arxiv: 2509.19445 · v3 · submitted 2025-09-23 · ✦ hep-ph

Study of Form Factors and Observables in B_c^- rightarrow bar{D}^{()0}ell^-bar{ν}_{ell} and B_c^- rightarrow D^{()-}ell^+ell^- decays

Utsab Dey , Soumitra Nandi This is my paper

Pith reviewed 2026-05-18 14:22 UTC · model grok-4.3

classification ✦ hep-ph PACS 13.20.He12.39.St14.40.Nd

keywords B_c meson decaysform factorsperturbative QCDheavy quark symmetryangular observableslepton flavor violationStandard Model predictionsrare decays

0 comments

The pith

The paper computes Standard Model predictions for branching fractions and angular observables in B_c decays to D mesons using perturbative QCD form factors and lattice inputs.

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

This paper calculates form factors for the semileptonic decays B_c^- to anti-D^(*)0 and the rare decays B_c^- to D^(*)- ell^+ ell^- within the Standard Model. It extracts meson wave function shape parameters from lattice QCD results for related transitions and applies heavy quark spin symmetry to determine the q^2 dependence of the B_c to D^* form factors. The work then delivers numerical predictions for branching fractions, lepton flavor violating observables, and a full angular analysis of the cascade decay B_c^- to D^*-(to D^0 pi^-) ell^+ ell^-, supplying expected values for several angular coefficients under Standard Model assumptions.

Core claim

Using perturbative QCD to model the wave functions of the B_c and D^(*) mesons together with lattice inputs for B to D^(*) and B_c to D transitions, the calculation determines the relevant form factors and their q^2 dependence via heavy quark spin symmetry; these form factors are then inserted into the decay amplitudes to obtain concrete Standard Model predictions for branching fractions, lepton-flavor-violating ratios, and the full set of angular observables in the four-body cascade decay.

What carries the argument

Perturbative QCD form factors whose shape parameters are fixed by lattice QCD inputs for related transitions, with q^2 dependence of the B_c to D^* form factors supplied by heavy quark spin symmetry.

If this is right

The computed branching fractions set a baseline that any observation of lepton flavor violation in these channels must exceed.
The angular observables provide additional handles that experiments can use to test the Standard Model in the presence of new physics contributions.
The same form-factor framework can be reused for related decays of the B_c meson once more lattice data become available.

Where Pith is reading between the lines

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

If the predicted angular distributions are measured, they could be combined with similar observables from B meson decays to test the consistency of heavy quark symmetry assumptions across different systems.
Discrepancies between these predictions and future LHCb or Belle II data would point toward specific new physics operators that modify the b to c or b to u transitions.
The lattice-constrained wave functions could be applied to estimate non-factorizable effects in other rare B_c decays not covered here.

Load-bearing premise

The q^2 dependence of the B_c to D^* form factors can be obtained reliably by applying heavy quark spin symmetry to the B_c to D form factors taken from lattice calculations.

What would settle it

A precision measurement of the branching fraction for B_c^- to D^- mu^+ mu^- or of one of the angular coefficients in the cascade decay that lies significantly outside the reported Standard Model range would falsify the central predictions.

read the original abstract

We investigate the decays $B_c^- \rightarrow \bar{D}^{(*)0}\ell^-\bar{\nu}_{\ell}$ and $B_c^- \rightarrow D^{(*)-}\ell^+\ell^-$ within the Standard Model (SM), employing perturbative QCD (pQCD) form factors that are sensitive to the wave functions of $B_c$ and $D^{(*)}$ mesons. Using lattice QCD inputs for $B \to D^{(*)}$ and $B_c \to D$ transitions, we extract the shape parameters of the meson wave functions and estimate the $q^2$-dependence of $B_c \to D^*$ form factors via heavy quark spin symmetry. We present predictions for branching fractions, lepton flavor violating observables, and perform a detailed angular analysis of the cascade decay $B_{c}^{-} \to D^{*-}(\to D^{0}\pi^{-}) \ell^+\ell^-$, providing SM expectations for several angular observables.

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

This paper offers new SM predictions for B_c decay observables using pQCD and lattice inputs, though the heavy quark spin symmetry step for vector form factors lacks quantified corrections.

read the letter

The punchline is that this paper generates new Standard Model predictions for branching fractions and angular observables in B_c to D and D star decays, but the form factor modeling for the vector channels depends on an extrapolation whose uncertainties are not fully addressed. What the paper does well is to take lattice QCD inputs for the B to D star and B_c to D transitions and use them to determine the shape parameters of the meson wave functions in the perturbative QCD framework. This makes the calculations for the semileptonic decays more anchored in first-principles results than a pure model would be. They then extend the same setup to the rare B_c to D star l plus l minus modes and include lepton flavor violating observables as well. The detailed angular analysis of the cascade decay B_c minus to D star minus to D zero pi minus l plus l minus stands out as a practical addition, giving specific SM expectations for several angular coefficients that could be compared with future data. On the soft side, the q squared dependence of the B_c to D star form factors is obtained by applying heavy quark spin symmetry to the B_c to D form factors. The stress test points out that these relations are reliable only in the infinite mass limit with small recoil, but here the charm mass is finite, the recoil is large, and the initial state has two heavy quarks. The paper does not appear to estimate the size of the symmetry breaking terms or include additional theoretical uncertainties from this step. As a result, the central values for the branching fractions and especially the angular observables in the dilepton channels may have larger errors than indicated. The citation pattern looks standard, referencing prior pQCD and lattice work without obvious gaps or over-reliance on self-citations. This work is aimed at readers in heavy flavor phenomenology who follow B_c physics and rare decays. Someone planning LHCb measurements or checking consistency with other form factor approaches would get value from the numerical results. I would recommend sending it for peer review. The core calculations are grounded enough to deserve referee feedback, particularly on whether the heavy quark symmetry application needs more support or error analysis.

