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## 物理代写|高能物理代写High Energy Physics代考|Event rates in pp or pp colliders

In $\bar{p} p$ or $p p$ colliders the total cross section is $60 \mathrm{mb}$ and above. At $\bar{p} p$ colliders the luminosity is limited by the number of antiprotons, as these cannot be produced in large quantities. A typical value of the luminosity is of the order of $10^{30} \mathrm{~cm}^{-2} \mathrm{~s}^{-1}$, which results in an event rate of $6 \times 10^{4}$ events per second. For selected reactions like the production of the intermediate vector boson $Z^{0}$ the cross section is only $2 \mathrm{nb}$, which results in a production rate of one $Z^{0}$ per $5 \times 10^{3} \mathrm{~s}$ or $19 Z^{0}$ per day. The planned hadron-hadron collider (LHC) at CERN will consist of two proton rings with magnetic fields in opposite directions. The $p p$ cross section is expected to rise to $135 \mathrm{mb}$ at $\sqrt{s}=17 \mathrm{TeV}$. It consists of three parts: the elastic, the diffractive and the inelastic cross section. Only the inelastic part contributes to the event rate of a general purpose detector. The particles emerging from elastic and diffractive events remain almost exclusively in the beam pipe. With an inelastic cross section of $60 \%$ of the total cross section and an expected peak luminosity of $L=10^{34} \mathrm{~cm}^{-2} \mathrm{~s}^{-1}$ the event rate becomes $(6-8) \times 10^{8} \mathrm{~Hz}$. With $25 \mathrm{~ns}$ between bunch crossings the average number of observed interactions in each crossing is about 15! If one wants to trigger on missing energy which is a signature of reactions with an escaping neutrino one has to limit the luminosity in such a way that one gets only one event per bunch crossing:
$$L_{\text {limit }}=\langle n\rangle /\left(\text { Time between bunches } \times \sigma_{p p}\right)$$
Even for $\langle n\rangle=1$ there is more than one event per crossing in $26 \%$ of the interactions. (Poisson distribution $P_{1}(>1)=1-P_{1}(0)-P_{1}(1)=1-2 e^{-1}=$ 0.26.)
1.1.6.3 Event rates in $e^{+} e^{-}$colliders. In $e^{+} e^{-}$machines on the other hand, the cross section is very small. The single photon exchange cross section is determined by the cross section for $e^{+} e^{-} \rightarrow \mu^{+} \mu^{-}$which is
$$\sigma_{\mu \mu}=\frac{4 \pi \alpha^{2}}{3 s}=\frac{21.9 \mathrm{nb} \mathrm{GeV}^{2}}{E_{\text {beam }}^{2}}$$
where $\alpha$ is the fine structure constant. The ratio of hadron production to $\mu^{+} \mu^{-}$production is given by the sum of the squared charges of possible quarks multiplied by 3 for the three colours:
$$R=3 \sum_{i=1}^{6} Q_{i}^{2}=5 .$$

## 物理代写|高能物理代写High Energy Physics代考|Event rates at electron-proton colliders

In electron-proton colliders the cross section has two parts: a neutral current $\left(\gamma, Z^{0}\right)$ and charged current $\left(W^{\pm}\right)$contribution. These contributions can be calculated and depend mostly on the momentum transfer $Q^{2}$. Above $Q^{2}=1000 \mathrm{GeV}^{2}$ the cross section for $27.5 \mathrm{GeV}$ electrons and $820 \mathrm{GeV}$ protons is of the order of $150 \mathrm{pb}$. For a luminosity $L=10^{31} \mathrm{~cm}^{-2} \mathrm{~s}^{-1}$ this results in 4 events per hour.

## 物理代写|高能物理代写High Energy Physics代考|Event rates in pp or pp colliders

$$L_{\text {limit }}=\langle n\rangle /\left(\text { Time between bunches } \times \sigma_{p p}\right)$$

1.1.6.3 事件发生率 $e^{+} e^{-}$对撞机。在 $e^{+} e^{-}$另一方面，机器的横截面非常小。单光子交换截面由截面决定 $e^{+} e^{-} \rightarrow \mu^{+} \mu^{-}$这是
$$\sigma_{\mu \mu}=\frac{4 \pi \alpha^{2}}{3 s}=\frac{21.9 \mathrm{nbGeV}^{2}}{E_{\text {beam }}^{2}}$$
$$R=3 \sum_{i=1}^{6} Q_{i}^{2}=5 .$$

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。