AI 中文总结
研究利用软共线有效理论框架下的光锥求和规则，对B→D1(2420)和B→D'1(2430)跃迁形状因子进行αs阶计算，给出相关求和规则及唯象预测，得到的数值结果可与未来实验对比。
AI 中文摘要
我们在软共线有效理论（SCET）框架内，首次利用光锥求和规则对B→D1(2420)和B→D'1(2430)跃迁形状因子进行了αs阶的计算。先将QCD跃迁流匹配到SCET_I，再在SCET_II中对相应的真空到B介子关联函数进行因式分解。所得因式分解公式用于构建有效SCET形状因子ξR∥/⊥和ΞR∥/⊥（R = D1，D'1）的领头幂次求和规则。计算了由有限粲夸克质量引起的附加纵向形状因子ξR∥,mc。为分离混合态，引入专用插值流组合并通过运动方程确定其衰变常数。为分离轨道激发态，从总求和规则中减去基态贡献并检验求和规则稳定性。利用Bourrely - Caprini - Lellouch参数化外推物理形状因子的q²依赖性。最后给出分支比、微分衰变宽度和轻子味普适性比的唯象预测。数值上得到R(D1)=0.070 +0.028 -0.018和R(D'1)=0.159 +0.032 -0.025，可与未来Belle II和LHCb的测量结果对比。
英文摘要
We present the first calculation of the $B \to D_1(2420)$ and $B \to D'_1(2430)$ transition form factors at ${\cal O}(α_s)$ using light-cone sum rules within the framework of soft-collinear effective theory (SCET). We first match the QCD transition currents onto ${\rm SCET_I}$ and then factorize the corresponding vacuum-to-$B$-meson correlation functions in ${\rm SCET_{II}}$. The resulting factorization formulae are used to construct the leading-power sum rules for the effective SCET form factors $ξ^R_{\parallel/\perp}$ and $Ξ^R_{\parallel/\perp}$ ($R=D_1,D'_1$). In particular, we calculate the additional longitudinal form factor $ξ^R_{\parallel,m_c}$ induced by the finite charm-quark mass, whose contribution depends only on the $B$-meson light-cone distribution amplitude $ϕ_B^+(ω,μ)$. To disentangle the mixed $D_1$ and $D'_1$ states, we introduce dedicated combinations of interpolating currents, with their decay constants determined via the equations of motion. To isolate the orbitally excited states from ground-state contamination, we subtract the ground-state contribution from the total sum rules and examine the stability of the resulting sum rules. Furthermore, the $q^2$-dependence of the physical form factors is extrapolated over the full kinematic region using the Bourrely--Caprini--Lellouch parameterization. Finally, we provide phenomenological predictions for the branching fractions, differential decay widths, and lepton flavor universality ratios. Numerically, we obtain $R(D_1) = 0.070^{+0.028}_{-0.018}$ and $R(D'_1) = 0.159^{+0.032}_{-0.025}$, which can be confronted with the future measurements at Belle~II and LHCb.
Comments40 pages, 9 figures, 3 tables
