Abstract
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}_qright) 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.
Highlights
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 αsn ln2n−1(mH /mq) to all orders in the strong coupling constant
We present the analysis of the light quark loop mediated gg → H amplitude in the next-to-leading logarithmic approximation which sums up the terms of the form αsn ln2n−1(mH /mq) to all orders in perturbation theory and use this result for the evaluation of the bottom quark effect on the Higgs boson production cross section near the threshold
We have derived the all-order next-to-leading logarithmic approximation for the light quark loop mediated amplitude of Higgs boson production in gluon fusion. To our knowledge this is the first example of the subleading logarithms resummation for a power-suppressed QCD amplitude
Summary
The logarithmically enhanced contributions under consideration appear in the high-energy or small-mass limit of the on-shell gauge theory amplitudes. The characteristic feature of the gg → H amplitude is that it vanishes in the limit of the massless quark mq → 0 i.e. is power-suppressed. The asymptotic behavior of the power suppressed amplitudes may be significantly different from the Sudakov case and attract a lot of attention in many various contexts At the same time the logarithmically enhanced corrections to the on-shell (or almost on-shell) amplitudes in the high energy limit are universally associated with the emission of the virtual particles which are soft and/or collinear to the large external momenta.
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