arXiv 1702.073472017-02hep-phhep-exhep-latnucl-th

强子光-光散射的色散关系：2 π介子贡献

Dispersion relation for hadronic light-by-light scattering: two-pion contributions

Gilberto Colangelo, Martin Hoferichter, Massimiliano Procura, Peter Stoffer

备注：: 70 pages, 14 figures, Mathematica notebook with full expressions for the basis change included as supplementary material. Version accepted for publication in JHEP
DOI：: 10.1007/JHEP04(2017)161

摘要：

在这一系列的第三篇论文致力于一个色散处理的强子光的光（HLbL）张量，我们推导出一个分波公式的2 π介子中间态的HLbL的贡献的异常磁矩的μ子$(g-2)_μ$，包括一个详细的讨论的么正关系的任意分波。我们表明，获得不受非物理螺旋度分波影响的最终表达式是一个微妙的问题，我们彻底澄清了这一点。作为副产品，我们得到了一组求和规则，可用于约束$γ^*γ^*\toππ$的未来计算。我们验证的形式主义广泛使用的π介子盒的贡献，定义的两个π介子中间态与π介子极左手切，并演示了如何充分已知的结果是再现时，重新计算的分波。使用色散拟合高统计数据的π矢量形状因子，我们提供了一个完整的π盒子，$a_μ^{π\text{-box}}=-15.9(2)\times 10^{-11}$的评价。作为分波形式的应用，我们首次计算了HLbL散射中的$ππ$ -再散射效应，其中使用从反振幅方法推导出的$ππ$相移分散地构建了$γ^*γ^*\toππ$螺旋分波。这样，我们计算的同位旋- $0$部分可以解释为$f_0(500)$对$(g-2)_μ$中HLbL散射的贡献。我们认为，由于带电π再散射的贡献实施相关的相应的π极化率的修正，并表明这些是温和的。我们对π介子盒贡献和它的$S$ -波再散射修正之和的最终结果读作$a_μ^{π\text{-box}} + a_{μ,J=0}^{ππ,π\text{-pole LHC}}=-24(1)\times 10^{-11}$。

英文摘要：

In this third paper of a series dedicated to a dispersive treatment of the hadronic light-by-light (HLbL) tensor, we derive a partial-wave formulation for two-pion intermediate states in the HLbL contribution to the anomalous magnetic moment of the muon $(g-2)_μ$, including a detailed discussion of the unitarity relation for arbitrary partial waves. We show that obtaining a final expression free from unphysical helicity partial waves is a subtle issue, which we thoroughly clarify. As a by-product, we obtain a set of sum rules that could be used to constrain future calculations of $γ^*γ^*\toππ$. We validate the formalism extensively using the pion-box contribution, defined by two-pion intermediate states with a pion-pole left-hand cut, and demonstrate how the full known result is reproduced when resumming the partial waves. Using dispersive fits to high-statistics data for the pion vector form factor, we provide an evaluation of the full pion box, $a_μ^{π\text{-box}}=-15.9(2)\times 10^{-11}$. As an application of the partial-wave formalism, we present a first calculation of $ππ$-rescattering effects in HLbL scattering, with $γ^*γ^*\toππ$ helicity partial waves constructed dispersively using $ππ$ phase shifts derived from the inverse-amplitude method. In this way, the isospin-$0$ part of our calculation can be interpreted as the contribution of the $f_0(500)$ to HLbL scattering in $(g-2)_μ$. We argue that the contribution due to charged-pion rescattering implements corrections related to the corresponding pion polarizability and show that these are moderate. Our final result for the sum of pion-box contribution and its $S$-wave rescattering corrections reads $a_μ^{π\text{-box}} + a_{μ,J=0}^{ππ,π\text{-pole LHC}}=-24(1)\times 10^{-11}$.

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