Quark Transverse Beam Function At N~3LO And Energy Correlation At NLO

The Large Hadron Collider(LHC)at the European Organization for Nuclear Research(CERN)has accumulated a large amount of experimental data.But through the detailed analysis of these data,there is still no sign of the existence of new physics.Therefore,it is becoming more and more important to accurately test the standard model and find small deviations with the experimental data.Strong interactions are ubiquitous at the LHC and quantum chromodynamics(QCD)is the most successful theory describing strong interactions.Therefore,QCD plays an indispensable role at the LHC.Regarding LHC physics,the accuracy of the standard model depends on the accuracy of QCD to some extent.To improve the accuracy of QCD's theoretical predictions,we need to consider several different aspects.This thesis focuses on the theme of high-order precision calculation in perturbation theory,and calculates the high-order correction effects of several observables.The main contents are as follows:The existence of the measurement function in the energy-energy correlation function(EEC)makes the traditional methods of calculating Feynman integrals no longer applicable,which has led to no significant breakthroughs in the analytical calculation of EEC for nearly 40 years.After proposing a set of generalized integration-by-part equations in this thesis,this problem has been completely solved,and for the first time the fully analytical results of EEC at the next-to-leading order in QCD have been obtained.The results obtained have an extremely simple and beautiful mathematical structure,and the asymptotic expansion of its endpoints can provide useful data for factorization and power correction in the corresponding regions.The developed method is also directly applied to calculate the energy correlation function for gluon-initiated Higgs decays,which is important for the study of Higgs physics;Suffering from the rapidity divergences,the calculation of transverse momentum dependent(TMD)beam function is non-trivial.In this thesis,we used the exponential regulator to regulate the rapidity divergences,and proposed a novel generalized integration-by-parts equation to deal with the exponential propagator for the first time.A series of self-written automatic code made this extremely complicated calculation possible.Finally,we were able to obtain the fully analytical results for quark TMD beam function at next-to-next-to-next-to leading order(N3LO)in QCD.Our results are for all color structures and all partonic channels.Though the intermediate calculation process is extremely complicated,the results are rather simple.These results represent the last missing ingredient for qT subtraction to obtain the fully differential distribution of Drell-Yan process at N3LO.Through analytic continuation,the TMD fragmentation function can be obtained from TMD beam function.In the mean while,the EEC in the back-to-back limit can be related with TMD fragmentation function through a factorization formula.These relations make the several seemingly different works closely related and the results have been cross checked with each other.