[论文解读] New results with colour-sextet quarks

D. K. Sinclair, J. B. Kogut|arXiv (Cornell University)|Aug 14, 2010

Quantum Chromodynamics and Particle Interactions被引用 5

一句话总结

该规范场论研究利用格点QCD方法，研究了含2种和3种色六重态夸克的QCD相结构，以区分行走行为与共形行为。在有限温度下，使用在$16^3\times8$和$24^3\times8$格点上的阶梯费米子，研究发现从$N_t=4$到$6$，手征对称性相变耦合常数显著增加，但从$6$到$8$的增加幅度小得多，表明存在强耦合动力学；该行为与共形区内的体相变一致，暗示$N_f=2$的理论更可能是共形理论而非行走理论。

ABSTRACT

We study QCD with 2 and 3 flavours of colour-sextet quarks. The 2-flavour theory is a candidate Walking Technicolor theory. Since we are attempting to distinguish whether this theory is walking or conformal, we also study the 3-flavour theory, which is believed to be conformal, for comparison. We simulate lattice QCD with 2 and 3 flavours of colour-sextet staggered quarks at finite temperatures to determine the scales of confinement and chiral-symmetry breaking from the positions of the deconfinement and chiral-symmetry restoration transitions. Unlike the case with fundamental quarks, these transitions are far apart. For 2 flavours the values of beta=6/g^2 for both transitions increase as Ta is decreased from 1/4 to 1/6 to 1/8, as expected for a theory whose coupling runs to smaller values as the lattice spacing is decreased. However, for the chiral transition, the increase in beta between Ta=1/4 and Ta=1/6 is much larger than the increase between Ta=1/6 and Ta=1/8. This suggests that between Ta=1/4 and Ta=1/6 we are at strong coupling where the theory is effectively quenched, while between Ta=1/6 and Ta=1/8 we are emerging into the weak coupling regime. It will require even smaller Ta values to determine whether the running of the chiral-transition coupling is controlled by asymptotic freedom and the theory walks, or if it reaches a non-zero limit when the transition becomes a bulk transition and the theory is conformal. The 3 flavour case at Ta=1/4 and Ta=1/6 behaves similarly to the 2 flavour case. Since this theory is expected to be conformal, the interpretation that we are seeing strong-coupling behaviour, inaccessible from the weak-coupling limit (continuum) is the most likely interpretation.

研究动机与目标

• 确定含2种色六重态夸克的QCD是否为行走或共形场论。
• 比较$N_f=2$与$N_f=3$六重态QCD的有限温度相变行为，其中后者预期为共形理论。
• 通过外推至大$N_t$，判断手征对称性相变是由渐近自由（行走）还是体相变（共形）控制。
• 研究强耦合动力学在手征对称性相变区域如何掩盖弱耦合行为。
• 评估有限尺寸效应，并指出未来模拟中需采用更大空间体积和更小夸克质量。

提出的方法

• 在有限温度下，使用威尔逊平面元作用和未改进的阶梯费米子，模拟$N_f=2$和$N_f=3$色六重态夸克的格点QCD。
• 使用RHMC算法在$16^3\times8$和$24^3\times8$格点上生成配置，其中$N_t=8$，夸克质量为$m_q=0.005, 0.01, 0.02$。
• 测量威尔逊线和手征凝聚$\langle\bar\psi\psi\rangle$作为序参量，以识别禁闭与手征对称性自发破缺的相变。
• 将威尔逊线数据分为三个相，以检测与$Z_3$中心对称性破缺相关的三态信号。
• 分析$\beta$对相变点$\beta_d$（禁闭相变）和$\beta_\chi$（手征对称性相变）在$N_t=4,6,8$下的依赖关系，推断耦合常数的跑动行为。
• 将结果与真空理论及已知的共形基准进行比较，评估$\beta_\chi$在连续极限下是否趋于有限值或趋于零。

实验结果

研究问题

• RQ1 在连续极限下，$N_f=2$色六重态QCD理论是否表现出行走或共形行为？
• RQ2 为何手征对称性相变耦合常数$\beta_\chi$从$N_t=4$到$6$的增加幅度远大于从$6$到$8$？
• RQ3 在$N_f=2$和$N_f=3$理论中观察到的行为是由强耦合动力学还是渐近自由引起的？
• RQ4 $N_f=3$理论的手征对称性相变是否可用强耦合区内的真空标度行为解释？
• RQ5 有限尺寸效应和夸克质量在所观察到的相变行为中起何作用？

主要发现

• 对于$N_f=2$，手征对称性相变耦合常数$\beta_\chi$从$N_t=4$到$6$显著增加，但从$6$到$8$仅略有增加，表明理论正从强耦合区过渡到弱耦合区。
• 从$N_t=4$到$6$时$\beta_\chi$的大幅增加表明，该理论处于强耦合区，费米子效应被抑制，类似于真空动力学。
• 从$N_t=6$到$8$时增加幅度较小，表明理论正进入弱耦合区，费米子效应开始显现。
• 对于$N_f=3$，手征对称性相变也表现出从$N_t=4$到$6$时$\beta_\chi$的大幅增加，但从$6$到$8$的增加幅度小得多，与强耦合标度行为一致。
• $N_f=3$理论在$N_t=4$时的$\beta_\chi$接近真空理论在$N_t=8$时的禁闭相变点，而在$N_t=6$时与真空理论在$N_t=12$时的$\beta_d$一致，表明存在真空标度行为。
• 结果表明，$\beta_\chi$在连续极限下可能趋于有限值，暗示两种理论（$N_f=2$与$N_f=3$）均存在体相变和共形行为。