arxiv: 2604.27970 · v1 · submitted 2026-04-30 · ✦ hep-ph · hep-ex

Recognition: unknown

b to c semileptonic sum rule: orbitally excited hadrons

Motoi Endo , Syuhei Iguro , Satoshi Mishima

Authors on Pith no claims yet

Pith reviewed 2026-05-07 05:00 UTC · model grok-4.3

classification ✦ hep-ph hep-ex

keywords semileptonic decaysb to c transitionsheavy quark symmetrysum rulesorbitally excited hadronslepton universalityform factorstensor contributions

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The pith

Sum rules for b to c tau nu decays show larger deviations from the small-velocity limit once orbitally excited charm hadrons are included.

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

The paper constructs sum rules relating semileptonic b to c tau antineutrino transitions that involve orbitally excited charm hadrons, beginning from an amplitude-level identity supplied by heavy quark symmetry. It then measures how far these relations depart from the small-velocity limit that had been assumed in earlier ground-state analyses. Numerical evaluation finds that the departures become larger with excited states and that tensor contributions often dominate the size of the corrections. Because the relevant transition form factors are still poorly known, the sum rules do not yet produce reliable forecasts for lepton-universality ratios. Better hadronic inputs are required before the relations can be used to search for new physics.

Core claim

Starting from the amplitude-level relation implied by heavy quark symmetry, we construct sum rules for b to c tau nu-bar transitions to orbitally excited charm hadrons. We examine the deviations from the small-velocity limit and find that these deviations generally increase once excited hadrons are involved, with tensor contributions often inducing sizable effects. At present the relevant form factors are not yet sufficiently constrained, so the sum rules cannot yet yield robust predictions for the corresponding lepton-universality ratios.

What carries the argument

Amplitude-level sum rules derived from the heavy-quark-symmetry relation, applied to transitions involving orbitally excited charm hadrons to quantify corrections beyond the small-velocity limit.

If this is right

Deviations from the small-velocity limit increase when orbitally excited hadrons are included in the sum rules.
Tensor contributions frequently produce sizable effects within those deviations.
The sum rules do not yet deliver robust predictions for lepton-universality ratios because the form factors remain too uncertain.
Further improvements in the hadronic inputs for the excited-state form factors are required before the relations become predictive.

Where Pith is reading between the lines

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

Once form-factor uncertainties shrink, the same sum rules could supply independent constraints on possible new-physics contributions to the tau modes.
The pattern of larger corrections in excited channels hints that including additional excited states could increase sensitivity to lepton-flavor non-universality.
Analogous constructions might be examined for other heavy-to-heavy transitions or for radially excited states.

Load-bearing premise

The numerical values adopted for the transition form factors to orbitally excited charm hadrons are accurate enough to establish the size and direction of the deviations from the small-velocity limit.

What would settle it

A lattice-QCD or model calculation that supplies revised form factors for the b to excited-c transitions and produces deviations smaller than those found for ground states would falsify the reported increase in deviations.

Figures

Figures reproduced from arXiv: 2604.27970 by Motoi Endo, Satoshi Mishima, Syuhei Iguro.

**Figure 1.** Figure 1: The deviations δ X ij (upper) and cancellation measures ϵ X ij (lower) for the sum rules relating pairs of decays into excited-state doublets. The left, middle, and right columns correspond to the combinations of decay channels (D1/2 + , Λ ∗ c ), (D3/2 + , Λ ∗ c ), and (D1/2 + , D3/2 + ), respectively. For each panel, the two groups labeled “SV” and “KIT” show the results obtained with the SV-limit prescri… view at source ↗

**Figure 2.** Figure 2: The sum rule violation δ X in the NP scenarios for the sum rules relating pairs of decays into excited-state hadrons. The left, middle, and right panels correspond to the combinations of decay channels (D1/2 + , Λ ∗ c ), (D3/2 + , Λ ∗ c ), and (D1/2 + , D3/2 + ), respectively. In each panel, the two groups labeled “SV” and “KIT” show the results obtained with the SV-limit prescription and the KIT prescript… view at source ↗

**Figure 3.** Figure 3: The deviations δ X ij (upper) and cancellation measures ϵ X ij (lower) for the sum rules relating B → D1/2− τν to decays into excited hadrons. Here, D1/2− belongs to a heavy-quark doublet. The left, middle, and right columns correspond to the combinations of decay channels (D1/2− , Λ ∗ c ), (D1/2− , D1/2 + ), and (D1/2− , D3/2 + ), respectively. The coefficients are determined within the KIT prescription,… view at source ↗

