arXiv 1202.47752012-02-21hep-ph

用有效拉格朗日方法研究重夸克偶素辐射跃迁

Investigating the heavy quarkonium radiative transitions with the effective Lagrangian method

Zhi-Guo He

备注：: 9 pages, no figures

摘要：

本文利用有效拉格朗日方法研究了重夸克偶素态的辐射衰变。首先，我们构造了$nP\leftrightarrow mS$跃迁有效拉格朗日量中的自旋破缺项，并通过拟合实验数据确定了部分耦合常数。结果表明，在$χ_{cJ}$、$ψ(2S)$、$Υ(2S)$和$Υ(3S)$辐射衰变中，自旋破缺效应很小，可以忽略.其次，我们研究了$c\bar{c}(1D)$态的辐射衰变宽度，发现如果$ψ(3770)$是纯$^3D_1$态，它辐射衰变到$χ_{cJ}+γ$态时基本上保持了重夸克自旋对称性，而如果它是具有混合角$12^{\circ}$的$S-D$混合态，它的辐射衰变和$ψ(3686)$的辐射衰变中的重夸克自旋对称性将被大大破坏。最后，我们证明了将$P$波$χ_{bJ}(1,2P)$的辐射衰变和轻强子衰变结合起来，可以在非相对论QCD（NRQCD）有效理论的背景下提供另一种提取色八重态矩阵元信息的方法，并且我们的结果与潜在的NRQCD假设是一致的.

英文摘要：

In this work, we study the radiative decay of heavy quarkonium states by using the effective Lagrangian approach. Firstly, we construct the spin-breaking terms in the effective Lagrangian for the $nP\leftrightarrow mS$ transitions and determine the some of the coupling constants by fitting the experimental data. Our results show that in $χ_{cJ}$, $ψ(2S)$, $Υ(2S)$, and $Υ(3S)$ radiative decays, the spin-breaking effect is so small that can be ignored. Secondly, we investigate the radiative decay widths of the $c\bar{c}(1D)$ states and find the if $ψ(3770)$ is a pure $^3D_1$ state its radiative decay into $χ_{cJ}+γ$ roughly preserve the heavy-quark spin symmetry, while if it is a $S-D$ mixing state with mixing angel $12^{\circ}$ the heavy quark-spin symmetry in its radiative decay and in the radiative decay of $ψ(3686)$ will be largely violated. In the end, we show that combining the radiative decay and the light hadron decay of $P$-wave $χ_{bJ}(1,2P)$ can provide another way to extract the information of the color-octet matrix element in the context of non-relativistic QCD (NRQCD) effective theory, and our result is consistent with potential NRQCD hypothesis.

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