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arXiv 1701.01633hep-phhep-ex
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$B$ -介子分布振幅下光锥求和规则的$B\toππ$形状因子

$B\toππ$ Form Factors from Light-Cone Sum Rules with $B$-meson Distribution Amplitudes

Shan Cheng, Alexander Khodjamirian, Javier Virto

摘要:

我们用QCD光锥求和规则和$B$介子分布振幅研究了$B\toππ$的形状因子。这些形状因子描述了半轻子衰变$B\to ππ\ell\barν_{\ell}$,并构成了$B\to ππ\ell^+\ell^-$和$B\to πππ$衰变的基本输入。我们采用的相关函数中的一个双介子的同位旋一状态是由矢量光夸克流插值。我们得到的总和规则的$P$波$\bar{B}^0\to π^+π^0$形状因子与类时π介子矢量形状因子的卷积与普适$B$介子分布振幅有关。这些求和规则在双介子态具有大能量和低不变质量的运动机制中是有效的,并且在$ρ$ -优势为零宽度的极限中解析地再现了已知的$B\to ρ$形状因子的光锥求和规则,从而为迄今为止未解释的$B\toρ$跃迁修正提供了系统。使用数据的π矢量形状因子,我们估计有限宽度的影响和贡献的激发$ρ$ -共振的$B\toππ$形状因子。我们发现,这些贡献金额高达$\sim 20\%$在小的双介子质量区域,它们可以有效地被视为一个非共振($P$波)背景的$B\toρ$过渡。

英文摘要:

We study $B\toππ$ form factors using QCD light-cone sum rules with $B$-meson distribution amplitudes. These form factors describe the semileptonic decay $B\to ππ\ell\barν_{\ell}$, and constitute an essential input in $B\to ππ\ell^+\ell^-$ and $B\to πππ$ decays. We employ the correlation functions where a dipion isospin-one state is interpolated by the vector light-quark current. We obtain sum rules where convolutions of the $P$-wave $\bar{B}^0\to π^+π^0$ form factors with the time-like pion vector form factor are related to universal $B$-meson distribution amplitudes. These sum rules are valid in the kinematic regime where the dipion state has a large energy and a low invariant mass, and reproduce analytically the known light-cone sum rules for $B\to ρ$ form factors in the limit of $ρ$-dominance with zero width, thus providing a systematics for so-far-unaccounted corrections to $B\toρ$ transitions. Using data for the pion vector form factor, we estimate finite width-effects and the contribution of excited $ρ$-resonances to the $B\toππ$ form factors. We find that these contributions amount up to $\sim 20\%$ in the small dipion mass region where they can be effectively regarded as a nonresonant ($P$-wave) background to the $B\toρ$ transition.

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