Using Heavy Quark Spin Symmetry in Semileptonic $B_c$ Decays

F. De Fazio; P. Colangelo

REVIEW

Using Heavy Quark Spin Symmetry in Semileptonic $B_c$ Decays

P. Colangelo, F. De Fazio

High Energy Physics - Phenomenology · Submitted 17 Sep 1999 · 38 references

Pith's verdict: A solid, honest model calculation whose zero-recoil numbers are real predictions but whose headline J/ψ and ηc rates ride on an extrapolated slope with no error band.

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arXiv IDhep-ph/9909423 (version 1)

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CitationF. De Fazio, P. Colangelo. "Using Heavy Quark Spin Symmetry in Semileptonic $B_c$ Decays." arXiv:hep-ph/9909423 (1999). https://pith.science/paper/HIAIOQZG

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Editor's note

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Worth reading, with one caveat that matters more than the paper lets on. The zero-recoil results are genuine; the rate tables are softer than they look. What's actually new here isn't the spin-symmetry reduction — that's Jenkins, Luke, Manohar and Savage, and the authors say so and rederive it for completeness. The new content is the model computation: Δ, Ω₁ and Σ₁ as overlap integrals of wave-functions from a relativistic potential model whose parameters (m_b, m_c, Λ) are fixed from charmonium and bottomonium spectra. That's the right way to do it. Nothing is tuned to the decay data, so Δ(0)≈0.94 and Ω₁(0)≈0.66 are real predictions, and the structural result that heavy-light final states pick up a 1/√2 relative to heavy-heavy ones is clean and worth having. The factorization tests in eqs. (5.3)–(5.5) are a sensible, falsifiable proposal. The soft spot is the y-dependence, and it is load-bearing for the numbers people will actually use. Eq. (3.10) is explicitly a near-zero-recoil construction. The paper then fits the three-parameter form (3.15) and reports ρ²=2.9, c=3 in Table I as though they were computed. For Bc→ηc and J/ψ the physical range reaches y≈1.29, and with ρ²=2.9 the form factor drops from 0.94 to roughly 0.4 — which is exactly the factor-of-two spread between the two columns of Table II (2.1 vs 6.9; 21.6 vs 48.3). So the headline J/ψ and ηc rates are controlled by the extrapolated slope, not by the overlap integral. The authors flag this (abstract:s0 aside, the Sec. II sentence 'admittedly a strong assumption' is the honest one) and I give them credit, but they attach no error band anywhere, so a reader cannot tell whether the bracket is model uncertainty or fit artifact. Second, Ω₂ and Σ₂ are set to zero outright. Fine for the narrow c→s,d modes; not fine for Bc→D*ℓν, where the paper's own text says the omission could matter. Neither problem is hidden, and the zero-recoil results stand. Read the rate tables as order-of-magnitude, not as predictions with a defensible uncertainty. This is for someone working on Bc semileptonic or non-leptonic modes who wants a benchmark and a set of experimental targets; the spin-symmetry review section alone is a decent entry point. It deserves a serious referee — the physics is sound and the authors are candid about the assumptions, which is more than most model papers manage.

Referee report

Significance

The zero-recoil results are genuine, parameter-free predictions in the sense that matters: the model inputs are fixed by the charmonium and bottomonium spectra and by heavy-light masses, not by the B_c decay data being predicted, so Δ(1) ≈ 1 and Ω₁(1) ≈ 1/√2 are not fits in disguise. The observation that Δ(1) is near unity because the B_c and η_c wave-functions are similar, while the heavy-light channels are suppressed by 1/√2, is a useful and physically transparent statement that deserves independent checks by QCD sum rules in the heavy quark limit, as the authors themselves note. The factorization tests of eqs. (5.3)–(5.5) are falsifiable relations between a two-body rate and a differential semileptonic spectrum, and are the kind of prediction that hadron-machine experiments can actually confront. The paper is also careful to state where it is assuming rather than deriving, which is a point in its favour.

