论文标题
$ b \ tox_sγ$ in n $^3 $ ll $'$的光子能量谱
The photon energy spectrum in $B\to X_sγ$ at N$^3$LL$'$
论文作者
论文摘要
我们介绍了由电磁企鹅操作员介导的X_Sγ$衰减中的Photon Energy Spectrum的预测。我们使用软共线有效理论（SCET）来恢复大型光子能量下峰区的单数贡献。在尾部区域中，重新定义的预测与n $^3 $ lo的固定顺序相匹配，在其中我们包括$ o_7 $的已知固定顺序贡献，最高为$ \ mathcal {o}（α_s^2）$。我们开发了一种方法来适当地参数仍然未知的$ \ MATHCAL {O}（α_s^3）$非校正在理论滋扰参数方面，其变化提供了相关理论不确定性的估计。在这种情况下，我们还研究了在匹配中处理高阶跨项的不同方法。我们分析的另一个重要方面是用于$ b $ QUARK MASS $ M_B $的短途计划。我们发现，在当前情况下，以前最多使用2循环订单的1 $ S $质量方案无法按3循环订单工作，因为质量方案以软尺度输入到这里的软尺度大得多，在这里，未设计1 $ s $方案。而是将MSR质量方案与$ r \ sim 1 \，\ mathrm {gev} $一起使用，我们获得了稳定的结果，具有良好的扰动收敛，最高为n $^3 $ ll $'$。
We present predictions for the photon energy spectrum in inclusive $B\to X_sγ$ decays mediated by the electromagnetic penguin operator $O_7$ to N$^3$LL$'$. We use soft-collinear effective theory (SCET) to resum the singular contributions in the peak region at large photon energy. In the tail region the resummed predictions are matched to fixed order at N$^3$LO, where we include the known fixed-order contributions for $O_7$ up to $\mathcal{O}(α_s^2)$. We develop a method to suitably parametrize the still unknown $\mathcal{O}(α_s^3)$ nonsingular corrections in terms of theory nuisance parameters, whose variations provide an estimate of the associated theory uncertainty. In this context, we also study different ways to treat higher-order cross terms in the matching. Another important aspect of our analysis is the short-distance scheme used for the $b$-quark mass $m_b$. We find that in the present context, the 1$S$ mass scheme, which was previously used up to 2-loop order, fails to work at 3-loop order, because the mass scheme enters at a soft scale much smaller than $m_b$ here, for which the 1$S$ scheme was not devised. Using instead the MSR mass scheme with $R\sim 1\,\mathrm{GeV}$, we obtain stable results with good perturbative convergence up to N$^3$LL$'$.
