论文标题
近代到领导级辐射校正到$ e^+e^ - \toχ_{cj}+γ$ at $ b $ factory at $ b $
Next-to-Next-to-Leading-Order Radiative Corrections to $e^+e^-\toχ_{cJ}+γ$ at $B$ factory
论文作者
论文摘要
Within the nonrelativistic QCD (NRQCD) factorization framework, we have computed the ${\mathcal O}(α_s^2)$ corrections to the exclusive production of $P$-wave spin-triplet charmonia $χ_{cJ}(J=0,1,2)$ accompanied by a hard photon at $B$ factories.我们首次明确验证了NRQCD分解对独家$ p $ p $ - 波Quarkonium生产的有效性。与$χ_{CJ} $电磁衰减过程不同，发现$ \ Mathcal {o}（α_s^2）$更正小于所有三个通道中的$ \ Mathcal {o}（α_s）$校正的所有三个通道$ e^+e^+e^+e^+e^ - \χ_\χ_{c0,1,1,1,1,1,1,2}+c。特别是，$ {\ mathcal o}（α_s^2）$校正对于$χ_{C1} $ case显得中度，而对于$χ_{C0} $而言无关紧要。此外，对$χ_{C0,1}+γ$的生产率的近隔到领先顺序（NNLO）预测对重新归一化和分解量表不敏感。所有这些特征都可能表明这两个通道中的扰动膨胀表现出不错的收敛行为。相比之下，$ {\ Mathcal O}（α_s）$和$ {\ Mathcal O}（α_s^2）$对$χ_{C2}+γ$生产横截面的校正都是可观的，甚至在包括nnlo of nnlo offertate cormection之后，born Order crots crots crots crots crots crots croth crots crots croth crote crote croments都是可观的。从非依赖性潜在模型中借助长距离NRQCD矩阵元素的值，我们的预测到$χ_{C1}+γ$生产率与最近的{\ tt belle}测量是一致的。 $χ_{C0,2}+γ$的生产率的NNLO预测远小于$χ_{C1}+γ$的NNLO预测，这似乎自然地解释了为什么$ e^+E^+E^ - \ toχ_toχ_{C0,2}+γ$通道已逃脱了实验检测。
Within the nonrelativistic QCD (NRQCD) factorization framework, we have computed the ${\mathcal O}(α_s^2)$ corrections to the exclusive production of $P$-wave spin-triplet charmonia $χ_{cJ}(J=0,1,2)$ accompanied by a hard photon at $B$ factories. For the first time, we have explicitly verified the validity of NRQCD factorization for exclusive $P$-wave quarkonium production at two-loop order. Unlike the $χ_{cJ}$ electromagnetic decay processes, the $\mathcal{O}(α_s^2)$ corrections are found to be smaller than the $\mathcal{O}(α_s)$ corrections in all three channels $e^+e^-\to χ_{c0,1,2}+γ$. In particular, the ${\mathcal O}(α_s^2)$ corrections appear moderate for $χ_{c1}$ case, and insignificant for $χ_{c0}$. In addition, the next-to-next-to-leading order (NNLO) predictions for the production rates of $χ_{c0,1}+γ$ are insensitive to the renormalization and factorization scales. All of these features may indicate that perturbative expansion in these two channels exhibits a decent convergence behavior. By contrast, both the ${\mathcal O}(α_s)$ and ${\mathcal O}(α_s^2)$ corrections to the $χ_{c2}+γ$ production cross section are sizable, which even reduces the Born order cross section by one order of magnitude after including the NNLO perturbative correction. Taking the values of the long-distance NRQCD matrix elements from nonrelativistic potential model, our prediction to $χ_{c1}+γ$ production rate is consistent with the recent {\tt Belle} measurement. The NNLO predictions for the $χ_{c0,2}+γ$ production rates are much smaller than that for $χ_{c1}+γ$, which seems to naturally explain why the $e^+e^-\to χ_{c0,2}+γ$ channels have escaped experimental detection to date.
