圈积分及相空间积分计算系列讲座

29 Oct 2020, 01:00 → 3 Nov 2020, 18:00 Asia/Shanghai

45161188005 (腾讯会议)

高精度物理是未来检验标准模型及探测新物理的主要手段。从理论角度，需要进行微扰论的高阶计算，其中核心困难是费曼圈积分和相空间积分的计算。本系列讲座将回顾过去几十年在圈积分及相空间积分计算方面的主流、非主流方法和想法。希望通过一两年的学习，国内同行能对相关知识有更全面的了解，从而能在高精度前沿领域作出更重要的贡献。幻灯片和参考文献将放在本网站供大家查阅及下载。

 

系列讲座分为六个主题，相应召集人为：

1、积分约化（张扬-中国科学技术大学）

2、解析计算（杨李林-浙江大学）

3、数值计算（马滟青-北京大学）

4、积分行为（王玉明-南开大学）

5、相空间积分（刘晓辉-北京师范大学）

6、程序使用（李钊-中科院高能所）

 

讲座时间：自2020年10月29日起，北京时间每周四7pm开始（1-2小时，依赖于报告人，节假日无报告）

 

讲座方式：腾讯会议 451 6118 8005，密码 123456（https://meeting.tencent.com/s/YeTK9EQclzCF）

 

报告视频下载密码：363K

完整资料下载地址：https://pan.baidu.com/s/12SOBiU1UKxZWeGbz3Tv4kQ

 

若对系列讲座有任何意见及建议，欢迎提出。

Thursday, 29 October

积分约化

Convener: 张扬

1 A Canonical Introduction to Feynman Integral Reduction

In order to get high order scattering amplitudes, it is essential to calculate corresponding Feynman integrals. However, for multi-loop orders, there will be a huge number of Feynman integrals for a physical process. Thanks to the integration-by-parts (IBP) identities, we can reduce these integrals to a small set of integrals, i.e., master integrals. Here I give an introduction on IBP identities and the Laporta algorithm, which is the standard algorithm for IBP reduction. I will also present the usage of FIRE6 --- a popular software on automatic IBP reduction.

Speaker: 徐英轩 (Humboldt-Universitat zu Berlin)

record https://pan.baidu.com/s/1k3JPCgyhlaYdCdDc7tHFMA

Slides 20201029_A_Canonical_Introduction_to_Feynman_Integral_Reduction.pdf

2 Usage of public IBP reduction packages: FIRE and Kira

FIRE 和 Kira 是目前最常使用的积分约化开源程序包。两者都主要基于 Laporta 算法，多核多节点并行，但又各有特色，FIRE 吸收了非交换代数构造递推关系的技巧，而 Kira 在大稀疏矩阵消元策略/代数运算底层并行上有专长。两者都可以和现代有限域计算方法相结合，提高计算速度。这次报告中，报告人将在线演示如何使用这两种软件。

Speakers: Mr Mingming Long, Prof. Yang Zhang

Slides FIRE6_tutorial-M.Long.pdf

software Demo_FIRE+LiteRed.zip

Video https://pan.baidu.com/s/1DTzyaw5zKQu2qmF23pjK3A

3 Syzygy for Feynman integral reduction

Speaker: Prof. Yang Zhang

Slides Syzygy4FIR_Yang_Zhang.pdf

Video https://pan.baidu.com/s/1S_QejFf6mQu0vEMOk6sAoA

4 Technique in Auxiliary Mass Flow

Speaker: Prof. Zhao Li

Slides AMF_ZLi.pdf

Video https://pan.baidu.com/s/1YDRrXP1Tvt8j3-8nLmPUkA

5 IBP for gravitational wave physics

We describe the calculations of multi-loop scattering amplitudes in the context of binary black hole dynamics. The method of regions is used to expand the amplitudes in the limit of small $\hbar$. The expansion reduces the number of dimensionless kinematic variables from 3 to 1, which dramatically speeds up the subsequent IBP reduction, allowing us to calculate the 3-loop conservative dynamics of binary black holes. Additionally, Using reverse unitarity, phase space integrals for graviton emissions are treated like loop integrals using standard techniques like IBP and differential equations, allowing us to obtain analytic results for energy loss in black hole scattering.