Major objections (3)

[Sec. III, eq. (3.10) and Table I] The slope ρ² = 2.9 and curvature c = 3 quoted for Δ in Table I are not independent computations: eq. (3.10) is explicitly a near-zero-recoil construction ('for a small momentum q'), and the y-dependence is then obtained by extrapolating that construction over the whole range and representing it in the form (3.15). This extrapolation, not the overlap integral, controls the physically interesting channels: with ρ² = 2.9 the form factor falls from 0.94 at y = 1 to roughly 0.4 at the kinematic endpoints of B_c → η_c and B_c → J/ψ, which is precisely the factor-of-two spread between the two columns of Table II (η_c: 2.1 vs 6.9; J/ψ: 21.6 vs 48.3). The text acknowledges the extrapolation as 'admittedly a strong assumption', but Table I presents ρ² and c as if they were computed quantities with no qualification, and Table II labels the t-independent column an 'upper bound' rather than a model bracket. What is missing is a statement of the range of q over which (3.10) is under control, and a demonstration that ρ² is stable against the truncation of the q-expansion used to extract it. Without that, a reader cannot tell whether the factor-of-two bracket on the flagship J/ψ channel is a genuine model uncertainty or an artifact of the extrapolation procedure.
[Table I] No uncertainty is attached to any entry of Table I, yet the two central quantitative claims of the paper are deviations of 5% (Δ(1) = 0.94 vs 1) and 7% (Ω₁(1) = 0.66 vs 1/√2) from limiting values. These deviations are the substance of the claim that the departure from the symmetry limit is due to the shapes of the wave-functions, so their significance depends entirely on the sensitivity of the overlap integrals to the model parameters. A study varying Λ, m_c and m_b within the ranges that still reproduce the charmonium and bottomonium spectra, and quoting the resulting spread on F(1), ρ² and c, is needed before the 5% and 7% numbers can be read as predictions rather than as the model's central values. The same applies to the quoted 'less than 3%' SU(3)_F breaking between Ω₁^d and Ω₁^s, which is not visible at all in Table I, where both entries read 0.66.
[Sec. II and Sec. IV] The symmetry relations (2.6) and (2.7) are derived near zero recoil and then applied over the full physical range, including the wide-recoil b → c transitions where the neglected O(q/m_c) terms are largest. The authors state this openly, so the issue is not concealment but the absence of any estimate of the size of the correction. For B_c → η_c and B_c → J/ψ the recoil is large over most of the phase space, and the leading spin-symmetry-breaking corrections grow with it; a power-counting estimate, even a crude one, of the leading correction to (2.7) at the upper end of the y range would let the reader judge how seriously to take the J/ψ branching ratio of 1.5 × 10⁻². If such an estimate cannot be made, the rate predictions for these two channels should be explicitly labelled illustrative, with the zero-recoil values Δ(1) and Ω₁(1) presented as the robust output of the paper.

Minor objections (7)

[Table III] Two entries in the D̄ column appear inconsistent with the quoted widths and the a₂² factor. For D^{*+}D̄^{*0} the width 2.4 × 10⁻¹⁵ GeV with a₂² and τ_{B_c} = 0.46 ps gives a branching ratio of order 1.4 × 10⁻⁵, not the listed 51.4 × 10⁻⁴; for D^{*+}D̄⁰ the width 1.46 × 10⁻¹⁵ GeV gives about 8.4 × 10⁻⁶, not 8.4 × 10⁻⁵. The neighbouring D⁺D̄⁰ entry is consistent, so these look like typographical errors; please check the whole column.
[Sec. V, Tables III–IV] The Γ columns carry explicit a₁², a₂² or (a₁x + a₂y)² factors while the BR columns have those factors already evaluated at c₁(m_b) = 1.132, c₂(m_b) = −0.286 and c₁(m_c) = 1.351, c₂(m_c) = −0.631. This is good practice, but a footnote stating it explicitly would save the reader the reconstruction, since the two columns otherwise appear to disagree by factors of order 1.3–1.8.
[Sec. III, eq. (3.14) and following text] The authors conclude that the expansion truncated at the first term 'appears to be of limited usefulness' because the next-to-leading corrections are sizeable. Since eq. (3.14) feeds no subsequent result, it would be cleaner either to remove it or to state the size of the neglected correction, so that the reader is not left with an unquantified caveat attached to the Ω₁–f_{B_s} relation.
[Fig. 2 and caption] The caption identifies solid lines as the present model and dashed lines as the ISGW model, but with five panels it does not say which panel corresponds to which channel, nor which of the several curves in a panel is which form factor. Labelling each panel with its channel and each curve with its symbol would make the figure usable.
[Sec. III, eq. (3.15)] It should be stated explicitly whether ρ² and c are obtained by fitting (3.15) to the model's own Δ(q) at small q or by analytic expansion of (3.10); the two procedures differ in their sensitivity to the truncation and the reader needs to know which was used.
[Sec. III, eq. (3.11)] The 1/√2 suppression is derived in the limits m_s → 0 and m_b → ∞ and then applied at finite masses. It would help to say how much of the 7% deviation of Ω₁(1) from 1/√2 is attributable to finite m_s and how much to the wave-function shapes, since the two effects are currently merged in a single number.
[General] There are several typographical and language slips that should be corrected: 'at odds of the heavy quark flavour symmetry' (Sec. I) should read 'unlike the heavy quark flavour symmetry'; 'istantaneous' (Sec. III) should be 'instantaneous'; 'nalogous' (Sec. I) should be 'analogous'; and the reference name 'Sanchiz-Lozano' in refs. [20] and [34] should presumably be 'Sanchis-Lozano'. The broken inter-word spacing throughout the arXiv version should also be cleaned up in the final manuscript.

