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Large corrections to asymptotic $F_{\eta_c \gamma}$ and $F_{\eta_b \gamma}$ in the light-cone perturbative QCD
High Energy Physics - Phenomenology · Submitted 11 Nov 1997
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim It is pointed out that the quark mass effect brings significant modifications to the asymptotic predictions of the transition form factors in a rather broad energy region, and this modification is much severer for $F_{\eta_b\gamma}(Q^2)$ than that for $F_{\eta_c\gamma}(Q^2)$ due to the $b$-quark being heavier than the $c$-quark.
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The abstract, sentence by sentence
The large-$Q^2$ behavior of $\eta_c$-$\gamma$ and $\eta_b$-$\gamma$ transition form factors, $F_{\eta_c\gamma}(Q^2)$ and $F_{\eta_b\gamma}(Q^2)$ are analyzed in the framework of light-cone perturbative QCD with the heavy quark ($c$ and $b$) mass effect, the parton's transverse momentum dependence and the higher helicity components in the light-cone wave function are respected. It is pointed out that the quark mass effect brings significant modifications to the asymptotic predictions of the transition form factors in a rather broad energy region, and this modification is much severer for $F_{\eta_b\gamma}(Q^2)$ than that for $F_{\eta_c\gamma}(Q^2)$ due to the $b$-quark being heavier than the $c$-quark. The parton's transverse momentum and the higher helicity components are another two factors which decrease the perturbative predictions. For the transition form factor $F_{\eta_c\gamma}(Q^2)$, they bring sizable corrections in the present experimentally accessible energy region ($Q^2 \leq 10 GeV^2$). For the transition form factor $F_{\eta_b\gamma}(Q^2)$, the corrections coming from these two factors are negligible since the $b$-quark mass is much larger than the parton's average transverse momentum. The coming $e^+ e^-$ collider (LEP2) will provide the opportunity to examine these theoretical predictions.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The large-$Q^2$ behavior of $\eta_c$-$\gamma$ and $\eta_b$-$\gamma$ transition form factors, $F_{\eta_c\gamma}(Q^2)$ and $F_{\eta_b\gamma}(Q^2)$ are analyzed in the framework of light-cone perturbative QCD with the heavy quark ($c$ and $b$) mass effect, the parton's transverse momentum dependence and the higher helicity components in the light-cone wave function are respected. | contribution 0.68 | 0.87 | 0.09 | asserted 0.99 |
| s1 | It is pointed out that the quark mass effect brings significant modifications to the asymptotic predictions of the transition form factors in a rather broad energy region, and this modification is much severer for $F_{\eta_b\gamma}(Q^2)$ than that for $F_{\eta_c\gamma}(Q^2)$ due to the $b$-quark being heavier than the $c$-quark. | result 0.96 | 0.81 | 0.51 | asserted 0.99 |
| s2 | The parton's transverse momentum and the higher helicity components are another two factors which decrease the perturbative predictions. | result 0.95 | 0.75 | 0.13 | asserted 1.00 |
| s3 | For the transition form factor $F_{\eta_c\gamma}(Q^2)$, they bring sizable corrections in the present experimentally accessible energy region ($Q^2 \leq 10 GeV^2$). | result 0.99 | 0.79 | 0.11 | asserted 1.00 |
| s4 | For the transition form factor $F_{\eta_b\gamma}(Q^2)$, the corrections coming from these two factors are negligible since the $b$-quark mass is much larger than the parton's average transverse momentum. | result 0.98 | 0.81 | 0.09 | asserted 1.00 |
| s5 | The coming $e^+ e^-$ collider (LEP2) will provide the opportunity to examine these theoretical predictions. | future work 0.91 | 0.06 | 0.03 | hedged possibility 0.56 |
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Original abstract
The large-$Q^2$ behavior of $\eta_c$-$\gamma$ and $\eta_b$-$\gamma$ transition form factors, $F_{\eta_c\gamma}(Q^2)$ and $F_{\eta_b\gamma}(Q^2)$ are analyzed in the framework of light-cone perturbative QCD with the heavy quark ($c$ and $b$) mass effect, the parton's transverse momentum dependence and the higher helicity components in the light-cone wave function are respected. It is pointed out that the quark mass effect brings significant modifications to the asymptotic predictions of the transition form factors in a rather broad energy region, and this modification is much severer for $F_{\eta_b\gamma}(Q^2)$ than that for $F_{\eta_c\gamma}(Q^2)$ due to the $b$-quark being heavier than the $c$-quark. The parton's transverse momentum and the higher helicity components are another two factors which decrease the perturbative predictions. For the transition form factor $F_{\eta_c\gamma}(Q^2)$, they bring sizable corrections in the present experimentally accessible energy region ($Q^2 \leq 10 GeV^2$). For the transition form factor $F_{\eta_b\gamma}(Q^2)$, the corrections coming from these two factors are negligible since the $b$-quark mass is much larger than the parton's average transverse momentum. The coming $e^+ e^-$ collider (LEP2) will provide the opportunity to examine these theoretical predictions.
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References
How the literature uses it
7 arXiv papers cite this in 8 sentences
Papers citing it · 2 sentences without a confident label
Uses its method or tool 4 papers
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Therefore, we present a model for $D$-meson leading-twist LCDA $ϕ_2;D(x,μ_0)$, which is constructed by the Brodsky-Huang-Lepage (BHL) prescription [ref] together with the Wigner-Melosh rotation effect [ref] .
Footprint in fitting $B \to D$ vector form factor and determination for $D$-meson leading-twist LCDA · Introduction · 0.96
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By using the Wigner-Melosh rotation [ref] , the different helicities of $χ_ω^h_1h_2(x,𝐤_)$ can be obtained [equation] where $m̂_q=300 GeV$ is constituent quark mass.
Non-perturbaitve effects for the isoscalar light vector $\omega$-meson in charmed meson semileptonic decays · Theoretical Framework · 1.00
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To obtain the behavior of twist-2 LCDAs for the $K^*0$ meson, we construct the corresponding LCDAs within the LCHO model following the BHL prescription [ref] .
Scrutinizing lepton flavor universality and transition form factor correlation from charmed meson semileptonic decay into light strange vector $K^*$ meson · Theoretical framework · 0.89
Cites it as background 1 paper
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So far, LCHO has been widely used in the study of various meson WFs or DAs and has been continuously improved [ref] .
$K_0^\ast(1430)$ Twist-2 Distribution Amplitude and $B_s,D_s \to K_0^\ast(1430)$ Transition Form Factors · LCHO model for $ϕ_2;K_0^∗(x,μ)$ based on BHL prescription · 0.91
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