Speaker: Prof. Mao Zeng

Slides IBP_talk-M.Zeng.pdf

Video https://pan.baidu.com/s/1eJToJXpXcpuDTp-m7CMgLQ

6 Counting Master Integral: A Fascinating Problem

Speaker: Jiuci Xu

References refs.zip

Slides CMI-J.Xu.pdf

Video https://pan.baidu.com/s/1HEUm11XAicMr3pCrvZG__A

Friday, 30 October

解析计算

Convener: 杨李林

7 Introduction to differential equation method for Feynman integral

Feynman integrals are one of the important ingredients to provide precise theoretical predictions for process at the LHC. Recently, there is significant progress in calculating Feynman integrals using differential equation method. In this lecture, I will introduce the canonical form of differential equations, the corresponding integrals called canonical basis, and I will discuss how to solve the equations. Finally, I will review recent progress in constructing canonical basis.

Speaker: 徐小峰

record https://pan.baidu.com/s/10s8_Wc0rRAd6VaKAymGGDA

Slides 20201105_Introduction_to_differential_equation_method.pdf

8 Analytic calculation--traditional methods for integrals

传统的积分方法在历史上起到了非常重要的作用。尽管目前微分方程的方法非常流行也非常强大，但是依然需要利用其它方法确定其边界条件。此外，在一些有效理论中出现的积分，微分方程的方法并不能很好的适用。此时，这些传统的方法便成为非常重要的处理手段。本次报告主要介绍三种传统的积分方法：parameterization，Mellin Barnes representation，Asymptotic expansions. 在报告中，报告人将分别介绍这些方法的基本概念和一些常用公式，并以一些简单的例子介绍如何在具体计算中使用这些积分方法。

Speaker: Dr Guo-Xing Wang

Slides integrals_Guoxing_Wang.pdf

Video https://pan.baidu.com/s/1dF5LX_xLq9Sasj7hF85hTw

9 Regularization and calculation of rapidity divergent Feynman integrals systematically

Speaker: Dr Tong-Zhi Yang

Slides TMDBeam_TongzhiYang.pdf

Video https://pan.baidu.com/s/19IRfQpoCImVgYxFbj5OgzA

10 Bootstrapping a two-loop four-point form factor

We explain a recent computation of a two-loop four-point form factor in planar N=4 SYM, which belongs to the class of two-loop five-point scattering observables with one off-shell color-singlet leg. A new bootstrapping strategy is developed to obtain this result by starting with an ansatz expanded in terms of master integrals and then solving the master coefficients via various physical constraints. We find that consistency conditions of infrared divergences and collinear limits, plus the cancellation of spurious pole, can fix a significant part of the ansatz. The remaining degrees of freedom can be fixed by one single type of two-double unitarity cut.

Speaker: Prof. Gang Yang

Slides Bootstrap_4pt_G.Yang.pdf

Video https://pan.baidu.com/s/1UplhM15tk8_eE9ZS7GX7Mg

11 Efficient NLO computation for gg->HH/ZH with top quark mass dependence

Recently, we present a precise and efficient computation of the two-loop amplitudes entering gg->HH/ZH and present for the first time a calculation of the complete NLO corrections to the gg->ZH process. We use the method of small mass expansion to tackle the most challenging two-loop virtual amplitude, in which the top quark mass dependence is retained throughout the calculations. Our results are necessary ingredients towards reducing the theoretical uncertainties of the pp->ZH cross sections down to the percent-level, and provide important theoretical inputs for future precision experimental collider programs. In this talk, I will start with a brief introduction to to the HH/ZH production and method of the small mass expansion and then show our new results for the ZH production at the LHC.

