{"arxiv_id":"hep-ph/0306306","incoming":{"papers":34,"sentences":69,"groups":[{"kind":"contests","label":"Contests it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"1607.06823","title":"Measurement of the ratio of branching fractions $\\mathcal{B}(B_{c}^{+} \\to J/\\psi K^{+})/\\mathcal{B}(B_{c}^{+} \\to J/\\psi\\pi^{+})$","url":"/paper/1607.06823","section":"Results and summary","sentence":"The result supersedes the previous measurement [ref] and agrees with the theoretical predictions in Refs. [ref] , but disfavours that based on QCD sum rules [ref] .","intent_p":0.68,"contests_p":0.8}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":6,"sentences":9,"quotes":[{"arxiv_id":"2604.01782","title":"Exclusive semileptonic and nonleptonic $J/\\psi$ decays","url":"/paper/2604.01782","section":"RELATIVISTIC QUARK MODEL","sentence":"This matrix element in the quasipotential approach is expressed [ref] through the overlap integral of the initial $J/ψ$ and final $D_(s)$ meson wave functions $Ψ_Mp_M$ ($M=J/ψ$ or $D_(s)$), which are projected on the positive energy states and boosted to the moving reference frame with the three-momentum $p_M$ [equation] Here the vertex function $Γ=Γ^(1)+Γ^(2)$ contains two contributions.","intent_p":0.97,"contests_p":null},{"arxiv_id":"2501.16406","title":"Exclusive semileptonic decays of $D$ and $D_s$ mesons into orbitally and radially excited states of strange and light mesons","url":"/paper/2501.16406","section":"Weak decay matrix elements","sentence":"The wave function of the moving meson $Ψ_F Δ$ is connected with the wave function in the rest frame $Ψ_F 0$ by the transformation [ref] [equation] where $R^W$ is the Wigner rotation, $L_Δ$ is the Lorentz boost from the meson rest frame to a moving one, and $D^1/2_q(R)$ is the rotation matrix in spinor representation.","intent_p":0.94,"contests_p":null},{"arxiv_id":"1401.6932","title":"Measurement of the $B_c^+$ meson lifetime using $B_c^+ \\to J\\!/\\!\\psi\\mu^+ \\nu_{\\mu} X$ decays","url":"/paper/1401.6932","section":"Signal model","sentence":"For the decay, three different decay models are implemented in the simulation, referred to as Kiselev [ref] , Ebert [ref] and ISGW2 [ref] .","intent_p":0.94,"contests_p":null},{"arxiv_id":"1711.05623","title":"Measurement of the ratio of branching fractions $\\mathcal{B}(B_c^+\\,\\to\\,J/\\psi\\tau^+\\nu_\\tau)$/$\\mathcal{B}(B_c^+\\,\\to\\,J/\\psi\\mu^+\\nu_\\mu)$","url":"/paper/1711.05623","section":"Introduction","sentence":"In this expansion, the form factors $V(q^2)$, $A_0(q^2)$, $A_1(q^2)$, and $A_2(q^2)$ (following the convention of Ref. [ref] ) are fit by functions of the form [equation] where $z(q^2)$ is defined in Ref. [ref] .","intent_p":0.81,"contests_p":null},{"arxiv_id":"1404.0287","title":"Evidence for the decay $B_c^+ \\rightarrow J/\\psi 3\\pi^+ 2\\pi^-$","url":"/paper/1404.0287","section":"Detector","sentence":"The model allows the implementation of different form factors for this decay, calculated using QCD sum rules [ref] or a relativistic quark model [ref] .","intent_p":0.83,"contests_p":null}]},{"kind":"data_used","label":"Uses its data or values","papers":5,"sentences":5,"quotes":[{"arxiv_id":"1810.04939","title":"$b\\to c\\tau\\nu$ Transitions in the Standard Model Effective Field Theory","url":"/paper/1810.04939","section":"$B_c→(J/ψ, η_c)τν$","sentence":"Similar to the definitions of $R(D^(∗))$, the ratios $R(J/ψ)$ and $R(η_c)$ for $B_c→(J/ψ, η_c)τν$ decays are defined, respectively, by [equation] Using the model-dependent calculations of $B_c→(J/ψ, η_c)$ transition form factors [ref] , the SM central values of $R(J/ψ)$ and $R(η_c)$ vary within the ranges $0.24-0.30$ and $0.25-0.35$, respectively, with the former being lower than the LHCb measurement $R(J/ψ)^exp=0.71(17)(18)$ [ref] by $1.7σ$.","intent_p":0.92,"contests_p":null},{"arxiv_id":"1401.6932","title":"Measurement of the $B_c^+$ meson lifetime using $B_c^+ \\to J\\!