Heavy pseudoscalar twist-3 distribution amplitudes within QCD theory in background fields

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• 作者：Tao Zhong ; Xing-Gang Wu ; Tao Huang ; Hai-Bing Fu
• 刊名：The European Physical Journal C - Particles and Fields
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：76
• 期：9
• 全文大小：1,047 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Elementary Particles and Quantum Field Theory
  Nuclear Physics, Heavy Ions and Hadrons
  Physics beyond the Standard Model
  Measurement Science and Instrumentation
  Astronomy, Astrophysics and Cosmology
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1434-6052
• 卷排序：76

文摘

In this paper, we study the properties of the twist-3 distribution amplitude (DA) of the heavy pseudoscalars such as \(\eta _c\), \(B_c\), and \(\eta _b\). New sum rules for the twist-3 DA moments \(\langle \xi ^n_P\rangle _\mathrm{HP}\) and \(\langle \xi ^n_\sigma \rangle _\mathrm{HP}\) up to sixth order and up to dimension-six condensates are deduced under the framework of the background field theory. Based on the sum rules for the twist-3 DA moments, we construct a new model for the two twist-3 DAs of the heavy pseudoscalar with the help of the Brodsky–Huang–Lepage prescription. Furthermore, we apply them to the \(B_c\rightarrow \eta _c\) transition form factor (\(f^{B_c\rightarrow \eta _c}_+(q^2)\)) within the light-cone sum rules approach, and the results are comparable with other approaches. It has been found that the twist-3 DAs \(\phi ^P_{3;\eta _c}\) and \(\phi ^\sigma _{3;\eta _c}\) are important for a reliable prediction of \(f^{B_c\rightarrow \eta _c}_+(q^2)\). For example, at the maximum recoil region, we have \(f^{B_c\rightarrow \eta _c}_+(0) = 0.674 \pm 0.066\), in which those two twist-3 terms provide \({\sim }33\) and \({\sim }22\,\%\) contributions. Also we calculate the branching ratio of the semi-leptonic decay \(B_c \rightarrow \eta _c l\nu \) as \(Br(B_c \rightarrow \eta _c l\nu ) = ( 9.31^{+2.27}_{-2.01} ) \times 10^{-3}\).