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arXiv 1503.00859hep-ph
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企鹅对$B_{d,s}$衰变到粲偶素的CP相的贡献

Penguin contributions to CP phases in $B_{d,s}$ decays to charmonium

Philipp Frings, Ulrich Nierste, Martin Wiebusch

备注：
typo in Eqs. (2) and (3) corrected, references updated.Matches version published in PRL
发表信息：
Phys. Rev. Lett. 115, 061802 (2015)
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摘要：

由$B_d\to J/ψK_S$和$B_s\to J/ψϕ$中混合诱导的CP不对称性分别确定的CP相位$2β$和$2β_s$的精度受到涉及上夸克的企鹅图的未知长距离贡献的限制。企鹅的贡献预计在大小上与LHCb和Belle II实验的精度相当，因此限制了测量量对新物理的敏感性。我们分析了红外QCD结构的贡献，发现所有的软和共线的分歧，或者取消不同的图表之间或分解成矩阵元素的本地四夸克算子的条款抑制$Λ_{QCD}/m_ψ$，其中$m_ψ$表示$J/ψ$质量。我们的研究结果，这是基于一个运营商的产品扩展，使我们能够计算企鹅树的比例$P/T$在这些运营商的矩阵元素，并限制企鹅的贡献相位$2β$为$|Δϕ_d|\leq {0.68}^\circ$。对于纵向、平行和垂直$ϕ$和$J/ψ$偏振的情况，企鹅对$2β_s$的贡献分别被限定为$|Δϕ_s^{0}|\leq {0.97}^\circ$、$|Δϕ_s^{\parallel}|\leq {1.22}^\circ$和$|Δϕ_s^{\perp}|\leq {0.99}^\circ$。我们进一步对$B_d\to ψ(2S) K_S$的$|Δϕ_d|$和$B_d\to J/ψK^*$中的偏振振幅进行了限制。在我们的方法中，它是进一步限制$P/T$的衰变，其中$P/T$是Cabibbo-unsuppressed，我们推导出上限的企鹅贡献的混合诱导CP不对称的$B_d\to J/ψπ^0$，$B_d\to J/ψρ^0$，$B_s\to J/ψK_S$，和$B_s\to J/ψK^*$。对于所有研究的衰变模式，我们也约束的直接CP不对称的大小。

英文摘要：

The precision of the CP phases $2β$ and $2β_s$ determined from the mixing-induced CP asymmetries in $B_d\to J/ψK_S$ and $B_s\to J/ψϕ$, respectively, is limited by the unknown long-distance contribution of a penguin diagram involving up quarks. The penguin contribution is expected to be comparable in size to the precision of the LHCb and Belle II experiments and therefore limits the sensitivity of the measured quantities to new physics. We analyze the infrared QCD structure of this contribution and find that all soft and collinear divergences either cancel between different diagrams or factorize into matrix elements of local four-quark operators up to terms suppressed by $Λ_{QCD}/m_ψ$, where $m_ψ$ denotes the $J/ψ$ mass. Our results, which are based on an operator product expansion, allow us to calculate the penguin-to-tree ratio $P/T$ in terms of the matrix elements of these operators and to constrain the penguin contribution to the phase $2β$ as $|Δϕ_d|\leq {0.68}^\circ$. The penguin contribution to $2β_s$ is bounded as $|Δϕ_s^{0}|\leq {0.97}^\circ$, $|Δϕ_s^{\parallel}|\leq {1.22}^\circ$, and $|Δϕ_s^{\perp}|\leq {0.99}^\circ$ for the case of longitudinal, parallel, and perpendicular $ϕ$ and $J/ψ$ polarizations, respectively. We further place bounds on $|Δϕ_d|$ for $B_d\to ψ(2S) K_S$ and the polarization amplitudes in $B_d\to J/ψK^*$. In our approach it is further possible to constrain $P/T$ for decays in which $P/T$ is Cabibbo-unsuppressed and we derive upper limits on the penguin contribution to the mixing-induced CP asymmetries in $B_d\to J/ψπ^0$, $B_d\to J/ψρ^0$, $B_s\to J/ψK_S$, and $B_s\to J/ψK^*$. For all studied decay modes we also constrain the sizes of the direct CP asymmetries.

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