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The paper

The paper claims

Heavy quark spin symmetry reduces the six form factors of semileptonic $B_c$ decays to one or two invariant functions, and a potential-model overlap integral fixes their normalizations near 0.94 and 0.66.

The reading

The $B_c$ meson holds a beauty and a charm quark at once, and both can decay weakly, so its semileptonic transitions span an unusually wide set of final states: charmonium ($J/ψ$, $η_c$), heavy-light mesons ($B_s$, $B_d$), and $D$ mesons. The paper's aim is to show that heavy quark spin symmetry — the decoupling of the heavy quark spins in the infinite-mass limit — collapses the six form factors of each transition into one invariant function for quarkonium finals and two for heavy-light finals, so the whole semileptonic landscape is governed by a handful of functions. What makes the paper more than a symmetry counting exercise is that it then computes those functions as overlap integrals of meson wave-functions taken from a QCD-motivated relativistic potential model, which fixes normalizations that the symmetry alone leaves free. The payoff is numerical: the quarkonium form factor at zero recoil comes out at 0.94, close to the symmetric value of 1, while the heavy-light one comes out at 0.66, close to $1/√2$, and these feed predictions for semileptonic and (under factorization) non-leptonic $B_c$ branching fractions. The reason a reader should care is that these numbers are checkable at hadron machines, and the ratios the authors write down turn decay-rate measurements into direct tests of spin symmetry itself.

What carries the argument

The load-bearing device is the trace formalism for heavy quark spin symmetry: the $B_c$ and the light-heavy or quarkonium final states are each packaged into a $4×4$ matrix field ($H_{c̄b}$ and $H_a$ in eqs. 2.2–2.3), and the weak current matrix element is written as a trace over these fields times a Dirac matrix $Ω$ built from the four-velocity $v$ and residual momentum $q$ (eq. 2.4). Because $Ω$ can only be expanded in a small number of structures, the six form factors of a given transition collapse onto one or two invariant functions. The second device is the overlap integral: the model's meson states (eq. 3.1) and the weak current written in quark creation and annihilation operators (eq. 3.5) reduce, via canonical anticommutation, to an integral over the reduced radial wave-functions $u_{B_c}(k)$ and $u_M(k)$ (eq. 3.6), which in the heavy-quark limit becomes the plain coordinate-space overlap of eq. 3.8. That integral is what converts a symmetry statement into a number, and it is also what produces the $1/√2$ suppression for heavy-light finals.

Extended reading notes

Core claim

The central claim is that spin symmetry plus a wave-function overlap calculation pins down the $B_c$ semileptonic form factors well enough to predict rates. Using the trace formalism, the authors show that the matrix elements for $B_c → B_a$ and $B_c → B^*_a$ (with $B_a$ a heavy-light meson) depend on two invariant functions $Ω^a_1$ and $Ω^a_2$, that $B_c → D, D^*$ depends on $Σ_1, Σ_2$, and that $B_c → η_c, J/ψ$ depends on a single function $Δ$ (eqs. 2.5–2.7). Symmetry alone does not normalize these functions; the model does. Writing $Δ$ at zero recoil as the coordinate-space overlap of the $B_c$ and $η_c$ wave-functions (eq. 3.8) shows that the deviation from 1 is purely a shape mismatch, and the numerical solution gives $Δ(0) = 0.94$, a 5% effect. The analogous heavy-light overlap carries an extra factor $1/√2$ (eq. 3.11), and the computed value is $Ω^s_1(0) = 0.66$, a 7% deviation from that limit, with $Σ_1(0) = 0.59$. Feeding these into phase space, the authors find that $B_c → B_s ℓν$ and $B_c → B^*_s ℓν$ together make up nearly 60% of the semileptonic width despite the narrow phase space, that $Γ(B_c → J/ψ ℓν) ≃ 21.6 × 10^{-15}$ GeV, and that the $J/ψ$ channel's longitudinal and transverse pieces (eq. 4.1) give access to the slope $ρ^2$ and to $V_{cb} Δ(1)$.

