At a hadron collider，diphoton (γγ）production allows detailedstudies of the Standard Model (SM)，as well as as searchesfor new phenomena，such as new heavy resonances，extra spatialdimensions or cascade decays of heavy new particles. Within theSM，continuum γγ+X production is characterized by a steeplyfallingγγ mass spectrum，on top of which a heavy resonancedecaying into γγ can potentially be observed. In particular，thisis considered one of the most promising discovery channels for aSM Higgs boson at the LHC，despite the small branching ratio ofBR (H →γγ)～0.2％ for 110 In this thesis，we present a search for a light Higgs boson in the diphoton final state using 4.2±0.3 fb?1 of the DφRun Iidata，collected at the Fermilab Tevatron collider from April 2002to December 2008. Good agreement between the data and theSM background prediction is observed. Since there is no evidencefor new physics，we set 95％ C.L. Limits on the productioncross section times the branching ratio (σ×BR(H →γγ)）relativeto the SM-like Higgs prediction for different assumed Higgsmasses. The observed limits (σ(limit)/σ(SM)）range from 11.9 to 35.2for Higgs masses from 100 to 150 GeV，while the expected limitsrange from 17.5 to 32.0. This search is also interpreted in thecontext of the particular fermiophobic Higgs model. The correspondingresults have reached the same sensitivity as a single LEPexperiement，setting a lower limit on the fermiophobic Higgs ofMhf>102.5 GeV (Mhf>107.5 GeV expected). We are slightlybelow the combined LEP limit (Mhf>109.7 GeV).We also provideaccess to theMhf>125 GeV region which was inaccessibleat LEP. During the study，we found the major and irreducible backgrounddirect γγ (DPP）production is not well modelled by thecurrent theoretical predictions：RESBOS，DIPHOX or PYTHIA. Thereis ～20％ theoretical uncertainty for the predicted values. Thus,for our Higgs search，we use the side-band fitting method to estimateDPP contribution directly from the data events. Furthermore,DPP production is also a significant background in searchesfor new phenomena，such as new heavy resonances，extra spatialdimensions，or cascade decays of heavy new particles. Thus,precise measurements of the DPP cross sections for various kinematicvariables and their theoretical understanding are extremelyimportant for future Higgs and new phenomena searches. In this thesis，we also present a precise measurement of theDPP single differential cross sections as a function of the diphotonmass，the transverse momentum of the diphoton system，theazimuthal angle between the photons，and the polar scattering angleof the photons，as well as the double differential cross sectionsconsidering the last three kinematic variables in three diphotonmass bins，using 4.2 fb?1 data. These results are the first oftheir kind at D? Run II，and in fact the double differential measurementsare the first of their kind at Tevatron. The results arecompared with different perturbative QCD predictions and eventgenerators.
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