论文标题
$ b- \ bar {b} $ system的宽度差异QCD的临时订单
The width difference in the $B-\bar{B}$ system at next-to-next-to-leading order of QCD
论文作者
论文摘要
我们将标准模型中中性$ b $ erson的宽度差$Δγ_Q$扩展到宽度差$Δγ_Q$的理论预测到$α_s$的近代到领先顺序。为此，我们在分析上使用两个$ |ΔB| = 1 $电流运算符计算三环图。在$ |ΔB| = 1 $和$ |ΔB| = 2 $之间的匹配中，我们将红外散布定于尺寸，并考虑到所有相关的evanevancent运算符。计算的进一步元素是$ |ΔB| = 2 $运算符和$ \ Mathcal {o}（α_S^2）$校正的两环恢复矩阵$ z_ {ij} $，以确保$ 1/m_b $ pussions $ 1/m_b $ pussiontriation $ 1/m_b $ pussiontriation $ 1/m_b $ r_ $ r_0 $ r_0订购。我们的理论预测读取$δγ_s/δm_s= {（4.33 \ pm 0.93）\ cdot 10^{ - 3}} $如果用$ \ edline {\ rm MS} $ pasterline {\ rm MS} $ pline {\ rm MS} $方案和$δγ_S/δm_s/δm_s= {4.20 \ pm pm pm pm pm \ rm ms} $ cd.95}的质量表示。潜在提取的质量的使用。 $ | v_ {cb} | $的争议影响$Δγ_s$和$Δm_s$，而比率$Δγ_s/δm_s$不受$ | v_ {cb} | $的不确定性的影响。
We extend the theoretical prediction for the width difference $ΔΓ_q$ in the mixing of neutral $B$ mesons in the Standard Model to next-to-next-to-leading order in $α_s$. To this aim we calculate three-loop diagrams with two $|ΔB|=1$ current-current operators analytically. In the matching between $|ΔB|=1$ and $|ΔB|=2$ effective theories we regularize the infrared divergences dimensionally and take into account all relevant evanescent operators. Further elements of the calculation are the two-loop renormalization matrix $Z_{ij}$ for the $|ΔB|=2$ operators and the $\mathcal{O}(α_s^2)$ corrections to the finite renormalization that ensures the $1/m_b$ suppression of the operator $R_0$ at two-loop order. Our theoretical prediction reads $ΔΓ_s/ΔM_s = {(4.33\pm 0.93)\cdot 10^{-3}}$ if expressed in terms of the bottom mass in the $\overline{\rm MS}$ scheme and $ΔΓ_s/ΔM_s = {(4.20\pm 0.95)\cdot 10^{-3}}$ for the use of the potential-subtracted mass. While the controversy on $|V_{cb}|$ affects both $ΔΓ_s$ and $ΔM_s$, the ratio $ΔΓ_s/ΔM_s$ is not affected by the uncertainty in $|V_{cb}|$ .
