论文标题
$η_{C2}（η_{B2}）$电磁衰减成双光子的研究
Study on $η_{c2}(η_{b2})$ electromagnetic decay into double photons
论文作者
论文摘要
在非依赖性QCD（NRQCD）分解形式主义的框架内，我们计算了$η_{q2} $（$ q = c，b $）电磁衰减的衰减宽度以及$η_{q2} $（$ q = c，b $）的衰减宽度，分为两个光子，直至两个光子，直至$ nnlo）$ nnlo $ spection $ allion。我们首次验证了NNLO的D-Wave Quarkonium衰减的NRQCD分解的有效性。我们发现，$ \ Mathcal {O}（α_s）$和$ \ Mathcal {O}（α_s^2）$对螺旋度振幅的校正为负和中等，尽管如此，这两种校正都结合了抑制衰减宽度的领先预测。通过将$η_{q2} $的总衰减宽度作为hadronic衰变和电$ e1 $过渡的总和，我们获得分支比率$ {\ rm br}（η_{η_{c2}} \2γ） 2γ）\大约4 \ times10^{ - 7} $。为了探索$η_{Q2} $的潜在测量值，我们进一步评估了$η_{q2} $的生产横截面，在LHCB处以最低顺序$α_s$扩展。 With the kinematic constraint on the longitudinal rapidity $4.5>y>2$ and transverse momentum $P_T>(2-4)m_Q$ for $η_{Q2}$, we find the cross section can reach $2-50$ nb for $η_{c2}$, and $1-22$ pb for $η_{b2}$.考虑集成的光度$ \ MATHCAL {l} = 10 \，{\ rm fb}^{ - 1} $ at $ \ sqrt {s} = 7 $ tev和$ \ sqrt {s} = 13 $ tev，我们估计有数百个$ pp pp \ pp \ pp \ pp \ pp \ pp \ pp \ pp \ pp \ pp pp \ toη_}由于背景相对干净，因此有望通过电磁衰减重建$η_{C2} $。相反，由于分支比和生产横截面很小，在LHCB处检测$η_{B2} \至2γ$是非常具有挑战性的。
Within the framework of nonrelativistic QCD (NRQCD) factorization formalism, we compute the helicity amplitude as well as the decay width of $η_{Q2}$ ($Q=c,b$) electromagnetic decay into two photons up to next-to-next-to-leading order (NNLO) in $α_s$ expansion. For the first time, we verify the validity of NRQCD factorization for the D-wave quarkonium decay at NNLO. We find that the $\mathcal{O}(α_s)$ and $\mathcal{O}(α_s^2)$ 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 $η_{Q2}$ as the sum of those for the hadronic decay and the electric $E1$ transition, we obtain the branching ratios ${\rm Br}(η_{c2}\to 2γ)\approx 5\times10^{-6}$ and ${\rm Br}(η_{b2}\to 2γ)\approx 4\times10^{-7}$. To explore the potential measurement on $η_{Q2}$, we further evaluate the production cross section of $η_{Q2}$ at LHCb at the lowest order in $α_s$ expansion. With the kinematic constraint on the longitudinal rapidity $4.5>y>2$ and transverse momentum $P_T>(2-4)m_Q$ for $η_{Q2}$, we find the cross section can reach $2-50$ nb for $η_{c2}$, and $1-22$ pb for $η_{b2}$. 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 $pp\to η_{c2}\to 2γ$. Since the background is relatively clean, it is promising to reconstruct $η_{c2}$ through its electromagnetic decay. On the contrary, due to small branching ratio and production cross section, it is quite challenging to detect $η_{b2}\to 2γ$ at LHCb.
