AI 中文总结
该研究指出大N_c手征拉格朗日量的算符结构会在特定低能常数间诱导关联方向，并以π介子衰变常数为例重新解释相关确定结果，为低能常数的现象学确定提供了实用方案。
AI 中文摘要
手征与大N_c相结合的展开正越来越多地应用于涉及η和η'介子的精确研究，包括近期在U(3)手征微扰论框架下对低能轴子现象学的应用。我们指出，大N_c手征拉格朗日量的算符结构会自然地在低能常数(F₀,L₄,C₁₆)与(F₀,L₆,C₂₀)之间诱导出关联方向，这意味着现象学分析确定的是耦合的关联组合，而非独立的低能常数。以π介子衰变常数的确定为例，我们根据这些关联方向重新解释了现有现象学和格点确定结果，表明F₀与L₄之间著名的反关联通过C₁₆自然延伸至NNLO。这些关联方向为在手征与大N_c相结合的框架内一致地解释和传播低能常数的现象学确定提供了实用方案。
英文摘要
The combined chiral and large-$N_c$ expansion is increasingly employed in precision studies involving the $η$ and $η'$ mesons, including recent applications to low-energy axion phenomenology within U(3) chiral perturbation theory. We point out that the operator structure of the large-$N_c$ chiral Lagrangian naturally induces correlated directions among the low-energy constants $(F_0,L_4,C_{16})$ and $(F_0,L_6,C_{20})$, implying that phenomenological analyses determine correlated combinations of couplings rather than independent low-energy constants. Using the determination of the pion decay constant as an illustrative example, we reinterpret existing phenomenological and lattice determinations in terms of these correlated directions, showing that the well-known anticorrelation between $F_0$ and $L_4$ extends naturally to NNLO through $C_{16}$. These correlated directions lead to a practical prescription for interpreting and propagating phenomenological determinations of the low-energy constants consistently within the combined chiral and large-$N_c$ framework.
CommentsShort letter of 7 pages with 2 figures
