In this paper, we summarize the existing methods of solving the evolution equation of the leading-twist $B$-meson LCDA. Then, in the Mellin space, we derive a factorization formula with next-to-leading-logarithmic (NLL) resummation for the form factors $F_{A,V}$ in the $B \to γ\ellν$ decay at leading power in $Λ/m_b$. Furthermore, we investigate the power suppressed local contributions, factorizable non-local contributions (which are suppressed by $1/E_γ$ and $1/m_b$), and soft contributions to the form factors. In the numerical analysis, which employs the two-loop-level hard function and the jet function, we find that both the resummation effect and the power corrections can sizably decrease the form factors. Finally, the integrated branching ratios are also calculated for comparison with future experimental data.
The Minimal Lepton Flavour Violation (MLFV) framework is discussed after the recent indication for CP violation in the leptonic sector. Among the three distinct versions of MLFV, the one with degenerate right-handed neutrinos will be disfavoured, if this indication is confirmed. The predictions for leptonic radiative rare decays and muon conversion in nuclei are analysed, identifying strategies to disentangle the different MLFV scenarios. The claim that the present anomalies in the semi-leptonic $B$-meson decays can be explained within the MLFV context is critically re-examined concluding that…
Precision measurement of the neutrino mixing parameters and the determination of mass hierarchy are the primary goals of the present and upcoming neutrino experiments. In this work, we study the sensitivity of T2K,NO$ν$A and LBNE experiments to discover leptonic CP violation and the determination of neutrino mass hierarchy. We obtain the correlation between the CP violating phase $δ_{CP}$ and the mixing angles $θ_{13}$, $θ_{23}$ and the sensitivity to determine the octant of atmospheric mixing angle $θ_{23}$. The entire analysis is done for a total 10 years (5$ν$+ 5$\bar ν$) of running of T2K,…
We study lifetimes of heavy mesons in the 't Hooft model, a large-$N_c$ theory of strong interaction in two-dimensional spacetime. Since this model is solvable, one can evaluate the total decay widths through hadronic amplitudes that are determined unambiguously within the formalism. We investigate quark-hadron duality by numerically comparing the exclusive result and one from the heavy quark expansion, with the contribution of Pauli interference being consistently incorporated. Within certain numerical accuracy, we find that the maximal difference between inclusive and exclusive rates for $τ[…
We revisit the heavy quarkonium leptonic decays $ψ(nS) \to \ell^+\ell^-$ and $Υ(nS) \to \ell^+\ell^-$ using the Bethe-Salpeter method. The emphasis is on the relativistic correction. For the $ψ(1S-5S)$ decays, the relativistic effects are $22^{+3}_{-2}\%$, $34^{+5}_{-5}\%$, $41^{+6}_{-6}\%$, $52^{+11}_{-13}\%$ and $62^{+14}_{-12}\%$, respectively. For the $Υ(1S-5S)$ decays, the relativistic effects are $14^{+1}_{-2}\%$, $23^{+0}_{-3}\%$, $20^{+8}_{-2}\%$, $21^{+6}_{-7}\%$ and $28^{+2}_{-7}\%$, respectively. Thus, the relativistic corrections are large and important in heavy quarkonium leptonic…
Rare radiative leptonic decay $B\to l\bar ν_l γ$ is studied in the instantaneous Bethe-Salpeter approach. The results are compared to other relativistic quark model predictions.
We show that the so-called parity-conserving amplitudes predicted in the a priori mixing scheme for non-leptonic and weak radiative decays of hyperons vanish in the strong-flavor symmetry limit.
A priori mixings of eigenstates in physical states are quantum mechanical effects well known in several realms of physics. The possibility that such effects are also present in particle physics, in the form of flavor and parity mixings, is studied. Applications to weak radiative and non-leptonic decays of hyperons are discussed.
The radiative leptonic $B_{c}\toτ\bar{ν_τ}γ$ decay is analysed in context of 2HDM. It is shown that with large values of $tanβ$, the contributions of Model II to the decay rate exceeds considerably the Standard Model ones, while the contributions of Model I overlap with the Standard Model predictions.
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.
In this work we study the radiative leptonic decays of $B^-$, $D^-$ and $D_s^-\to γl \barν$, including both the short-distance and long-distance contributions. The short-distance contribution is calculated by using the relativistic quark model, where the bound state wave function we used is that obtained in the relativistic potential model. The long-distance contribution is estimated by using vector meson dominance model.
