论文标题
两种中微子双β衰减中的洛伦兹违规效果
Lorentz violation effects in two neutrino double-beta decay
论文作者
论文摘要
还可以在双β衰减（DBD）中研究对洛伦兹不变性违规（LIV）的可观察效应。例如，通过将理论预测与对$2νβ$衰减的电子的总结能量谱进行比较，可以约束$ \ Mathring {a} _ {a} _ {of}^{（3）} $系数，该系数控制着违反标准模型的lorentz不变性运算师的时间型诸如lorentz不变性的成分。在这项工作中，我们对电子的相位因子和求和能量谱进行计算，以及由于在此类实验研究中所需的LIV而导致的偏差。计算中所需的费米函数是通过通过数值求解有限的核大小和筛选效应的逼真的库仑型电势中数字求解狄拉克方程来构建的。我们将我们的结果与以前使用近似（分析）费米函数获得的LIV研究中使用的结果进行了比较，发现较重的核的差异高达$ 30 \％$。我们的工作包括八个实验有趣的核。接下来，我们估计并讨论与Q值测量中的不确定性相关的计算的不确定性以及由于形式主义中的运动术语所带来的差异。最后，我们提供了标准相空间因子及其LIV偏差与预期LIV效应最大的能量之间的比率。我们希望我们的研究对当前的$2νβ$衰减的LIV研究有用，并会改善对$ \ Mathring {a} _ {of}^{（3）} $系数的约束。
Observable effects for the Lorentz invariance violation (LIV) at a low energy scale can also be investigated in double beta decay (DBD). For example, by comparing the theoretical predictions with a precise analysis of the summed energy spectra of electrons in $2νββ$ decay, one can constrain the $\mathring{a}_{of}^{(3)}$ coefficient that governs the time-like component of the Lorentz invariance violating operator that appears in the Standard Model extension theory. In this work, we perform calculations of the phase space factors and summed energy spectra of electrons as well as of their deviations due to LIV necessary in such experimental investigations. The Fermi functions needed in the calculation are built up with exact electron wave functions obtained by numerically solving the Dirac equation in a realistic Coulomb-type potential with the inclusion of the finite nuclear size and screening effects. We compared our results with those used in previous LIV investigations that were obtained with approximate (analytical) Fermi functions and found differences of up to $30\%$ for heavier nuclei. Our work includes eight experimentally interesting nuclei. Next, we estimate and discuss the uncertainties of our calculations associated with uncertainties in Q-values measurements and the differences raised from the inclusion of the kinematic terms in the formalism. Finally, we provide the ratio between the standard phase space factors and their LIV deviations and the energies where the LIV effects are expected to be maximal. We expect our study to be useful in the current LIV investigations in $2νββ$ decay and to lead to improved constraints on the $\mathring{a}_{of}^{(3)}$ coefficient.
