【作者】 张云；

【导师】 张若筠； Konstantin G.Savvidy； 陈刚；

【作者基本信息】 南京大学 ， 理论物理， 2013， 博士

【摘要】 我将在这篇论文里描述我在高能物理中的两类散射振幅方面的研究工作.论文由两部分组成：一是利用质子-Delta共振态统一模型研究质子的康普顿散射；另一部分是关于杨-米尔斯规范场散射振幅的计算.首先,为了更好地了解质子的电磁性质,比如质子的电磁极化率,我们用有效场论方法研究了第一共振区质子的康普顿散射.这项工作是由我和Konstantin G. Sawidy博士合作完成.我们用Sawidy博士推广的Rarita-Schwinger理论统一描述质子和Delta重子—以质子和Delta分别作为自旋为二分之一和自旋为二分之三的子态.最近Sawidy博士已经提出能满足流守恒的、自洽地描述自旋二分之三的费米子和电磁场的最小相互作用的规范场论.为了描述质子康普顿散射,我们引入了六项以形状因子为系数并且满足规范不变性要求的非最小顶角以及用以描述固有极化率的有效拉氏量.从而我们得到了用形状因子表达的质子和Delta共振态磁矩的表达式。然后我们计算了质子的康普顿散射振幅,得出了总极化率与形状因子及固有极化率的关系；同时我们分析了在Delta极点附近振幅的近似行为.最后我们利用实验数据得到了形状因子和极化率的最佳拟合值,并且从这些最佳拟合值得出了Delta共振态的磁矩作为我们的理论预言.在回顾了一些关于杨-米尔斯场振幅的背景知识和描述了我们研究不在壳振幅的边界行为的动机后,我介绍我和陈刚博士合作研究的在有一对外线动量被复化的情况下杨-米尔斯的不在壳振幅的边界行为.在费曼规范下,我们引入了一套“约化顶角”用以计算边界行为的领头两阶,并且用之极大地简化了接下来的分析.在相邻线被复化的情况下,散射振幅边界行为可以从约化顶角中直接读出.然后我们证明了一个关于既定色排序的置换求和定理,并且用它来分析不相邻线复化之散射振幅的边界行为.利用分析得出的边界行为,我们把Britto-Cachazo-Feng-Witten(BCFW)递归关系突破性地推广到不在壳的树图上.作为应用,我们计算了杨-米尔斯规范场论中的四点不在壳散射振幅,并分析了多点不在壳振幅之间的关系.最后,我们从被复化的Ward恒等式推出树图项次和单圈图项次的不在壳振幅的递归关系.此项工作是基于陈刚博士之前用Ward恒等式导出的树图边界项的递归关系.我和陈刚博士共同将其推广到了树图和单圈图的完整振幅的递归关系.我们用费曼规则在树图和单圈图水平上严格地证明了Ward恒等式；然后给出对应的任意点不在壳振幅的递归关系.作为应用,我们计算了三点和四点单圈图的不在壳散射振幅.更多还原

【Abstract】 I will describe my work on two classes of scattering amplitudes in high energy physics. The thesis consists of two parts:one is on the proton Compton scattering in a Unified Proton-Delta theory, and the other is on the computation of scattering amplitudes in Yang-Mills theory.We study the proton Compton scattering in the first resonance region in an effective field theory approach, in an effort to better understand the proton’s electromagnetic properties, ie. its electric and magnetic polarizabilities. This part is done together with my advisor Dr. Konstantin G. Savvidy. The consistent electrodynamic interaction of the spin3/2field, which respects current conservation, has re-cently been developed by Savvidy in his generalized Rarita-Schwinger theory for the spin3/2particle, resolving the long standing superluminal propagation problem of the old Rarita-Schwinger theory. The proton and△+are naturally unified in this generalized Rarita-Schwinger theory with the proton being the spin1/2component and the△+being the spin3/2component. To describe the proton Compton scat-tering, we introduce six non-minimal electromagnetic interactions--with their coefficients being called "form factors"--and bare polarizabilities in an effective Lagrangian, consistent with the requirement of gauge invariance. We express the proton and△+magnetic moments in terms of the form factors. We then compute the proton Compton scattering amplitudes, and obtain the total electric and magnetic polariz-abilities in terms of the bare ones and the form factors. We also study an approximation of the amplitudes around the△+pole. Using experimental data, we obtain the best fit values for the form factors and bare polarizabilities. As a prediction, we derive the△+magnetic moment from the best fit values of the parameters.After some background preparation, we present our joint work with advisor Dr. Gang Chen on the study of boundary behavior of off-shell Yang-Mills amplitudes with a pair of external momenta complex-ified. In Feynman gauge, we introduce a set of "reduced vertices" which effectively capture the boundary behavior up to the first two leading orders and greatly simplify subsequent analysis. The boundary be-havior of amplitudes with two adjacent legs complexified can be read off from the reduced vertices. We then prove a theorem on the permutation sum for a given color ordering, and use it to analyze the boundary behavior of amplitudes with two non-adjacent legs complexified. Based on the boundary be-haviors, we construct off-shell Britto-Cachazo-Feng-Witten (BCFW) recursion relations for general tree level amplitudes. As applications, we calculate off-shell amplitudes and study relations between off-shell amplitudes.Finally, we study the recursion relations for off-shell Yang-Mills amplitudes at tree and one loop levels as deduced from imposing complexified Ward identity, also in collaboration with Dr. Gang Chen. It is based on a previous work by Gang Chen in which the Ward identity is used to derive a recursion relation for calculating tree level boundary terms. We extend his work to derive recursion relations of the full scattering amplitudes at both tree and one loop levels. Using Feynman rules, we explicitly prove the Ward identity at tree and one loop levels. We then give recursion relations for general N-point off-shell amplitudes. We calculate three and four point one loop off-shell amplitudes as applications of our method.更多还原