We present an accurate theoretical prediction for the production of Higgs boson through bottom quark annihilation at the LHC up to next-to-next-to-next-to leading order (N 3 LO) plus next-to-next-to-next-to-leading logarithmic (N 3 LL) accuracy. We determine the third order perturbative Quantum Chromodynamics (QCD) correction to the process dependent constant in the resummed expression using the three loop bottom quark form factor and third order quark soft distribution function. Thanks to the recent computation of N 3 LO corrections to this production cross-section from all the partonic channels, an accurate matching can be obtained for a consistent predictions at N 3 LO+N 3 LL accuracy in QCD. We have studied in detail the impact of resummed threshold contributions to inclusive cross-sections at various centre-of-mass energies and also discussed their sensitivity to renormalization and factorization scales at next-to-next-to leading order (NNLO) matched with next-to-next-to leading logarithm (NNLL). At N 3 LO+N 3 LL, we predict the cross-section for different centre-of-mass energies using the recently available results in [1] as well as study the renormalization scale dependence at the same order.

We study the threshold corrections for inclusive deep-inelastic scattering (DIS) and their all-order resummation. Using recent results for the QCD form factor, related anomalous dimensions and Mellin moments of DIS structure functions at four loops we derive the complete soft and collinear contributions to the DIS Wilson coefficients at four loops. For a general SU (n c ) gauge group the results are exact in the large-n c approximation and for QCD with n c = 3 we present precise approximations. We extend the threshold resummation exponent G N in Mellin-N space to the fifth logarithmic (N 4 LL) order collecting the terms α 3 s (α s ln N ) n to all orders in the strong coupling constant α s . We study the numerical effect of the N 4 LL corrections using both the fully exponentiated form and the expansion of the coefficient function in towers of logarithms. As a byproduct, we derive a numerical result for the complete pole structure of the QCD form factor in the parameter of dimensional regularization ε at four loops.

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