relation by direct analogy to bottom-hadron sum rules.
  • domain assumption Deviations from the sum rule arise only from new-physics operators already constrained by low-energy and high-p_T data.
    The abstract states that these constraints restrict deviations to below the percent level.

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discussion (0)

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Reference graph

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