/\\!\\psi\\mu^+ \\nu_{\\mu} X$ decays","url":"/paper/1401.6932","section":"Systematic uncertainties and checks","sentence":"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] .","intent_p":0.92,"contests_p":null},{"arxiv_id":"1711.05623","title":"Measurement of the ratio of branching fractions $\\mathcal{B}(B_c^+\\,\\to\\,J/\\psi\\tau^+\\nu_\\tau)$/$\\mathcal{B}(B_c^+\\,\\to\\,J/\\psi\\mu^+\\nu_\\mu)$","url":"/paper/1711.05623","section":"Introduction","sentence":"The pole mass $M_pole$ is the mass of the excited state with quantum numbers corresponding to the form factor: the $J^P = 1^-$ state for the form factor $V(q^2)$, taken to be 6.33; the $0^-$ state for $A_0(q^2)$, which is the mass itself; and finally the $1^+$ state for $A_1(q^2)$ and $A_2(q^2)$, taken to be 6.73 [ref] .","intent_p":0.98,"contests_p":null},{"arxiv_id":"1407.2126","title":"Measurement of the ratio of $B_c^+$ branching fractions to $J/\\psi\\pi^+$ and $J/\\psi\\mu^+\\nu_\\mu$","url":"/paper/1407.2126","section":"Extraction of the $$ signal","sentence":"0.009–0.185 [ref] .","intent_p":0.91,"contests_p":null},{"arxiv_id":"1309.0587","title":"Observation of the decay $B_c \\rightarrow J/\\psi K^+ K^- \\pi^+ $","url":"/paper/1309.0587","section":"Introduction","sentence":"The predictions for the ratio of branching fractions $(→)/(→)$ are 0.49 and 0.47 [ref] , using form factor contributions from Refs. [ref] and [ref] , respectively.","intent_p":0.83,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":11,"sentences":15,"quotes":[{"arxiv_id":"2301.11107","title":"Covariant Light-Front Approach for $B_c$ Decays into Charmonium: Implications on Form Factors and Branching Ratios","url":"/paper/2301.11107","section":"Transition form factors","sentence":"One can find that our results are consistent with those calculated using the relativistic quark model (RQM) [ref] , while they are too large for the results given by the relativistic constituent quark model (RCQM) [ref] , the light-cone sum rule (LCSR) [ref] , and the QCD sum rules [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1407.2126","title":"Measurement of the ratio of $B_c^+$ branching fractions to $J/\\psi\\pi^+$ and $J/\\psi\\mu^+\\nu_\\mu$","url":"/paper/1407.2126","section":"Summary","sentence":"Extrapolating to the full mass range, we obtain a value of $()/()=0.0469 ±0.0028 ±0.0046$, which is in good agreement with the theoretical predictions by Ebert [ref] and El-Hady [ref] , and consistent with the prediction by Ke [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"2601.01305","title":"$B_c$ meson decays into $S$-wave charmonium plus light meson pairs in the perturbative QCD approach","url":"/paper/2601.01305","section":"Numerical Analysis","sentence":"For a comparison, the previous PQCD predictions [ref] and the results from other theoretical approaches [ref] are also listed in Tables [ref] and [ref].","intent_p":1.0,"contests_p":null},{"arxiv_id":"1304.4530","title":"Observation of $B^+_c \\rightarrow J/\\psi D_s^+$ and $B^+_c \\rightarrow J/\\psi D_s^{*+}$ decays","url":"/paper/1304.4530","section":"Results and summary","sentence":"The fraction of the $𝒜_±±$ amplitude in the decay is measured to be [equation] in agreement with a simple estimate of $23$, the measurements [ref] and factorization predictions [ref] for $→^*-_^∗+$ decays, and expectations for $→ℓ^+_ℓ$ decays from Refs. [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"1404.0287","title":"Evidence for the decay $B_c^+ \\rightarrow J/\\psi 3\\pi^+ 2\\pi^-$","url":"/paper/1404.0287","section":"Results and