Heavy quarkonium potential from Bethe-Salpeter wave function on the lattice
Heavy quarkonium potential from Bethe-Salpeter wave function on the lattice
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DOI：
10.1103/physrevd.89.054507
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发表时间：
2013-11
影响因子：
5
通讯作者：
T. Kawanai;S. Sasaki
中科院分区：
文献类型：
--
作者：
T. Kawanai;S. Sasaki
本文提出了一种新的方法，由格点QCD中的等时$Q\bar{Q}$ Bethe-Salpeter（BS）振幅确定夸克间势和夸克“运动质量”$mQ $.我们的方法允许我们计算自旋相关的$Q\bar{Q}$势，例如自旋-自旋势。为了调查几个系统的不确定性，这样的$Q\bar{Q}$潜力，我们进行晶格QCD模拟使用淬火规范配置产生的单格元规范行动与三个不同的晶格间距，$a \approximately $0.093，0.068和0.047调频，和两个不同的物理量，$L \approximately $2.2和3.0调频。对于重夸克，我们采用相对论重夸克作用量，它可以控制大质量夸克引起的大的离散误差。粲偶素系统的自旋独立的中心$Q\bar{Q}$势产生“库仑加线性”行为，具有良好的标度和小的体积依赖性。我们研究了从粲夸克到底区以外的宽质量范围内夸克质量的依赖性，并证明了在m_Q \to \infty$极限下的自旋无关中心$Q\bar{Q}$势与由Wilson环得到的静态$Q\bar{Q}$势是相当一致的.有限夸克质量下的自旋-自旋势提供了一个有限范围的排斥相互作用，随着夸克质量的增加，这个范围变得越来越窄。我们还讨论了自旋-自旋势的$1/m_Q$展开方法的适用性。
We propose a novel method for the determination of the interquark potential together with quark "kinetic mass'' $m_Q$ from the equal-time $Q\bar{Q}$ Bethe-Salpeter (BS) amplitude in lattice QCD. Our approach allows us to calculate spin-dependent $Q\bar{Q}$ potentials, e.g. the spin-spin potential, as well. In order to investigate several systematic uncertainties on such $Q\bar{Q}$ potentials, we carry out lattice QCD simulations using quenched gauge configurations generated with the single plaquette gauge action with three different lattice spacings, $a \approx$ 0.093, 0.068 and 0.047 fm, and two different physical volumes, $L \approx$ 2.2 and 3.0 fm. For heavy quarks, we employ the relativistic heavy quark (RHQ) action which can control large discretization errors introduced by large quark mass $m_Q$. The spin-independent central $Q\bar{Q}$ potential for the charmonium system yields the "Coulomb plus linear'' behavior with good scaling and small volume dependence. We explore the quark mass dependence over the wide mass range from the charm to beyond the bottom region, and then demonstrate that the spin-independent central $Q\bar{Q}$ potential in the $m_Q \to \infty$ limit is fairly consistent with the static $Q\bar{Q}$ potential obtained from Wilson loops. The spin-spin potential at finite quark mass provides a repulsive interaction with a finite range, which becomes narrower as the quark mass increases. We also discuss the applicability of the $1/m_Q$ expansion approach for the spin-spin potential.