QCD Corrections and Resummation Beyond Threshold in Hadronic Collisions [HBNI Th196]

Abstract

This thesis mainly focus on the perturbative calculations of hadronic cross sections in Quantum Chromodynamics (QCD).

I study the infrared structure of the form factor and inclusive real emission cross section that contribute to inclusive production of color neutral states, namely Drell-Yan and Higgs boson in bottom quark annihilation, in the threshold limit. I also compute the mixed gauge group anomalous dimensions and universal quantities, that contribute to the threshold gross section.

I provide the analytic results of two-loop massless QCD corrections to the b-quark- induced ZH process involving non-vanishing b-quark Yukawa coupling λ b. I perform this computation by projecting the D-dimensional scattering amplitude directly onto a set of Lorentz structures related to the linear polarization states of the Z boson. Through this computation I conclude, that for physical observables, an ultimate D-dimensional form factor decomposition of amplitudes is not necessary rather an acrobatic version of axial form factor decomposition, adopted for this computation, is sufficient. This conclusion has the potential to simplify multi-loop calculations, particularly those involving axial coupling regularized in D dimensions.

I study the impact of threshold resummation for the production of Higgs Boson via bot- tom quark annihilation at next-to-next-to-next-to-leading logarithmic (N 3 LL) accuracy. I determine the third order QCD correction to the process dependent constant in the re- summed expression using the three loop bottom quark form factor and third order quark soft distribution function. At N 3 LO+N 3 LL, I predict the cross-section for different center- of-mass energies and also study the renormalization scale dependence at the same order.

With the understanding of threshold logarithms and their high energy resummation, I ex- plore the territory of next-to-threshold contributions to rapidity distribution for Drell-Yan, Higgs boson production through gluon fusion and bottom quark annihilation. Using IR factorization and solutions from the renormalization group equations, I develop a formal- ism which accounts for both soft-virtual (SV) and next-to-SV (NSV) logarithms for the diagonal channels. I present an ansatz, the soft-collinear function, which has the correct logarithmic structure to account for soft and collinear contributions from the differential real emission cross section. This ansatz along with the other threshold components plays a crucial role in predicting the NSV logarithms to all-orders. I present the first results for all the NSV terms till third order for DY and Higgs boson in bottom quark annihilation. I also compute the first three NSV logarithms till a 7 s for all the aforementioned processes. I also present the integral representation of the NSV improved solution which resums these logarithms. The resummed exponents which sums up SV and NSV logarithms till N 2 LL accuracy is also included in this thesis.