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arXiv 2302.13587hep-lathep-phnucl-th
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利用格点QCD研究最大同位旋下$πK$、$ππK$和$KKπ$系统的相互作用

Interactions of $πK$, $ππK$ and $KKπ$ systems at maximal isospin from lattice QCD

Zachary T. Draper, Andrew D. Hanlon, Ben Hörz, Colin Morningstar, Fernando Romero-López, Stephen R. Sharpe

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64 pages, 26 tables, 13 figures. Energy levels provided in ancillary files. v3: new appendix C, updated fig 6 and other minor changes
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AI总结：

本文用格点QCD和随机LapH方法测定最大同位旋下$π^+K^+$、$π^+π^+K^+$及$K^+K^+π^+$能谱，首次约束相关三粒子K矩阵并与手征微扰论比较。

摘要：

我们利用格点QCD研究了由π介子和K介子组成的两个和三个非简并介子系统在最大同位旋下的相互作用，具体为$π^+K^+$、$π^+π^+K^+$和$K^+K^+π^+$。借助随机LapH方法，我们在两套CLS $N_f=2+1$组态系综（π介子质量分别为200 MeV和340 MeV）上测定了这些系统的能谱，并纳入了不同动量框架中的多个能级。我们通过将能谱拟合到有限体积形式体系所预测的结果（最高包含$p$波），对描述两粒子和三粒子相互作用的K矩阵进行约束。这还需要$π^+π^+$和$K^+ K^+$能谱的结果，这些结果此前已在相同组态上获得。我们探索了不同的拟合策略，比较了对能量移动的拟合与对提升至静止系的能量的拟合，同时也比较了对所有相关两粒子和三粒子道的同步全局拟合，与先拟合两粒子道再加入三粒子信息的拟合。我们首次给出了$π^+π^+K^+$和$K^+ K^+ π^+$系统中三粒子K矩阵的测定，在大多数情况下发现了具有统计显著性的非零结果。我们在$π^+ K^+$散射的K矩阵中纳入$s$波和$p$波，发现了存在吸引性$p$波散射长度的证据。我们将结果与手征微扰论进行了比较，包括考察离散化误差的影响，并为此给出了利用Wilson手征微扰论获得的领头阶预测。

英文摘要：

We study the interactions of systems of two and three nondegenerate mesons composed of pions and kaons at maximal isospin using lattice QCD, specifically $π^+K^+$, $π^+π^+K^+$ and $K^+K^+π^+$. Utilizing the stochastic LapH method, we determine the spectrum of these systems on two CLS $N_f=2+1$ ensembles with pion masses of $200$ MeV and $340$ MeV, and include many levels in different momentum frames. We constrain the K matrices describing two- and three-particle interactions by fitting the spectrum to the results predicted by the finite-volume formalism, including up to $p$ waves. This requires also results for the $π^+π^+$ and $K^+ K^+$ spectrum, which have been obtained previously on the same configurations. We explore different fitting strategies, comparing fits to energy shifts with fits to energies boosted to the rest frame, and also comparing simultaneous global fits to all relevant two- and three-particle channels to those where we first fit two-particle channels and then add in the three-particle information. We provide the first determination of the three-particle K matrix in $π^+π^+K^+$ and $K^+ K^+ π^+$ systems, finding statistically significant nonzero results in most cases. We include $s$ and $p$ waves in the K matrix for $π^+ K^+$ scattering, finding evidence for an attractive $p$-wave scattering length. We compare our results to Chiral Perturbation Theory, including an investigation of the impact of discretization errors, for which we provide the leading order predictions obtained using Wilson Chiral Perturbation Theory.

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