Speaker: Dr Guo-Xing Wang

Slides HH_ZH_Guoxing_Wang.pdf

Video https://pan.baidu.com/s/1wCDMpVt1lJX739FYjKdAfQ

12 Compton Scattering at Next-to-leading Order

The analytic form for the total QED scattering cross section of an electron and a photon at order \alpha^3 is computed. This includes both the double-Compton scattering real-emission contribution as well as the virtual Compton scattering part. When combined with the recent analytic result for the pair-production cross section, the complete \alpha^3 cross section is now known. Both the next-to-leading order calculation as well as the pair-production cross section are computed using modern multi-loop calculation techniques, where cut diagrams are decomposed into a set of master integrals that are then computed using differential equations.

Speaker: Xiaoyuan Zhang

Slides CSTCS@NLO-X.Zhang.pdf

Video https://pan.baidu.com/s/1ggF_9Owyvj0-eUU5gNQh4g

Saturday, 31 October

数值计算

Convener: 马滟青

13 Introduction to sector decomposition

简要介绍sector decomposition的基本原理，其方法的优势及局限性，介绍几个主流的工具。

Speaker: 李钊

Slides 20201112_Sector.pdf

Video https://pan.baidu.com/s/1pxbRjMDZDydNUKmVEJBlnA

14 Calculation of master integrals using difference equation method

差分方程是计算主积分的一个重要方法。本次报告将介绍如何构建差分方程、求解差分方程，并给出科研中用到的具体例子。

Speakers: Mr Zheng-Yang Li, Mr Zhi-Feng Liu

Slides Feynman_integrals_calculation_by_difference_equations-Zhi-Feng_Liu.pdf Feynman_integrals_calculation_by_difference_equations-Zhi-Feng_Liu.pdf

Video https://pan.baidu.com/s/1qA5wRrw7-1p9DacGg3NCww

15 Solving Master Integrals via Numerical Differential Equations

Speaker: Xiao Liu

Slides Solving_Master_Integrals_via_NDE-Xiao_Liu.pdf

Video https://pan.baidu.com/s/13oBJ0-NHiY3EU8JrVzDkqg

16 圈积分的解析与数值计算若干方法与程序简介

本次报告将简单介绍圈积分的一些解析和数值计算方法，以及相关程序包的使用。例如微分方法方法来解析或数值计算圈积分，利用DiffExp 程序包来数值计算微分方程。 应用基于sector decomposition 方法的 FIESTA 程序包来对积分进行数值计算，以及利用GINAC来数值计算Goncharov Polylogarithms。

Speaker: Prof. Long-Bin Chen

notes 3loop-H2L-FIESTA.nb

Slides MI-calc-num-L.B.Chen.pdf

Video https://pan.baidu.com/s/1UErZmxVvKceiwqdTMuylbg

17 On the evaluation of two-loop electroweak box diagrams for e+ e- to HZ production

Precision studies of the Higgs boson at future e+e- colliders can help to shed light on fundamental questions related to electroweak symmetry breaking, baryogenesis, the hierarchy problem, and dark matter. The main production process, e+ e- to HZ, will need to be controlled with sub-percent precision, which requires the inclusion of next-to-next-to-leading order (NNLO) electroweak corrections. The most challenging class of diagrams are planar and non-planar double-box topologies with multiple massive propagators in the loops. We generate a new technique for computing these diagrams numerically, by transforming one of the sub-loops through the use of Feynman parameters and a dispersion relation, while standard one-loop formulae can be used for the other sub-loop. This approach can be extended to deal with tensor integrals. The resulting numerical integrals can be evaluated in minutes on a single CPU core, to achieve about 0.1% relative precision.

Speaker: Qian Song

Slides 2loop-EW-box-Q.Song.pdf

Video https://pan.baidu.com/s/1LdYXg4ABDQnCUjQH1Qh2mA

18 AMF method 程序AMFlow

这将是首个能够高精度计算任意圈积分、相空间积分的程序。

Speaker: Dr Xiao Liu

Slides X.Liu.pdf

Video https://pan.baidu.com/s/1HHgacYo69Gic3R6Xc8Liow

Sunday, 1 November

积分行为

Convener: 王玉明

19 EFT perspectives on Feynman integrals/Matching QCD currents(operators) onto SCET

Speakers: Prof. Xin-Qiang Li, Prof. Yu-Ming Wang

Slides Loop_Integrals_from_EFT-Y.M.Wang.pdf NNLO_matching-X.Q.Li.pdf

Video https://pan.baidu.com/s/11_FIy3tuGF9COAN6YdzP-Q

20 Applications of conformal symmetry in QCD

Conformal symmetry provides significant simplifications to loop calculations in QCD for non-forward kinematics. In this talk, I will explain the relevant ideas detailing the procedures for applying conformal symmetry in QCD. I will review some recent results obtained through the conformal technique, which are immediately applicable to EIC physics, and meson decays.

