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arXiv 0901.1172hep-ph
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μ介子g-2中的强子光-光散射:π介子交换的一个新的短距离约束

Hadronic light-by-light scattering in the muon g-2: a new short-distance constraint on pion exchange

Andreas Nyffeler

摘要:

最近有人指出,为了评价μ介子g-2中占主导地位的π介子交换对强子光-光散射修正的贡献,应该使用完全离壳的π介子-光子-光子形状因子。在此基础上,我们首先导出了一个新的短距离约束,即μ子g-2的离壳形状因子从外顶点进入,并证明了它与QCD中的夸克凝聚磁化率有关.然后,我们在大N_C QCD框架下,使用满足所有短距离约束的离壳形状因子计算了π介子交换的贡献。在同样的大N_C框架下,利用磁化率的估计值,我们得到a_μ(LbyL; π^0)=(72 \pm 12)× 10^{-11}。利用简单的矢量介子优势形状因子修正了我们先前关于eta和eta-素数交换贡献的结果,得到了所有轻赝标量之和的a_μ(LbyL; PS)=(99 \pm 16)× 10^{-11}。结合对强子光-光散射的其他贡献的现有估计,这导致新的估计a_μ(LbyL; had)=(116 \pm 40)x 10^{-11}。

英文摘要:

Recently it was pointed out that for the evaluation of the numerically dominant pion-exchange contribution to the hadronic light-by-light scattering correction in the muon g-2, a fully off-shell pion-photon-photon form factor should be used. Following this proposal, we first derive a new short-distance constraint on the off-shell form factor which enters at the external vertex for the muon g-2 and show that it is related to the quark condensate magnetic susceptibility in QCD. We then evaluate the pion-exchange contribution in the framework of large-N_C QCD using an off-shell form factor which fulfills all short-distance constraints. With a value for the magnetic susceptibility as estimated in the same large-N_C framework, we obtain the result a_μ(LbyL; π^0) = (72 \pm 12) x 10^{-11}. Updating our earlier results for the contributions from the exchanges of the eta and eta-prime using simple vector-meson dominance form factors, we obtain a_μ(LbyL; PS) = (99 \pm 16) x 10^{-11} for the sum of all light pseudoscalars. Combined with available evaluations for the other contributions to hadronic light-by-light scattering this leads to the new estimate a_μ(LbyL; had) = (116 \pm 40) x 10^{-11}.

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