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A factorization theorem connecting the light-cone distribution amplitudes of heavy-flavor mesons in QCD and HQET
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abstract
The light-cone distribution amplitude (LCDA) of a heavy-light meson defined in heavy quark effective theory (HQET), is a fundamental nonperturbative input to account for innumerable $B$ meson exclusive decay and production processes. On the other hand, the conventional heavy-flavored meson LCDA defined in QCD, also ubiquitously enters the factorization formula for hard exclusive $B$ production processes. Inspired by the observation that these two LCDAs exhibit the identical infrared behaviors, yet differ in the ultraviolet scale of order $m_b$ or greater, we propose a novel factorization theorem for the heavy-light mesons, that the LCDA defined in QCD can be further expressed as a convolution between the LCDA in HQET and a perturbatively calculable coefficient function thanks to asymptotic freedom. This refactorization program can be invoked to fully disentangle the effects from three disparate scales $Q$, $m_b$ and $\Lambda_{\rm QCD}$ for a hard exclusive $B$ production process, particularly to facilitate the resummation of logarithms of type $\ln Q/m_b$ and $\ln m_b/\Lambda_{\rm QCD}$ in a systematic fashion.
Forward citations
Cited by 4 Pith papers
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Factorization Formula Connecting the Shape Functions of Heavy Meson in QCD and Heavy Quark Effective Theory
The QCD B-meson shape function in the endpoint region equals the HQET shape function multiplied by a perturbative matching coefficient whose one-loop form is derived in this paper.
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$B$-meson light-cone distribution amplitude from the Euclidean quantity
The paper derives a hard-collinear factorization formula with a one-loop matching coefficient connecting the B-meson quasi-distribution amplitude to the physical light-cone distribution amplitude.
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Heavy quark mass dependence of the $\Lambda_Q$ light-cone distribution amplitude in QCD
The Lambda_Q baryon LCDA at mass m_Q equals (m_Q/m_Q^0)^2 times the LCDA at m_Q^0 evaluated at rescaled fractions x_i*m_Q/m_Q^0, times an exponentiated anomalous dimension, plus renormalon-model power corrections.
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Power corrections in the determination of heavy meson LCDAs: A renormalon-based estimation
Using the renormalon model, the paper estimates that power corrections to the QCD-to-HQET light-cone distribution amplitude matching are around 22% for the D meson and 7% for the B meson in the peak region.
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