Speaker: Dr Yao JI

Slides Applications_of_conformal_symmetry_in_QCD-Yao_JI.pdf

Video https://pan.baidu.com/s/1EpJa405dCLLChZ4lE80-AA

21 Analyticity, renormalization, and evolution of the soft-quark function

Speaker: Dr Xiang-Peng Wang

Slides Analycity,Renormaliztion_and_Evolution_of_SQF_X.P.Wang.pdf

Video https://pan.baidu.com/s/1DHI0gMyzTJ-eIpHnBsY8Sg

22 An introduction to the basics of SCET and method of regions

Soft collinear effective theory is an effective theory of QCD in the infrared regions. It has been used widely in the study of infrared divergnces of scattering amplitudes and of resummation of large logarithms in cross sectons. It helps one to obtain much information about the higher order corrections. The method of regions is another useful tool to calculate loop integrals up to certain power corrections, and can thus help to check the analytic result or to set the boundary constants for differential equations.

Speaker: Prof. Jian Wang

Slides introduction-to-Method-of-regions-and-SCET-WangJian.pdf

Video https://pan.baidu.com/s/1nzHAVSUAMG_t8mrN7O-xQA

23 Resummation of Super-Leading Logarithms

Jet cross sections at high-energy colliders exhibit intricate patterns of logarithmically enhanced higher-order corrections. In particular, so-called non-global logarithms emerge from soft radiation emitted off energetic partons inside jets. While this is a single-logarithmic effect at lepton colliders, at hadron colliders phase factors in the amplitudes lead to double-logarithmic corrections starting at four-loop order. This effect was discovered a long time ago, but not much is known about the higher-order behavior of these terms and their process dependence. We derive, for the first time, the all-order structure of these “super-leading logarithms” for generic 2->N scattering processes at hadron colliders and resum them in closed form.

Speaker: Prof. Ding-Yu Shao

Slides Resum_SLL-DYShao.pdf

Video https://pan.baidu.com/s/1azo-WqddVzf7_f8pJH3yFA

24 SCET factorization for the radiative leptonic B-meson decays

The radiative leptonic B-meson decays are extremely important to the study of the exclusive B-meson decays. I will concentrate on the factorization properties of the radiative leptonic B decay with an energetic photon in the final states. Employing the method of regions, we can derive the factorization formula of the decay form factors at the leading power. The factorization formula could be proved to be valid to all orders in QCD with the help of the soft collinear effective theory (SCET). The SCET also provides an elegant approach to obtain the evolution behavior of the factorization formula. In the framework of the SCET, we can further study systematically the factorization properties of the radiative leptonic B decay beyond the leading power.

Speaker: Dr Yan-Bing Wei

Slides Y.B.Wei.pdf

Video https://pan.baidu.com/s/1IPdqHo5QIJPQNV2U8yVc9Q

Monday, 2 November

相空间积分

Convener: 刘晓辉

25 Phase space integration-overview/Slicing method and soft function at NNLO

Speakers: Prof. Jian Wang, Prof. Xiao-Hui Liu

Slides overview.pdf slicing-w-jian.pdf

Video https://pan.baidu.com/s/1Po23qUh_KMq8lIdWfLyGKQ

26 Calculation of phase-space integration of sufficient inclusive processes

In this talk, I will introduce a systematic method (inverse unitarity+differential equations+auxiliary mass flow) to calculate phase-space integration for sufficient inclusive processes. With this method, we can get numerical results with high precision efficiently.