We analyze the radiative leptonic $B_c$ decay mode: $B_c \to \ell νγ$ ($\ell=e, μ$) using a QCD-inspired constituent quark model. The prediction: ${\cal B}(B_c \to \ell νγ)\simeq 3 \times 10^{-5}$ makes this channel experimentally promising in view of the large number of $B_c$ mesons which are expected to be produced at the future hadron facilities.
The radiative corrections to the pure leptonic decay $D_s{\longrightarrow} {\ell}{ν}_{\ell}$ up-to one-loop order is presented. We find the virtual photon loop corrections to $D_s{\longrightarrow} τ{ν}_τ$ is negative and the corresponding branching ratio is larger than $3.51\times 10^{-3}$. Considering the possible experimental resolutions, our prediction of the radiative decay $D_s{\longrightarrow} τ{ν}_τγ$ is not so large as others, and the best radiative channel to determine the $V_{cs}$ or $f_{D_s}$ is $D_s{\longrightarrow} μ{ν}_μγ$.
The well-known leptonic U(1) symmetry of the standard model of quarks and leptons is extended to include a number of new fermions and scalars. The resulting theory has an invisible QCD axion (thereby solving the strong CP problem), a candidate for weak-scale dark matter, as well as radiative neutrino masses. A possible key connection is a color-triplet scalar, which may be produced and detected at the Large Hadron Collider.
We discuss factorization in exclusive radiative leptonic B->γeνdecays using the soft-collinear effective theory. The form factors describing these decays can be expanded in a power series in Lambda/E_γwith E_γthe photon energy. We write down the most general operators in the effective theory which contribute to the form factors at leading order in Lambda_QCD/E_γ, proving their factorization into hard, jet and soft contributions, to all orders in alpha_s.
To the leading order, the radiative leptonic decays $B_c \to γ\ell \bar ν$ ($ \ell=e, μ$) are studied carefully. In the study, a non-relativistic constituent quark model and the effective Lagrangian for the heavy flavour decays are used. As a result, the branching ratios turn out to be of the orders of $10^{-5}$ for $B_c \to γμ\bar ν$ or for $B_c \to γe \bar ν$. Based on this study, we point out the decays being accessible experimentally at the future LHC, and the possibility to determine the decay constant $f_{B_c}$ through the radiative decays.
The radiative corrections to the pure leptonic decay $B_c \to \ellν_{\ell}$ up-to one-loop order is presented. How to cancel the infrared divergences appearing in the loop calculations, and the radiative decay $B_c \to \ellν_{\ell}γ$ is shown precisely. It is emphasized that the radiative decay may be separated properly and may compare with measurements directly as long as the theoretical `softness' of the photon corresponds to the experimental resolutions. Furthermore with a kind of non-relativistic constituent quark model, a kind of typical long distance contributions to the radiative decays…
It is interesting to investigate the OZI-forbidden radiative orthoquarkonium decays $J/ψ\to γπ^0, γη$ and $γη'$ in perturbative QCD. In this work without the approximations adopted in literature we carry out a full one-loop calculation which involves integrations of 4-point and 5-point loop functions. Our numerical results are in agreement with the present data. We also briefly discuss the decays of $J/ψ\to γ+ρ^0$, as well as $Υ\to π^0γ, ηγ, η'γ$.
We introduce the Working Group 2 proceedings contributions from the 2nd workshop on the CKM Unitarity Triangle and note their connection to the proceedings of the first workshop. The topic of WG2 was the determination of the CKM matrix elements Vtd and Vts from B-Bbar mixing, radiative penguin B to X{s/d} gamma decays and rare (semi)leptonic decays such as B to Xs l+ l-.
