AI 中文总结
该研究构建重QCD轴子的软共线有效理论框架，以B→Ka为基准，分析两种低能实现方式下旁观者散射对稀有B介子衰变重轴子产生的影响，并推导轴子衰变常数界限。
AI 中文摘要
我们针对重QCD轴子构建了软共线有效理论（SCET）框架，考虑两种低能实现方式，并以B→Ka作为基准模式。第一种实现方式假设在标度μ~m_b处，aG∧G是唯一独立的轴子相互作用。我们证明，在弱有效理论中消除冗余的味改变导数-胶子算符会生成一个新的七维轴子算符，记为O_∂ag。我们将该算符匹配到SCET中，推导得到B→Ka对应的领头幂次软贡献和旁观者散射贡献。我们用微扰硬核以及B介子和K介子的光锥分布振幅得到旁观者贡献的因子化表达式。旁观者贡献在幂次展开中与软重叠项处于同一阶，约为软贡献的25%。第二种实现方式假设aG∧G的威尔逊系数在电弱标度以上存在，重整化群演化和匹配会诱导出直接的b→sa算符，进而产生主导的软形状因子贡献，而胶子旁观者项在数值上是次领头的（约6-7%）。我们由此确定了旁观者散射在稀有B介子衰变的重轴子产生中变得相关的条件，最终推导得到两种实现方式下轴子衰变常数f_a的对应界限，并比较了它们的唯象学意义。
英文摘要
We develop a soft-collinear effective theory (SCET) framework for heavy QCD axion, considering two low-energy realizations and taking $B\to Ka$ as a benchmark mode. In the first realization, $aG\widetilde G$ is assumed to be the only independent axion interaction at the scale $μ\sim m_b$. We show that eliminating the redundant flavor-changing derivative-gluon operator in the weak effective theory generates a new dimension-seven axion operator identified as $\mathrm{O}_{\partial ag}$. We match this operator onto SCET and derive the corresponding leading-power soft and spectator-scattering contributions to $B\to Ka$. We obtain a factorized expression for the spectator contribution in terms of perturbative hard kernels and the $B$- and $K$-meson light-cone distribution amplitudes. The spectator contribution arises at the same order in the power expansion as the soft-overlap term and amounts to approximately $25\%$ of the soft contribution. In the second realization, the Wilson coefficient of $aG\widetilde G$ is assumed to be present above the electroweak scale. Renormalization-group evolution and matching then induce a direct $b\to sa$ operator, which subsequently results in a dominant soft form-factor contribution, whereas the gluonic spectator term turns out to be numerically subleading ($\sim 6-7\%$). We thus identify the conditions under which spectator scattering becomes relevant for heavy-axion production in rare $B$-meson decays. Finally, we derive the corresponding bounds on the axion decay constant $f_a$ for both realizations and compare their phenomenological implications.
Comments18 pages, 1 figure
