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arXiv 2004.09527hep-phhep-ex
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Darwin算符对重夸克非轻子衰变的贡献

Contribution of the Darwin operator to non-leptonic decays of heavy quarks

Alexander Lenz, Maria Laura Piscopo, Aleksey V. Rusov

摘要:

我们计算了达尔文算符对$B$介子($B^+$、$B_d$或$B_s$)的包容性非轻子衰变宽度的贡献($1/m_b^3$修正),这些衰变源于夸克变味跃迁$b \to q_1 \bar q_2 q_3$,其中$q_1,q_2 = u, c$和$q_3 = d, s$。计算的核心思想是夸克传播子在外胶子场中的局域展开,包括胶子场强度张量的协变导数项和重夸克展开(HQE)的标准技术。我们确认以前已知的表达式的$1/m_b^3$贡献的半轻子衰变$b \to q_1 \ell \bar ν_\ell$,与$\ell = e, μ, τ$和$1/m_b^2$的贡献的非轻子模式。我们发现这个新项可以对$B$介子的非轻子衰变宽度给出约$- 4 \, \%$的相当大的修正。对于$B_d$和$B_s$介子,这是对自由b夸克衰变的主要修正,而对于$B^+$介子,达尔文项给出了第二重要的修正--大约是相空间增强的泡利干涉贡献的1/2到1/3。由于寿命测量中微小的实验不确定性,达尔文项的贡献对于标准模型的精度测试至关重要。

英文摘要:

We compute the Darwin operator contribution ($1/m_b^3$ correction) to the width of the inclusive non-leptonic decay of a $B$ meson ($B^+$, $B_d$ or $B_s$), stemming from the quark flavour-changing transition $b \to q_1 \bar q_2 q_3$, where $q_1,q_2 = u, c$ and $q_3 = d, s$. The key ideas of the computation are the local expansion of the quark propagator in the external gluon field including terms with covariant derivative of the gluon field strength tensor and the standard technique of the Heavy Quark Expansion (HQE). We confirm the previously known expressions of the $1/m_b^3$ contributions to the semi-leptonic decay $b \to q_1 \ell \bar ν_\ell$, with $\ell = e, μ, τ$ and of the $1/m_b^2$ contributions to the non-leptonic modes. We find that this new term can give a sizeable correction of about $- 4 \, \%$ to the non-leptonic decay width of a $B$ meson. For $B_d$ and $B_s$ mesons this turns out to be the dominant correction to the free b-quark decay, while for the $B^+$ meson the Darwin term gives the second most important correction - roughly 1/2 to 1/3 of the phase space enhanced Pauli interference contribution. Due to the tiny experimental uncertainties in lifetime measurements the incorporation of the Darwin term contribution is crucial for precision tests of the Standard Model.

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