We revisit rare radiative leptonic decays $B_{s,d}\to γe^+e^-$ and $B_{s,d}\to γμ^+μ^-$ in the Standard Model and provide the updated estimates for various differential distributions (the branching ratios, the forward-backward asymmetry, and $R_{μ/e}$, the ratio of the differential distribution for muons over electrons in the final state). The new ingredients of this work compared to the existing theoretical analyses are the following: (i) we calculate all $B_d\toγ$ and $B_s\toγ$ form factors induced by the vector, axial-vector, tensor and pseudotensor quark currents within the relativistic di…
We reconsider the QCD predictions for the radiative decay $B\to γ\ell ν_\ell$ with an energetic photon in the final state by taking into account the $1/E_γ, 1/m_b$ power-suppressed hard-collinear and soft corrections from higher-twist $B$-meson light-cone distribution amplitudes (LCDAs). The soft contribution is estimated through a dispersion relation and light-cone QCD sum rules. The analysis of theoretical uncertainties and the dependence of the decay form factors on the leading-twist LCDA $ϕ_+(ω)$ shows that the latter dominates. The radiative leptonic decay is therefore well suited to cons…
The radiative corrections to the pure leptonic decay $D_s{\longrightarrow} {\ell}{ν}_{\ell}$ up-to one-loop order is presented. We find the virtual photon loop corrections to $D_s{\longrightarrow} τ{ν}_τ$ is negative and the corresponding branching ratio is larger than $3.51\times 10^{-3}$. Considering the possible experimental resolutions, our prediction of the radiative decay $D_s{\longrightarrow} τ{ν}_τγ$ is not so large as others, and the best channel to determine the $V_{cs}$ or $f_{D_s}$ is $D_s{\longrightarrow} μ{ν}_μγ$. How to cancel the infrared divergences appearing in the loop calcu…
The notion of U(1) lepton number (which may only be softly broken) is applied to models of dark matter which interacts with leptons. Previous scotogenic models of Majorana or Dirac neutrino mass are shown to be derivable in this framework without additional symmetries. Only complete renormalizable theories are considered. An explicit class of models with $Z_n$ ($n \geq 5$) lepton and dark symmetry for Dirac neutrinos is derived, as well as an example of $Z_3$ dark symmetry.
The radiative and leptonic decays of $η_c\to γγ$ and $η_c\to l^+l^-$ are studied. For $η_c\to γγ$ decay, the second-order electromagnetic tree-level diagram gives the leading contribution. The decay rate of $η_c\to γγ$ is calculated, the prediction is in good agreement with the experimental data. For $η_c\to l^+ł^-$, both the tree and loop diagrams are calculated. The analysis shows that the loop contribution dominates, the contribution of tree diagram with $Z^0$ intermediate state can only modifies the decay rate by less than 1%. The prediction of the branching ratios of $η_c\to e^+e^-$ and $…
As one of the extensions of the Standard Model, we investigate the anomalous four-point $τ-W-ν_τ-γ$ scalar- and tensor-type interactions, which originate from the gauge invariant dimension-five operators. The coupling constants are constrained by the measured branching ratio of the $τ^- \rightarrow μ^- ν_τ \bar{ν_μ} γ$ decay: $-4.9<κ_τ^S<9.4$ and $-1.4<κ_τ^T<2.8$ at the 95% confidence level for the scalar and tensor interactions, respectively.
In this work, we study the factorization of the radiative leptonic decays of $B^-$ and $D^-$ mesons, the contributions of the order $O(Λ_{\rm QCD}\left/m_Q\right.)$ are taken into account. The factorization is proved to be valid explicitly at the order $O(α_sΛ_{\rm QCD}\left/m_Q\right.)$. The hard kernel is obtained. The numerical results are calculated using the wave-function obtained in relativistic potential model. The $O(Λ_{\rm QCD}\left/m_Q\right.)$ contribution is found to be very important, the correction to the decay amplitudes of $B^-\to γe\barν$ is about $20\% - 30\%$. For $D$ mesons…
We compute the form factors parametrizing radiative leptonic decays of heavy mesons B^+\toγe^+νfor photon energies much larger than Λ_{QCD}, where perturbative QCD methods for exclusive processes can be combined with the heavy quark effective theory. The form factors can be reliably obtained in this region in an expansion in powers of Λ/E_γ. The leading term in this expansion displays an additional spin symmetry manifested in the equality of form factors of vector and axial currents. The leading twist form factors can be written as the convolution of the B meson light-cone wave function with a…
We obtain predictions for $B_{(s)}\to e^+e^-γ$ and $B_{(s)}\to μ^+μ^-γ$ decays. All the contributions containing long-distance QCD effects are calculated in the framework of relativistic quark model. The contributions of the light vector-meson resonances related to the virtual photon emission from valence quarks of the $B$-meson are included. The highest branching ratios for the radiative leptonic B-decays are ${\cal B}(\bar B^0_s\to e^+e^-γ)=18.8\times10^{-9}$ and ${\cal B}(B^0_s\to μ^+μ^-γ)=12.2\times10^{-9}$. We also give the distribution of the foward-backward asymmetry.