Load-bearing premise

The symmetry relations are derived only near zero recoil, yet the authors apply them across the entire physical range of momentum transfer — including the wide $b → c$ transitions to $η_c$ and $J/ψ$ — an extrapolation they themselves call admittedly a strong assumption.

Editorial extensions

If this is right

If the normalization is right, $B_c → J/ψ ℓν$ has a width near $21.6 × 10^{-15}$ GeV (branching fraction about $1.5×10^{-2}$ at the CDF lifetime), with a $t$-independent form factor giving an upper bound of $48 × 10^{-15}$ GeV.
The two $B_s$ semileptonic modes should dominate the semileptonic width at roughly 60%, even though their phase space is the narrowest of all the channels considered.
The ratio $Γ_T/Γ_L$ in $B_c → J/ψ ℓν$ measures the slope $ρ^2$ of $Δ(y)$ if the curvature term is dropped, and the combination $V_{cb}Δ(1)$ can be extracted from $Γ_L$ — offering an independent handle on $V_{cb}$.
Under factorization, the ratio of the two-body rate $Γ(B_c → J/ψ π^+)$ to the differential semileptonic width at $y = y_π$ is fixed by $V_{ud}$, $a_1$ and $f_π$ alone (eq. 5.3), giving a direct test of both factorization and spin symmetry.
The charm-induced non-leptonic channel $B_c → B^*_s ρ^+$ should exceed 10% of the total $B_c$ width, making it the single largest two-body mode in the tables.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The prediction that $Δ(0)$ sits within 5% of 1 while $Ω_1(0)$ sits within 7% of $1/√2$ suggests a pattern worth stating: the symmetry-limit values are recovered to within roughly the size of the wave-function shape mismatch, so the model's real content is that shape mismatch is small. That is a claim about wave-function universality, not about the symmetry, and it is the part most likely to fail f
Because the model predicts both $Δ(0)$ and $f_{B_c}$ from the same wave-functions, an independent lattice determination of $f_{B_c}$ would indirectly constrain the overlap integral and hence $Δ(0)$, even without any semileptonic measurement.
The authors set $Ω_2$ and $Σ_2$ to zero for lack of a rest-frame calculation. For the Cabibbo-suppressed $B_c → D^* ℓν$ channel the neglected term is not small in principle, so a future rest-frame treatment of the subleading functions would change the smallest entries of the semileptonic table by more than the quoted $t$-dependence does.
The SU(3) breaking between $Ω^d_1$ and $Ω^s_1$ comes out below 3%, which is smaller than typical model spreads; a measurement of the $B_d$ to $B_s$ semileptonic ratio at the few-percent level would therefore discriminate between this model and ISGW-type treatments, where the two differ more.

Original abstract

The form factors parameterizing the B_c semileptonic matrix elements can be related to a few invariant functions if the decoupling of the spin of the heavy quarks in B_c and in the mesons produced in the semileptonic decays is exploited. We compute the form factors as overlap integral of the meson wave-functions obtained using a QCD relativistic potential model, and give predictions for semileptonic and non-leptonic B_c decay modes. We also discuss possible experimental tests of the heavy quark spin symmetry in B_c decays.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,016 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

The form factors parameterizing the B_c semileptonic matrix elements can be related to a few invariant functions if the decoupling of the spin of the heavy quarks in B_c and in the mesons produced in the semileptonic decays is exploited. We compute the form factors as overlap integral of the meson wave-functions obtained using a QCD relativistic potential model, and give predictions for semileptonic and non-leptonic B_c decay modes. We also discuss possible experimental tests of the heavy quark spin symmetry in B_c decays.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The form factors parameterizing the B_c semileptonic matrix elements can be related to a few invariant functions if the decoupling of the spin of the heavy quarks in B_c and in the mesons produced in the semileptonic decays is exploited.	background 0.68	0.16	0.25	asserted 0.78
s1	We compute the form factors as overlap integral of the meson wave-functions obtained using a QCD relativistic potential model, and give predictions for semileptonic and non-leptonic B_c decay modes.	contribution 0.59	0.96	0.27	asserted 1.00
s2	We also discuss possible experimental tests of the heavy quark spin symmetry in B_c decays.	contribution 0.55	0.73	0.07	hedged possibility 0.63

