近几十年，在欧洲核子中心的大型强子对撞机 (LHC) 中，喷注一直是精确验证粒子物理标准模型和发现新物理的不可缺少的工具。在相对论重离子对撞机 (RHIC) 中的研究显示，喷注也可以用来研究一些非微扰动力学。
想要对喷注进行理论研究，就必须计算喷注截面。要计算这些截面必须对这些喷注进行合适的定义，这些定义由一系列的算法来实现，这些算法提供了将粒子组合成喷注的规则。一个合适的喷注算法应该得到红外安全的结果，且能方便地在理论计算和实验中使用。
目前关于喷注和喷注算法在理论上和实验上都有很多的研究。特别是 NLO 喷注函数在很多算法下都已经被很好地计算。随着喷注截面精度需求增加，这些 NLO 结果的精度显然不足够。无论是固定阶计算还是重求和，都要求截面因子化中的组分精度在 NLO 以上，而人们对其中软和硬的部分在 NNLO已经有了一定的了解。本文基于软-共线有效理论，将夸克喷注截面因子化，分离出共线的部分，即喷注函数。先用 anti-kT 算法计算 NLO喷注函数，用于后面 NNLO 数值计算的验证。然后用相同的思路尝试计算 NNLO 喷注函
数。

In recent decades, jet have been an essential tool for accurately validating the particle physics Standard Model and discovering new physics in the Large Hadron Collider (LHC) at CERN. Studies at the Relativistic Heavy Ion Collider (RHIC) have also shown that jet can be used to investigate some aspects of non-perturbative physics.
In order to conduct theoretical research on jet, it is necessary to calculate the cross-sections of the jet. To calculate these cross-sections, it is necessary to define the jet appropriately, which is achieved through a series of algorithms. These algorithms provide rules for combining particles into the jet. An appropriate jet algorithm should produce infrared-safe results and be conveniently used in theoretical calculations and experiments.
Currently, there is a lot of research on jet and jet algorithms in both theory and experiments. In particular, the NLO jet function has been well calculated with other algorithms. However, as the demand for jet cross-section accuracy increases, the precision of these NLO results is obviously not sufficient. Whether it is fixed-order calculation or re-summation, the component precision in the factorization of the cross-section needs to be at least NLO. People already have some understanding of the soft and hard components at NNLO. This article is based on the soft-collinear effective theory to factorize the quark jet cross-section and separate the collinear part, which is the jet function. In this article, we first calculated the NLO jet function using the anti-kT algorithm. Then, the same approach is used to implement the calculation of the NNLO jet function.