Beyond the Conventional Quark Model: Theoretical Studies of QCD Exotics

传统的夸克模型将介子归类为夸克-反夸克($Q\bar Q$)态，将重子归类为$QQQ$三夸克态。虽然传统的夸克模型代表了可以形成彩色单态的夸克的最简单的组合，但也有丰富的其他彩色单态的可能性，如胶子(完全由胶子组成)、杂化(与胶子含量相结合的传统强子)和多夸克态，如四夸克$q\bar q\bar q$介子和五夸克$qq\bar q$重子。这些超越传统夸克模型的构型统称为奇异强子。直到2003年，关于奇异强子的证据仅限于胶子和轻介子中的混合体的迹象。然而，2003年X(3872)的发现标志着强子光谱学新纪元的开始，发现了大量无法用传统夸克模型描述的XYZ介子。我研究计划的长期激情是从量子色动力学(QCD)的理论角度来推进我们对奇异强子的理解：量子色动力学是强相互作用的基本理论。尽管进行了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。四夸克态的情景包括介子-介子分子，结合到四个夸克中的双夸克-反双夸克团簇，以及具有重夸克-反夸克核心和轻夸克云的强夸克。这些不同形式的夸克内部聚集有望在强子性质中显现出来。这项研究的一个关键主题是开发和使用新的QCD求和算符，这些算符由不同的时空点上的介子或双夸克算符组成，以模拟内部分子结构或四夸克结构。我们的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配置的新见解。这项拟议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上的不确定性所掩盖。绝大多数奇异体的QCD求和规则研究都是在前导阶进行的，所以这项拟议的研究将考察包括混合介子、多夸克态和混合重子在内的各种奇特系统中的高圈效应对质谱和衰变的影响。涉及混合、夸克-反夸克和多夸克成分的混合解释将是一个研究领域。我的研究计划已经突破了QCD求和规则解析计算的边界，下一个前沿是使用扇区分解方法来实现在pySecDec中实现的数值循环积分技术。结合新的理论方法，这项研究将开创这些数值方法在奇异强子QCD求和规则研究中的先河。

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.