论文标题
最小的su（$ n $）哈德子
The Smallest SU($N$) Hadrons
论文作者
论文摘要
如果新的物理学包含与伴随或（反）基本不同的不可约（3）表示不可约定表示的新的，强烈的相互交互的颗粒，那么计算出最小数量的夸克/反quarks/gluon是一个非平凡的问题，以形成一个颜色界面的状态（“ hadron”（“ hadron）”（“ hadron）”（hadron），或者构成了persient a perter auns new abar abar abar a n abar abar a pertrust a pertrust a nert and a n abar abar a ner pertrust a。在这里，我证明，对于带有Dynkin标签$（P，Q）$的SU（3）表（3）表示，形成包含（0,0）表示的产品所需的最小数量为$ 2P+Q $。我将此结果推广到SU（$ n $），并带有$ n> 3 $。我还计算了与$（p，q）$表示中的新粒子绑定的夸克/古夸克/gl子的最小总数，给出了一个颜色的状态，或者等效地，包括最小的尺寸量表式操作员，其中包括Quark/Antiquark/Gluon Fields和新的强烈的Intermantilly Intercracting Mattalsacting Mattalacting Matteracting Matteracting Matteracting Matteracting。最后，我列出了包含新的外来粒子的最小的黑龙的电荷的所有可能值，并讨论了QCD和大统一嵌入的渐近自由的约束。
If new physics contains new, heavy strongly-interacting particles belonging to irreducible representations of SU(3) different from the adjoint or the (anti)fundamental, it is a non-trivial question to calculate what is the minimum number of quarks/antiquarks/gluons needed to form a color-singlet bound state ("hadron"), or, perturbatively, to form a gauge-invariant operator, with the new particle. Here, I prove that for an SU(3) irreducible representation with Dynkin label $(p,q)$, the minimal number of quarks needed to form a product that includes the (0,0) representation is $2p+q$. I generalize this result to SU($N$), with $N>3$. I also calculate the minimal total number of quarks/antiquarks/gluons that, bound to a new particle in the $(p,q)$ representation, give a color-singlet state, or, equivalently, the smallest-dimensional gauge-invariant operator that includes quark/antiquark/gluon fields and the new strongly-interacting matter field. Finally, I list all possible values of the electric charge of the smallest hadrons containing the new exotic particles, and discuss constraints from asymptotic freedom both for QCD and for grand unification embeddings thereof.
