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Factorization of radiative leptonic D-meson decay with sub-leading power corrections
High Energy Physics - Phenomenology · Submitted 4 Apr 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Finally, we find that all the sub-leading power contributions are significant at $\lambda_D(\mu_0)=354\,\rm MeV$, and the next-to-leading power contributions will lead to $143\%$ in $\phi_{D,\rm I}^+$ and $120\%$ in $\phi_{D,\rm II}^+$ corrections to leading power vector form factors with $E_{\gamma}=0.5\,\rm GeV$.
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In this work, we calculate the sub-leading power contributions to the radiative leptonic $D\to\gamma \,\ell \,\nu$ decay. For the first time, we provide the analytic expressions of next-to-leading power contributions and the error estimation associated with the power expansion of ${\cal O}(\Lambda_{\rm QCD}/m_c)$. In our calculation, we adopt two different models of the $D$-meson distribution amplitudes $\phi_{D,\rm I}^+$ and $\phi_{D,\rm II}^+$. Within the framework of the QCD factorization as well as the dispersion relation, we evaluate the soft contribution up to the next-to-leading logarithmic accuracy, and the higher-twist contribution from the two-particle and three-particle distribution amplitudes is also considered. Finally, we find that all the sub-leading power contributions are significant at $\lambda_D(\mu_0)=354\,\rm MeV$, and the next-to-leading power contributions will lead to $143\%$ in $\phi_{D,\rm I}^+$ and $120\%$ in $\phi_{D,\rm II}^+$ corrections to leading power vector form factors with $E_{\gamma}=0.5\,\rm GeV$. As the corrections from the higher-twist and local sub-leading power contributions will be enhanced with the growing of the inverse moment, it is difficult to extract an appropriate inverse moment of the $D$-meson distribution amplitude. The predicted branching fractions are $(1.88_{-0.29}^{+0.36})\times10^{-5}$ for $\phi_{D,\rm I}^+$ and $(2.31_{-0.54}^{+0.65})\times10^{-5}$ for $\phi_{D,\rm II}^+$, respectively.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this work, we calculate the sub-leading power contributions to the radiative leptonic $D\to\gamma \,\ell \,\nu$ decay. | contribution 1.00 | 0.97 | 0.04 | asserted 0.99 |
| s1 | For the first time, we provide the analytic expressions of next-to-leading power contributions and the error estimation associated with the power expansion of ${\cal O}(\Lambda_{\rm QCD}/m_c)$. | contribution 0.94 | 0.97 | 0.11 | asserted 1.00 |
| s2 | In our calculation, we adopt two different models of the $D$-meson distribution amplitudes $\phi_{D,\rm I}^+$ and $\phi_{D,\rm II}^+$. | method 0.99 | 0.92 | 0.02 | asserted 1.00 |
| s3 | Within the framework of the QCD factorization as well as the dispersion relation, we evaluate the soft contribution up to the next-to-leading logarithmic accuracy, and the higher-twist contribution from the two-particle and three-particle distribution amplitudes is also considered. | method 1.00 | 0.94 | 0.04 | asserted 1.00 |
| s4 | Finally, we find that all the sub-leading power contributions are significant at $\lambda_D(\mu_0)=354\,\rm MeV$, and the next-to-leading power contributions will lead to $143\%$ in $\phi_{D,\rm I}^+$ and $120\%$ in $\phi_{D,\rm II}^+$ corrections to leading power vector form factors with $E_{\gamma}=0.5\,\rm GeV$. | result 1.00 | 0.97 | 0.73 | asserted 1.00 |
| s5 | As the corrections from the higher-twist and local sub-leading power contributions will be enhanced with the growing of the inverse moment, it is difficult to extract an appropriate inverse moment of the $D$-meson distribution amplitude. | limitation 0.78 | 0.53 | 0.06 | asserted 0.95 |
| s6 | The predicted branching fractions are $(1.88_{-0.29}^{+0.36})\times10^{-5}$ for $\phi_{D,\rm I}^+$ and $(2.31_{-0.54}^{+0.65})\times10^{-5}$ for $\phi_{D,\rm II}^+$, respectively. | result 1.00 | 0.95 | 0.18 | asserted 1.00 |
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The paper
Original abstract
In this work, we calculate the sub-leading power contributions to the radiative leptonic $D\to\gamma \,\ell \,\nu$ decay. For the first time, we provide the analytic expressions of next-to-leading power contributions and the error estimation associated with the power expansion of ${\cal O}(\Lambda_{\rm QCD}/m_c)$. In our calculation, we adopt two different models of the $D$-meson distribution amplitudes $\phi_{D,\rm I}^+$ and $\phi_{D,\rm II}^+$. Within the framework of the QCD factorization as well as the dispersion relation, we evaluate the soft contribution up to the next-to-leading logarithmic accuracy, and the higher-twist contribution from the two-particle and three-particle distribution amplitudes is also considered. Finally, we find that all the sub-leading power contributions are significant at $\lambda_D(\mu_0)=354\,\rm MeV$, and the next-to-leading power contributions will lead to $143\%$ in $\phi_{D,\rm I}^+$ and $120\%$ in $\phi_{D,\rm II}^+$ corrections to leading power vector form factors with $E_{\gamma}=0.5\,\rm GeV$. As the corrections from the higher-twist and local sub-leading power contributions will be enhanced with the growing of the inverse moment, it is difficult to extract an appropriate inverse moment of the $D$-meson distribution amplitude. The predicted branching fractions are $(1.88_{-0.29}^{+0.36})\times10^{-5}$ for $\phi_{D,\rm I}^+$ and $(2.31_{-0.54}^{+0.65})\times10^{-5}$ for $\phi_{D,\rm II}^+$, respectively.
