标题： 研究在SMEFT框架下LHC中$H\to ZZ^\star$的量子纠缠 显示英文标题

标题： Looking into the quantum entanglement in $H\to ZZ^\star$ at LHC within SMEFT framework

摘要： 我们研究在SMEFT框架下，$13$TeV LHC中最终四个轻子态的$H\to ZZ^\star$产生过程。 异常的$HZZ$耦合用维度-6的$SU(2)_L\times U(1)_Y$规范不变算符进行参数化。 我们计算每个$Z$玻色子的八种极化以及$64$自旋相关性，作为在$Z$玻色子静止系中最终衰变轻子角度函数中的不对称性。 我们对这些不对称性进行敏感性分析，并在$95\%$置信水平上获得这些耦合的一个参数限制。 这些不对称性进一步用于构建$ZZ^\star$系统的联合密度矩阵（DM）。 然而，这种 DM 存在负概率和特征值的问题。 为了缓解负面问题，我们利用由于两个$Z$玻色子不可区分性而产生的对称化角度函数的不对称性来重构 DM。 对称化的 DM 进一步用于计算纠缠的下限，作为对撞机实验中可测量的纠缠的判据。 发现$ZZ^\star$系统在所有异常耦合值下都处于纠缠态。 值得注意的是，虽然下限相比不对称性对异常耦合的敏感性较差，但它对 CP 偶和奇耦合表现出不同的行为。 显示英文摘要

摘要： We study $H\to ZZ^\star$ production process in final four lepton states at $13$ TeV LHC within SMEFT framework. The anomalous $HZZ$ couplings are parameterized with dimension-6 $SU(2)_L\times U(1)_Y$ gauge invariant operators. We compute the eight polarizations of each $Z$ boson and $64$ spin-correlations as asymmetries in angular functions of final decayed leptons in the rest frame of the $Z$ boson. We perform the sensitivity analysis of these asymmetries to anomalous couplings and one parameter limits on these couplings at $95\%$ confidence level are obtained. These asymmetries are further used to construct the joint density matrix (DM) for $ZZ^\star$ system. However, such DM suffers from negative probability and eigenvalues. To alleviate the negativity issues, we reconstruct the DM using asymmetries of symmetrized angular functions owing to the indistinguishability of two $Z$ bosons. The symmetrized DM is further employed to compute lower bound for concurrence as a witness of entanglement measurable at the collider experiments. The $ZZ^\star$ system is found to be in an entangled state for all values of the anomalous couplings. Notably, while the lower bound exhibits poorer sensitivity to anomalous couplings compared to asymmetries, it demonstrates distinct behavior for CP-even and odd couplings.