arXiv 1901.030452019-01hep-ph

裸夸克质量为零时的非零π质量

Nonvanishing pion masses for vanishing bare quark masses

Aiichi Iwazaki

备注：: revised version, 6 pages, no figures. arXiv admin note: text overlap with arXiv:1809.00279

摘要：

一般认为，当裸轻夸克质量$m_q$消失时，π介子质量也消失了。π介子是具有手征$SU_{A}(2)$对称性的南武-戈德斯通玻色子。我们讨论了一种可能性，即即使当$m_q=0$时，强耦合QCD中的手征对称性也被显式破缺，而弱耦合QCD中的手征对称性没有破缺。问题的关键是，在强耦合QCD中，QCD单极子是动力学自由度。我们发现，夸克相互作用打破手征$U_5(1)$对称性以及手征$SU_{A}(2)$对称性。它们相对于夸克和胶子的其他手征对称相互作用是弱的。这些弱相互作用产生小的π介子质量以及夸克质量$\sim 20$ MeV的阶段与凝聚。相互作用的存在修改了盖尔曼奥克斯伦纳关系。使用该关系，我们预测值$(-\langle\bar{q}q\rangle)^{1/3}\simeq 160$ MeV。我们还证明了双超导模型中的夸克相互作用并不阻止夸克凝聚。

英文摘要：

It is generally thought that pion masses vanish when bare light quark masses $m_q$ vanish. The pions are Nambu-Goldstone bosons of chiral $SU_{A}(2)$ symmetry. We discuss a possibility that even when $m_q=0$, the chiral symmetry is explicitly broken in strong coupled QCD, while it is not in weakly coupled QCD. The point is that QCD monopoles are dynamical degrees of freedom in the strong coupled QCD. We show that the monopole quark interactions break the chiral $U_5(1)$ symmetry as well as the chiral $SU_{A}(2)$ symmetry. They are weak relative to the other chiral symmetric interactions of quarks and gluons. These weak interactions produce small pion masses as well as quark masses $\sim 20$MeV in the phase with the monopole condensation. The presence of the interactions modifies the Gell-Mann Oakes Renner relation. Using the relation we predict the value $(-\langle\bar{q}q\rangle)^{1/3}\simeq 160$MeV. We also show that the monopole quark interactions do not prevent the monopole condensation in dual superconducting model.

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