Within the light front framework, we calculate the form factors for $B\toγ$ transitions directly in the entire physical range of momentum transfer. Using these form factors, we study the radiative decays of $B\to lν_lγ$ and $B_{s(d)}\toν\barνγ$. We show that the decay rates of $B\to lν_lγ(l=e,μ)$ and $B\toν\barνγ$ are larger than that of the corresponding purely leptonic modes. Explicitly, in the standard model, we find that the branching ratios of $B\to μν_μγ$ and $B_s\toν\barνγ$ are $3.7\times 10^{-6}$ and $5.0\times 10^{-8}$, in contrast with $3\times 10^{-7}$ and 0 for $B\toμν_μ$ and $B\to…
In this work, we study the radiative leptonic decays of $B^-$ and $D^-$ mesons in the standard model and the two-Higgs-doublet-model type II. The results are obtained using the factorization procedure, and the contribution of the order $O(Λ_{\rm QCD}\left/m_Q\right.)$ is included. The numerical results are calculated using the wave-function obtained in relativistic potential model. As a result, the decay mode $B\to γτν_τ$ is found to be sensitive to the effect of the charged Higgs boson. Using the constraint on the free parameters of the two Higgs doublet model given in previous works, we find…
Triggered by experimentally driven renewed interest in hyperon properties we address the subject of weak radiative hyperon decays (WRHD). We start with the issue of Hara's theorem and briefly discuss the question of its possible evasion. Then, we give a short review of the story of vector-meson-dominance (VMD) approach to WRHD. We stress the shift from the Hara's-theorem-violating to Hara's-theorem-satisfying version of the VMD approach that did occur over time. Finally, spurred by a recent theoretical paper, we discuss the pole model description of WRHD, putting special attention to the issue…
The model--independent QED radiative corrections to polarization observables in elastic scattering of unpolarized and longitudinally--polarized electron beam by the deuteron target have been calculated in leptonic variables. The experimental setup when the deuteron target is arbitrarily polarized is considered and the procedure for applying derived results to the vector or tensor polarization of the recoil deuteron is discussed. The basis of the calculations consists of the account for all essential Feynman diagrams which results in the form of the Drell-Yan representation for the cross-sectio…
In this work, we study the radiative leptonic decays of $B^-$ and $D^-$ mesons using factorization approach. Factorization is proved to be valid explicitly at 1-loop level at any order of $O(Λ_{\rm QCD}\left/m_Q\right.)$. We consider the contribution in the soft photon region that $E_γ \sim \left. Λ^2_{\rm QCD} /\right. m_Q$. The numerical results shows that, the soft photon region is very important for both the $B$ and $D$ mesons. The branching ratios of $B\to γeν_e$ is $5.21\times 10^{-6}$, which is about $3$ times of the result obtained by only considering the hard photon region $E_γ\sim m_…
We study rare radiative leptonic decays $B_{(s)}\to e^+e^-γ$ and $B_{(s)}\to μ^+μ^-γ$ within relativistic quark model. In addition to previous analysis we give the estimations of the branching ratios for four values of the minimal photon energy, which correspond to photon selection criteria of the Belle and LHCb detectors. We find out that the branching ratios only slightly change. The highest values corresponding to $E^γ_{min}=80 \textrm{MeV}$ are ${\cal B}(\bar B^0_s\to e^+e^-γ)=18.5\times10^{-9}$ and ${\cal B}(B^0_s\to μ^+μ^-γ)=11.9\times10^{-9}$. We present the distribution of the forward-…
We study the radiative leptonic $D$ meson decays of $D^+_{(s)}\to ł^+ν_łγ$ ($ł=e,μ,τ$), $D^0\to ν\barνγ$ and $D^0\to ł^+ł^-γ$ ($l=e,μ$) within the light front quark model. In the standard model, we find that the decay branching ratios of $D^+_{(s)}\to e^+ν_eγ$, $D^+_{(s)}\toμ^+ν_μγ$ and $D^+_{(s)}\toτ^+ν_τγ$ are $6.9\times 10^{-6}$ ($7.7\times 10^{-5}$), $2.5\times 10^{-5}$ ($2.6\times 10^{-4}$), and $6.0\times 10^{-6}$ ($3.2\times 10^{-4}$), and that of $D^0\toł^+ł^-γ$ ($ł=e,μ$) and $D^0\toν\barνγ$ are $6.3\times 10^{-11}$ and $2.7\times 10^{-16}$, respectively.
