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arXiv 2101.08071hep-phhep-ex
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τ轻子电偶极矩的再认识

The electric dipole moment of the tau lepton revisited

Werner Bernreuther, Long Chen, Otto Nachtmann

备注：
Two tables, one figure, and references added. Version to be published in Phys. Rev. D
发表信息：
Phys. Rev. D 103, 096011 (2021)
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摘要：

我们重新考虑使用$e^+ e^-$碰撞产生的$τ^+τ^-$中的最佳可观测量来寻找非零电偶极形状因子（EDM）$d_τ(s)$的问题，该可观测量在从$τ$对阈值到大约$\sqrt{s} \sim 15$ GeV的质心能量范围内。我们讨论了一般形式主义的最佳观测量，并将其应用到两个$CP$奇观测量，是敏感的实部和虚部的$d_τ(s)$，分别。我们计算这些最佳$CP$观测值的期望值和协方差的$τ$对生产在$\sqrt{s}=10.58$ GeV与随后的$τ^\pm$衰变成主要轻子或半强子模式。对于$τ$衰变为两个π介子和三个带电π介子，我们考虑了强子系统的全部运动学信息。假设KEKB加速器上的Belle II实验最终将分析对应于50 ab $^{-1}$的积分光度的数据，并对末态π介子应用接受切割，我们发现1~s.d.灵敏度$δ{\rm Re} d_τ= 6.8 \times 10^{-20}$ e cm和$δ{\rm} Im d_τ= 4.0 \times 10^{-20}$ e cm可以用两个$τ$都半强子衰变的事件获得。在没有对最终态粒子进行切割的理想情况下，我们发现在对应于$4.5 \times 10^{10}$ $τ^+ τ^-$事件的$\sqrt{s}=10.58$ GeV处具有50 ab $^{-1}$的1 s.d.灵敏度$δ{\rm Re} d_τ= 5.8 \times 10^{-20}$ e cm和$δ{\rm} Im d_τ= 3.2 \times 10^{-20}$ e cm，同样适用于两个$τ$轻子都以半强子衰变的事件。此外，我们分析了$τ$ EDM形状因子在II型两希格斯偶极子扩展和两个标量leptoquark扩展的标准模型中的潜在幅度。

英文摘要：

We reconsider the issue of the search for a nonzero electric dipole form factor (EDM) $d_τ(s)$ using optimal observables in $τ^+τ^-$ production by $e^+ e^-$ collisions in the center-of-mass energy range from the $τ$-pair threshold to about $\sqrt{s} \sim 15$ GeV. We discuss the general formalism of optimal observables and apply it to two $CP$-odd observables that are sensitive to the real and imaginary part of $d_τ(s)$, respectively. We compute the expectation values and covariances of these optimal $CP$ observables for $τ$-pair production at $\sqrt{s}=10.58$ GeV with subsequent decays of $τ^\pm$ into major leptonic or semihadronic modes. For the $τ$ decays to two pions and three charged pions we take the full kinematic information of the hadronic system into account. Assuming that the Belle II experiment at the KEKB accelerator will eventually analyze data corresponding to an integrated luminosity of 50 ab$^{-1}$ and applying acceptance cuts on the final-state pions we find that 1~s.d. sensitivities $δ{\rm Re} d_τ= 6.8 \times 10^{-20}$ e cm and $δ{\rm} Im d_τ= 4.0 \times 10^{-20}$ e cm can be obtained with events where both $τ$'s decay semihadronically. In the ideal case where no cuts on the final-state particles are applied we find with 50 ab$^{-1}$ at $\sqrt{s}=10.58$ GeV corresponding to $4.5 \times 10^{10}$ $τ^+ τ^-$ events the 1 s.d. sensitivities $δ{\rm Re} d_τ= 5.8 \times 10^{-20}$ e cm and $δ{\rm} Im d_τ= 3.2 \times 10^{-20}$ e cm, again for events where both $τ$ leptons decay semihadronically. Furthermore, we analyze the potential magnitude of the $τ$ EDM form factor in the type-II two-Higgs doublet extension and in two scalar leptoquark extensions of the Standard Model.

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