Deviation from the standard model prediction is observed in many semileptonic $B$ decays mediated via $b \to c$ charged current interactions. In particular, current experimental measurements of the ratio of branching ratio $R_D$ and $R_{D^{\ast}}$ in $B \rightarrow D^{(*)}l ν$ decays disagree with standard model expectations at the level of about $4.1σ$. Moreover, recent measurement of the ratio of branching ratio $R_{J/Ψ}$ by LHCb, where $R_{J/Ψ} = \mathcal B(B_c \to J/Ψ\,τν)/\mathcal B(B_c \to J/Ψ\,μν)$, is more than $2σ$ away from the standard model prediction. In this context, we consider an effective Lagrangian in the presence of vector and scalar new physics couplings to study the implications of $R_D$ and $R_{D^{\ast}}$ anomalies in $B_s \to D_s\,τν$ decays. We give prediction of several observables such as branching ratio, ratio of branching ratio, forward backward asymmetry parameter, $τ$ polarization fraction, and the convexity parameter for the $B_s \to D_s\,τν$ decays within the standard model and within various new physics scenarios.
We make predictions for the exclusive semileptonic and the non-leptonic decay widths of the B_c meson. We evaluate the B_c semileptonic form factors for different decay channels in a relativistic model, and use factorization to obtain the non-leptonic decay widths.
We summarize the status of semileptonic and leptonic $B$ decays, including $|V_{cb}|$ and $|V_{ub}|$ exclusive and inclusive determinations, decays to excited states of the charm meson spectrum and decays into $τ$ leptons.
In this talk, we review the QCD calculation of the lepton spectrum from inclusive semileptonic $B$ decay. We compare this prediction to that of the ACCMM model. This latter work was done in collaboration with Csaba Csaki.
We present Standard Model predictions for lepton flavour universality ratios of inclusive $B\to X_{(c)} \ell \barν_\ell$. For the $\ell=μ,e$, these ratios are very close to unity as expected. For the $τ$ mode, we update the SM prediction for the branching ratio including power-corrections in the heavy-quark expansion up to $1/m_b^3$. These inclusive ratios serve as an important cross-check of the exclusive $B\to D^{(*)}\ell\barν_\ell$ modes, in which tensions exists between the predictions and measurements in those modes.
We employ the relativistic constituent quark model to give a unified description of the leptonic and semileptonic decays of pseudoscalar mesons (π, K, D, D_s, B, B_s). The calculated leptonic decay constants and form factors are found to be in good agreement with available experimental data and other approaches. We reproduce the results of spin-flavor symmetry in the heavy quark limit.
We study the forward-backward and the CP-violating asymmetries (both time-independent and time-dependent) in rare semileptonic and radiative leptonic B_{d,s}-decays and investigate the sensitivity of these asymmetries to the extensions of the Standard model.
We study the lepton angular distributions in $B\to D^{(*)} \ell ν_{\ell}$ decays. The lepton angular asymmetries in the decays with the general effective interactions are examined. We demonstrate that the asymmetries are sensitive to new physics with a right-handed quark current.
The status of lattice calculations of heavy quark phenomenology is reviewed. Particular emphasis is placed on the understanding and control of the calculational uncertainties. The ensuing implications for constraining the CKM matrix elements are discussed.
Perturbative corrections of the order of $α_s$ to inclusive double differential lepton distribution from $b$ quark decay are considered. A perturbative correction to the charged lepton energy spectrum has been calculated for an arbitrary charged lepton mass. The perturbative contribution suppresses the partial rate but almost does not change the shape of energy distribution. Applications of our result to semileptonic B meson decays are briefly discussed.
Starting from an Operator Product Expansion in the Heavy Quark Effective Theory up to order 1/m_b^2 we calculate the inclusive semileptonic decays of unpolarized bottom hadrons including lepton mass effects. We calculate the differential decay spectra dΓ/(dE_τ), and the total decay rate for B meson decays to final states containing a τlepton.
We present a global analysis of leptonic and semileptonic kaon decays data, including all recent results by BNL-E865, KLOE, KTeV, ISTRA+, and NA48. Experimental results are critically reviewed and combined, taking into account theoretical (both analytical and numerical) constraints on the semileptonic kaon form factors. This analysis leads to a very accurate determination of Vus and allows us to perform several stringent tests of the Standard Model.
