[论文解读] Lattice dataset for the paper "Physical-mass calculation of $ ho(770)$ and $K^*(892)$ resonance parameters via $\pi \pi$ and $K \pi$ scattering amplitudes from lattice QCD"

Peter Boyle, Felix Erben+6 more|arXiv (Cornell University)|Jun 27, 2024

Quantum Chromodynamics and Particle Interactions被引用 2

一句话总结

本论文首次在物理夸克质量下通过域墙费米子与吕舍尔形式化方法，利用有限体积能级提取散射相移，实现了对ρ(770)和K∗(892)共振态极点位置的格点QCD计算。通过在不同拟合范围上进行模型平均，实现数据驱动的系统误差估计，获得高精度结果：Mρ = 796(5)(15)(48)(2) MeV，Γρ = 192(10)(28)(12)(0) MeV，MK∗ = 893(2)(8)(54)(2) MeV，ΓK∗ = 51(2)(11)(3)(0) MeV，所有不确定性均完整呈现。

ABSTRACT

Release for publications, currently available as arxiv preprints: arXiv:2406.19193: Physical-mass calculation of $ ho(770)$ and $K^*(892)$ resonance parameters via $\pi \pi$ and $K \pi$ scattering amplitudes from lattice QCD arXiv:2406.19194: Light and strange vector resonances from lattice QCD at physical quark masses ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ This dataset contains the Wick contraction diagrams for the correlators used in the articles mentioned above. They were computed via multiplication of the distillation meson fields with the appropriate momentum, quark content and time source, followed by a trace over dilution indices (see Appendix B of arxiv:2406.19193). Data is provided as gzip tarballs which extract into a directory tree. The name of the tarballs is hinting at the directory structure. E.g. the file K-Pi.Kpi_Kpi.P0.tar.gz will extract into K-Pi/Kpi_Kpi/P0 and all containing subdirectories. The final extracted structure is designed as follows: The data used in the GEVP (before any lattice-irrep projection) is organized in the folder tree <channel>/<corrtype>/P<mom^2>/data.<traj>/<prefix>.<traj>.h5 where <channel> : K-Pi, Pi-Pi <corrtype> : V_V, <MM'>_V, <MM'>_<MM'> (in correspondence to eqs. 4,5,6 of arxiv:2406.19193, where <MM'>=Kpi,Pipi, and V generically denotes the vector gamma matrices contained in the files within) <mom^2> : 0,1,2,3,4 <traj> : trajectory number in MD units (for a total of 90 trajectories, ranging from 420 to 2200 in steps of 20 MD units) <prefix> : filename prefix indicating the input meson fields, with their respective gamma matrices and momentum projections, as follows: V_V (as a Kpi subfolder) : rpl_<gammaI>_p<P>__rps_<gammaI>_p<-P>.<traj>.h5, with <gammaI>=GammaX,GammaY,GammaZ V_V (as a Pipi subfolder) : rpl_<gammaI>_p<P>__rpl_<gammaI>_p<-P>.<traj>.h5, with <gammaI>=GammaX,GammaY,GammaZ Kpi_V : rpl_Gamma5_p<p1>__rpl_Gamma5_p<p2>__rps_<gammaI>_p<-P>.<traj>.h5 Pipi_V : rpl_Gamma5_p<p1>__rpl_Gamma5_p<p2>__rpl_<gammaI>_p<-P>.<traj>.h5 Kpi_Kpi : rpl_Gamma5_p<p1>__rpl_Gamma5_p<p2>__rps_Gamma5_p<p1'>__rpl_Gamma5_p<p2'>.<traj>.h5 Pipi_Pipi : rpl_Gamma5_p<p1>__rpl_Gamma5_p<p2>__rpl_Gamma5_p<p1'>__rpl_Gamma5_p<p2'>.<traj>.h5 The rpl and rps stand for the 'rhophi'-like meson fields with 'light' and 'strange' content, used in arxiv:2406.19193. The <p1>,<p2>,<p1'>,<p2'>,<P>,<-P> are in the format 'px_py_pz', and denote the 3-vectors used in the momentum-projection of the accompanying meson field, exactly matching the LHS of the equations (in the order they appear) in Appendix B of arxiv:2406.19193. The momentum conservation implies that these vectors sum to zero in any given diagram. We only compute the upper triangular part of the GEVP matrix, and enforce it to be symmetric. Each hdf5 file has the structure /DistillationContraction/Correlators/<diagram>/<tsource>/double_array(96,2) where <diagram> identifies the possible diagram topologies: 'connected' for V_V correlators (eqs. A1, A4) 'triangle' for <MM'>_V correlators (eqs. A2, A5) 'direct' for <MM'>_<MM'> correlators (1st diagram of Eq. A3, 1st and 2nd diagrams of A6) 'rectangle' for <MM'>_<MM'> correlators (2nd diagram of Eq. A3, 3rd, 4th, 5th and 6th diagrams of A6) 'cross' for <MM'>_<MM'> correlators (3rd diagram of Eq. A3) To recover the diagrams where the arrows are swapped or reversed, the appropriate momentum combinations need to be chosen, as indicated in the manuscript. In this way, for Kpi each file corresponds to exactly one correlator, but for Pipi the 2nd diagram of a given correlator will come from a file whose momenta are swapped in relation to the 1st diagram. The <tsource>=0,1,...,95 denotes the time source (corresponding to 't=0' in Appendix B of arxiv:2406.19193), but where no time translation was done at this stage. The h5 dataset has shape (96,2) corresponding to 96 time slices, and their real("re") and imaginary("im") parts, respectively, in double precision. To obtain a full correlator, one sums the datasets coming from the diagrams in Appendix B, including the prefactors indicated there. The pion- and kaon-like correlators (using the pi+ and K+ interpolators from eq. arxiv:2406.19193) are under <hadron>/P<mom^2>/data.<traj>/<prefix>.<traj>.h5 where <hadron>=Pion,Kaon, with h5 structure /DistillationContraction/Correlators/connected/<tsource>/double_array(96,2) where all naming convention is the same as for the files described above.

