Study on ηc2(ηb2) electromagnetic decay into double photons
Study on ηc2(ηb2) electromagnetic decay into double photons
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DOI：
10.1103/physrevd.103.034018
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发表时间：
2020-10
影响因子：
5
通讯作者：
Li Yang;Wen-Long Sang;Hong-Fei Zhang;Yu-Dong Zhang;Ming-Zhen Zhou
中科院分区：
文献类型：
--
作者：
Li Yang;Wen-Long Sang;Hong-Fei Zhang;Yu-Dong Zhang;Ming-Zhen Zhou
在非相对论QCD(NRQCD)因式分解的框架下，计算了α-S展开中电磁衰变为两个光子的螺旋度振幅和衰变宽度.首次验证了NRQCD因式分解在非线性光学D波夸克衰变中的有效性。我们发现，螺旋度振幅的数学{O}(\α_S)$和数学{O}(\α_S^2)$校正是负的和适度的，但这两个校正结合在一起显著地抑制了对衰变宽度的前级预测。通过将强子衰变的总衰变宽度近似为强子衰变的总衰变宽度和电性衰变的总衰变宽度之和，我们得到了约5倍10^-6}$和约4倍10^-7}$的分支比${rM BR}(eTA{c2})。为了探索$eta{q2}$的势度量，我们进一步计算了在$α_S$展开中最低阶的LHCb的$eta{q2}$的产生截面。在运动学约束下，对纵向速度$4.5>；y>；2$和横向动量$P_T>；(2-4)m_q$，我们发现，对于$eta{c2}$，横截面可以达到$2-50$nb，对于$eta{b2}$，可以达到$1-22$pb。考虑到积分光度{L}=10，{rM fb}^-1}在$\Sqrt{S}=7$TeV和$\Sqrt{S}=13$TeV，我们估计有数百个事件从$pp到eTa_{c2}到2\伽马$。由于背景相对干净，通过其电磁衰变来重建ETA_{c2}$是很有前途的。相反，由于LHCb的分支比和产物截面较小，因此在LHCb上检测αeTA{b2}到2γ$是相当困难的。
Within the framework of nonrelativistic QCD (NRQCD) factorization formalism, we compute the helicity amplitude as well as the decay width of $\eta_{Q2}$ ($Q=c,b$) electromagnetic decay into two photons up to next-to-next-to-leading order (NNLO) in $\alpha_s$ expansion. For the first time, we verify the validity of NRQCD factorization for the D-wave quarkonium decay at NNLO. We find that the $\mathcal{O}(\alpha_s)$ and $\mathcal{O}(\alpha_s^2)$ corrections to the helicity amplitude are negative and moderate, nevertheless both corrections combine to suppress the leading-order prediction for the decay width significantly. By approximating the total decay width of $\eta_{Q2}$ as the sum of those for the hadronic decay and the electric $E1$ transition, we obtain the branching ratios ${\rm Br}(\eta_{c2}\to 2\gamma)\approx 5\times10^{-6}$ and ${\rm Br}(\eta_{b2}\to 2\gamma)\approx 4\times10^{-7}$. To explore the potential measurement on $\eta_{Q2}$, we further evaluate the production cross section of $\eta_{Q2}$ at LHCb at the lowest order in $\alpha_s$ expansion. With the kinematic constraint on the longitudinal rapidity $4.5>y>2$ and transverse momentum $P_T>(2-4)m_Q$ for $\eta_{Q2}$, we find the cross section can reach $2-50$ nb for $\eta_{c2}$, and $1-22$ pb for $\eta_{b2}$. Considering the integrated luminosity $\mathcal{L}=10\, {\rm fb}^{-1}$ at $\sqrt{s}=7$ TeV and $\sqrt{s}=13$ TeV, we estimate that there are several hundreds events of $pp\to \eta_{c2}\to 2\gamma$. Since the background is relatively clean, it is promising to reconstruct $\eta_{c2}$ through its electromagnetic decay. On the contrary, due to small branching ratio and production cross section, it is quite challenging to detect $\eta_{b2}\to 2\gamma$ at LHCb.