What kind of paper the classifier reports this is: theoretical result 0.96 · evidence from simulation or computation 0.97.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** Reduced L = 0 wave-functions uM(k) of heavy-heavy (Bc, J/Ψ, ψ(2S)) and heavy-light (Bs, Bd, D) mesons. The wave-functions are obtained by solving the wave equation (3.2); they describe both the pseudoscalar 0− and vector 1− mesons

**Figure 2.** Form factors of Bc semileptonic decays. The variable y is related to the squared momentum t, transferred to the lepton pair, by the relation: y = M2 Bc +M2 M−t 2MBcMM . The solid lines correspond to the form factors obtained by the model discussed in the paper; the dashed lines refer to the model in ref. [15]. 20

Figures reproduced from arXiv:hep-ph/9909423 by the authors.

References

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View on Pith 1992

Forward citations

Cited by 11 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 162 citations worldwide. Full citation record

Observation of the decay Bc+ -> Bs0 pi+
hep-ex 2013-08 accept novelty 7.0 of 10

The Bc+ meson is observed decaying to Bs0 pi+ with a rate ratio times branching fraction of (2.37 ± 0.31 ± 0.11 +0.17/-0.13) x 10^-3, the first weak decay of one B meson into another.
$|V_{ub}|$ determination and testing of lepton flavour universality in semileptonic $B_c \rightarrow D^{(\ast)}$ decays
hep-ph 2019-09 conditional novelty 6.0 of 10

A three-point QCD sum-rule calculation of B_c to D^(*) form factors supports a new |Vub| extraction channel and predicts lepton universality ratios R_c(D^0) = 0.64 +/- 0.05 and R_c(D*) = 0.55 +/- 0.05.
Observation of $B^+_c \rightarrow J/\psi D_s^+$ and $B^+_c \rightarrow J/\psi D_s^{*+}$ decays
hep-ex 2013-04 accept novelty 6.0 of 10

LHCb observes the decays Bc+ to J/psi Ds+ and Bc+ to J/psi Ds*+ for the first time, measures their branching-fraction ratios, and determines the Bc mass to be 6276.28 +/- 1.44 (stat) +/- 0.36 (syst) MeV/c^2.
$B_c$ meson decays into $S$-wave charmonium plus light meson pairs in the perturbative QCD approach
hep-ph 2026-01 unverdicted novelty 5.0 of 10

pQCD calculations predict ~90% longitudinal polarization in B_c to J/psi or psi(2S) plus rho or K* mediated light meson pairs, with one branching ratio ratio matching LHCb at 2.67 vs 2.80.
On lepton flavour universality in semileptonic $B_c \to \eta_c, J/\psi$ decays
hep-ph 2019-01 conditional novelty 5.0 of 10

Sum-rule form factors give R(eta_c) = 0.32 +/- 0.02 and R(J/psi) = 0.23 +/- 0.01 in the Standard Model, and no new-physics scenario fitted to B -> D(*) data reproduces the measured R(J/psi).

Show 6 more citing papers

Constraint on the branching ratio of B_c \to tau nu from LEP1 and consequences for R(D(*)) anomaly
hep-ph 2017-08 accept novelty 5.0 of 10

LEP1 data at the Z peak implies BR(B_c to tau nu) below about 10%, a stronger constraint than the B_c lifetime bound, which narrows the charged-Higgs explanation of the R(D(*)) anomaly.
Implications of new physics in the decays $B_c \to (J/\psi,\eta_c)\tau\nu$
hep-ph 2018-01 conditional novelty 4.0 of 10

With covariant confined quark model form factors, scalar new-physics operators in b to c tau nu are excluded at 2 sigma by current data, while vector and tensor operators survive and would leave distinctive imprints o...
\large\bf $B_c \to (J/\Psi,\,\eta_c)\tau\nu$ semileptonic decays within Standard model and beyond
hep-ph 2017-01 conditional novelty 4.0 of 10

Constraining new-physics couplings with the measured R_D and R_D* ratios, the authors predict ranges for branching ratios, tau polarization fractions, and forward-backward asymmetries in B_c → (J/Ψ, η_c) τν decays acr...
Sensitivity to Majorana neutrinos in $\Delta L=2$ decays of $B_c$ meson at LHCb
hep-ph 2016-04 conditional novelty 4.0 of 10

