论文标题
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Nonleptonic decays of $Ξ_{cc}\to Ξ_c π$ with $Ξ_c-Ξ_c'$ mixing
论文作者
论文摘要
为了测试$ξ_c-ξ_c'$混合，我们研究了$ξ_{cc} \ to $ξ_cπ$的衰减，并使用$ξ_{cc} =（ξ_{cc} ^{cc} ^{++}， （ξ_c^{（\ prime）+}，ξ_c^{（\ prime）0}）$和$π=（π^+，π^0）$。软膜极限与极模型一起考虑，并通过有没有删除质量中心运动（CMM）的BAG模型来评估Baryon矩阵元素。我们发现，一旦删除了不需要的CMM，四夸克操作员矩阵元素大约大两倍。我们获得该$ {\ cal r} = {\ cal b}（ξ_{cc}^+ \ toξ_c^{\ prime+}π^+）/ {\ cal b}（ξ__{cc}^+ \ to $ 1.45 $，没有删除CMM，前者接近下限，较晚的$与$ {\ cal r} = 1.41 \ pm 0.17 \ pm 0.10 $ 0.10 $一致。此外，我们表明，包括混合后，$α（ξ_{cc}^+ \ toξ_c^{（\ prime）0}π^+）$ flips符号的上向下不对称。明确地，我们获得了$α（ξ_{cc}^{+} \ toξ_c^{\ prime+}π^0）= 0.52 $和$α（ξ_{C {cc}^{+}^{+} \ toξ_c^{0} {0}π^+0.31 $ cimm and Commistion of and commistion of and Commistion of Comm comportion commistion，缺席。作为奖励，实验中的$α（ξ_{cc}^{+} \ toξ_c^{\ prime 0}π^+）$的正值也可以作为$ W $ -ExChange贡献的证据。
Aiming on testing the $Ξ_c-Ξ_c'$ mixing, we study the decays of $Ξ_{cc}\to Ξ_c π$ with $Ξ_{cc} = (Ξ_{cc}^{++} , Ξ_{cc} ^+ )$, $Ξ_c = (Ξ_c^{(\prime)+},Ξ_c^{(\prime)0})$ and $π= (π^+ , π^0)$. The soft-meson limit is considered along with the pole model, and the baryon matrix elements are evaluated by the bag model with and without removing the center-of-mass motion (CMM). We find that the four-quark operator matrix elements are about twice larger once the unwanted CMM is removed. We obtain that ${\cal R} = {\cal B}(Ξ_{cc}^+ \to Ξ_c^{\prime +} π^+ )/ {\cal B}(Ξ_{cc}^+ \to Ξ_c^{ +} π^+ ) = 0.87^{+0.17}_{-0.11} $ and $1.45$ with and without removing the CMM, where the former is close to the lower bound and the later is well consistent with ${\cal R} = 1.41 \pm 0.17 \pm 0.10$ measured at LHCb. In addition, we show that after including the mixing, the up-down asymmetry of $α( Ξ_{cc}^+ \to Ξ_c^{(\prime)0 } π^+)$ flips sign. Explicitly, we obtain that $α(Ξ_{cc}^{+} \to Ξ_c^{\prime +} π^0) = 0.52$ and $α(Ξ_{cc}^{+} \to Ξ_c^{ 0 } π^+) = 0.31$ with and without the CMM corrections, respectively, which are all negative if the mixing is absence. As a bonus, a positive value of $α(Ξ_{cc}^{+} \to Ξ_c^{\prime 0} π^+)$ in experiments can also serve as the evidence of the $W$-exchange contributions.