summary","sentence":"The result is in agreement with theoretical predictions [ref] of 0.95 and 1.1 using the form factors from Refs. [ref] and [ref] , respectively.","intent_p":0.98,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":13,"sentences":13,"quotes":[{"arxiv_id":"2411.11413","title":"Unravelling theoretical challenges in understanding $B_c$ meson decay","url":"/paper/2411.11413","section":"Semi-leptonic decays","sentence":"Some of them include the potential model approach [ref] , the Bethe-Salpeture approach [ref] , relativistic constituent quark model on the light front [ref] , three-point sum rule of QCD, and non-relativistic QCD (NRQCD) [ref] , relativistic quark model based on the quasi-potential approach [ref] , the Baur, Stech-Wirbel framework [ref] , perturbative QCD(PQCD) approach [ref] , and the lattice QCD approach [ref] .","intent_p":0.92,"contests_p":null},{"arxiv_id":"1809.02968","title":"Relativistic effects in the semileptonic $B_c$ decays to charmonium with the Bethe-Salpeter method","url":"/paper/1809.02968","section":"Introduction","sentence":"A great deal of work has been done on various $B_c$ decays under different approaches, such as NRQCD approach [ref] , the perturbative QCD approach (PQCD) [ref] , the relativistic quark model (RQM) [ref] , Light-cone sum rules (LCSR) [ref] , the non-relativistic constituent quark model (NCQM) [ref] and QCD sum rules (QCDSR) [ref] .","intent_p":0.99,"contests_p":null},{"arxiv_id":"1801.06927","title":"Implications of new physics in the decays $B_c \\to (J/\\psi,\\eta_c)\\tau\\nu$","url":"/paper/1801.06927","section":"Introduction","sentence":"In the literature, a wide range of different approaches has been used to compute the $B_c→J/ψ(η_c)$ transition form factors, such as the potential model approach [ref] , the Bethe-Salpeter equation [ref] , the relativistic constituent quark model on the light front [ref] , three-point sum rules of QCD and nonrelativistic QCD [ref] , the relativistic quark model based on the quasipotential approach [ref] , the nonrelativistic quark model [ref] , the Bauer-Stech-Wirbel framework [ref] , the perturbative QCD (pQCD) [ref] , and the covariant quark model developed by our group [ref] .","intent_p":0.93,"contests_p":null},{"arxiv_id":"2302.13743","title":"$B_c^- \\to J/\\psi (\\to \\mu^+ \\mu^-)\\tau^- (\\to \\pi^- \\nu_\\tau, \\rho^- \\nu_\\tau, \\ell^-\\bar{\\nu}_\\ell\\nu_\\tau)\\bar{\\nu}_\\tau$ decays with visible final-state kinematics","url":"/paper/2302.13743","section":"Introduction","sentence":"In the literature, a wide range of different approaches has been used to evaluate these form factors, such as the quark models [ref] , the QCD sum rules [ref] , the Bethe-Salpeter equation [ref] , the relativistic constituent quark model on the light front [ref] , the perturbative QCD calculations [ref] , as well as the nonrelativistic QCD (NRQCD) approach [ref] .","intent_p":0.96,"contests_p":null},{"arxiv_id":"2311.00758","title":"Analyzing the semileptonic and nonleptonic $B_c \\to J/\\psi, \\eta_c$ decays","url":"/paper/2311.00758","section":"Extractions of $ψ^R_M(0)$ for $M = B_c, J/ψ, η_c$","sentence":"Apart from the lattice, to date, several theoretical approaches have been incorporated in order to estimate the $B_c→J/ψ(η_c)$ form factors such as perturbative QCD (PQCD) [ref] , the constituent quark model [ref] , the relativistic quark model [ref] , the non-relativistic quark model [ref] , QCD sum rules [ref] , the relativistic constituent quark model [ref] , the light-front covariant quark model (LFCQ) [ref] .","intent_p":1.0,"contests_p":null}]}],"unlabelled_sentences":26},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":null,"_links":{"html":"https://pith.science/paper/hep-ph/0306306"}}