Higher-order calculations and collider analyses with Mellin-space techniques

使用梅林空间技术进行高阶计算和碰撞分析

• 批准号: PP/E007414/1
• 负责人: Andreas Vogt
• 金额: $ 27.04万
• 依托单位: University of Liverpool
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2008
• 资助国家: 英国
• 起止时间: 2008 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=PP%2FE007414%2F1
• 关键词: Higher; order; calculations; collider; analyses

The proposed research focuses on higher-order calculations in perturbative quantum field theory, in particular quantum chromodynamics (QCD, the theory of the interactions of quarks and gluons), and the efficient application of such calculations to analyses of experimental data, especially from present and forthcoming high energy electron-proton and proton-proton colliders. Quantum field theory, the merger of quantum mechanics and the theory of special relativity for pointlike fundamental objects, is the mathematical framework for particle physics phenomenology, the theoretical research with direct relevance to experimental investigations. Even for simple processes, the predictions of phenomenologically relevant quantum field theories cannot be calculated exactly by present or foreseeable mathematical methods. Lattice theory offers a way out by discretizing space-time and numerically solving the resulting equations on supercomputers. This method, however, is not applicable to a large amount of scattering observables, thus leaving perturbation theory, i.e., the evaluation of the predictions in terms of a series expansion in a small parameter (coupling constant) such as the fine-structure constant of quantum electrodynamics. In order to derive quantitatively reliable predictions, this expansion has to be extended beyond the first term (the leading order). In fact, for many important processes even contributions beyond the second term (the next-to-leading order) need to be computed. Such higher-order calculations also help to uncover general structural features of the theory under consideration, thus stimulating also research in formal quantum field theory and, via `duality' relations, even string theory. During the time span of the proposed research, particle physics will take the next big step by starting experimentation at the Large Hadron Collider (LHC) at CERN, a proton-proton accelerator with an unprecedented collision energy of 14 TeV. Research at this facility will shed light on fundamental questions like the mechanism of electroweak symmetry breaking and the realization of supersymmetry, or other `new physics', at the TeV scale. At a proton collider, perturbation theory can be applied only after factorizing the non-perturbative structure of the protons encoded in the momentum distributions of the quarks and gluons (`partons') in the proton. These universal quantities cannot be obtained from lattice theory either, but have to be fitted from experimental data, including results from the 320 GeV electron-proton collider HERA at DESY which is now in its final phase of high-luminosity data taking. Hence it is vital to perform sufficiently accurate calculations not only for proton-proton cross sections, but also the electron-proton observables employed for the determination of the parton distributions. Furthermore the resulting, usually very complex higher-order results need to be included in a highly efficient numerical setup, improving on codes so far used for the determination of parton distributions and collider cross sections. The proposed research will address these issues by 1. performing higher-order QCD calculations relevant to collider processes. These calculations will be performed via an integral transform (leading to integer Mellin-moments), a technique already used in the past years for pioneering third-order calculations by the applicant and his collaborators. 2. setting up, applying and publicizing an efficient platform for the numerical analysis of proton collider data which incorporates the above calculations and relevant results by other groups. This platform will be based on a technique using complex Mellin moments, for which the applicant is one of the leading international experts. This project is a novel initiative at Liverpool University which will considerably strengthen the synergy between the theory group in Mathematical Sciences and the experimental group in the Physics Department.

提出的研究重点是微扰量子场论中的高阶计算，特别是量子色动力学（QCD，夸克和胶子相互作用的理论），以及这些计算在实验数据分析中的有效应用，特别是来自现有和即将到来的高能电子-质子和质子-质子对撞机的数据。量子场论是量子力学和点状基本物体的狭义相对论的融合，是粒子物理现象学的数学框架，是与实验研究直接相关的理论研究。即使对于简单的过程，现象学相关量子场论的预测也不能用现有的或可预见的数学方法精确计算。晶格理论提供了一种方法，将时空离散化，并在超级计算机上数值求解得到的方程。然而，这种方法不适用于大量的散射观测值，因此留下了微扰理论，即根据小参数（耦合常数）（如量子电动力学的精细结构常数）的级数展开来评估预测。为了得出定量上可靠的预测，这种展开必须延伸到第一项（先导阶）之后。事实上，对于许多重要的流程，甚至超过第二项（仅次于领先的顺序）的贡献也需要计算。这种高阶计算也有助于揭示所考虑的理论的一般结构特征，从而也刺激了形式量子场论的研究，甚至通过“对偶”关系，甚至弦理论。在拟议研究的时间跨度内，粒子物理学将迈出下一步，在欧洲核子研究中心的大型强子对撞机（LHC）上开始实验，这是一个质子-质子加速器，具有前所未有的14 TeV的碰撞能量。该设施的研究将揭示一些基本问题，如电弱对称破缺机制和超对称的实现，或其他“新物理学”，在TeV尺度上。在质子对撞机中，摄动理论只能在分解质子中夸克和胶子（“部分”）的动量分布中编码的质子的非摄动结构后才能应用。这些通用量也不能从晶格理论中获得，但必须从实验数据中进行拟合，包括来自DESY的320 GeV电子-质子对撞机HERA的结果，该对撞机目前处于高亮度数据采集的最后阶段。因此，不仅要对质子-质子横截面进行足够精确的计算，而且要对用于确定部分子分布的电子-质子观测值进行足够精确的计算。此外，所得到的通常非常复杂的高阶结果需要包含在高效的数值设置中，从而改进迄今用于确定部分子分布和对撞机截面的代码。拟议的研究将在1年前解决这些问题。执行与对撞机过程相关的高阶QCD计算。这些计算将通过积分变换（导致整数梅林矩）来执行，这是一种在过去几年被申请人和他的合作者用于开创性三阶计算的技术。2. 建立、应用和宣传一个高效的质子对撞机数据数值分析平台，将上述计算和其他小组的相关结果结合起来。该平台将基于使用复杂梅林矩的技术，申请人是国际领先的专家之一。这个项目是利物浦大学的一个新项目，它将大大加强数学科学理论组和物理系实验组之间的协同作用。

项目成果

Higher-order threshold resummation for semi-inclusive e^+e^- annihilation

半包含 e^ e^- 湮灭的高阶阈值恢复

• DOI: 10.48550/arxiv.0908.2746
• 发表时间: 2009
• 作者: Moch S

On the next-to-next-to-leading order QCD corrections to heavy-quark production in deep-inelastic scattering

关于深非弹性散射中重夸克产生的次次次前导 QCD 校正

• DOI: 10.1016/j.nuclphysb.2012.07.001
• 发表时间: 2012
• 期刊: Nuclear Physics B
• 影响因子: 2.8
• 作者: Kawamura H

Threshold improved predictions for charm production in DIS

改进了 DIS 魅力生产的预测阈值

• DOI: 10.22323/1.106.0163
• 发表时间: 2010
• 作者: Lo Presti N

Operator product expansion for B-meson distribution amplitude and dimension-5 HQET operators

• DOI: 10.1016/j.physletb.2009.02.028
• 发表时间: 2008-10
• 期刊: Physics Letters B
• 影响因子: 4.4
• 作者: H. Kawamura;Kazuhiro Tanaka Univ. of Liverpool;Juntendo Univ.

Double Transverse-Spin Asymmetries for Small-Q[sub T] Drell-Yan Pair Production in pp¯ Collisions

pp 碰撞中小 Q[sub T] Drell-Yan 对产生的双横向自旋不对称

• DOI: 10.1063/1.3215698
• 发表时间: 2009
• 作者: Kawamura H