Light Quark Mediated Higgs Boson Threshold Production in the Next-to-Leading Logarithmic Approximation

We study the amplitude of the Higgs boson production in gluon fusion mediated by a light quark loop and evaluate the logarithmically enhanced radiative corrections to the next-to-leading logarithmic approximation which sums up the terms of the form $$ {\alpha}_s^n{\ln}^{2n-1}\left({m}_H/{m}_q\right) $$ to all orders in the strong coupling constant. This result is used for the calculation of the process cross section near the production threshold and gives a quantitative estimate of the three and four-loop bottom quark contribution to the Higgs boson production at the Large Hadron Collider.