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arxiv: 2606.30881 · v1 · pith:DIF4324Fnew · submitted 2026-06-29 · ✦ hep-ph

Search for New Physics through the Observables of Semileptonic B_(c)^+to D^(ast+)ell⁺ell⁻ Decay

Zohaib Aarfi , Qazi Maaz Us Salam , Faisal Munir Bhutta , Ishtiaq Ahmed , M. Ali Paracha This is my paper

Pith reviewed 2026-07-01 01:15 UTC · model grok-4.3

classification ✦ hep-ph
keywords B_c decaysemileptonic decayNew Physicsangular observablesb to d transitionflavor anomaliesweak annihilationform factors
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0 comments X

The pith

The decay B_c^+ to D^{*+} lepton pair shows sensitivity to New Physics in b to d transitions through several observables.

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

This paper performs a model-independent analysis of the rare semileptonic decay B_c^+ → D^{*+} ℓ^+ ℓ^- for muons and taus. It includes penguin-box terms, resonance contributions, and weak-annihilation amplitudes to test for New Physics. Form factors from the covariant confined quark model and Bethe-Salpeter approach are used to compute the differential branching fraction, forward-backward asymmetry, helicity fractions, and angular observables. In multiple New Physics scenarios, the branching fraction, forward-backward asymmetry, and coefficients such as I_{2c}, I_3, I_5, and I_{6s} deviate from Standard Model expectations. The results position this decay as a complementary probe for the flavor structure of New Physics.

Core claim

Using B_c to D^* transition form factors from the covariant confined quark model and weak-annihilation form factors from the Bethe-Salpeter approach, the branching fraction, forward-backward asymmetry, and normalized angular coefficients ⟨I_{2c}⟩, ⟨I_3⟩, ⟨I_5⟩, and ⟨I_{6s}⟩ exhibit clear sensitivity to New Physics effects in one- and two-dimensional scenarios, while other observables remain closer to Standard Model values.

What carries the argument

The B_c → D^* transition form factors from the covariant confined quark model combined with weak-annihilation form factors from the Bethe-Salpeter approach, incorporating penguin-box and resonance effects to compute differential and angular observables.

Load-bearing premise

The hadronic matrix elements for the B_c to D^* transition and weak annihilation are accurately captured by the form factors from the covariant confined quark model and Bethe-Salpeter approach.

What would settle it

A measurement at LHCb of the differential branching fraction or forward-backward asymmetry that matches Standard Model predictions within experimental errors across the full dilepton mass range would show no detectable New Physics sensitivity in this channel.

Figures

Figures reproduced from arXiv: 2606.30881 by Faisal Munir Bhutta, Ishtiaq Ahmed, M. Ali Paracha, Qazi Maaz Us Salam, Zohaib Aarfi.

Figure 1
Figure 1. Figure 1: FIG. 1: Predictions for the differential branching fraction [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Predictions for the normalized angular coefficients [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Predictions for the normalized angular coefficients [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Binned predictions for the observables in the 1D NP scenarios SI–SIV. For each observable, the results are [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Correlations between the integrated branching fraction and the observables [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Predictions for the differential branching fraction [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Predictions for the normalized angular coefficients [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Predictions for the normalized angular coefficients [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Binned predictions for the observables of [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Correlation plots between the integrated branching fraction and the observables [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
read the original abstract

Motivated by the current flavor anomalies and the comparatively less explored nature of the $b\to d$ sector, we present a model-independent study of the rare semileptonic $B_c^{+}\to D^{\ast+}\ell^{+}\ell^{-}$ ($\ell=\mu,\tau$) decay, to investigate its sensitivity to New Physics effects. The analysis incorporates penguin-box contributions, long-distance resonance effects, and the sizable weak-annihilation amplitudes. Using the $B_c\to D^\ast$ transition form factors calculated in the covariant confined quark model and the weak-annihilation form factors obtained within the Bethe--Salpeter approach, we analyze the differential branching fraction, forward-backward asymmetry, longitudinal helicity fraction, and a comprehensive set of normalized angular observables in several one- and two-dimensional New Physics scenarios and compare our results with the Standard Model predictions. Notably, the branching fraction, forward-backward asymmetry, and the normalized angular coefficients such as, $\langle I_{2c}\rangle$, $\langle I_{3}\rangle$, $\langle I_{5}\rangle$, and $\langle I_{6s} \rangle$, show clear sensitivity to New Physics effects. Our results indicate that the decay $B_c^{+}\to D^{\ast+}\ell^{+}\ell^{-}$ serves as a complementary probe of the flavor structure of New Physics and can therefore be investigated in future measurements at LHCb and other high-luminosity flavor experiments.