We extend previous computations of the second order QCD corrections to semileptonic b \to c inclusive transitions, to the case where the charged lepton in the final state is massive. This allows accurate description of b \to c τ\bar ν_τdecays. We review techniques used in the computation of O(α_s^2) corrections to inclusive semileptonic b \to c transitions and present extensive numerical studies of O(α_s^2) QCD corrections to b \to c l \bar ν_l decays, for l =e, τ.
We complement the results for the radiative corrections to the s2.l angular correlation of baryon semileptonic decays of Ref. [1] with the final results in the rest frame of the decaying baryon.
We put constraints on several products of R-parity violating lambda lambda' and lambda' lambda' type couplings from leptonic and semileptonic tau, B_d and B_s decays. Most of them are one to two orders of magnitude better than the existing bounds, and almost free from theoretical uncertainties. A significant improvement of these bounds can be made in high luminosity tau-charm or B factories.
Analytic formulae for the one-loop order QCD corrections to the differential width of the semileptonic b decay are given with the tau polarization taken into account. Thence the polarization of tau is expressed by its energy and the invariant mass of the tau + antineutrino system. The non-perturbative corrections by Falk et al. are incorporated in the calculation.
Analytic formulae are given for order alpha_s perturbative QCD corrections to the double differential distribution of the tau lepton energy and the invariant mass of the tau + antineutrino system in semileptonic decays of the bottom quark. The corresponding distribution for B meson decays are obtained by combining these results and the nonperturbative QCD corrections calculated by Falk et al. The moments of the energy distribution of the tau lepton are calculated.
We compute O(alpha_s^2) QCD corrections to the lepton invariant mass spectrum in the decay b --> u l nu_l, relevant for the determination of the CKM matrix element |V_{ub}|. Our method can also be used to evaluate moments of the lepton energy distribution with an O(alpha_s^2) accuracy. The abelian part of our result gives the neutrino invariant mass spectrum in the muon decay and, upon integration, the O(alpha^2) correction to the muon lifetime.
We discuss the possibilities of extracting the constraints on New Physics by using the current data on the leptonic and semileptonic decays of pseudoscalar mesons. In doing so we use a general low energy Lagrangian that besides the vector and axial operators also includes the (pseudo-)scalar and tensor ones. In obtaining constraints on New Physics couplings we combine the experimental information concerning several decay modes with the accurate lattice QCD results for the hadronic matrix elements. We propose to study new observables that can be extracted from the angular analysis of the semile…
Large long-distance standard model effects in FCNC semileptonic D decays can make observable these processes in future measurements. Eventual disagreements in this sector and/or the observation of lepton family violating (LFV) D decays would require an explanatio beyond the SM framework. In this paper we confront present experimental data on leptonic and semileptonic FCNC and LFV D meson decays with a version of the two-Higgs doublet model that allows these effects to occur at tree- level. The stringent bounds on the parameters of the model are obtained from D^0 --> l^+l'^- and D --> pi l^+l'^…
Recently, Neubert has suggested that a certain class of nonperturbative corrections dominates the shape of the electron spectrum in the endpoint region of semileptonic $B$ decay. Perturbative QCD corrections are important in the endpoint region. We study the effects of these corrections on Neubert's proposal. The connection between the endpoint of the electron spectrum in semileptonic $B$ decay and the photon spectrum in $b\rightarrow sγ$ is outlined.
The evaluation, systematic analysis and numerical study of the semileptonic $τ$-lepton decays with two mesons in the final state has been made in the frame of the standard model extended by right handed neutrinos. In the analysis, heavy-neutrino nondecoupling effects, finite quark masses, quark and meson mixings, finite widths of vector mesons, chiral symmetry breakings in vector-meson--pseudoscalar-meson vertices and effective Higgs-boson--pseudoscalar-meson couplings have been included. Numerical estimates reveal that the decays $τ^-\to e^-π^-π^+$, $τ^-\to e^-K^-K^+$ and $τ^-\to e^-K^0\bar{K…
Analytical radiative corrections of order (alpha/pi)(q/M) are calculated for the four-body region of the Dalitz plot of baryon semileptonic decays when the s1.l correlation is present. Once the final result is available, it is possible to exhibit it in terms of the corresponding final result of the three-body region following a set of simple changes in the latter, except for a few exceptions. We cover two cases, a charged and a neutral polarized decaying baryon.
