AI 中文总结
研究长基线中微子振荡中CP - CPT简并问题，发现用单一路径平均值近似地球密度分布会产生联合参数简并，多通道组合无法解决，通过分析证明偏差形成二维谷，还指出恒定密度假设会带来错误结果，强调完整空间分辨PREM传播的必要性。
AI 中文摘要
我们证明，用单一路径平均值而非空间分辨的初步参考地球模型（PREM）来近似地球密度分布，会在（δ_CP，Δ_CPT，θ_CPT）空间产生联合参数简并。在长基线（L≥5000 km）时，这种几何伪像与真正的超出标准模型（BSM）的物理现象完全无法区分。此前研究分别确定了各通道偏差，本研究首次给出分析证明，这些偏差在完整的三参数空间内形成一个扩展的二维谷。此外，我们严格证明仅多通道组合不足以解决这种简并。泊松对数似然卡方分析证实，像DUNE那样采用恒定密度近似的曝光会错误地将此伪像报告为±3σ的BSM发现。具体而言，在L = 7000 km时，恒定密度假设使恢复的δ_CP偏移17.8°，并在Δ_CPT = 4.1×10^(-4) eV²处制造出虚假的CPT违反。因此，完整的空间分辨PREM传播是对包括DUNE、超级神冈和P2O在内的下一代长基线实验数据进行正确物理解释的严格数学要求，而非可选的改进。
英文摘要
We demonstrate that approximating the Earth's density profile with a single path averaged value instead of the spatially resolved Preliminary Reference Earth Model PREM generates a joint parameter degeneracy in the $(δ_{\text{CP}}, Δ_{\text{CPT}}, θ_{\text{CPT}})$ space. At long baselines ($L \geq 5000\text{ km}$), this geometric artifact becomes entirely indistinguishable from genuine Beyond the Standard Model (BSM) physics. While previous studies established individual channel biases separately, this work provides the first analytic proof that these biases form an extended two dimensional valley within the full three-parameter space. Furthermore, we rigorously demonstrate that multi channel combinations alone are insufficient to resolve this degeneracy. A Poisson loglikelihood chi square analysis confirms that DUNE like exposures utilizing a constant density approximation would erroneously report this artifact as a $\pm3σ$ BSM discovery. Specifically, at $L = 7000\text{ km}$, the constant-density assumption shifts the recovered $δ_{\text{CP}}$ by $17.8^\circ$ and fabricates a spurious CPT violation at $Δ_{\text{CPT}} = 4.1 \times 10^{-4}\text{ eV}^2$. Consequently, full spatially resolved PREM propagation is established as a strict mathematical requirement rather than an optional refinement for the correct physical interpretation of data from next-generation long baseline experiments, including DUNE, HyperKamiokande, and P2O.
