粒子物理实验中的统计学¶
Abstract
- Quarks *6
- Leptons *6
- Bosons *5
- Higgs boson
SM
大型强子对撞机（LHC）
- ATLAS
- CMS
- ALICE
- LHCb
25 ns 碰撞一次，数据量巨大
A portrait of the Higgs boson in the CMS experiment ten years after the discovery
假设检验¶
自旋 \(0^+\) / \(1^+\)
ROOT 简介¶
CERN 开发的数据分析 Python 库
系统误差¶
Nuisance parameters：影响参数估计，但不是我们关心的物理量
Systematic uncertainties
单摆
测量周期：测量 \(N\) 个周期的时间 \(\tau\)，计算平均周期 \(T = \tau / N\) 测量摆长：如果尺子每次给出的结果
用似然函数和高斯限定条件纠正¶
\[L(\mu,\theta) = \prod_c \prod_i P_c(x_i|\mu,\theta) \cdot \prod_j C_j(g_j|\theta_j)\]
- \(\mu\)：感兴趣的物理量（POI）
- \(P_c(x_i|\mu,\theta)\)：Channel c 的概率密度函数（PDF）
- \(C_j(g_j|\theta_j)\)：额外的概率密度函数，不依赖于数据
- \(x_i\)：测量量（observables）
- binned dataset: each entry contains the contents of a bin
- unbinned dataset
- \(\theta\)：Nuisance parameters（NPs）
- 系统误差的主要来源
Likelihood ratio:¶
\[\Lambda(\mu) = \frac{L(\mu,\hat{\hat{\theta}(\mu)})}{L(\hat{\mu},\hat{\theta})}\]
Discovery Significance¶
- In the asymptotic limit (large N), the PLR, \(\Lambda(\mu) = \frac{L(\mu,\hat{\hat{\theta}(\mu)})}{L(\hat{\mu},\hat{\theta})}\), gives the compatibility between \(\mu\) and \(\hat{\mu}\) hypothesis.
Discovery with toys¶
- Toy MC(Monte Carlo pseudo-experiments) can be generated directly from the components of the likelihood function.