We compute the first two moments of the final hadronic invariant mass in inclusive semileptonic B decay, in the presence of a cut on the charged lepton energy. These moments may be measured directly by experiments at the Upsilon(4S) using the neutrino reconstruction technique, which requires such a cut. Measurement of these moments will place constraints on the nonperturbative parameters \barΛand λ_1, which are relevant for extracting the quark masses m_b and m_c, as well as the CKM angle V_cb. We include terms of order α_s^2β_0 and 1/m_b^3 in the operator product expansion, and use the latter…
Leptonic and semileptonic decays in the charm sector have been well studied in recent years. With the largest data sample near $D\bar D$ threshold, precision measurements of leptonic and semileptonic decays of charm meson and baryon are perfromed at BESIII. Test for letpon flavor universality is also performed. Sensitivity for rare leptonic and semileptonic charm decays is significantly improved taking advantage of the huge statistics in LHCb and the $B$ factories.
The exclusive semileptonic heavy baryon decay Λ_b\to p l\barνis investigated using light-cone sum rule method in both full QCD and HQET. The form factors describing the decay are calculated and used to predict the decay width and differential distribution. The total decay width obtained from full QCD is in agreement with the previous theoretical predictions while the HQET result are typically one order smaller. Both results are consistent with the experimental upper limit and can be compared to the refined experimental data in the future.
We obtain a model-independent expression for the Dalitz plot of semileptonic decays of polarized hyperons including radiative corrections to order alpha and neglecting terms of order (alpha q)/(pi M_1), where q is the four-momentum transfer and M_1 is the mass of the decaying hyperon. We specialize our results to exhibit the correlation between the charged-lepton momentum and the spin of the decaying hyperon. We present results for the three-body region of the Dalitz plot and for the complete Dalitz plot (which includes the four-body region). From these results we also obtain the corresponding…
Several beyond the Standard Model scenarios introduce new heavy neutrinos, whose Dirac or Majorana nature could be tested by comparing the rates of lepton number violating and lepton number conserving processes: a Dirac fermion induces only the latter, while a Majorana one predicts the same rate for both of them. Nevertheless, in the presence of more than one Majorana fermion, this picture may change drastically due to interference effects. We focus on lepton number violating and lepton flavour violating semileptonic meson decays induced by two heavy Majorana fermions, exploring the necessary …
We employ OPE techniques within HQET to calculate the inclusive semileptonic decays of polarized $Λ_b$ baryons. Lepton mass effects are included which enables us to also discuss rates into polarized $τ$-leptons. We present explicit results for the longitudinal polarization of the $τ$ in the $Λ_b$ rest frame as well as in the $(τ^-, \bar ν_τ)$ c.m. frame. In both cases we make use of novel calculational techniques which considerably simplify the calculations. The transverse polarization components of the $τ$ are calculated in the $(τ^-,\barν_τ)$ c.m. frame. We delineate how to measure the full …
We address the impact of a modified $W \ell ν$ coupling on a wide range of observables, such as $τ$ leptonic and mesonic decays, leptonic decays of pseudoscalar mesons, as well as semileptonic meson decays. In particular, we concentrate on deviations from lepton flavour universality, focusing on the ratios $R_{P} = Γ(P \to \ell ν) / Γ(P \to \ell' ν)$, with $P=K, π, D, D_s$, $R(D)={Γ(B^+ \to D τ^+ ν)}/{Γ(B^+ \to D\ell^+ ν)}$, $R τ={Γ(τ\to μνν)}/{Γ(τ\to eνν)}$, $R^{\ell τ}_P=Γ(τ\to Pν)/Γ(P\to \ell ν)$, and $\text{BR}(B \to τν)$. We further consider leptonic gauge boson decays, such as $W\to \ell…
It has been known that there exists a disagreement emerged between the determination of $|V_{ub}|$ from inclusive $B \to X_u\ellν$ decays and exclusive $B \to π\ellν$ decays. In order to solve the mismatch, we investigate the left-right (LR) mixing effects, denoted by $ξ_u$, in leptonic and semileptonic $b \to u$ decays. We find that the new interactions $(V+A)\times (V-A)$ induced via the LR mixing can explain the mismatch between the values of $|V_{ub}|$ if Re$(ξ_{u})=-(0.14 \pm 0.12)$. Furthermore, we also find that the LR mixing effects can enhance the branching fractions for $B \to τν$ an…
We search for signals of Weak Annihilation in inclusive semileptonic D decays. We consider both the widths and the lepton energy moments, which are quite sensitive probes. Our analysis of Cleo data shows no clear evidence of Weak Annihilation, and allows us to put bounds on their relevance in charmless B semileptonic decays.
