AI 中文总结
该研究构造重夸克偶素的 QCD 到 BOEFT 匹配，通过规范协变投影分离 BO 道与有能隙区域，将响应简化为 Peskin 构造，推导自旋单态 1S 态的磁匹配系数相关项，为 BOEFT 与 Peskin OPE 的连接提供关键结果。
AI 中文摘要
我们针对致密重夸克偶素的胶子响应构造了依赖源的量子色动力学（QCD）到玻恩-奥本海默有效场论（BOEFT）的匹配。一个规范协变的投影响应将动力学保留的玻恩-奥本海默（BO）道与由局域逆矩描述的有能隙区域分离开来。传播-顶点界为道分解的局域算符乘积展开（OPE）提供了充分判据，而额外的弱耦合和源-能隙层级将该响应简化为 Peskin 构造。在库仑极限下，已确立的 Bhanot-Peskin 电矩和解离割来自同一谱测度。作为磁扩展，对于自旋单态 1S 态，各向同性序列 M1 逆矩给出 $c_{B,GG}^{(1)ij}=5\pi\alpha_s^2 (c_FV_{\rm iso}^{(s)})^2\delta^{ij}/16$，而领头阶协变动能海鸥项给出 $c_{B,{\rm dia}}^{(1)ij}=-\pi\alpha_s^2\delta^{ij}/4$，这些是磁匹配系数的可识别贡献，而非其完整值。
英文摘要
We formulate a source-dependent QCD-to-BOEFT matching for the gluonic response of a stable compact heavy-quarkonium state. The matched complementary-space resolvent preserves coupled Born-Oppenheimer dynamics, while an exact Feshbach decomposition separates channels retained explicitly from sectors integrated out at the next matching step. Spectral separation, kernel analyticity, and joint propagation-source bounds provide sufficient conditions for a local channel-factorized OPE; otherwise low-energy BO poles and cuts remain dynamical. The weak-coupling pNRQCD response is recovered as a limiting reference problem. With the additional leading-$E1$, large-$N_c$/free-octet assumptions, the source-weighted spectral measure reproduces the established Bhanot-Peskin electric moments and dissociation cut. For a Coulombic spin-singlet $1S$ state we also obtain the sequential-$M1$ contribution $c_{B,GG}^{(1)ij} =5πα_s^2(c_FV_{\rm iso}^{(s)})^2δ^{ij}/16$ and the covariant-kinetic seagull contribution $c_{B,\mathrm{dia}}^{(1)ij} =-πα_s^2δ^{ij}/4$. These are identifiable components, not the complete magnetic matching coefficient.
Comments19 pages
