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.

Production of the Higgs boson, H in association with a massive vector boson, V , i.e., the V H process, plays an important role in the explorations of Higgs physics at the Large Hadron Collider, both for a precise study of Higgs' Standard Model couplings and for probing New Physics. In this publication we present the two-loop corrections in massless quantum chromodynamics (QCD) to the amplitude of the Higgs production associated with a Z boson via the bottom quark-antiquark annihilation channel with a non-vanishing bottom-quark Yukawa coupling, which is a necessary ingredient of the full next-to-nextto-leading-order QCD corrections to the V H process in the five-flavour scheme. The computation is performed by projecting the D-dimensional scattering amplitude directly onto an appropriate set of Lorentz structures related to the linear polarisation states of the Z boson. We provide analytic expressions of the complete set of renormalised polarised amplitudes in terms of polylogarithms of maximum weight four. To give an estimation of the size of contributions from amplitudes considered in this work, we compute numerically the resulting cross sections under the soft-virtual approximation. We also take the opportunity to make a dedicated discussion regarding an interesting subtlety appearing in the conventional form factor decomposition of amplitudes involving axial currents regularised in D dimensions.

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We present the resummed predictions for inclusive cross-section for Drell-Yan (DY) production as well as onshell Z, W± productions at next-to-next-to-next-to leading logarithmic (N3LL) accuracy. Using the standard techniques, we derive the N-dependent coefficients in the Mellin-N space as well as the N-independent constants and match the resummed result through the minimal prescription procedure with the fixed order results. In addition to the standard ln N exponentiation, we study the numerical impacts of exponentiating N-independent part of the soft function and the complete $$ {\overline{g}}_0 $$ g ¯ 0 that appears in the resummed predictions in N space. All the analytical pieces needed in these different approaches are extracted from the soft-virtual part of the inclusive cross section known to next-to-next-to-next-to leading order (N3LO). We perform a detailed analysis on the scale and parton distribution function (PDF) variations and present predictions for 13 TeV LHC for the neutral Drell-Yan process as well as onshell charged and neutral vector boson productions.

We present the first results on the two-loop massless QCD corrections to the four-point amplitude $$ b+\overline{b}\to H+H $$ b + b ¯ → H + H in the five flavor scheme, treating bottom quarks as massless. This amplitude is sensitive to the trilinear Higgs boson coupling. Our two-loop result for this amplitude constitutes of purely virtual contributions to the next-to-next-to-leading order QCD predictions for the production of a pair of Higgs bosons at the Large Hadron Collider. Using these two loop amplitudes and exploiting the universality of the soft contributions in perturbative QCD, we obtain the NNLO QCD effects in the soft plus virtual approximation. We find that the inclusion of higher order terms reduce the uncertainties resulting from the unphysical renormalisation and factorisation scales.