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

1 major / 0 minor

Summary. The paper claims to perform a model-independent analysis of the rare semileptonic decay B_c^+ → D^{*+} ℓ^+ ℓ^- (ℓ=μ,τ), incorporating penguin-box, resonance, and weak-annihilation contributions. Using B_c → D^* transition form factors from the covariant confined quark model and weak-annihilation form factors from the Bethe-Salpeter approach, it computes the differential branching fraction, forward-backward asymmetry, longitudinal helicity fraction, and normalized angular observables (including ⟨I_{2c}⟩, ⟨I_3⟩, ⟨I_5⟩, ⟨I_{6s}⟩) in several one- and two-dimensional NP scenarios parameterized by Wilson coefficients, reporting clear deviations from SM predictions in multiple observables and concluding that the decay is a complementary probe of NP flavor structure for future LHCb measurements.

Significance. If the results hold, the work adds a useful theoretical exploration of the less-studied b→d sector with explicit inclusion of weak-annihilation amplitudes, which strengthens the analysis relative to simpler treatments. This could help motivate targeted experimental searches at high-luminosity flavor facilities.

major comments (1)
  1. [hadronic form factor section] Hadronic form factor section: the central claim that observables such as the branching fraction, A_FB, ⟨I_{2c}⟩, ⟨I_5⟩ and ⟨I_{6s}⟩ exhibit clear NP sensitivity rests on the accuracy of the B_c → D^* form factors computed in the covariant confined quark model and the weak-annihilation form factors from the Bethe-Salpeter approach. The manuscript provides no cross-validation against lattice QCD, no systematic uncertainty estimates from these specific model choices, and no discussion of how O(1) variations in the inputs would affect the reported deviations; this is load-bearing for the sensitivity conclusions.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for the constructive comments, which help strengthen the presentation of our results. We respond to the major comment below.

read point-by-point responses

  1. Referee: [hadronic form factor section] Hadronic form factor section: the central claim that observables such as the branching fraction, A_FB, ⟨I_{2c}⟩, ⟨I_5⟩ and ⟨I_{6s}⟩ exhibit clear NP sensitivity rests on the accuracy of the B_c → D^* form factors computed in the covariant confined quark model and the weak-annihilation form factors from the Bethe-Salpeter approach. The manuscript provides no cross-validation against lattice QCD, no systematic uncertainty estimates from these specific model choices, and no discussion of how O(1) variations in the inputs would affect the reported deviations; this is load-bearing for the sensitivity conclusions.

    Authors: We agree that the form factor inputs underpin the reported NP sensitivities and that a quantitative discussion of their uncertainties is needed. The covariant confined quark model and Bethe-Salpeter approach were adopted because they furnish the complete set of required form factors and have been validated against data in related channels. In the revised manuscript we will add a dedicated subsection that varies the input parameters within their quoted uncertainties (O(1) ranges) and shows the resulting bands on the branching fraction, A_FB, ⟨I_{2c}⟩, ⟨I_5⟩ and ⟨I_{6s}⟩; this will demonstrate that the deviations from the SM remain visible. Direct cross-validation with lattice QCD is not possible at present, as no lattice results exist for the B_c → D^* transition form factors. revision: partial

standing simulated objections not resolved
  • Cross-validation of the B_c → D^* form factors against lattice QCD, as no such lattice calculations are currently available in the literature.

Circularity Check

0 steps flagged

No significant circularity: external form factors and independent NP parameterization

full rationale

The paper conducts a model-independent NP analysis by varying Wilson coefficients in one- and two-dimensional scenarios and computing observables (branching fraction, A_FB, angular coefficients) using B_c to D* transition form factors from the covariant confined quark model plus weak-annihilation amplitudes from the Bethe-Salpeter approach. These hadronic inputs are cited as external calculations rather than derived or fitted internally. The NP effects are parameterized independently of the form-factor values, and the reported sensitivities are forward predictions for future data rather than statistical fits or self-definitions. No load-bearing step reduces by construction to a self-citation chain, fitted input, or ansatz smuggled from prior author work; the derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 3 axioms · 0 invented entities

The central claim rests on the accuracy of the chosen form factor models for hadronic transitions and the validity of the effective field theory parameterization for New Physics contributions. No new particles or forces are postulated.

axioms (3)
  • domain assumption The form factors from the covariant confined quark model accurately describe the B_c to D* transition
    Invoked to compute the hadronic matrix elements for the decay amplitudes.
  • domain assumption Weak annihilation form factors from the Bethe-Salpeter approach are reliable inputs
    Used because the amplitudes are sizable in this decay.
  • domain assumption New Physics effects can be parameterized through modifications to Wilson coefficients in the effective operators
    Standard framework for model-independent analysis of flavor anomalies.

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discussion (0)

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Reference graph

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