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We sketch how the R*-operation can be used to compute the pole terms of Feynman diagrams. We identify computational difficulties when performing five-loop calculations, and provide four solutions that drastically reduce the number of terms that are generated. Using these methods, we have computed the beta function for Yang-Mills theory with fermions, the R-ratio in electron-positron annihilation, and Higgs decays to quarks and gluons at five-loop accuracy. The results for the beta function and Higgs decay width to gluons in the heavy-top limit are briefly discussed. There is no need for six-loop extensions of these calculations in the near future.
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We provide an update on a long-term project that aims at evaluating massive vacuum integrals at the five-loop frontier, with high precision and in various space-time dimensions. A number of applications are sketched, mainly concerning the determination of anomalous dimensions, for quantum field theories in four, three and two dimensions.
Recently, the deviation of the ratios $R(D)$, $R(D^{*})$ and $R(J/psi)$ have been found between experimental data and the Standard Model predictions, which may be the hint of New Physics. In this work, we calculate these ratios within the Standard Model by using the improved instantaneous Bethe-Salpeter method. The emphasis is pad to the relativistic correction of the form factors. The results are $R(D)=0.312 ^{+0.006}_{-0.007}$, $R(D^*)= 0.249^{+0.001}_{-0.002}$, $R(D_s)=0.320 ^{+0.009}_{-0.009}$, $R(D^*_s)=0.251 ^{+0.002}_{-0.003}$, $R(eta_c)=0.384 ^{+0.032}_{-0.042}$, and $R(J/psi)=0.267 ^{+0.009}_{-0.011}$, which are consistent with predictions of other models and the experimental data. The semileptonic decay rates and corresponding form factors at zero recoil are also given.
We briefly review numerical methods for calculations beyond one loop and then describe new developments within the method of sector decomposition in more detail. We also discuss applications to two-loop integrals involving several mass scales.
We discuss the impact of the recent $mathcal{O}(alpha_s^3)$ calculations of the semileptonic width of the $b$ quark and of the relation between pole and kinetic heavy quark masses by Fael et al. on the inclusive determination of $|V_{cb}|$. The most notable effects are a small increase in the value $|V_{cb}|$ and a reduction of the uncertainty. Our final result is $|V_{cb}|=42.16(50), 10^{-3}$.
In this talk, the program package GOSAM is presented, which can be used for the automated calculation of one-loop amplitudes for multi-particle processes. The integrands are generated in terms of Feynman diagrams and can be reduced by d-dimensional integrand-level decomposition, or tensor reduction, or a combination of both. Through various examples we show that GOSAM can produce one-loop amplitudes for both QCD and electroweak theory; model files for theories Beyond the Standard Model can be linked as well.
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