In the Standard Model (SM) of the elementary particles, the interactions among the known fundamental fermions (leptons and quarks) are mediated through gauge bosons which obey the symmetry: SU(3) {circle_times} SU(2) {circle_times} U(1). More precisely, the electroweak interaction [4-6] is described by a gauge symmetry SU(2) {circle_times} U(1) which is broken spontaneously. The electroweak symmetry breaking is implemented by the introduction of a complex scalar Higgs field which has a non-zero vacuum expectation value (vev). This way, the lagrangian of the theory remains invariant under SU(2) transformations, but quantization of the fields must start from a ground state which does not exhibit this symmetry, and therefore the full symmetry of the lagrangian is not manifest. Invariance of the theory under local SU(2) transformations implies the presence of vectorial gauge fields which mediate the electroweak interactions. The so called spontaneous symmetry breaking allows the quanta of these gauge fields, the W and Z bosons, to acquire a finite mass. The photon, the particle which mediates the electromagnetic interaction, remains massless. The Higgs boson is one of only two particles in the SM which have not yet been directly observed (the other is the {nu}{sub {tau}}, although there is indirect evidence of its existence). Although the SM does not predict the Higgs mass, a lower limit {approx} 100 GeV/c{sup 2} is set by LEPII data, and theoretical considerations prefer Higgs masses not higher than a few hundred GeV/c{sup 2}. At the Tevatron, a search for the Higgs boson is hard due to the small production cross section and the huge backgrounds that do not allow to see the signal clearly. It is still interesting, however, to perform sensitivity studies at the Tevatron. The easiest production channel to observe at the Tevatron is the associated production of Higgs with weak (W or Z) bosons. The Higgs boson coupling to the fermions increases with fermion mass, so the most likely decay in the mass range they are interested, M(H{sup 0}) {approx} 100 GeV/c{sup 2}, in is H {yields} b{bar b}. There are different possible final states depending on the decay of the associated vector boson: two jets plus lepton plus missing transverse energy (leptonic channel) and four jets (hadronic channel). In the former, the presence of a highly energetic, isolated lepton makes it relatively easy to reduce the background, while the latter has a larger production cross section times branching fraction, but it also has a huge amount of irreducible QCD background. CDF has searched for the Higgs boson in both final states, setting upper limits on the production cross sections.