Long-distance QCD effects in $B_{d,s}\to\ell^+\ell^-γ$ decays are analyzed. We show that the contribution of the light vector-meson resonances related to the virtual photon emission from valence quarks of the $B$-meson, which was not considered in previous analyses, strongly influences the dilepton differential distrubution. Taking into account photon emission from the $b$-quark loop, weak annihilation, and Bremsstrahlung from leptons in the final state, we give predictions for dilepton spectrum in $B_{d, s}\to \ell^+\ell^-γ$ decays within the Standard model.
We study the radiative leptonic decays of heavy mesons within the covariant light-front model. Using this model, both the form factors F_V and F_A have the same form when the heavy quark limit is taken. In addition, the relation between the form factor F_V and the decay constant of heavy meson F_H is obtained. The hadronic parameter βcan be determine by the parameters appearing in the wave function of heavy meson. We find that the value of βis not only quite smaller than the one in the non-relativistic case, but also insensitive to the value of light quark mass m_q. These results mean that the…
The recent discovery of the B_c meson by the CDF collaboration and proposed new experiments at Fermilab and CERN motivate new theoretical studies of the B_c system. Here we investigate the radiative leptonic decay B_c -> gamma l nu. This process is an important background to the annihilation process B_c -> l nu, which will be used to extract the B_c decay constant. We perform a model-independent calculation, based on QCD, of the partial width and various kinematic distributions. We also examine the decay within the framework of NRQCD, an effective field theory of nonrelativistic quarks, genera…
With a consistent definition of transverse-momentum-dependent(TMD) light-cone wave function of $B$-meson, we show that the amplitude of the radiative leptonic B-decay can be factorized at one-loop level as a convolution with the wave function and a perturbative coefficient function, combined with a soft factor. In this TMD factorization, the transverse momenta of partons in the $B$-meson are taken into account and all soft divergences are contained in the wave function and the soft factor. The coefficient function is infrared-safe. The factorization works on a diagram-by-diagram basis and is p…
We revisit the calculation of the width for the radiative decay of a $1^{+-}$ heavy $Q \bar Q$ meson via the channel $1^{+-} \to 0^{-+} +γ$ in the covariant light-front quark model. We carry out the reduction of the light-front amplitude in the non-relativistic limit, explicitly computing the leading and next-to-leading order relativistic corrections. This shows the consistency of the light-front approach with the non-relativistic formula for this electric dipole transition. Furthermore, the theoretical uncertainty in the predicted width is studied as a function of the inputs for the heavy qua…
We calculate the radiative corrections to the unpolarized and the four polarized spectrum and rate functions in the leptonic decay of a polarized $ μ$ into a polarized electron. The new feature of our calculation is that we keep the mass of the final state electron finite which is mandatory if one wants to investigate the threshold region of the decay. Analytical results are given for the energy spectrum and the polar angle distribution of the final state electron whose longitudinal and transverse polarization is calculated. We also provide analytical results on the integrated spectrum functio…
Adding a hard photon to the final state of a leptonic pseudoscalar-meson decay lifts the helicity suppression and can provide sensitivity to a larger set of operators in the weak effective Hamiltonian. Furthermore, radiative leptonic $B$ decays at high photon energy are well suited to constrain the first inverse moment of the $B$-meson light-cone distribution amplitude, an important parameter in the theory of nonleptonic $B$ decays. We demonstrate that the calculation of radiative leptonic decays is possible using Euclidean lattice QCD, and present preliminary numerical results for $D_s^+ \to …
The interpretation of high-precision lepton-nucleon scattering experiments requires the knowledge of higher-order radiative corrections. We present a calculation of the cross section for unpolarized lepton-proton scattering including leptonic radiative corrections up to second order, including one- and two-loop corrections, radiation of one and two photons and one-loop corrections for one-photon radiation. Numerical results are given for the planned P2 experiment at the MESA facility in Mainz, and some results are also discussed for Qweak and the suggested MUSE experiment.
