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arXiv 1603.04575hep-phhep-lathep-th
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π介子和介子的低能有效action

Low-energy effective action for pions and a dilatonic meson

Maarten Golterman, Yigal Shamir

摘要:

在类似量子色动力学的理论中,口味的数量被调整,使β函数非常小,但限制和手征对称性破缺仍然发生,数值模拟似乎揭示了一个口味单重标量介子的存在,它可以像π介子一样轻。由于由β函数量化的伸缩对称性破缺相对于QCD来说很小,一个可能的解释是标量介子是与近似伸缩对称性相关的伪南武-戈德斯通玻色子。我们利用这一观测结果系统地发展了一个低能有效作用量,该作用量同时考虑了π介子和标量介子。为了证明控制介子耦合的功率计数的合理性,我们引用了Veneziano极限,在这个极限中,基本表象的味道$N_f$的数量与颜色$N_c$的数量成比例地增长,而比率$N_f/N_c$保持接近但低于进入共形窗口的临界值。

英文摘要:

Numerical simulations of QCD-like theories in which the number of flavors is adjusted so that the beta function is very small, but confinement and chiral symmetry breaking nevertheless take place, appear to reveal the presence of a flavor-singlet scalar meson which can be as light as the pions. Because the breaking of dilatation symmetry, quantified by the beta function, is small relative to QCD, a possible explanation is that the scalar meson is a pseudo Nambu-Goldstone boson associated with the approximate dilatation symmetry. We use this observation to systematically develop a low-energy effective action that accounts for both the pions and the "dilatonic" scalar meson. In order to justify the power counting that controls the couplings of the dilatonic meson we invoke the Veneziano limit, in which the number of fundamental-representation flavors $N_f$ grows in proportion with the number of colors $N_c$, while the ratio $N_f/N_c$ is kept close to, but below, the critical value where the conformal window is entered.

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