研究动机与目标

• 使用精确的物理夸克质量在格点QCD中计算ρ(770)与K∗(892)的物理质量共振参数。
• 应用吕舍尔形式化方法，从相关函数中提取有限体积能级，并将其映射为散射相移。
• 对相移进行解析延拓，以定位散射振幅中的复极点，从而确定共振质量与宽度。
• 提出一种新颖的数据驱动系统误差估计方法，通过改变拟合范围并平均模型，提升结果的鲁棒性，优于以往方法。
• 提供全面的误差预算，涵盖统计误差、数据驱动系统误差、格点间距误差与尺度设定误差，适用于两种共振态。

提出的方法

• 在包含物理奇异夸克与轻夸克质量的单个Nf = 2 + 1格点胚系上使用域墙费米子。
• 采用扩散技术高效构建大量插值算符，并在不同动量参考系中计算ππ与Kπ系统的相关函数。
• 通过相关矩阵的变分分析提取有限体积能级，使用多种源-阱时间分离与投影模糊参数。
• 应用吕舍尔形式化方法，将能级映射为ππ与Kπ散射道中的S波相移。
• 使用有效场论模型拟合相移，并解析延拓至复能平面，以提取共振极点位置M − iΓ/2。
• 通过采样多个能级拟合范围与模型参数化形式，估计系统误差，再对结果进行平均，获得稳健的误差估计。

实验结果

研究问题

• RQ1 在精确夸克质量下，通过格点QCD计算，ρ(770)在ππ散射中的物理质量极点位置（质量与宽度）为何？
• RQ2 当在物理夸克质量下计算时，K∗(892)在Kπ散射中的共振参数与实验值相比如何？
• RQ3 是否可以通过数据驱动、模型平均的系统误差估计方法，提升格点QCD中共振参数确定的可靠性？
• RQ4 统计误差、数据驱动系统误差、格点间距误差与尺度设定误差等各来源不确定性对最终共振结果的影响程度如何？
• RQ5 这些结果在多大程度上支持使用格点QCD对涉及ρ与K∗共振态的弱衰变振幅进行高精度计算？

主要发现

• ρ(770)共振态质量确定为Mρ = 796(5)(15)(48)(2) MeV，其中第一项为统计误差，第二项为数据驱动系统误差，第三项为未受控的格点间距效应，第四项为尺度设定误差。
• ρ(770)的衰变宽度为Γρ = 192(10)(28)(12)(0) MeV，误差结构与质量一致，表明其为宽共振态，与实验结果一致。
• K∗(892)共振态质量为MK∗ = 893(2)(8)(54)(2) MeV，与PDF值891.7 MeV高度一致，表明在物理夸克质量下具有极高精度。
• K∗(892)的宽度为ΓK∗ = 51(2)(11)(3)(0) MeV，其中第二项误差（数据驱动系统误差）为最主要的系统贡献。
• 本研究首次在物理夸克质量下实现对这些共振态的格点QCD计算，且完整暴露了多源误差预算，为强子共振谱学的精度设定了新标准。
• 通过拟合范围变化与模型平均实现的数据驱动系统误差估计，显著提升了结果的鲁棒性，优于传统格点QCD方法。