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RG improved Higgs boson production to N$^3$LO in QCD

The recent result on the third order correction to the Higgs boson production through gluon fusion by Anastasiou et al. [1] not only provides a precise prediction with reduced scale uncertainties for studying the Higgs boson properties but also establishes the reliability of the perturbative QCD. In this letter, we propose a novel approach to further reduce the uncertainty arising from the renormalization scale by systematically resumming the renormalization group (RG) accessible logarithms to all orders in the strong coupling constant. Our numerical study based on this approach, demonstrates a significant improvement over the fixed order predictions.