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arXiv 1402.6855hep-phhep-ex
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$B^0 \to K^* μ^+μ^-$中$A_{FB}$零点与$P_5^\prime$中反常点的新关系

A new relation between the zero of $A_{FB}$ in $B^0 \to K^* μ^+μ^-$ and the anomaly in $P_5^\prime$

Joaquim Matias, Nicola Serra

摘要:

本文给出了四体衰变$B \to K^*(\to Kπ) l^+l^-$的角分布的观测量$P_i$和$P_i^{CP}$之间的两个精确关系,该关系适用于任何双轻子不变质量区(大的和低的反冲),并且与任何有效的哈密顿量计算无关.这些关系从角分布的对称性中显现出来。我们讨论了这些关系的影响下(可检验)的假设没有标量或张量的贡献,没有新物理弱相的威尔逊系数。在这些假设下,观测量$P_{1}$、$P_2$和$P_{4,5}^\prime$之间存在直接关系。这可以作为一个独立的一致性测试的角度观测量的测量。或者,这些关系可以直接应用于数据拟合,减少拟合中自由参数的数量。这开辟了将可观察值与现有数据集进行完全角度拟合的可能性。所发现的关系的重要结果是,先验的两个不同的测量,即前后不对称性$A_{FB}$的零点的测量位置($q_0^2$)和在该相同点处评估的$P_5^\prime$的值,通过$P_4^2(q_0^{2})+P_5^2(q_0^{2})=1$相关。在真实Wilson系数和$P_4^\prime$为SM样的假设下,我们证明了$q_0^{2}$的位置越高,在同一点上评价的$P_5^\prime$的值越小。$A_{FB}$零点位置的精确确定以及在该位置处$P_4^\prime$(和$P_1$)的测量可用作$P_5^\prime$异常的独立实验测试。我们还指出了$P_1$的上、下界的存在性,即$P_5^{\prime 2}-1 \leq P_1 \leq 1-P_4^{\prime 2}$,它限制了观测量的物理区域。

英文摘要:

We present two exact relations, valid for any dilepton invariant mass region (large and low-recoil) and independent of any effective Hamiltonian computation, between the observables $P_i$ and $P_i^{CP}$ of the angular distribution of the 4-body decay $B \to K^*(\to Kπ) l^+l^-$. These relations emerge out of the symmetries of the angular distribution. We discuss the implications of these relations under the (testable) hypotheses of no scalar or tensor contributions and no New Physics weak phases in the Wilson coefficients. Under these hypotheses there is a direct relation among the observables $P_{1}$,$P_2$ and $P_{4,5}^\prime$. This can be used as an independent consistency test of the measurements of the angular observables. Alternatively, these relations can be applied directly in the fit to data, reducing the number of free parameters in the fit. This opens up the possibility to perform a full angular fit of the observables with existing datasets. An important consequence of the found relations is that a priori two different measurements, namely the measured position of the zero ($q_0^2$) of the forward-backward asymmetry $A_{FB}$ and the value of $P_5^\prime$ evaluated at this same point, are related by $P_4^2(q_0^{2})+P_5^2(q_0^{2})=1$. Under the hypotheses of real Wilson coefficients and $P_4^\prime$ being SM-like, we show that the higher the position of $q_0^{2}$ the smaller should be the value of $P_5^\prime$ evaluated at the same point. A precise determination of the position of the zero of $A_{FB}$ together with a measurement of $P_4^\prime$ (and $P_1$) at this position can be used as an independent experimental test of the anomaly in $P_5^\prime$. We also point out the existence of upper and lower bounds for $P_1$, namely $P_5^{\prime 2}-1 \leq P_1 \leq 1-P_4^{\prime 2}$, which constraints the physical region of the observables.

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