| η$_{jet}$ | < 2 . 5 | η$_{jet}$ | < 2 Process σ$_{LO}$ [fb] σ$_{NLO}$ [fb] σ$_{LO}$ [fb] σ$_{NLO}$ [fb] Higgs + 0 jets 1 . 25 1 . 98 1 . 25 2 . 05 Higgs + 1 jets 0 . 84 1 . 16 0 . 74 1 . 07 Higgs + ≥ 2 jets 0 . 35 0 . 48 0 . 28 0 . 39 TABLE I: Cross section for Higgs + jet production and decay into W $^{−}$( → µ $^{−}$¯ ν ) W $^{+}$( → νe $^{+}$) at √ s = 1 . 96 TeV for M$_{H}$ = µ = 160 GeV. In the second and third columns, only the cuts of Eq. (11) are applied. For the results in the final two columns the more stringent cut, | η$_{jet}$ | < 2 is applied, in order to allow a comparison with Ref. [29]. of the partial width, Γ( W → ℓ ¯ ν ) = G$_{F}$ √$_{2}$ m 2 W 6 π . (10) This ensures that our calculation incorporates the best possible value for the W branching ratio which is determined to about 1%. The values of the total Higgs width are taken from the program hdecay [27], version 3.51. To define the jets we perform clustering according to the k$_{T}$ algorithm [28], with jet definitions detailed further below. IV. TEVATRON RESULTS We use a very simple set of inclusive cuts, with no requirements on the Higgs boson decay products, p$_{t}$ (jet) > 15 GeV , | η$_{jet}$ | < 2 . 5 , R$_{jet}$$_{,}$$_{jet}$ > 0 . 4 . (11) At the Tevatron the search for the Higgs boson has been divided into jet bins. To set the stage for this we show in Table I the expected cross section in each bin due to the gluon fusion mechanism. The parameter µ is the renormalization and factorization scale, which we set equal to m$_{H}$ here. We note that next-to-next-to-leading order (NNLO) results for the Higgs + 0 jet cross section are given in [29], based on the earlier calculations in Refs. [30–32]. From table I columns 3 and 5, we see that the Higgs + ≥ 2 jets bin constitutes about 13% of the cross section for | η$_{jet}$ | < 2 . 5 and 11% with | η$_{jet}$ | < 2. It is interesting to compare the number for the fraction of Higgs + ≥ 2 jet events ( | η$_{jet}$ | < 5