Beyond the Conventional Quark Model: Theoretical Studies of QCD Exotics

传统的夸克模型将介子分类为夸克-反夸克（$q\bar q$）态，重子分类为$qqq$三夸克态。虽然传统的夸克模型代表了可以形成彩色单线态的最简单的夸克组合，但也有丰富的其他颜色单线态的可能性，如胶子（完全由胶子组成），杂子（传统强子与胶子内容结合），以及多夸克态，如四夸克$q\bar qq\bar q$介子和五夸克$qqq\bar qq $重子。这些超出常规夸克模型的构型被统称为外来强子。在2003年之前，关于奇异强子的证据仅限于在轻介子中存在的gluonium和一种杂合体。然而，2003年X（3872）的发现标志着强子光谱新时代的开始，它发现了大量无法用传统夸克模型描述的XYZ介子。我的研究项目的长期热情是从量子色动力学（QCD）的理论角度推进我们对外来强子的理解，量子色动力学是强相互作用的基本理论。尽管有激烈的理论和实验活动，XYZ介子的内部结构仍然是一个悬而未决的问题。四夸克态的情形包括介子-介子分子，重夸克-反夸克团簇结合成四夸克，以及具有重夸克-反夸克核和轻夸克云的硬夸克。这些不同形式的夸克内部聚类预计将在强子性质中表现出来。提出的研究主题之一是开发和使用由介子或双夸克算子在不同时空点组成的新的QCD和规则算子来模拟内部分子或四夸克结构。目标是确定内部结构对强子性质的影响，以获得对可能的内部构型的新见解。提出的研究的另一个主要主题是提高我们对奇异强子的理论计算的精度，以确保重要的物理见解不会被理论不确定性所掩盖。绝大多数关于外来粒子的QCD和规则研究都是在领先阶上进行的，因此提出的研究将检查各种外来系统（包括混合介子、多夸克态和混合重子）对质谱和衰变的高环效应。混合解释包括混合、夸克-反夸克和多夸克成分将是一个研究领域。我的研究项目已经推动了奇异强子的QCD和规则分析计算的边界，下一个前沿是在pySecDec中实现的数值环路积分技术中使用扇区分解方法。结合新的理论方法，提出的研究将开拓这些数值方法在奇异强子的QCD和规则研究中的应用。

The conventional quark model classifies mesons as quark-antiquark ($q\bar q$) states and baryons as $qqq$ three-quark states. Although the conventional quark model represents the simplest combinations of quarks that can form colour singlets, there is a rich range of other colour-singlet possibilities such as gluonium (consisting entirely of gluons), hybrids (a conventional hadron combined with gluonic content), and multiquark states such as four-quark $q\bar q q\bar q$ mesons and pentaquark $qqq\bar q q$ baryons. These configurations that lie beyond the conventional quark model are collectively known as exotic hadrons. Until 2003, evidence for exotic hadrons was limited to hints of gluonium and a hybrid within the light mesons. However, the 2003 discovery of the X(3872) marked the beginning of a new era in hadron spectroscopy with the discovery of a multitude of XYZ mesons that cannot be described within the conventional quark model.  The long-term passion of my research program is to advance our understanding of exotic hadrons from the theoretical perspective of quantum chromodynamics (QCD): the fundamental theory of the strong interactions. Despite intense theoretical and experimental activity, the internal structure of the XYZ mesons remains an open question. Scenarios for four-quark states include meson-meson molecules, diquark-antidiquark clusters binding into tetraquarks, and hadro-quarkonium with a heavy quark-antiquark core and a cloud of light quarks. These distinct forms of quark internal clustering are expected to manifest themselves in hadronic properties. One of the key themes in the proposed research is to develop and use new QCD sum-rule operators consisting of meson or diquark operators at separate spacetime points to model the internal molecular or tetraquark structure. The goal is to determine the effect of the internal structure on hadronic properties to gain new insights on possible internal configurations. Another main theme of the proposed research is to advance the precision of our theoretical calculations for exotic hadrons to ensure that important physics insights are not obscured by theoretical uncertainties. The vast majority of QCD sum-rule studies of exotics have been performed at leading order, so the proposed research will examine higher-loop effects on the mass spectrum and decays in a variety of exotic systems including hybrid mesons, multiquark states, and hybrid baryons. Mixed interpretations involving hybrid, quark-antiquark, and multi-quark components will be an area of investigation. My research program has pushed the boundaries of QCD sum-rule analytic calculations for exotic hadrons, and the next frontier is the use of sector decomposition methods for numerical loop-integration techniques implemented in pySecDec. Combined with novel theoretical approaches, the proposed research will pioneer the use of these numerical methods in QCD sum-rule studies of exotic hadrons.