**Figure 4.** Figure 4: The deviations δ X ij (upper) and cancellation measures ϵ X ij (lower). The left-most column shows, for comparison, the sum rule relating the ground-state decays Λb → Λcτν and B → D1/2− τν. The second, third, and fourth columns correspond to the sum rules relating Λb → Λcτν to Λb → Λ ∗ c τν, B → D1/2 + τν, and B → D3/2 + τν, respectively. For the left-most column, the results obtained with both the SV-limi… view at source ↗

**Figure 5.** Figure 5: The sum rule violation δ X in the NP scenarios for the sum rules relating B → D1/2− τν to decays into excited hadrons. The left, middle, and right panels correspond to the combinations of decay channels (D1/2− , Λ ∗ c ), (D1/2− , D1/2 + ), and (D1/2− , D3/2 + ), respectively. The coefficients are determined within the KIT prescription. SV KIT δ[Λc,D1/2- ] -0.010 -0.005 0.000 0.005 KIT δ[Λc,D1/2+ ] -0.25 -0… view at source ↗

**Figure 6.** Figure 6: The sum rule violation δ X in the NP scenarios. The left-most panel shows, for comparison, the sum rule relating the ground-state decays Λb → Λcτν and B → D1/2− τν. The second, third, and fourth panels correspond to the sum rules relating Λb → Λcτν to Λb → Λ ∗ c τν, B → D1/2 + τν, and B → D3/2 + τν, respectively. For the left-most panel, both the SV-limit and KIT prescriptions are shown, whereas for the ot… view at source ↗

read the original abstract

We study semileptonic sum rules for $b \to c \tau \overline{\nu}$ transitions involving orbitally excited charm hadrons. Starting from the amplitude-level relation implied by the heavy quark symmetry, we construct sum rules relating these decays. We then examine deviations from the small-velocity limit. Our numerical analysis shows that the deviations generally increase once excited hadrons are involved, with tensor contributions often inducing sizable effects. At present, however, the relevant form factors are not yet sufficiently constrained. Further improvements in the hadronic inputs are essential for these sum rules to yield robust predictions for the corresponding lepton-universality ratios.

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.

Desk Editor's Note private letter to a colleague

The paper extends sum rules to orbitally excited charm states but its numerical claims on growing deviations rest on poorly constrained form factors.

read the letter

The main takeaway is that this work takes the usual heavy-quark-symmetry sum rules for b to c semileptonic decays and applies them to orbitally excited charm hadrons instead of just the ground states. The authors build the relations from the amplitude-level HQS identity, then check deviations from the small-velocity limit in a numerical scan. They report that the deviations tend to get larger with excited states and that tensor pieces can contribute noticeably. They also state outright that the relevant form factors are not yet tight enough for solid predictions on lepton-universality ratios. That last point is important and correctly placed in the abstract and conclusion. The extension itself is the new element; prior sum-rule papers stayed with ground-state mesons, so moving to orbital excitations is a legitimate next step rather than a rehash. The construction of the sum rules follows standard HQS logic without obvious circularity or invented assumptions. The soft spot is exactly what the authors flag: the numerical trends on deviation size come from choosing specific form-factor values or parametrizations. Since those inputs remain loose, shifting them within present uncertainties could shrink or flip the reported increase in deviations. The paper does not claim the trends are model-independent, which keeps the issue from being fatal, but it does mean the central numerical statements are illustrative rather than robust. This is a niche paper aimed at people already following B-decay anomalies and R(D)-type ratios. A reader who works on excited-state form factors or who wants to see how sum rules might eventually constrain excited-channel lepton universality would get some value, mainly as a prompt for better hadronic inputs. The derivations look standard and the limitation is stated plainly, so the paper shows clear thinking on its own terms. I would send it to peer review. A referee could usefully press on the form-factor sensitivity and ask whether the numerics should be framed more as a proof-of-concept than as firm trends.

Referee Report

1 major / 0 minor

Summary. The paper develops semileptonic sum rules for b → c transitions to orbitally excited charm hadrons using relations from heavy quark symmetry at the amplitude level. It constructs these sum rules and performs a numerical analysis of deviations from the small-velocity limit, reporting that deviations generally increase with the involvement of excited hadrons and that tensor contributions often have sizable effects. The authors conclude that while these sum rules could inform lepton-universality ratios, the current lack of sufficient constraints on the relevant form factors prevents robust predictions, calling for further improvements in hadronic inputs.

