At a hadron collider, diphoton （γγ） production allows de-tailed studies of the Standard Model （SM）, as well as as searches for new phenomena, such as new heavy resonances, extra spatial dimensions or cascade decays of heavy new particles. Within the SM, continuumγγ+X production is characterized by a steeply-fallingγγmass spectrum, on top of which a heavy resonance decaying intoγγcan potentially be observed. In particular, this is considered one of the most promising discovery channels for a SM Higgs boson at the LHC, despite the small branching ratio of BR （H→γγ）-0.2% for 110<MHiggs<140 GeV. At the Tevatron, the dominant SM Higgs boson production mechanism is gluon fusion, followed by associated production with a W or Z boson, and vector boson fusion. While the SM Higgs produc-tion rate at the Tevatron is not sufficient to observe it in theγγmode, the Hgg and Hγγcouplings, being loop-mediated, are par-ticularly sensitive to new physics effects. Furthermore, in some models beyond the SM, for instance, fermiophobic Higgs, with no couplings to fermions, the BR （H→γγ） can be enhanced significantly relative to the SM prediction, while has the SM-like production cross sections except the gluon fusion is absent.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 D（?） RunⅡdata, collected at the Fermilab Tevatron collider from April 2002 to December 2008. Good agreement between the data and the SM background prediction is observed. Since there is no evi-dence for new physics, we set 95% C.L. limits on the production cross section times the branching ratio （σ×BR（H→γγ）） rela-tive to the SM-like Higgs prediction for different assumed Higgs masses. The observed limits （?） range from 11.9 to 35.2 for Higgs masses from 100 to 150 GeV, while the expected lim-its range from 17.5 to 32.0. This search is also interpreted in the context of the particular fermiophobic Higgs model. The corre-sponding results have reached the same sensitivity as a single LEP experiement, setting a lower limit on the fermiophobic Higgs of Mhf>102.5 GeV（Mhf> 107.5 GeV expected）. We are slightly below the combined LEP limit （Mhf> 109.7 GeV）. We also pro-vide access to the Mhf> 125 GeV region which was inaccessible at LEP.During the study, we found the major and irreducible back-ground directγγ（DPP） production is not well modelled by the current theoretical predictions:RESBOS,DIPHOXorPYTHIA. There is-20% theoretical uncertainty for the predicted values. Thus, for our Higgs search, we use the side-band fitting method to es-timate DPP contribution directly from the data events. Further-more, DPP production is also a significant background in searches for new phenomena, such as new heavy resonances, extra spa-tial dimensions, or cascade decays of heavy new particles. Thus, precise measurements of the DPP cross sections for various kine-matic variables and their theoretical understanding are extremely important for future Higgs and new phenomena searches.In this thesis, we also present a precise measurement of the DPP single differential cross sections as a function of the dipho-ton mass, the transverse momentum of the diphoton system, the azimuthal angle between the photons, and the polar scattering an-gle of the photons, as well as the double differential cross sections considering the last three kinematic variables in three diphoton mass bins, using 4.2 fb-1 data. These results are the first of their kind at D（?） RunⅡ, and in fact the double differential mea-surements are the first of their kind at Tevatron. The results are compared with different perturbative QCD predictions and event generators.