论文标题
两杆对辐射真空极化的贡献的约束
Constraints on the two-pion contribution to hadronic vacuum polarization
论文作者
论文摘要
在低能量下，HADRONIC真空极化（HVP）由两杆式中间状态强烈主导，这将使HVP的HVP贡献约为70美元，对MUON的异常磁矩，$A_μ^\ text {HVP} $。后者的晶状体QCD评估表明，它可能比$ e^+e^ - \ to \ tox {hadrons} $ data的分散计算得出的水平，这将使长期存在的差异与$a_μ$ $ $的测量。在这封信中，我们研究了$2π$贡献的程度，而没有同时在低能源的黑积木现象学中引起冲突。为此，我们考虑了$ e^+e^ - \至2π$过程的分散表示，并研究了$a_μ^\ text {hvp} $之间出现的相关性，即$ p $ - p $ -p $ -wave $ππ$相位移位以及Pion的电荷radius的宽带运行。尽管受到Eidelman-Lukaszuk结合的约束，但非弹性效应起着重要作用。我们确定$a_μ^\ text {hvp} $的方案，这是由相移和/或非弹性贡献的变化驱动的，并说明了$ e^+e^ - \ to2π$横截面的随后变化。在最小化横截面中效果的组合情况下，需要在$ 4 \％$上进行均匀的偏移。同时，分析延续到太空区域和旋转电荷半径都受到可能在未来的晶格QCD计算中探测的水平。
At low energies hadronic vacuum polarization (HVP) is strongly dominated by two-pion intermediate states, which are responsible for about $70\%$ of the HVP contribution to the anomalous magnetic moment of the muon, $a_μ^\text{HVP}$. Lattice-QCD evaluations of the latter indicate that it might be larger than calculated dispersively on the basis of $e^+e^-\to\text{hadrons}$ data, at a level which would contest the long-standing discrepancy with the $a_μ$ measurement. In this Letter we study to which extent this $2π$ contribution can be modified without, at the same time, producing a conflict elsewhere in low-energy hadron phenomenology. To this end we consider a dispersive representation of the $e^+e^- \to 2π$ process and study the correlations which thereby emerge between $a_μ^\text{HVP}$, the hadronic running of the fine-structure constant, the $P$-wave $ππ$ phase shift, and the charge radius of the pion. Inelastic effects play an important role, despite being constrained by the Eidelman-Lukaszuk bound. We identify scenarios in which $a_μ^\text{HVP}$ can be altered substantially, driven by changes in the phase shift and/or the inelastic contribution, and illustrate the ensuing changes in the $e^+e^-\to 2π$ cross section. In the combined scenario, which minimizes the effect in the cross section, a uniform shift around $4\%$ is required. At the same time both the analytic continuation into the space-like region and the pion charge radius are affected at a level that could be probed in future lattice-QCD calculations.
