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arXiv 2008.00346hep-phnucl-th
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风味依赖的U（3）Nambu Jona Lasinio耦合常数

Flavor-dependent U(3) Nambu Jona Lasinio coupling constant

Fabio L. Braghin

备注：
18 pages, revised, improved and extended version, accepted for publication
发表信息：
Phys. Rev. D 103, 094028 (2021)
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摘要：

考虑非微扰的单胶子交换夸克-反夸克相互作用，从非简并u-d-s夸克有效质量的单圈极化过程出发，计算了形式为$G_{ij, Γ} (\barψ λ_i Γψ) ( \barψ λ_j Γψ)$（$i,j=0...8$和$Γ=I, i γ_5$）的味相关U（3）Nambu-Jona-Lasinio（NJL）型相互作用.所得到的NJL型耦合常数在所有通道中的解决在长波长的限制和数值结果，提出了不同的选择一个有效的胶子传播子。对于$n=1,2$，发现相对于味对称耦合常数的领先偏差为$(M_{f_2}^*-M_{f_1}^*)^n/(M_{f_2}^*+M_{f_1}^*)^n$的量级，其中$M_{f_i}^*$是夸克$f_1,f_2=u, d$和$s$的有效质量。标量沟道耦合常数$G_{ij, s}$可以比赝标量沟道耦合常数小得多。π介子和K介子质量的耦合常数的味道依赖性的影响可能与u，d和s夸克质量非简并性的影响几乎是相同的数量级。这些耦合常数的效果也验证了一些轻标量介子的质量，通常描述的夸克-反夸克态，并为一些可观的赝标量介子。

英文摘要：

A non-perturbative one gluon exchange quark-antiquark interaction is considered to compute flavor dependent U(3) Nambu-Jona-Lasinio (NJL)-type interaction of the form $G_{ij, Γ} (\barψ λ_i Γψ) ( \barψ λ_j Γψ)$ for $i,j=0...8$ and $Γ=I, i γ_5$ from one loop polarization process with non degenerate u-d-s quark effective masses. The resulting NJL-type coupling constants in all channels are resolved in the long-wavelength limit and numerical results are presented for different choices of an effective gluon propagator. Leading deviations with respect to a flavor symmetric coupling constant are found to be of the order of $(M_{f_2}^*-M_{f_1}^*)^n/(M_{f_2}^*+M_{f_1}^*)^n$, for $n=1,2$, where $M_{f_i}^*$ are the effective masses of quarks $f_1,f_2=u, d$ and $s$. The scalar channel coupling constants $G_{ij, s}$ can be considerably smaller than pseudoscalar ones. The effect of the flavor-dependence of coupling constants for the masses of pions and kaons may be nearly of the same order of magnitude as the effect of the u,d and s quark mass non-degeneracy. The effect of these coupling constants is also verified for some of the light scalar mesons masses, usually described by quark-antiquark states, and for some observables of the pseudoscalar mesons.

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