arXiv 2408.047192024-08hep-phhep-exhep-lat

一个玻恩-奥本海默有效理论统领一切：混杂态、四夸克态、五夸克态、双重重子与夸克偶素

One Born$-$Oppenheimer Effective Theory to rule them all: hybrids, tetraquarks, pentaquarks, doubly heavy baryons and quarkonium

Matthias Berwein, Nora Brambilla, Abhishek Mohapatra, Antonio Vairo

备注：: 115 pages, 13 figures, 13 tables; v2: Minor updates, Journal version
发表信息：: Phys. Rev. D 110, 094040 (2024)
DOI：: 10.1103/PhysRevD.110.094040

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AI总结：

本文提出基于QCD的玻恩-奥本海默有效场论（BOEFT），统一描述含两个重夸克的XYZ奇特态，推导了涵盖混杂态、四夸克态、五夸克态、双重重子和夸克偶素的耦合薛定谔方程，并阐明能级免交叉如何统一四夸克与分子图像。

摘要：

在强子领域中发现含有两个重夸克的XYZ奇特态，对粒子理论构成了重大挑战。理解并预言它们的本质仍然是一个悬而未决的问题。在这项工作中，我们展示了如何利用基于尺度分离和对称性从量子色动力学（QCD）导出的玻恩-奥本海默（BO）有效场论（BOEFT）来处理任意组分的XYZ奇特态。我们推导了在领头阶描述混杂态、四夸克态、五夸克态、双重重子和夸克偶素的薛定谔耦合方程，纳入了非绝热项，并给出了预言的多重态。我们针对所有相关情形，用QCD静态能量定义了静态势。我们给出了BOEFT所需的非微扰低能规范不变关联函数的精确形式：静态能量、广义威尔逊圈、胶球团和伴随介子。这些量需要在格点上计算，我们在此计算了它们的短距离行为。此外，我们概述了如何利用匹配计算纳入自旋相关修正和混合项。最后，我们讨论了具有相同BO量子数的静态能量如何在大距离处发生混合，从而导致能级免交叉现象。这一效应对于理解具有分子特征的奇特态（如$χ_{c1}(3872)$）的出现至关重要。借助BOEFT，四夸克图像和分子图像都成为同一描述的一部分。

英文摘要：

The discovery of XYZ exotic states in the hadronic sector with two heavy quarks, represents a significant challenge in particle theory. Understanding and predicting their nature remains an open problem. In this work, we demonstrate how the Born$-$Oppenheimer (BO) effective field theory (BOEFT), derived from Quantum Chromodynamics (QCD) on the basis of scale separation and symmetries, can address XYZ exotics of any composition. We derive the Schrödinger coupled equations that describe hybrids, tetraquarks, pentaquarks, doubly heavy baryons, and quarkonia at leading order, incorporating nonadiabatic terms, and present the predicted multiples. We define the static potentials in terms of the QCD static energies for all relevant cases. We provide the precise form of the nonperturbative low-energy gauge-invariant correlators required for the BOEFT: static energies, generalized Wilson loops, gluelumps, and adjoint mesons. These are to be calculated on the lattice and we calculate here their short-distance behavior. Furthermore, we outline how spin-dependent corrections and mixing terms can be incorporated using matching computations. Lastly, we discuss how static energies with the same BO quantum numbers mix at large distances leading to the phenomenon of avoided level crossing. This effect is crucial to understand the emergence of exotics with molecular characteristics, such as the $χ_{c1}(3872)$. With BOEFT both the tetraquark and the molecular picture appear as part of the same description.

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