Speaker: Peng Zhang

Slides Calculation_of_phase_space_integration_of_sufficient_inclusive_processes-Peng_Zhang.pdf

Video https://pan.baidu.com/s/159lcvUgrZgjH9qoNmCc6DA

27 高精度现象学和减除法

Speaker: Dr Xuan Chen

Slides HPP&SM_XuanChen.pdf

Video https://pan.baidu.com/s/1A4j7ZaGeotcAA7VstpNhiA

28 Introduction to parton shower

Monte-Carlo event generators have been widely used to simulate the processes in high-energy physics. Parton shower plays a central role in Monte-Carlo event generators which provides a reliable tool to perform the leading logarithms resummation. Precision prediction from parton shower requires more theory developments such as proof of NLL resummation and NLO shower framework. Beyond the resummation region, matching or merging with fixed-order calculations can improve the description of hard radiation. This talk will be aiming to give a comprehensive review of parton showers and matching/merging techniques.

Speaker: Dr Hai-Tao Li

Slides parton_shower-H.T.Li.pdf

Video https://pan.baidu.com/s/1ml6-489PzN703X6T4WaycA

29 Light-ray OPE in QCD

Light-ray operators play an important role in various areas of physics and, in particular, are natural language for an interesting class of observables in collider physics, including energy-energy correlator (EEC). Similar to operator product expansion (OPE) of local operators, OPE of light-ray operators governs the collinear behavior of these observables. In this talk, I will first briefly review Hofman and Maldacena’s basic idea about Conformal Collider Physics and recent development of light-ray OPE in conformal field theory. In the second part, I will describe the application of light-ray OPE in perturbative QCD and how it helps us understand jet substructures.

Speaker: Hao Chen

Slides Light-ray_OPE_in_QCD-H.Chen.pdf

Video https://pan.baidu.com/s/1SmckuVFCHtzOHikvtnBMqQ

30 The pion-photon transition form factor at two loops in QCD

In this talk, I will report on our recent fully analytic calculation of the leading-power contribution to the photon-pion transition form factor at two loops in QCD. The applied techniques rely on hard-collinear factorization, together with modern multi-loop methods. I will focus both on the technical details, such as the treatment of evanescent operators, and the phenomenological implications. Our results indicate that the two-loop correction is numerically comparable to the one-loop effect in the same kinematic domain. I will also demonstrate that our results will play a key role in disentangling various models for the twist-two pion distribution amplitude thanks to the envisaged precision at future experimental facilities.

Speaker: Dr Yao Ji

Slides TFF@2loop-Y.Ji.pdf

Video https://pan.baidu.com/s/1C8Ticwvbuq1UwQe8n6Ccfg

Tuesday, 3 November

程序使用

Convener: 李钊

31 pfd: a Singular Library to Simplify IBP Reduction Coefficients

Speaker: Mr Zihao Wu

Slides Simple_IBP-Zihao_Wu.pptx

Video https://pan.baidu.com/s/1XCzVyJhzeFRBQ8167F4E2A

32 Introduction to FDC project

Speaker: Prof. Bin Gong

Slides FDC_Project-Bin_Gong.pdf

Video https://pan.baidu.com/s/1WodUL_rUY0SfUI5KBln1sw

33 Introduction to FORM

Speaker: Prof. Zhao Li

Slides FORM_intro_Z.Li.pdf play_form.tar.bz2

Video https://pan.baidu.com/s/1N9wFF143q9Ja3C0_5i7tSw

34 An introduction to the computer algebra system Singular

Speaker: Prof. Yang Zhang

Slides Singular-Y_Zhang.pdf

Video https://pan.baidu.com/s/1zaGS5YaVR7ROifoW2uXGEg

35 FiniteFlow程序的物理和使用

Speakers: Chuan-Qi He, Xin Guan

notebook fflow-X.Guan.zip

Slides FFlow-C.Q.He.pdf FFlow-X.Guan.pdf

Vedio https://pan.baidu.com/s/19Cq-YLk6C40p2YixuzDh-w

36 Julia编程语言介绍

Speaker: Prof. Zhao Li

Slides Julia-Z.Li.pdf

Video https://pan.baidu.com/s/192R9hDcR9uTPb4pnaGM9Mw