标题： 格点QCD中的强子散射长度 显示英文标题

标题： Hadron Scattering Lengths in Lattice QCD

摘要： 在 quenched QCD 的框架下，在$\beta=6/g^2=5.7$处对 s 波介子散射长度进行了计算，涉及的道包括\pi -\pi 、\pi -N、K-N、{\bar K}-N 和 N-N。 为此开发了一种改进的壁源方法，与传统的点源方法相比，在 L^3xT 晶格上可将计算机时间减少一个因子 L^3，并且避免了费米子混合问题。 一种不对规范构型做任何规范固定的该方法版本可以扩展到计算由夸克圈贡献的介子两、三点函数中的非连接项。 为该方法推导出了统计误差的解析估计，并比较了\pi -\pi 四点函数在用 KS 夸克作用量计算时固定规范和未固定规范情况下的误差大小。 对于 \pi -\pi 散射，使用KS和Wilson夸克作用量在 \( 12^3 \times 20 \) 网格上评估了I=0和2两种散射长度。对于相同大小的网格，使用Wilson夸克作用量计算了 \pi -N、K-N和 {\bar K}-N的散射长度。 对于\pi -\pi 和\pi -N 情况，模拟结果与当前代数和PCAC的预测一致，偏差在一到两个标准差之内，直到对应于$m_\pi/m_\rho\approx 0.74$的相当重的夸克质量；而对于 K-N 和{\bar K}-N 情况，一致性在一个因子二之内。 对于在20⁴格子上使用Wilson作用的N-N散射模拟，其中重夸克具有$m_\pi/m_\rho\approx 0.74-0.95$，从一种具有单玻色子交换势的经验研究预计氘核在这种情况下将变得无结合能，显示核子-核子力对自旋三重态和单重态通道都是有吸引力的，并且即使在这种重夸克的情况下，散射长度也比\pi -\pi 和\pi -N 情况下的散射长度大得多。 显示英文摘要

摘要： Lattice QCD calculation of s-wave hadron scattering lengths in the channels \pi-\pi, \pi-N, K-N, {\bar K}-N and N-N is carried out in the quenched QCD at $\beta=6/g^2=5.7$. A variant of the method of wall sourceis developed for this purpose, which reduces the computer time by a factor L^3 on an L^3xT lattice compared to the conventional point source method and avoids the Fierz mixing problem. A version of the method in which gauge configurations are not fixed to any gauge can be extended to calculate disconnected quark loop con- tributions in hadron two- and three-point functions. An analytical estimate of statistical errors for this method is worked out, and the magnitude of errors without and with gauge fixing is compared for the case of \pi-\pi four-point functions calculated with the KS quark action. For \pi-\pi scattering both I=0 and 2 scattering lengths are evaluated using the KS and Wilson quark actions on a 12^3x20 lattice. For the same size of lattice, \pi-N, K-N and {\bar K}-N scattering lenghts are calculated with the Wilson quark action. For the \pi-\pi and \pi-N cases simulation results are consistent with the predictions of current algebra and PCAC within one to two standard deviations up to quite heavy quark masses corresponding to $m_\pi/m_\rho\approx 0.74$, while for the K-N and {\bar K}-N cases the agreement is within a factor of two. For N-N scat- tering simulations with the Wilson action on a 20^4 lattice with heavy quarks with $m_\pi/m_\rho\approx 0.74-0.95$, where the deuteron is expected to become unbound from a phenomenological study with one-boson exchange potentials, show that the nucleon-nucleon force is attractive for both spin triplet and singlet channels, and that the scattering lengths are substantially larger compared to those for the \pi-\pi and \pi-N cases even for such heavy quarks.