The leading order contribution to the direct CP asymmetry in tau^{+/-} -> K^{+/-} pi^0 nu_{tau} decay rates is evaluated within the Standard Model. The weak phase required for CP violation is introduced through an interesting mechanism involving second order weak interactions, which is also responsible for tiny violations of the Delta S= Delta Q rule in K_{l3} decays. The calculated CP asymmetry turns out to be of order 10^{-12}, leaving a large window for studying effects of non-standard sources of CP violation in this observable.
New universality appears for the baryon Isgur--Wise form factor in the large $N_c$ limit. It is found that the semileptonic $Λ_b \rightarrow Λ_c$ and $Σ_b^{(*)} \rightarrow Σ^{(*)}_c$ decays are described by the same form factor, which can be calculated analytically. In the exact chiral $SU(3)$ limit, the same form factor is applicable to semileptonic $Ω_b^{(*)} \rightarrow Ω^{(*)}_c$ decays.
In this work we study the Lepton Flavour Violating semileptonic $τ$ decays: 1) $τ\to μPP$ with $PP= π^+π^-, π^0π^0, K^+K^-, K^0 {\bar K}^0$; 2) $τ\to μP$ with $P=π^0, η, η'$ and 3) $τ\to μV$ with $V = ρ^0, ϕ$. We work within the context of two constrained MSSM scenarios: the CMSSM and NUHM. A full one-(SUSY)loop computation is presented and the importance of the various contributions, the $γ$-, $Z$-, and Higgs bosons mediated ones are analysed. The hadronization of quark bilinears is performed within the chiral framework. Some discrepancies in the predicted rates for BR($τ\to μη$), BR($τ\to μη…
In this paper, we review recent calculations of the CKM matrix elements $|V_{cd}|$ and $|V_{cs}|$ from semileptonic and leptonic decays of $D$ and $D_s$ mesons using lattice QCD methods.
The paper gives the polarization of the tau lepton in the semileptonic B decays with respect to the direction of the virtual W boson. The result is given including the nonperturbative HQET corrections.The perturbative QCD corrections are probably negligible as suggested by the existing results for the longitudinal polarization of the charged lepton (Jezabek and Urban, 1998).
We discuss $B_c \to η_c$ and $B_c \to J/ψ$ semileptonic decays within the Standard Model (SM) and beyond. The relevant transition form factors, being the main source of theoretical uncertainties, are calculated in the sum rule approach and are provided in a full $q^2$ range. We calculate the semileptonic branching fractions and find for the ratios, $R_{η_c}|_{\rm SM}= 0.32 \pm 0.02$, $R_{J/ψ}|_{\rm SM} = 0.23 \pm 0.01$. Both predictions are in agreement with other existing calculations and support the current tension in $R_{J/ψ}$ at 2$σ$ level with the experiment. To extend the potential of te…
We have calculated the radiative corrections to the Dalitz plot of baryon semileptonic decays with angular correlation between polarized emitted baryons and charged leptons. This work covers both charged and neutral decaying baryons and is restricted to the so-called three-body region of the Dalitz plot. Also it is specialized at the center-of-mass frame of the emitted baryon. We have considered terms up to order (alpha/pi)(q/M_1)^0, where q is the momentum-transfer and M_1 is the mass of the decaying baryon, and neglected terms of order (alpha/pi)(q/M_1)^n$ for n >= 1. The expressions display…
We study the scalar leptoquark effects on the rare semileptonic decays of $Λ_b$ baryon, governed by the quark level transition $b \to s l^+ l^-$. We estimate the branching ratios, forward-backward asymmetries, lepton polarization parameters and the lepton flavour non-universality effects in these decay channels. We find significant deviations from the corresponding standard model predictions in some of the observables due to leptoquark effects. We also investigate the lepton flavour violating decays $Λ_b \to Λl_i^- l_j^+$, the branching ratios of which are found to be ${\cal O}(10^{-10} - 10^{…
We review semi-inclusive charmless B decays, focussing on threshold logarithmic resumming and on universality of QCD dynamics in radiative and semileptonic decays.
