30 years, some 700 integrals, and 1 dessert, or: Electroweak two-loop corrections to the Zbb vertex
30 years, some 700 integrals, and 1 dessert, or: Electroweak two-loop corrections to the Zbb vertex
复制标题
30 年，大约 700 个积分和 1 个甜点，或者：对 Zbb 顶点的电弱二环校正
DOI：
10.1007/jhep11(2013)111
复制
发表时间：
2016
影响因子：
5.4
通讯作者：
J. Usovitsch
中科院分区：
文献类型：
--
作者：
I. Dubovyk;A. Freitas;J. Gluza;T. Riemann;J. Usovitsch
The one-loop corrections to the weak mixing angle $\sin^2\theta_{eff}^b$ derived from the $Z{\bar b}b$ vertex, are known since 1985. It took another 30 years to calculate the complete electroweak two-loop corrections to $\sin^2\theta_{eff}^b$. The main obstacle was the calculation of the O(700) bosonic two-loop vertex integrals with up to three mass scales, at $s=M_Z^2$. We did not perform the usual integral reduction and master evaluation, but chose a completely numerical approach, using two different calculational chains. One method relies on publicly available sector decomposition implementations. Further, we derived Mellin-Barnes (MB) representations, exploring the publicly available MB suite. We had to supplement the MB suite by two new packages: AMBRE~3, a Mathematica program, for the efficient treatment of non-planar integrals and MBnumerics for advanced numerics in the Minkowskian space-time. Our preliminary result for LL2016, the"dessert", for the electroweak bosonic two-loop contributions to $\sin^2\theta_{eff}^b$ is: $\Delta \sin^2\theta_{eff}^{b(\alpha^2,\rm bos)} = \sin^2\theta_W ~ \Delta\kappa_b^{(\alpha^2,bos)}$, with $\Delta\kappa_b^{(\alpha^2,bos)} = -1.0276 x 10^{-4}$. This contribution is about a quarter of the corresponding fermionic corrections and of about the same magnitude as several of the known higher-order QCD corrections. The $\sin^2\theta_{eff}^b$ is now predicited in the Standard Model with a relative error of $10^{-4}$ [1].
The one-loop corrections to the weak mixing angle $\sin^2\theta_{eff}^b$ derived from the $Z{\bar b}b$ vertex, are known since 1985. It took another 30 years to calculate the complete electroweak two-loop corrections to $\sin^2\theta_{eff}^b$. The main obstacle was the calculation of the O(700) bosonic two-loop vertex integrals with up to three mass scales, at $s=M_Z^2$. We did not perform the usual integral reduction and master evaluation, but chose a completely numerical approach, using two different calculational chains. One method relies on publicly available sector decomposition implementations. Further, we derived Mellin-Barnes (MB) representations, exploring the publicly available MB suite. We had to supplement the MB suite by two new packages: AMBRE~3, a Mathematica program, for the efficient treatment of non-planar integrals and MBnumerics for advanced numerics in the Minkowskian space-time. Our preliminary result for LL2016, the"dessert", for the electroweak bosonic two-loop contributions to $\sin^2\theta_{eff}^b$ is: $\Delta \sin^2\theta_{eff}^{b(\alpha^2,\rm bos)} = \sin^2\theta_W ~ \Delta\kappa_b^{(\alpha^2,bos)}$, with $\Delta\kappa_b^{(\alpha^2,bos)} = -1.0276 x 10^{-4}$. This contribution is about a quarter of the corresponding fermionic corrections and of about the same magnitude as several of the known higher-order QCD corrections. The $\sin^2\theta_{eff}^b$ is now predicited in the Standard Model with a relative error of $10^{-4}$ [1].
DOI：
10.1016/j.cpc.2005.12.009
发表时间：
2005-07
期刊：
Comput. Phys. Commun.
影响因子：
--
作者：
A. Arbuzov;M. Awramik;M. Czakon;A. Freitas;M. Grünewald;K. Mönig;S. Riemann;T. Riemann
通讯作者：
A. Arbuzov;M. Awramik;M. Czakon;A. Freitas;M. Grünewald;K. Mönig;S. Riemann;T. Riemann