arXiv 2102.034912021-02hep-ph

轻子数破坏$τ$衰变的有效场论方法

Effective field theory approach to lepton number violating $τ$ decays

Yi Liao, Xiao-Dong Ma, Hao-Lin Wang

备注：: 16 pages, 4 figures, 4 tables
发表信息：: Chin. Phys. C 45, no.7, 073102 (2021)
DOI：: 10.1088/1674-1137/abf72e

摘要：

我们继续在有效场论（EFT）框架下研究低能轻子数破坏（LNV）过程。本文研究了LNV τ衰变$τ^+\rightarrow \ell^-P_i^{+}P_j^{+}$，其中$\ell=e,~μ$和$P^+_{i,j}$是最低层带电赝标量$π^+,~K^+$ .我们分析了一系列从高到低能量尺度的EFT中的主要贡献，即标准模型有效场论（SMEFT），低能有效场论（LEFT）和手征微扰理论（$χ$ PT）。衰变分支比用SMEFT中五维和七维算符的Wilson系数和强子低能常数表示。这些威尔逊系数涉及第一代和第二代夸克以及所有代轻子，因此无法在低能过程中进行探索，例如核无中微子双衰变或LNV K介子衰变。不幸的是，目前的实验上限的分支比太弱，设置有用的约束这些系数。或者，如果我们假设新的物理尺度大于1 TeV，则分支比远低于当前的实验界限。通过计算单圈手征谱估计了将$χ$ PT应用于$τ$衰变中所产生的强子不确定性，并试图通过在衰变振幅的短距离部分引入色散关系来改善手征微扰的收敛性.

英文摘要：

We continue our endeavor to investigate lepton number violating (LNV) processes at low energy in the framework of effective field theory (EFT). In this work we study the LNV tau decays $τ^+\rightarrow \ell^-P_i^{+}P_j^{+}$, where $\ell=e,~μ$ and $P^+_{i,j}$ are the lowest-lying charged pseudoscalars $π^+,~K^+$. We analyze the dominant contributions in a series of EFTs from high to low energy scales, namely, the standard model effective field theory (SMEFT), the low-energy effective field theory (LEFT), and the chiral perturbation theory ($χ$PT). The decay branching ratios are expressed in terms of the Wilson coefficients of dimension-five and -seven operators in SMEFT and hadronic low energy constants. These Wilson coefficients involve the first and second generations of quarks and all generations of leptons and thus cannot be explored in low energy processes such as nuclear neutrinoless double decay or LNV kaon decays. Unfortunately, the current experimental upper limits on the branching ratios are too weak to set useful constraints on those coefficients. Or, if we assume the new physics scale is larger than 1 TeV, the branching ratios are well below the current experimental bounds. We also estimate hadronic uncertainties incurred in applying $χ$PT to $τ$ decays by computing one-loop chiral logarithms and attempt to improve convergence of chiral perturbation by employing dispersion relations in the short-distance part of the decay amplitudes.

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