用拉普拉斯模投影计算核子的磁极化率
Magnetic polarisability of the nucleon using a Laplacian mode projection
摘要：
传统的强子内插场利用规范协变的高斯涂抹，在均匀背景磁场中分离基态核子是无效的。有证据表明，即使存在QCD相互作用，剩余朗道模物理仍然保持在夸克水平。在这项工作中，夸克级投影算子构造的$SU(3) \times U(1)$本征模的二维晶格拉普拉斯算子与朗道模式。这些夸克能级模是由一个周期性的有限晶格形成的，其中背景场和强相互作用都存在。利用这些本征模，夸克传播子投影算符提供了计算磁场中核子能移所必需的增强的强子能量-本征态隔离。在PACS-CS协作组提供的$32^3 \times 64$动力学QCD格点上，用这种方法计算了质子和中子的磁极化率。手征有效场论分析用于连接格点量子色动力学结果的物理制度，获得磁极化率$β^p = 2.79(22)({}^{+13}_{-18}) \times 10^{-4}$ fm $^3$和$β^n = 2.06(26)({}^{+15}_{-20}) \times 10^{-4}$ fm $^3$，其中parantheses中的数字描述统计和系统的不确定性。
英文摘要：
Conventional hadron interpolating fields, which utilise gauge-covariant Gaussian smearing, are ineffective in isolating ground state nucleons in a uniform background magnetic field. There is evidence that residual Landau mode physics remains at the quark level, even when QCD interactions are present. In this work, quark-level projection operators are constructed from the $SU(3) \times U(1)$ eigenmodes of the two-dimensional lattice Laplacian operator associated with Landau modes. These quark-level modes are formed from a periodic finite lattice where both the background field and strong interactions are present. Using these eigenmodes, quark-propagator projection operators provides the enhanced hadronic energy-eigenstate isolation necessary for calculation of nucleon energy shifts in a magnetic field. The magnetic polarisability of both the proton and neutron is calculated using this method on the $32^3 \times 64$ dynamical QCD lattices provided by the PACS-CS Collaboration. A chiral effective-field theory analysis is used to connect the lattice QCD results to the physical regime, obtaining magnetic polarisabilities of $β^p = 2.79(22)({}^{+13}_{-18}) \times 10^{-4}$ fm$^3$ and $β^n = 2.06(26)({}^{+15}_{-20}) \times 10^{-4}$ fm$^3$, where the numbers in parantheses describe statistical and systematic uncertainties.
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