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arXiv 1302.3528hep-phhep-exhep-latnucl-th
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pNRQCD中重夸克偶素磁偶极跃迁的改进测定

Improved determination of Heavy Quarkonium magnetic dipole transitions in pNRQCD

Antonio Pineda, J. Segovia

备注：
42 pages, 15 figures. Numbering of references on figure 9 has been corrected
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摘要：

我们用模型无关的方法计算了低重夸克偶素态之间的磁偶极跃迁。我们使用弱耦合版本的有效场理论命名为潜在的NRQCD与静态的潜力，正是纳入领先的一级哈密顿量。对于允许跃迁和禁止跃迁，我们分别达到了$k_γ^3/m^2\times{\cal O}(α_s^2,v^2)$和$k_γ^3/m^2\times{\cal O}(v^4)$的精度。我们还计算了与重夸克质量标度有关的大质量标度。本文考虑的具体跃迁如下：$Υ(1S) \to η_b(1S)\,γ$、$J/ψ(1S) \to η_c(1S)\,γ$、$h_b(1P) \to χ_{b0,1}(1P)\,γ$、$χ_{b2}(1P) \to h_b(1P)\,γ$、$Υ(2S) \to η_b(2S)\,γ$、$Υ(2S) \to η_b(1S)\,γ$和$η_b(2S)\toΥ(1S)\,γ$。新的功率计数的效果被发现是大的，并且静电势的软矩阵的精确处理使得因子分解尺度依赖性小得多。对$b\bar b$基态的收敛性很好，对$c\bar c$基态和$b\bar b$ 1P态的收敛性也很合理。对于所有这些，我们都给出了可靠的预测。对于2S衰变的情况是不太确定的，但我们的结果是完全符合现有的数据，因为以前的分歧与实验的$Υ(2S) \to η_b(1S)\,γ$衰变消失。我们还可以计算一些期望值，如电磁半径r^2或p^2。我们发现r^2在所有情况下都很好地收敛，而p^2的收敛通常更差。

英文摘要：

We compute the magnetic dipole transitions between low lying Heavy Quarkonium states in a model independent way. We use the weak-coupling version of the effective field theory named potential NRQCD with the static potential exactly incorporated in the leading order Hamiltonian. The precision we reach is $k_γ^3/m^2\times{\cal O}(α_s^2,v^2)$ and $k_γ^3/m^2\times{\cal O}(v^4)$ for the allowed and forbidden transitions respectively. We also resum the large logarithms associated to the heavy quark mass scale. The specific transitions considered in this paper are the following: $Υ(1S) \to η_b(1S)\,γ$, $J/ψ(1S) \to η_c(1S)\,γ$, $h_b(1P) \to χ_{b0,1}(1P)\,γ$, $χ_{b2}(1P) \to h_b(1P)\,γ$, $Υ(2S) \to η_b(2S)\,γ$, $Υ(2S) \to η_b(1S)\,γ$ and $η_b(2S)\toΥ(1S)\,γ$. The effect of the new power counting is found to be large and the exact treatment of the soft logarithms of the static potential makes the factorization scale dependence much smaller. The convergence for the $b\bar b$ ground state is quite good, and also quite reasonable for the $c\bar c$ ground state and the $b\bar b$ 1P state. For all of them we give solid predictions. For the 2S decays the situation is less conclusive, yet our results are perfectly consistent with existing data, as the previous disagreement with experiment for the $Υ(2S) \to η_b(1S)\,γ$ decay fades away. We also profit to compute some expectation values like the electromagnetic radius, r^2, or p^2. We find r^2 to be nicely convergent in all cases, whereas the convergence of p^2 is typically worse.

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