The Precise Study Of The H~0W~+W~- Coupling And J/ψ Production Associated With A W/Z Boson At High-energy Colliders

Although the Standard Model (SM) achieves great success, the Higgs boson hasnot been discovered yet. The search for the Higgs boson and exploring the electroweaksymmetrybreakingmechanismarethemainmissionsforpresentandfuturehigh-energyexperiments. In order to reconstruct Higgs potential, the precise study of the couplingsbetween Higgs boson and other particles are necessary and their observable predictionswill provide strong support for exploring the new physics beyond the SM.In this thesis, we calculate the next-to-leading-order (NLO) Quantum Chromody-namics (QCD) and electroweak (EW) radiative corrections to Higgs boson productionassociatedwith a W boson pair at the LargeHadron Collider (LHC)and the Internation-al Linear Collider (ILC), respectively. We present the accurate theoretical predictionsfor the integrated cross sections, the distributions of invariant mass of W boson pairand the transverse momenta of final W and Higgs boson up to NLO. We find that theNLOQCDcorrectionstotheH0W+W? productionprocessattheLHCcanreach50%,and the NLO EW corrections to the H0W+W? production process at the ILC can alsoreach ?19% at most. Those corrections must be considered in the future experiments.The precise predictions for the Higgs production associated with a W pair at the LHCand the ILC will be very useful for probing the Higgs coupling with W bosons. Inthe calculations of the NLO corrections, we use dimensional regularization method toregularizetheinfrared(IR)divergences. Wegivealltheanalyticformulasofscalarone-loop integrals with the IR divergences in the virtual correction, and adopt the two-cutoffphase space slicing (TCPSS) method to isolate the IR divergences for the real emissionprocess.The decay and production of heavy quarkonium are important topics in heavyquarkonium physics. Non-relativistic quantum chromodynamics (NRQCD) is an at-tractive theory in heavy quarkonium physics. An important feature of the NRQCD isthe prediction of Color Octet. In order to investigate the effects of the Color OctetMechanism (COM) in heavy quarkonium, it is an urgent task to study the processeswhich heavily depend on the production mechanism. The J/ψproduction associatedwith a gauge boson at LHC, is a suitable process for studying COM. In high-energycollider experiments, W±, Z0 and J/ψcan be identified by using their purely leptonicdecays, whichareparticularlyusefulinhadroncolliders, becausetheyprovideanheavysuppression of the background. Recently, substantial progress has been achieved in the calculation of high order QCD corrections to J/ψhadroproduction and we find that theNLO effects are usually significant. In this thesis, we calculate the NLO QCD correc-tions to the associated J/ψproduction with a gauge boson in the NRQCD at the LHC.We present the distribution of the transverse momenta of J/ψand the correspondingK-factor. For the process pp→J/ψ+ W + X, we find that when we take into ac-count both the NLO short-distance part and long-distance matrix contributions, the IRdivergences can be completely eliminated.In this thesis, there are the following innovations:Inthisthesis,wehavesystematicallystudiedtheHiggsproductionassociatedwitha W pair at the high-energy collider, and calculated NLO QCD and electroweakcross sections at LHC and ILC, respectively. We present the most accurate the-oretical predictions of this process so far, which will provide theoretical supportfor the test of the H0W+W? coupling at the LHC and the ILC.We use dimensional regularization (D = 4?2?) to regularize the IR divergencesand give all the related analytical formulas of bubble, triangle and box integralswithinfrareddivergences. WefirstaddedtheseanalyticalresultstotheLoopToolsprogram, which can also be applicable to other processes.Inthisthesis, wefirstcalculatetheJ/ψproductionassociatedwithagaugebosonat the LHC up toαs3v7 order within the NRQCD framework, which is useful forstudying COM and the universal LDMEs. Here, we use the dimensional regu-larization method to regularize UV and IR divergences. As the structures of theIR divergences are very complex, we have analyzed the IR divergences from allparts, and demonstrated an overview of the IR singularity structure.