有效价夸克模型和$d Br(B \to K \ell \bar{\ell})/dq^2$的一个可能的倾角
Effective Valence Quark Model and a Possible Dip in $d Br(B \to K \ell \bar{\ell})/dq^2$
摘要：
在稀有的$B$介子衰变$B\rightarrow K \ell^+ \ell^-$中，除了传统的$\bar{b} \rightarrow \bar{s} +γ\rightarrow \bar{s}+\ell^+ + \ell^-$外，还研究了$B$介子$(q\bar{b})$中“旁观者”夸克$q$（$q=u,d$）对$\ell^+\ell^-$辐射的可能贡献.如果与$B\rightarrow K \ell^+ \ell^-$的标准估计值相比，这种贡献相当大，则我们将观察到$d Γ(B^0\rightarrow K^0 \ell^+ \ell^-)/d q^2$和$d Γ(B^+\rightarrow K^+ \ell^+ \ell^-)/d q^2$在$q^2$依赖性（$q^2 \equiv m_{\ell\ell}^2$）方面的明显差异。此外，由于传统的$d Γ(B\rightarrow K \ell^+ \ell^-)/d q^2$和新的$d Γ(B\rightarrow K \ell^+ \ell^-)/d q^2$之间的干扰，在$q^2$的一个小区域处，$d Γ(B\rightarrow K \ell^+ \ell^-)/d q^2$中出现凹陷。在$B^0$衰变中的干涉效应也将与在$B^+$衰变中的干涉效应不同地观察到。计算是基于半经典的方法，一个价夸克模型。在本模型中，旁观夸克$q$，$d \rightarrow d+γ$（$u \rightarrow u+γ$）的光子发射与$b$-$s$跃迁机制无关，特征结果是由于对夸克传播子的直接估计，而这种估计不能纳入因子分解方法.这个模型不是一个价夸克“占主导地位”的模型，因此，例如，处于末态的价夸克只携带K介子能量动量的$24\%$。
英文摘要：
In rare $B$ meson decays $B\rightarrow K \ell^+ \ell^-$, a possible contribution of $\ell^+\ell^-$ emission via photon from the "spectator" quark $q$ ($q=u,d$) in the $B$ meson $(q\bar{b})$ is investigated in addition to the conventional one $\bar{b} \rightarrow \bar{s} +γ\rightarrow \bar{s}+\ell^+ + \ell^-$. If such a contribution is sizable compared with the standard estimation of $B\rightarrow K \ell^+ \ell^-$, we will observe visible difference between $d Γ(B^0\rightarrow K^0 \ell^+ \ell^-)/d q^2$ and $d Γ(B^+\rightarrow K^+ \ell^+ \ell^-)/d q^2$ in $q^2$ dependence ($q^2 \equiv m_{\ell\ell}^2$). Besides, as a result of the interference between the conventional one and a new one, a dip appears in $d Γ(B\rightarrow K \ell^+ \ell^-)/d q^2$ at a small region of $q^2$. The interference effect in the $B^0$ decay will also be observed differently from that in the $B^+$ decay. The calculation is done based on a semi-classical approach, a valence quark model. In the present model, the photon emission from the spectator quark $q$, $d \rightarrow d+γ$ ($u \rightarrow u+γ$) is independent of the $b$-$s$ transition mechanism, and the characteristic results are due to a straightforward estimate of the quark propagator which cannot be incorporated into the factorization method. The model is not a valence quark "dominant" model, so that, for example, the valence quarks in the final state carry only $24\%$ of the energy-momentum of the kaon.
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