In this work, we present the calculation of the production cross sections of bottomonia states using Non-Relativistic Quantum Chromodynamics (NRQCD) formalism. The direct production cross-section of a resonance can be factorised in terms of short distance Quantum Chromodynamics (QCD) cross sections and long distance matrix elements (LDMEs) under NRQCD. We use a large set of measured ϒ(nS) production data at Tevatron and LHC energies in both central and forward rapidity regions to extract the LDMEs with better precision. The feed down contributions from the higher states including the ${\chi }_b$(3P) state are taken into account for the LDME extraction. The formalism provides a good description of the bottomonia data in wide transverse momentum range at different collision energies.

在这项工作中，我们使用非相对论量子色动力学 (NRQCD) 形式来计算巴托尼亚状态的产生截面。共振的直接产生截面可以根据 NRQCD 下的短距离量子色动力学 (QCD) 截面和长距离矩阵元素 (LDME) 进行分解。我们在中央和前向快速区域的 Tevatron 和 LHC 能量处使用大量测量的 ϒ(nS) 生产数据，以更准确地提取 LDME。来自包括美国在内的更高州的馈送贡献${\chi }_{乙}$(3P) 状态被考虑用于 LDME 提取。形式主义提供了在不同碰撞能量下宽横向动量范围内的巴托尼亚数据的良好描述。