LHCb could reach branching fractions near 10^-7 (10^-8) in B_c to pion mu mu and B_c to J/psi pion mu mu at LHC runs 2 (3), probing Majorana neutrino mixing |V_muN|^2 of order 10^-5 to 10^-4.
Exclusive semileptonic and nonleptonic decays of the Bc meson
hep-ph 2006-02 conditional novelty 4.0 of 10

The paper tabulates branching ratios for about eighty exclusive Bc decay channels in a fitted relativistic constituent quark model and gives full angular decay distributions for two J/psi cascade modes.
The decays $B_{c}\to J/\psi+\bar\ell\nu_\ell$ and $B_{c}\to J/\psi + \pi(K)$ in covariant confined quark model
hep-ph 2018-04 conditional novelty 3.0 of 10

A covariant confined quark model reproduces the LHCb ratios R(K/pi) and R(pi/mu nu) for B_c decays but underpredicts R(J/psi) by more than 2 sigma.

How the literature uses it

32 arXiv papers cite this in 54 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 25 sentences without a confident label

Contests it 1 paper

All other currently available models [ref] overestimate this ratio.

Measurement of the ratio of $B_c^+$ branching fractions to $J/\psi\pi^+$ and $J/\psi\mu^+\nu_\mu$ · Summary · contest 0.79

Uses its method or tool 2 papers

Within the framework of heavy quark spin symmetry, the hadronic current can be expressed as [ref]

Role of heavy neutral lepton in lepton number violating $B$ meson decays · Semileptonic decay $B_c^- →J/ψμ^-N$ · 0.91
Based on the framework of a QCD relativistic potential model [ref] , the form factor can be represented by the three-parameter formula Eq. [ref].

Sensitivity to Majorana neutrinos in $\Delta L=2$ decays of $B_c$ meson at LHCb · Semileptonic decay $B_c^- →J/ψμ^-N$ · 0.86

Uses its data or values 4 papers

We use the lattice QCD $B_c →B_d$ form factors in [ref] , and the $B_c →B_d^*$ form factors derived in [ref] applying the heavy quark spin symmetry [ref] .

$c \to u \nu {\bar \nu}$ transitions of $B_c$ mesons: 331 model facing Standard Model null tests · Relating the $c →u$ dineutrino and charged dilepton modes using SMEFT · 0.95
in terms of the value at zero recoil $Δ(0)=0.94$, the slope $ρ^2 = 2.9$ and the curvature $c=3$ [ref] .

Sensitivity to Majorana neutrinos in $\Delta L=2$ decays of $B_c$ meson at LHCb · $B_c^- →J/ψπ^+μ^-μ^-$ · 1.00
For the feed-down contributions, the relative decay widths with respect to the decay are varied according to the range of values predicted in Refs. [ref] .

Measurement of the $B_c^+$ meson lifetime using $B_c^+ \to J\!/\!\psi\mu^+ \nu_{\mu} X$ decays · Systematic uncertainties and checks · 0.92

Compares with it 8 papers

We compare our results with Refs. [ref] in the forth column.

Study of charm and beauty mass spectra, semileptonic decays of $B_{(s,c)}$ and ${B_c} \to J/\psi ({\eta _c}) + P(V)$ in a phenomenological potential model · Isgur-Wise function parameters, Semileptonic decay widths of $B$, $B_s$ and $B_c$ to charmed mesons · 1.00
For a comparison, the previous PQCD predictions [ref] and the results from other theoretical approaches [ref] are also listed in Tables [ref] and [ref].

$B_c$ meson decays into $S$-wave charmonium plus light meson pairs in the perturbative QCD approach · Numerical Analysis · 1.00
Overall the best description of all the ratios of branching fraction is given by the predictions of a QCD relativistic potential model [ref] .

Electroweak, QCD and flavour physics studies with ATLAS data from Run 2 of the LHC · Precision measurement of decays · 0.85

Cites it as background 10 papers

This remark has prompted a number of phenomenological analyses of $B_c$ decays [ref] .

Relations among $B_c \to J/\psi, \eta_c$ form factors · Introduction · 0.84
There are a good number of theoretical models that study leptonic, semileptonic and hadronic decay channels of $cb̅$ state [ref] .

Mass spectra and decays of ground and orbitally excited $c\bar{b}$ states in non relativistic quark model · INTRODUCTION · 0.91
Beside the $b→c$ tree diagrams, the annihilation topology can also contribute, although it is not expected to have a large effect and is therefore often neglected [ref] .

Electroweak, QCD and flavour physics studies with ATLAS data from Run 2 of the LHC · Precision measurement of decays · 0.86

Discussion

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