The inclusive spectra of radiative and semi-leptonic B-meson decays near the endpoint is computed taking into account renormalons in the Sudakov exponent (Dressed Gluon Exponentiation). In this framework we demonstrate the factorization of decay spectra into hard, jet and soft functions and discuss the universality of the latter two. Going beyond perturbation theory the soft function, which we identify as the longitudinal momentum distribution in an on-shell b quark, is replaced by the b-quark distribution in the B meson. The two differ by power corrections. We show how the resummation of runn…
I discuss the two-particle subleading power corrections in radiative leptonic $B \to γ\ell ν$ decay at next-to-leading order in $α_s$ with the dispersion approach. Employing the method of regions, factorization of the $B \to γ^{\ast}$ form factors is demonstrated explicitly, at one loop, for a space-like hard-collinear photon. The two-particle soft (end-point) contribution is shown to be suppressed by one power of $Λ/m_b$, in the heavy quark limit, compared with the leading power contribution computed from QCD factorization. I further report the recent calculation on the three-particle sublead…
Soft-collinear effective theory is used to prove factorization of the B->gamma+l+nu decay amplitude at leading power in Lambda/m_b, including a demonstration of the absence of non-valence Fock states and of the finiteness of the convolution integral in the factorization formula. Large logarithms entering the hard-scattering kernel are resummed by performing a two-step perturbative matching onto the low-energy effective theory, and by solving evolution equations derived from the renormalization properties of the leading-order B-meson light-cone distribution amplitude. As a byproduct, the evolut…
There are several anomalous measurements in the decays induced by the quark level transition $b \to s μ^+ μ^-$, which do not agree with the predictions of the Standard Model. These measurements could be considered as signatures of physics beyond the Standard Model. Working within the framework of effective field theory, several groups have performed global fits to all $b \to s μ^+ μ^-$ data to identify the Lorentz structure of possible new physics. Many new physics scenarios have been suggested to explain the anomalies in the $b \to s μ^+ μ^-$ sector. In this work, we investigate the impact of…
We show results from calculations in full lattice QCD of the mass, leptonic width and radiative decay rate to eta_c of the J/psi meson. These provide few % tests of QCD. Another (1.5%) test comes from comparison of time-moments of the vector charmonium correlator with results derived from the experimental values of R(e+e- to hadrons) in the charm region.
We revisit electroweak radiative corrections to Standard Model Effective Field Theory (SMEFT) operators which are relevant for the $B$-meson semileptonic decays. The one-loop matching formulae onto the low-energy effective field theory are provided without imposing any flavor symmetry. The on-shell conditions are applied especially in dealing with quark-flavor mixings. Also, the gauge independence is shown explicitly in the $R_ξ$ gauge.
The branching fractions of radiative leptonic $τ$ decays $(τ\to l ν\barν γ$, $l=e,μ)$ were recently measured by the Babar collaboration with a relative error of about 3%. The measurement of the branching ratio $\mathcal{B} (τ\to e \barν νγ)$, for a minimum photon energy of 10 MeV in the $τ$ rest frame, differs from our recent SM prediction by 3.5 standard deviations, whereas our result agrees with Babar's value for $\mathcal{B} (τ\to μ\barν νγ)$. Our predictions also agree with the measurement of $\mathcal{B} (μ\to e \barν νγ)$ by the MEG collaboration. We also report on a recent proposal to t…
We present a detailed analysis together with exact numerical calculations on one-loop contributions to the branching ratio of the radiative decay of $μ$ and $τ$, namely $μ\to e γ$, $τ\to e γ$, and $τ\toμγ$ from supersymmetry without R parity, focusing on contributions involving bilinear couplings. A numerical study is performed to obtain explicit bounds on the parameters under the present experimental limit. We present, and use in the calculation, formulas for exact mass eigenstate effective couplings. In this sense, we present an exact analysis free from approximation for the first time. Afte…
In this work, we investigate the radiative leptonic decays D_(s)^- \to γ\ell \barν(\ell = e, μ) at tree level within the non-relativistic consistuent quark model and the effective Lagrangian for the heavy flavor decays. We find that the contributions for the three Feynman diagrams are all important. With the full calculation, the decay branching ratios are of the order of 10^-5 for D_s^- \to γ\ell \barνand 10^-6 for D^- \to γ\ell \barν, respectively. These decays can be measured at B factories and future CLEO-C experiments to determine the decay constants f_D_s and f_D.
