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arXiv 1007.5277hep-phnucl-th
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低能下$π^-γ\to 3π$过程的手性修正

Chiral corrections to $π^-γ\to 3π$ processes at low energies

N. Kaiser

备注：
19 pages, 14 figures, submitted to Nuclear Physics A
发表信息：
Nucl.Phys.A848:198-217,2010
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摘要：

本文用手征微扰理论计算了低能下双π光生过程$π^-γ\to π^- π^0π^0$和$π^-γ\to π^+π^-π^-$。在主导级，这些反应受手性π介子-π介子相互作用控制。次领先阶修正来自π介子环图和涉及低能常数$\bar\ell_1,\, \bar\ell_2,\, \bar\ell_3$和$\bar\ell_4$的手征不变反项。以封闭的解析形式给出了与五个运动学变量有关的生产幅度$A_1$和$A_2$。我们发现，中性π介子对产生的总截面$π^-γ\toπ^-π^0π^0$得到增强的区域$\sqrt{s}< 7m_π$的一个因素$1.5 - 1.8$的次领先的顺序修正。与此相反，在$π^-γ\to π^+ π^-π^-$区域中，带电π介子对产生的总截面与其树级结果相比几乎保持不变。虽然π介子对生成反应的动力学要丰富得多，但这种观察到的模式可以从手性修正对π介子-π介子终态相互作用（$π^+π^- \to π^0π^0$与$π^-π^- \to π^-π^-$）的不同影响来理解。我们还提出了完整的一套两π不变的质谱的结果。手征微扰理论对$π^-γ\to 3π$过程的预测可以通过COMPASS实验来检验，COMPASS实验使用高能π介子在重核库仑场中的Primakoff散射来提取具有各种终态的$π^-γ$反应的截面。

英文摘要：

We calculate in chiral perturbation theory the double-pion photoproduction processes $π^-γ\to π^- π^0π^0$ and $π^-γ\to π^+π^-π^-$ at low energies. At leading order these reactions are governed by the chiral pion-pion interaction. The next-to-leading order corrections arise from pion-loop diagrams and chiral-invariant counterterms involving the low-energy constants $\bar\ell_1,\, \bar\ell_2,\, \bar\ell_3$ and $\bar\ell_4$. The pertinent production amplitudes $A_1$ and $A_2$ depending on five kinematical variables are given in closed analytical form. We find that the total cross section for neutral pion-pair production $π^-γ\toπ^-π^0π^0$ gets enhanced in the region $\sqrt{s}< 7m_π$ by a factor $1.5 - 1.8$ by the next-to-leading order corrections. In contrast to this behavior the total cross section for charged pion-pair production $π^-γ\to π^+ π^-π^-$ remains almost unchanged in the region $\sqrt{s}< 6m_π$ in comparison to its tree-level result. Although the dynamics of the pion-pair production reactions is much richer, this observed pattern can be understood from the different influence of the chiral corrections on the pion-pion final state interaction ($π^+π^- \to π^0π^0$ versus $π^-π^- \to π^-π^-$). We present also results for the complete set of two-pion invariant mass spectra. The predictions of chiral perturbation theory for the $π^-γ\to 3π$ processes can be tested by the COMPASS experiment which uses Primakoff scattering of high-energy pions in the Coulomb field of a heavy nucleus to extract cross sections for $π^-γ$ reactions with various final states.

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