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arXiv 1607.00338hep-ph
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手征微扰理论中$η\to 3π$衰变的收敛性质

Convergence properties of $η\to 3π$ decays in chiral perturbation theory

Marian Kolesar, Jiri Novotny

摘要:

描述和解释$η\to 3π$衰变的理论努力可以追溯到很久以前。即使在今天,在低能QCD中,衰变宽度和一些Dalitz图参数的收敛似乎是有问题的。在框架内的mammed CHPT,我们探讨了一个仔细定义的手征系列,其中NNLO的mammers被假定为小的合理收敛的实验数据的兼容性的问题。通过处理高阶统计的不确定性,我们在数值上产生了一个大的理论预测,然后面对实验信息。在衰减宽度的情况下,实验值可以重建为一个合理的自由参数范围,因此没有观察到张力,尽管一些传统的计算建议。Dalitz图参数$a$和$d$也可以很好地描述。当考虑参数$b$和$α$时,我们发现在整个自由参数范围内,在小于2 $σ$ C. L.这可以用两种方式来解释--或者一些高阶修正确实出乎意料地大,或者有一个特定的配置,然而,这并不是完全不可能的。此外,发现理论不确定度的分布是显著非高斯的,因此不能简单地通过1个$σ$误差条来判断一致性。

英文摘要:

Theoretical efforts to describe and explain the $η\to 3π$ decays reach far back in time. Even today, the convergence of the decay widths and some of the Dalitz plot parameters seems problematic in low energy QCD. In the framework of resummed CHPT, we explore the question of compatibility of experimental data with a reasonable convergence of a carefully defined chiral series, where NNLO remainders are assumed to be small. By treating the uncertainties in the higher orders statistically, we numerically generate a large set of theoretical predictions, which are then confronted with experimental information. In the case of the decay widths, the experimental values can be reconstructed for a reasonable range of the free parameters and thus no tension is observed, in spite of what some of the traditional calculations suggest. The Dalitz plot parameters $a$ and $d$ can be described very well too. When the parameters $b$ and $α$ are concerned, we find a mild tension for the whole range of the free parameters, at less than 2$σ$ C.L. This can be interpreted in two ways - either some of the higher order corrections are indeed unexpectedly large or there is a specific configuration of the remainders, which is, however, not completely improbable. Also, the distribution of the theoretical uncertainties is found to be significantly non-gaussian, so the consistency cannot be simply judged by the 1$σ$ error bars.

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