The contributions of the neutral top-pion $π_{t}^{0}$ and the non-universal gauge boson $Z'$ predicted by topcolor scenario to the lepton flavor violating $(LFV)$ semileptonic $τ$ decays $τ\to lP(V)$ $(P=π^{0}, η, η' $ and $ V=ρ^{0}, ϕ)$ are discussed. We find that the contributions of $Z'$ to these decay processes are generally larger than those from $π_{t}^{0}$. $π_{t}^{0}$ can only make the value of the branching ratio $Br(τ\to lP)$ in the range of 1$\times10^{-11}$ $\sim$ 1$\times10^{-16}$, which is far below the sensitivity of foreseeable experiments. With reasonable values of the free pa…
A heavy-quark limit of the Dyson-Schwinger equations is introduced and used in an exploratory study of leptonic and semileptonic decays of heavy mesons. The application of this framework to heavy-to-light semileptonic decays, which require a good knowledge of light-quark propagation characteristics and light-meson bound state amplitudes, is illustrated.
Recently there has been much interest in the tauonic semileptonic meson decays B -> D + tau + nu_tau and B -> D* + tau + nu_tau where one has found larger rates than what is predicted by the Standard Model. We analyze the corresponding semileptonic baryon decays Lambda_b(0) -> Lambda_c(+) + tau(-) + antinu_tau with particular emphasis on the lepton helicity flip and scalar contributions which vanish for zero lepton masses. We calculate the total rate, differential decay distributions, the longitudinal and transverse polarization of the daughter baryon Lambda_c(+) and the tau-lepton, and the le…
Deviation from the standard model prediction is observed in many semileptonic $B$ decays mediated via $b \to c$ charged current interactions. In particular, current experimental measurements of the ratio of branching ratio $R_D$ and $R_{D^{\ast}}$ in $B \rightarrow D^{(*)}l ν$ decays disagree with standard model expectations at the level of about $4.1σ$. Moreover, recent measurement of the ratio of branching ratio $R_{J/Ψ}$ by LHCb, where $R_{J/Ψ} = \mathcal B(B_c \to J/Ψ\,τν)/\mathcal B(B_c \to J/Ψ\,μν)$, is more than $2σ$ away from the standard model prediction. In this context, we consider …
Semileptonic $B$ meson decays into the four lightest excited charmed meson states ($D_0^*$, $D_1^*$, $D_1$, and $D_2^*$) and their counterparts with $s$ quarks are investigated, including the full lepton mass dependence. We derive the standard model predictions for the differential branching fractions, as well as predictions for the ratios of the semi-tauonic and light lepton semileptonic branching fractions. These can be systematically improved using future measurements of the total or differential semileptonic rates to $e$ and $μ$, as well as the two-body hadronic branching fractions with a …
In the semileptonic decays of heavy mesons and baryons the lepton-mass dependence factors out in the quadratic $\cos^2θ$ coefficient of the differential $\cosθ$ distribution. We call the corresponding normalized coefficient the convexity parameter. This observation opens the path to a test of lepton universality in semileptonic heavy meson and baryon decays that is independent of form-factor effects. By projecting out the quadratic rate coefficient, dividing out the lepton-mass-dependent factor and restricting the phase space integration to the $τ$ lepton phase space, one can define optimized …
A summary of WG II of the CKM 2018 conference on semileptonic and leptonic $b$-hadron decays is presented. This includes discussions on the CKM matrix element magitudes $|V_{ub}|$ and $|V_{cb}|$, lepton universality tests such as $R(D^{*})$ and leptonic decays. As is usual for semileptonic and leptonic decays, much discussion is devoted towards the interplay between theoretical QCD calculations and the experimental measurements.
A recent calculation by Chay and Rey has shown that instantons may make a significant contribution to the lepton energy spectrum near its endpoint. Using an ansatz borrowed from the study of high energy baryon number violating processes, we investigate whether these corrections could spoil the relation between the nonperturbative contributions to this spectrum and to the photon energy spectrum in radiative $B$ decays. We find, in general, that this universality may well fail unless the spectrum is smeared over a region which is considerably larger than had previously been thought necessary. Th…
The perturbative QCD corrections to the semileptonic decay width of the tau lepton are evaluated in the next-next-to-leading order from the contour integral representation in various renormalization schemes, using numerical solution of the renormalization group equation for complex energies. A quantitative estimate of the ambiguities resulting from the freedom of choice of the renormalization scheme is obtained by taking into account predictions in all schemes that do not involve large cancellations in the expression for the scheme invariant combination of the expansion coefficients. The probl…
Within the framework of the factorization approximation, two body non-leptonic decays of $B$ mesons are related to semileptonic matrix elements and form factors, evaluated with an effective lagrangian incorporating both chiral and heavy quark symmetries. Using semileptonic $D$-decay data, estimates for nonleptonic processes are obtained.
