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Factorization of Radiative Leptonic Decays of $B^-$ and $D^-$ Mesons Including the Soft Photon Region
High Energy Physics - Phenomenology · Submitted 28 Apr 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The numerical results shows that, the soft photon region is very important for both the $B$ and $D$ mesons.
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The abstract, sentence by sentence
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 $O(\Lambda_{\rm QCD}\left/m_Q\right.)$. We consider the contribution in the soft photon region that $E_{\gamma} \sim \left. \Lambda^2_{\rm QCD} /\right. m_Q$. The numerical results shows that, the soft photon region is very important for both the $B$ and $D$ mesons. The branching ratios of $B\to \gamma e\nu_e$ is $5.21\times 10^{-6}$, which is about $3$ times of the result obtained by only considering the hard photon region $E_{\gamma}\sim m_Q$. And for the case of $D\to \gamma e\nu_e$, the result of the branching ratio is $1.92\times 10^{-5}$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this work, we study the radiative leptonic decays of $B^-$ and $D^-$ mesons using factorization approach. | contribution 0.98 | 0.93 | 0.06 | asserted 0.85 |
| s1 | Factorization is proved to be valid explicitly at 1-loop level at any order of $O(\Lambda_{\rm QCD}\left/m_Q\right.)$. | result 0.68 | 0.85 | 0.24 | asserted 1.00 |
| s2 | We consider the contribution in the soft photon region that $E_{\gamma} \sim \left. | contribution 0.66 | 0.81 | 0.04 | unclear 0.61 |
| s3 | \Lambda^2_{\rm QCD} /\right. m_Q$. | method 0.54 | 0.37 | 0.04 | unclear 0.92 |
| s4 | The numerical results shows that, the soft photon region is very important for both the $B$ and $D$ mesons. | result 0.62 | 0.93 | 0.44 | asserted 1.00 |
| s5 | The branching ratios of $B\to \gamma e\nu_e$ is $5.21\times 10^{-6}$, which is about $3$ times of the result obtained by only considering the hard photon region $E_{\gamma}\sim m_Q$. | result 1.00 | 0.92 | 0.27 | asserted 1.00 |
| s6 | And for the case of $D\to \gamma e\nu_e$, the result of the branching ratio is $1.92\times 10^{-5}$. | result 1.00 | 0.92 | 0.11 | asserted 1.00 |
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The paper
Original abstract
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 $O(\Lambda_{\rm QCD}\left/m_Q\right.)$. We consider the contribution in the soft photon region that $E_{\gamma} \sim \left. \Lambda^2_{\rm QCD} /\right. m_Q$. The numerical results shows that, the soft photon region is very important for both the $B$ and $D$ mesons. The branching ratios of $B\to \gamma e\nu_e$ is $5.21\times 10^{-6}$, which is about $3$ times of the result obtained by only considering the hard photon region $E_{\gamma}\sim m_Q$. And for the case of $D\to \gamma e\nu_e$, the result of the branching ratio is $1.92\times 10^{-5}$.
Human review
How the literature uses it
4 arXiv papers cite this in 7 sentences
Papers citing it · 3 sentences without a confident label
Uses its data or values 1 paper
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with $λ_B=0.360$ GeV [ref] and $λ_D_s=0.294$ GeV [ref] .
$W$ radiative decay to heavy-light mesons in HQET factorization through ${\cal O}(\alpha_s)$ · Numerical results · 1.00
Compares with it 2 papers
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This result is in agreement with the LP predictions [ref] .
Factorization of radiative leptonic D-meson decay with sub-leading power corrections · Introduction · 0.80
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The result approaches the theoretical predictions in Refs. [ref] ; more data may help to discriminate among the full suite of theoretical models.
Search for the Radiative Leptonic Decay $D^{+}\to \gamma e^{+} {\nu}_{e}$ · Summary · 0.97
Cites it as background 1 paper
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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 D-meson decay with sub-leading power corrections · Introduction · 0.96
What it cites · 20 sentences without a confident label
Builds on 2 papers
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So we can extend the valid region of factorization in Refs. [ref] to $E_γ∼. Λ^2 _QCD/ . m_Q$.
Factorization of Radiative Leptonic Decays of $B^-$ and $D^-$ Mesons · 1-loop result summery · 1.00
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So we can extend the valid region of factorization in Refs. [ref] to $E_γ∼. Λ^2 _QCD/ . m_Q$.
Factorization, the light-cone distribution amplitude of the B-meson and the radiative decay B -> gamma l nu_l · 1-loop result summery · 1.00
Uses the method or tool of 2 papers
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The matrix element can be decomposed as [ref] [equation] To calculate the form factors $F_A$ and $F_V$ in Eq. ([ref]), we introduce $6$ operators [equation]
Factorization, the light-cone distribution amplitude of the B-meson and the radiative decay B -> gamma l nu_l · expansion and large logarithms · 0.87
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In the calculation we use Integral by part(IBP) method [ref] .
Integration by parts: An introduction · the details of $Φ_q̅^(1)⊗T^(0)$ and $Φ_Q^(1)⊗T^(0)$ · 1.00
Uses data or values from 1 paper
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On the other hand, $F_c$ can be related to the decay constant [ref] by [equation] Using the fitted results of $F_A$, $F_V$ and $F_c$, and using the Cabibbo - Kobayashi - Maskawa (CKM) matrix elements [ref] and the decay constant $f_B$ [ref] as following [equation] we can obtain the branching ratios.
Radiative Leptonic Decays of the charged $B$ and $D$ Mesons Including Long-Distance Contribution · Numerical Results · 0.94
Compares with 3 papers
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The branching ratios of $B→γeν_e$ can be increased to $5.21×10^-6$, which is about $3$ times of the result we obtained in Ref. [ref] , where only hard photon region is seriously treated.
Factorization of Radiative Leptonic Decays of $B^-$ and $D^-$ Mesons · Introduction · 0.97
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The branching ratio of $B^-→γeν̅$ is found to be at the order of $5.21×10^-6$, which is a little larger then the previous works [ref] .
Radiative Leptonic Decays of the charged $B$ and $D$ Mesons Including Long-Distance Contribution · Summary · 1.00
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The branching ratio of $B^-→γeν̅$ is found to be at the order of $5.21×10^-6$, which is a little larger then the previous works [ref] .
Radiative leptonic decays of B mesons in QCD · Summary · 1.00
Cites as support 1 paper
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The IR Div in $F^(1)EM_a$ can be canceled to all orders, which has been proved in Ref. [ref] .
Factorization of Radiative Leptonic Decays of $B^-$ and $D^-$ Mesons · the details of $Φ_q̅^(1)⊗T^(0)$ and $Φ_Q^(1)⊗T^(0)$ · 0.97
Cites as background 2 papers
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The study of the heavy meson decays is an important subject for understanding the high energy physics and standard model [ref] .
B Decays and CP Violation · Introduction · 0.99
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In recent years, both experimental and theoretical studies have been improved greatly [ref] .
BaBar B Decay Results · Introduction · 0.87
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