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arXiv 0905.2729hep-ph
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B介子分布振幅的OPE和5维HQET算符

OPE for B-meson distribution amplitude and dimension-5 HQET operators

Hiroyuki Kawamura, Kazuhiro Tanaka

摘要:

$B$ -介子光锥分布振幅(LCDA)是重夸克有效理论(HQET)中夸克-反夸克双局域光锥算符的矩阵元,是$B$ -介子衰变的QCD因子化公式的基础。当相应的双局域HQET算符在夸克场和反夸克场之间具有类光距离$t$时,尺度$\sim 1/t$将紫外区和红外区分开,分别导致辐射修正中的尖点奇异性和非微扰修正中的多粒子态混合.我们处理的双局域HQET算子的基础上的运营商的产品展开(OPE),解开奇异的红外和紫外区域系统。在下一个到领先的顺序$α_s$的匹配是在$\overline{\rm MS}$计划与一套完整的本地运营商的尺寸$d \le 5$,通过一个明显的规范不变的计算组织在坐标空间中的所有贡献。结果显示了Wilson系数与Sudakov型双算符和高维算符与附加胶子的关系。用$\barΛ= m_B - m_b$和两个附加的HQET参数作为5维算符的矩阵元,得到了$t$小于$\sim 1$ GeV $^{-1}$的$B$介子LCDA.这些新的HQET参数的影响有关的独家$B$衰变,$λ_B$的积分,也进行了讨论。

英文摘要:

The $B$-meson light-cone distribution amplitude (LCDA) is defined as the matrix element of a quark-antiquark bilocal light-cone operator in the heavy-quark effective theory (HQET) and is a building block of QCD factorization formula for exclusive $B$-meson decays. When the corresponding bilocal HQET operator has a light-like distance $t$ between the quark and antiquark fields, the scale $\sim 1/t$ separates the UV and IR regions, which induce the cusp singularity in radiative corrections and the mixing of multiparticle states in nonperturbative corrections, respectively. We treat the bilocal HQET operator based on the operator product expansion (OPE), disentangling the singularities from the IR and UV regions systematically. The matching at the next-to-leading order $α_s$ is performed in the $\overline{\rm MS}$ scheme with a complete set of local operators of dimension $d \le 5$, through a manifestly gauge-invariant calculation organizing all contributions in the coordinate space. The result exhibits the Wilson coefficients with Sudakov-type double logarithms and the higher-dimensional operators with additional gluons. This OPE yields the $B$-meson LCDA for $t$ less than $\sim 1$ GeV$^{-1}$, in terms of $\barΛ= m_B - m_b$ and the two additional HQET parameters as matrix elements of dimension-5 operators. The impact of these novel HQET parameters on the integral relevant to exclusive $B$ decays, $λ_B$, is also discussed.

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