Significance. Should the numerical trends be confirmed with better-constrained form factors, this study would contribute meaningfully to the field by illustrating the enhanced role of orbitally excited states in b to c semileptonic sum rules. It provides a concrete framework for incorporating these states and highlights the potential impact of tensor operators, which could aid in refining tests of lepton flavor universality in heavy flavor decays. The work also serves as a motivation for dedicated lattice calculations of the excited-state form factors.

major comments (1)

[Numerical analysis] The assertion that 'the deviations generally increase once excited hadrons are involved, with tensor contributions often inducing sizable effects' is presented as a result of the numerical analysis. However, this relies on specific parametrizations or values for the form factors of the orbitally excited states, which the manuscript itself identifies as 'not yet sufficiently constrained' (see abstract and the discussion following the numerical results). Without an accompanying analysis of how the trends vary under changes to these inputs within their current uncertainties, it is difficult to assess whether the reported increase and sizable effects are robust features or artifacts of the chosen inputs. Including such a sensitivity study would strengthen the central claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive comments. We are pleased that the referee recognizes the potential contribution of this work to understanding the role of orbitally excited states in b to c semileptonic transitions and lepton universality tests. We address the major comment in detail below and agree to incorporate the suggested sensitivity analysis in the revised version.

read point-by-point responses

Referee: [Numerical analysis] The assertion that 'the deviations generally increase once excited hadrons are involved, with tensor contributions often inducing sizable effects' is presented as a result of the numerical analysis. However, this relies on specific parametrizations or values for the form factors of the orbitally excited states, which the manuscript itself identifies as 'not yet sufficiently constrained' (see abstract and the discussion following the numerical results). Without an accompanying analysis of how the trends vary under changes to these inputs within their current uncertainties, it is difficult to assess whether the reported increase and sizable effects are robust features or artifacts of the chosen inputs. Including such a sensitivity study would strengthen the central claim.

Authors: We agree with the referee that a sensitivity analysis is necessary to substantiate the robustness of our numerical findings. The form factors for the orbitally excited charm hadrons are indeed subject to significant uncertainties at present, as stated in the manuscript. In the revised version, we will add a dedicated subsection or appendix performing a sensitivity study. Specifically, we will vary the input form factors (e.g., the Isgur-Wise functions or their equivalents for excited states) within reasonable ranges based on existing estimates from quark models, sum rules, and available lattice results. We will then recompute the sum rules and deviations, presenting the results as bands or ranges to show that the qualitative trends—larger deviations with excited states and sizable tensor effects—persist across these variations. This will be illustrated with updated figures. We believe this addition will strengthen the paper without altering its main conclusions. revision: yes

Circularity Check

0 steps flagged

No significant circularity: sum rules built from external heavy-quark symmetry; numerical trends presented with explicit caveats on inputs

full rationale

The derivation begins from the amplitude-level relation implied by heavy quark symmetry (an established external framework) and constructs sum rules relating the decays. Deviations from the small-velocity limit are then examined numerically. The paper explicitly states that the relevant form factors 'are not yet sufficiently constrained' and that further improvements are essential for robust predictions, so the reported trends on increasing deviations and tensor effects are not claimed as forced consequences or predictions equivalent to the inputs. No self-definitional reduction, no fitted parameter renamed as a prediction, and no load-bearing self-citation chain appears in the provided derivation steps. The chain is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central construction rests on heavy quark symmetry providing amplitude-level relations for b to c transitions. Numerical results depend on external form factor inputs that the paper itself flags as insufficiently constrained.

free parameters (1)

form factors for orbitally excited states
These are used as inputs in the numerical analysis of deviations; the paper states they are not yet sufficiently constrained.

axioms (1)

domain assumption Heavy quark symmetry implies amplitude-level relations for b to c semileptonic transitions.
This is the starting point for constructing the sum rules, as stated in the abstract.

pith-pipeline@v0.9.0 · 5405 in / 1337 out tokens · 64432 ms · 2026-05-07T05:00:55.976380+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

$b \to c$ semileptonic sum rule: SU(3)$_{\rm{F}}$ symmetry violation
hep-ph 2026-04 unverdicted novelty 5.0

The SU(3) flavor symmetry violation in the extended b to c semileptonic sum rule is smaller than expected future experimental uncertainties, supporting new physics-agnostic consistency checks.

Reference graph

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