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How the literature uses it
4 arXiv papers cite this in 4 sentences
Papers citing it · 2 sentences without a confident label
Cites it as background 2 papers
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The TFFs for heavy-to-light decay processes have been calculated under various approaches, such as the QCD sum rules (QCDSR) [ref] , the covariant light-front quark model (CLFQM) [ref] , the constituent quark model (CQM) [ref] , the light-cone sum rules (LCSR) [ref] , the relativistic quark model (RQM) [ref] , the perturbative QCD (PQCD) [ref] , the QCD factorization (QCDF) [ref] , the three-point QCD sum rules (3PSR) [ref] , and etc.
$a_1(1260)$-meson longitudinal twist-2 distribution amplitude and the $D\to a_1(1260)\ell^+\nu_\ell$ decay processes · Introduction · 0.96
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Radiative leptonic decays have been gaining interest in recent years [ref] .
Controlling unwanted exponentials in lattice calculations of radiative leptonic decays · Introduction · 1.00
What it cites · 10 sentences without a confident label
Builds on 1 paper
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The local sub-leading power contribution in this procedure is given by evaluating the second diagram and the local term of the first diagram in figure [ref], which is the same as [ref] by just changing bottom quark to charm quark according to the symmetry of heavy quarks [equation] where the first term and second term correspond to the photon emission from the down quark and charm quark, respectively.
B meson distribution amplitude from B --> \gamma l \nu · The local sub-leading power contribution and higher-twist contribution · 0.93
Uses the method or tool of 6 papers
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We consider two models of the two-particle $D$-meson DA $ϕ_D^+(ω,μ_0)$ [ref] in our calculation [equation] where $ω_0=λ_D(μ_0)$, and $k= ω/(1 GeV)$. $ϕ_D,I^+(ω,μ_0)$ and $ϕ_D,II^+(ω,μ_0)$ are based upon the Grozin-Neubert parametrization (left panel) and Braun-Ivanov-Korchemsky parametrization (right panel) respectively.
Factorization and dispersion relations for radiative leptonic $B$ decay · Numerical analysis · 0.86
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In this work, we will study the radiative leptonic $D$-meson decay within the framework of the QCD factorization (QCDF) [ref] as well as the dispersion relation [ref] .
Soft contribution to $B\to \gamma \ell \nu_\ell$ and the $B$-meson distribution amplitude · Introduction · 0.95
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In this work, we will study the radiative leptonic $D$-meson decay within the framework of the QCD factorization (QCDF) [ref] as well as the dispersion relation [ref] .
QCD Factorization in B -> pi K, pi pi Decays and Extraction of Wolfenstein Parameters · Introduction · 0.95
Uses data or values from 2 papers
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The value of $λ_D(μ_0)$ is taken from the lattice simulations [ref] .
Review of lattice results concerning low-energy particle physics · Numerical analysis · 1.00
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In 2017, the BES-III Collaboration measured the radiative leptonic $D^+→γ e^+ ν_e$ decay [ref] , and the upper limit on the branching fraction is about $3.0×10^-5$ with $E_cut=10 MeV$.
Search for the Radiative Leptonic Decay $D^{+}\to \gamma e^{+} {\nu}_{e}$ · Introduction · 0.86
Compares with 3 papers
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This result is in agreement with the LP predictions [ref] .
Factorization of Radiative Leptonic Decays of $B^-$ and $D^-$ Mesons · Introduction · 0.80
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This result is in agreement with the LP predictions [ref] .
Factorization of Radiative Leptonic Decays of $B^-$ and $D^-$ Mesons Including the Soft Photon Region · Introduction · 0.80
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This expression is the same as the first term in [ref] .
Radiative leptonic decay $B\to \gamma \ell \nu_\ell$ with subleading power corrections · The local sub-leading power contribution and higher-twist contribution · 0.98
Cites as background 12 papers
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In the heavy quark limit, both the $B$- and $D$-meson decays could be studied within the factorization approach, the leading power (LP) predictions of $D→e ν_e γ$ are presented in [ref] , where the final state photon can be either hard or soft.
Factorization of Radiative Leptonic Decays of $B^-$ and $D^-$ Mesons Including the Soft Photon Region · Introduction · 0.96
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In the heavy quark limit, both the $B$- and $D$-meson decays could be studied within the factorization approach, the leading power (LP) predictions of $D→e ν_e γ$ are presented in [ref] , where the final state photon can be either hard or soft.
Factorization of Radiative Leptonic Decays of $B^-$ and $D^-$ Mesons · Introduction · 0.96
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In the framework of QCDF, one can separate long-distance and short-distance contributions via a simultaneous expansion in the power of strong coupling constant and $Λ_QCD/m_Q$, and the factorization approach has been applied to various radiative heavy meson decays [ref] , and other processes such as factorization of the correlation function in light-cone sum rules [ref] .
Perturbative corrections to $B \to D$ form factors in QCD · Introduction · 0.81
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