Higher order corrections and soft gluon resummation in perturbative QCD[HBNI Th137]

Abstract

With the increasing accurate measurements of various observables at the Large Hadron Collider (LHC), precise theoretical predictions are of paramount importance which will help not only to understand the Standard Model (SM) better but also to constrain various observables beyond the SM (BSM) scenarios. In this light, the main aim of this thesis is to provide precise theoretical predictions to some important observables at the LHC. This thesis is divided into two parts: the first part deals with the QCD radiative corrections to few important field theory quantities in BSM and the second part discusses threshold resummation to one of the very important observables called rapidity distribution associated with the Higgs boson production. After giving a brief introduction, in the second chapter, we have presented two-loop massless virtual corrections to the decay of a pseudo-scalar Higgs boson to three gluons and also to quark, anti-quark and a gluon in an effective field theory framework. We perform our computation in dimensional regularization and use minimal subtraction scheme to renormalize strong coupling constant as well as composite operators. To put a check on our computation, we have compared the infrared (IR) pole part of ultra violet (UV) renormalized amplitude against the prediction given by Catani and found agreement. With appropriate crossing, these amplitudes are well suited for predicting the differential distribution of a pseudo-scalar production associated with a jet in hadron colliders up to next-to-next-to-leading order in strong coupling constant. In the next chapter, we have calculated for the first time the third order corrections to the on-shell form factor (FF) of the Konishi operator in N=4 super Yang-Mills (SYM) theory using Feynman diagrammatic approach in modified dimensional reduction scheme. We have shown the advantage of dimensional reduction scheme over four dimensional helicity scheme for the composite operators which are not protected by supersymmetry such as the Konishi. In the fourth chapter, we went on to calculate three point FFs in N=4 SYM theory for both the half-BPS and the Konishi operators at two loops level between two different sets of final states. Exploiting the factorization property of the IR singularities, we determine two-loop finite remainders of them. We find that the finite remainders of FFs of the half-BPS operator for both the choices of final states give not only identical results but also contain terms of uniform transcendentality of weight two and four at one and two loop levels, respectively. However, in the case of the Konishi operator, the finite remainders depend on the external states and do not exhibit uniform transcendentality. We have also observed some beautiful connections between the scattering amplitudes in QCD and in N=4 SYM theory after modifying the color factor of the former in a specific way. Before concluding in sixth chapter, fifth chapter of the thesis deals with the threshold resummation technique and its application to a very important observable in the context of the Higgs boson production at the LHC. Inclusive production of the Higgs boson in the final state has been studied both in fixed order as well as in resummed frameworks. The perturbative predictions for differential observables like rapidity, transverse momentum distributions are underway. In this chapter, we have demonstrated how the threshold resummation in the rapidity distribution of the Higgs production helps to stabilise the perturbative predictions as well as reduce theoretical uncertainties resulting from unphysical scales such as renormalization and factorization scales.