关于格点场论中能量和矩阵元的广义本征值方法
On the generalized eigenvalue method for energies and matrix elements in lattice field theory
摘要：
讨论了格点规范理论中计算能量和矩阵元的广义本征值问题，包括HQET等有效理论。分析了当时间间隔较大时，提取的有效能量和矩阵元如何收敛。这表明一个特别有效的应用程序的方法，我们可以证明，修正消失渐近为$\exp(-(E_{N+1}-E_n) t)$。间隙$E_{N+1}-E_n$可以通过增加相关矩阵中的内插字段的数目$N$而变大。我们还展示了如何提取激发态矩阵元素，使得来自所有其他状态的污染随时间呈指数规律消失。作为演示，我们给出了在静态近似下提取基态和激发态B介子质量和衰变常数的数值结果，以及在HQET中对$1/m_b$进行排序的数值结果。
英文摘要：
We discuss the generalized eigenvalue problem for computing energies and matrix elements in lattice gauge theory, including effective theories such as HQET. It is analyzed how the extracted effective energies and matrix elements converge when the time separations are made large. This suggests a particularly efficient application of the method for which we can prove that corrections vanish asymptotically as $\exp(-(E_{N+1}-E_n) t)$. The gap $E_{N+1}-E_n$ can be made large by increasing the number $N$ of interpolating fields in the correlation matrix. We also show how excited state matrix elements can be extracted such that contaminations from all other states disappear exponentially in time. As a demonstration we present numerical results for the extraction of ground state and excited B-meson masses and decay constants in static approximation and to order $1/m_b$ in HQET.
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