Referee Report

1 major / 2 minor

Summary. The paper computes form factors for the decays B_c^- → D̄^{(*)0} ℓ^- ν̄_ℓ and B_c^- → D^{(*)-} ℓ^+ ℓ^- in the Standard Model using perturbative QCD, with meson wave-function shape parameters fixed from lattice QCD results on B → D^{(*)} and B_c → D transitions. It applies heavy quark spin symmetry to estimate the q^2 dependence of the B_c → D^* form factors, then derives predictions for branching fractions, lepton-flavor-violating observables, and a full angular analysis of the cascade B_c^- → D^{*-}(→ D^0 π^-) ℓ^+ ℓ^-.

Significance. If the form-factor inputs are reliable, the work supplies concrete SM benchmarks for branching ratios and angular coefficients that can be tested at LHCb or future facilities. The combination of pQCD with external lattice constraints on related channels is a methodological strength, and the detailed angular analysis of the cascade decay adds experimental utility beyond rate predictions alone.

major comments (1)

[form-factor section (estimation of B_c → D^* form factors via HQSS)] The central predictions for the B_c → D^* ℓ^+ ℓ^- observables, including the angular coefficients in the cascade decay, rest on the q^2-dependent form factors obtained by applying heavy quark spin symmetry to the lattice-constrained B_c → D results. No quantitative estimate of 1/m_c or recoil corrections is provided, despite the large recoil and m_c ≈ 1.5 GeV regime where HQSS is expected to receive sizable corrections. This directly impacts the reliability of the reported SM expectations for the angular observables.

minor comments (2)

[parameter extraction] Clarify in the text how the extracted shape parameters from B → D^{(*)} and B_c → D are combined and whether any tension between the two lattice sets is propagated into the final uncertainties.
[results section] Add a brief comparison of the obtained B_c → D form factors with existing literature results to help readers assess consistency.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We address the single major comment below and outline the revisions we will make.

read point-by-point responses

Referee: [form-factor section (estimation of B_c → D^* form factors via HQSS)] The central predictions for the B_c → D^* ℓ^+ ℓ^- observables, including the angular coefficients in the cascade decay, rest on the q^2-dependent form factors obtained by applying heavy quark spin symmetry to the lattice-constrained B_c → D results. No quantitative estimate of 1/m_c or recoil corrections is provided, despite the large recoil and m_c ≈ 1.5 GeV regime where HQSS is expected to receive sizable corrections. This directly impacts the reliability of the reported SM expectations for the angular observables.

Authors: We thank the referee for this observation. The use of heavy quark spin symmetry to obtain the q^2 dependence of the B_c → D^* form factors from the lattice-constrained B_c → D results is indeed an approximation whose validity is limited by the charm-quark mass and the large recoil. In the original manuscript we did not supply a quantitative estimate of the associated 1/m_c and recoil corrections. In the revised version we will add a dedicated paragraph in the form-factor section that (i) recalls the size of analogous corrections observed in B → D^* transitions, (ii) provides a conservative uncertainty band for the B_c → D^* form factors, and (iii) propagates this uncertainty into the angular observables of the cascade decay. This addition will make the limitations of the present approach explicit while preserving the utility of the SM benchmarks we report. revision: partial

Circularity Check

0 steps flagged

No significant circularity: external lattice inputs and HQSS applied to new channels

full rationale

The derivation extracts meson wave-function shape parameters from independent lattice QCD calculations on B → D^{(*)} and B_c → D transitions, then applies heavy quark spin symmetry to generate q^2 dependence for the B_c → D^* form factors used in the new decay channels. These steps rely on external data and a standard symmetry relation rather than fitting parameters to the target observables or renaming fitted quantities as predictions. The central predictions for branching fractions, LFV observables, and angular coefficients therefore remain independent of the paper's own outputs and do not reduce to the inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Central results rest on applicability of pQCD to these transitions, validity of heavy quark spin symmetry for relating form factors, and accuracy of lattice inputs for shape parameters; no new particles or forces are introduced.

free parameters (1)

meson wave function shape parameters
Extracted from lattice QCD inputs for B → D(*) and B_c → D transitions to determine the q^2 dependence of the form factors.

axioms (2)

domain assumption Heavy quark spin symmetry relates the form factors for B_c → D and B_c → D* transitions sufficiently well to estimate the q^2 dependence.
Invoked explicitly to extend lattice results on B_c → D to the D* case.
domain assumption Perturbative QCD factorization applies to the B_c → D(*) transitions at the relevant energy scales.
Basis for computing the form factors from meson wave functions.

pith-pipeline@v0.9.0 · 5734 in / 1560 out tokens · 49557 ms · 2026-05-18T14:22:24.967675+00:00 · methodology

discussion (0)

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Relation between the paper passage and the cited Recognition theorem.

estimate the q²-dependence of B_c → D^* form factors via heavy quark spin symmetry... using lattice QCD inputs for B→D(*) and B_c→D transitions
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express all the 10 form factors... in terms of just two universal soft functions Σ1 and Σ2

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Forward citations

Cited by 1 Pith paper

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

Weak Annihilation Contribution to Angular Observables in $B_{c}^+\to D^{\ast+}\ell^{+}\ell^{-}$ Decays
hep-ph 2026-02 unverdicted novelty 4.0

Weak annihilation contributions are sizable in B_c^+ to D^{*+} lepton pair decays and must be included to obtain reliable Standard Model predictions for angular observables.

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