A relativistic constituent quark model is adopted to give an unified description of the leptonic and semileptonic decays of pseudoscalar mesons (π, K, D, D_s, B, B_s). The calculated leptonic decay constants and form factors are found to be in good agreement with available experimental data and the results of other approaches. Eventually, the model is found to reproduce the scaling behaviours of spin-flavor symmetry in the heavy-quark limit.
The recent significant progress on both the experimental and theoretical sides on the study of leptonic and semileptonic kaon decays allows to precisely test the Standard Model. Here we present results for the determination of Vus from experimental data, the comparison between the values of Vus obtained from data on semileptonic and leptonic kaon decays, and tests of lepton universality in semileptonic kaon decays.
Motivated by the recent observation of lepton universality violation in the flavour changing charged current transitions $b \to c l \barν_l$, we intend to scrutinize the lepton non-universality effects in rare semileptonic $B$ meson decays involving the quark level transitions $b \to u l \barν_l$. In this regard, we envisage the model-independent approach and consider the generalized effective Lagrangian in the presence of new physics and constrain the new parameters by using the experimental branching fractions of $B_u^+ \to l^+ ν_l$ and $B^- \to π^0 μ^- \bar ν_μ$ processes, where $l=e, μ, τ$…
The semileptonic decays of $Λ_{b}\toΛ_{c}^{(*)}\ellν_\ell$ and $Λ_{c}\toΛ^{(*)}\ellν_\ell$ are studied in the light-front quark model in this work. Instead of the quark-diquark approximation, we use the three-body wave functions obtained by baryon spectroscopy. The ground states $(1/2^{+})$, the $λ$-mode orbital excited states $(1/2^{-})$, and the first radial excited states $(1/2^{+})$ of $Λ_{(c)}^{(*)}$ are considered. The discussions are given for the form factors, partial widths, branching fractions, leptonic forward-backward asymmetries, hadron polarizations, lepton polarizations, and the…
We summarize recent results on QCD corrections to various observables in semileptonic $b$ quark decays. For massless leptons in the final state we present effects of such corrections on triple differential distribution of leptons which are important in studies of polarized $b$ quark decays. Analogous formulas for distributions of neutrinos are applicable in decays of polarized $c$ quarks. In the case of decays with a $τ$ lepton in the final state mass effect of $τ$ has to be included. In this case we concentrate on corrections to the total decay width.
The decay width of b to c,c,c,l,nu has been computed as an expansion in limit (1- 3*(m_c/m_b)) << 1 with zero lepton invariant mass. Considering O(alpha_s^2) corrections to b to c,l,nu with zero invariant lepton mass, inclusion of our result is shown to rectify the disagreement between the expansions around (1-(m_c/m_b)) << 1 and m_c/m_b << 1 at smaller values.
We present a complete $O(α_s^2)$ correction to the differential width of the inclusive semileptonic decay $b\to clν_l$ at the kinematical point of vanishing invariant mass of the leptons, $q^2=0$. Together with the recently computed $O(α_s^2)$ correction at the upper boundary of the lepton invariant mass spectrum, this new information permits an estimate of the $O(α_s^2)$ effect in the total inclusive semileptonic decay width $b\to clν_l$. We argue that the non-BLM part of the $O(α_s^2)$ correction gives at most 1% correction to the inclusive semileptonic decay width $b\to clν_l$. This signifi…
We review the experimental measurements and theoretical descriptions of leptonic and semileptonic decays of particles containing a single heavy quark, either charm or bottom. Measurements of bottom semileptonic decays are used to determine the magnitudes of two fundamental parameters of the standard model, the Cabibbo-Kobayashi-Maskawa matrix elements $V_{cb}$ and $V_{ub}$. These parameters are connected with the physics of quark flavor and mass, and they have important implications for the breakdown of CP symmetry. To extract precise values of $|V_{cb}|$ and $|V_{ub}|$ from measurements, howe…
