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The total cross sections for Higgs production at the Tevatron as a function of the Higgs mass. The MSTW set of PDFs has been used andthe higher order corrections are included as discussed in the text.

The $gg \to H$ cross section at the Tevatron as a function of $M_H$: at NNLO for central scales at $\mu_{0}=M_H$ and $\mu_0= \frac12 M_{H}$ and at NNLL for a scale $\mu_0=M_H$. In the insert, shown are the deviations when one normalizes to $\sigma^{\rm NNLO}_{\rm gg\to H}(\mu_0=\frac12 M_H)$.

Left: the scale dependence of $\sigma^{\rm LO} (gg \to H)$ at the Tevatron as a function of $M_H$ for scale variations $M_H/{\kappa} \le \mu_R, \mu_F \le \kappa M_H$ with $\kappa=2,3,4$ and 5 compared to $\sigma^{\rm NNLO}$ for the central scale choice $\mu_R=\mu_F=M_H$. Right: the scale dependence of $\sigma^{\rm NLO} (gg \to H)$ at the Tevatron as a function of $M_H$ for variations $M_H/{\kappa} \le \mu_R, \mu_F \le \kappa M_H$ with $\kappa=2,3$ and 4 compared to $\sigma^{\rm NNLO}$ evaluated at the central scale $\mu_R=\mu_F=M_H$.

Left: the scale variation of $\sigma^{\rm LO}_{gg\to H}$ as a function of $M_H$ in the domain $ \mu_0/\kappa \leq \mu_R=\mu_F \leq \kappa \mu_0$ for $\mu_0= \frac12 M_H$ with $\kappa=2,3$ and $4$ compared to $\sigma^{\rm NNLO}_{gg\to H} (\mu_R=\mu_F=\frac12 M_H)$. Right: the uncertainty band of $\sigma^{\rm NNLO}_{gg\to H}$ as a function of $M_H$ for a scale variation $\mu_0/\kappa \leq \mu_R= \mu_F \leq \kappa \mu_0$ with $\mu_0=\frac12 M_H$ and $\kappa=3$. In the inserts shown are the relative deviations.

Left: the scale dependence of $\sigma^{\rm LO} (gg \to H)$ at the Tevatron as a function of $M_H$ for scale variations $M_H/{\kappa} \le \mu_R, \mu_F \le \kappa M_H$ with $\kappa=2,3,4$ and 5 compared to $\sigma^{\rm NNLO}$ for the central scale choice $\mu_R=\mu_F=M_H$. Right: the scale dependence of $\sigma^{\rm NLO} (gg \to H)$ at the Tevatron as a function of $M_H$ for variations $M_H/{\kappa} \le \mu_R, \mu_F \le \kappa M_H$ with $\kappa=2,3$ and 4 compared to $\sigma^{\rm NNLO}$ evaluated at the central scale $\mu_R=\mu_F=M_H$.

Left: the scale variation of $\sigma^{\rm LO}_{gg\to H}$ as a function of $M_H$ in the domain $ \mu_0/\kappa \leq \mu_R=\mu_F \leq \kappa \mu_0$ for $\mu_0= \frac12 M_H$ with $\kappa=2,3$ and $4$ compared to $\sigma^{\rm NNLO}_{gg\to H} (\mu_R=\mu_F=\frac12 M_H)$. Right: the uncertainty band of $\sigma^{\rm NNLO}_{gg\to H}$ as a function of $M_H$ for a scale variation $\mu_0/\kappa \leq \mu_R= \mu_F \leq \kappa \mu_0$ with $\mu_0=\frac12 M_H$ and $\kappa=3$. In the inserts shown are the relative deviations.

The uncertainty bands of the NNLO $gg \to H$ cross section at the Tevatron as a function of $M_H$ for scale variation in the domains $\frac13 M_H \le \mu_R,\mu_F \le 3 M_H$ and $\frac12 M_H \le \mu_R, \mu_F \le 2 M_H$.

Left: the $gg\to H$ cross section at NNLO for $\mu_{0}=\frac12 M_{H}$ as a function of $M_H$ when the MSTW, CTEQ and ABKM parameterizations are used. Left: the 90\%CL PDF, PDF+$\Delta^{\rm exp}\alpha_{s}$ and PDF+$ \Delta^{\rm exp+th}\alpha_{s}$ uncertainties on $\sigma^{\rm NNLO}_{gg\to H}$ in the MSTW parametrisation. In the inserts, shown in \% are the deviations with respect to the central MSTW value.

Relative difference (in \%) at Tevatron energies and as a function of $M_H$ between the exact NLO and NNLO $gg\to H$ cross sections $\sigma^{\rm exact}_{\rm NLO/NNLO}$ and the cross section in the effective approach with aninfinite top quark mass $\sigma^{m_t \! \to \! \infty}_{\rm NLO/NNLO}$.

Left: the $gg\to H$ cross section at NNLO for $\mu_{0}=\frac12 M_{H}$ as a function of $M_H$ when the MSTW, CTEQ and ABKM parameterizations are used. Left: the 90\%CL PDF, PDF+$\Delta^{\rm exp}\alpha_{s}$ and PDF+$ \Delta^{\rm exp+th}\alpha_{s}$ uncertainties on $\sigma^{\rm NNLO}_{gg\to H}$ in the MSTW parametrisation. In the inserts, shown in \% are the deviations with respect to the central MSTW value.

Relative difference (in \%) between the complete factorisation and partial factorisation approaches for the electroweak radiative corrections tothe NLO $gg \to H$ cross section at the Tevatron as a function of $M_H$.

The production cross section $\sigma(gg\to H)$ at NNLO for the QCD and NLO for the electroweak corrections at the Tevatron at a central scale $\mu_F=\mu_R= \frac12 M_H$ with the uncertainty band when all theoretical uncertainties are added using our procedure. It is compared to $\sigma(gg \to H)$ at NNLL~\cite{ggH-FG} with the errors quoted by the CDF/D0 collaboration \cite{Tev1}. In the insert, the relative deviations compared to the central value are shown.

The central values and the 90\% CL PDF uncertainty bands in the NNLO cross section $\sigma(gg \to H+X)$ at the Tevatron when evaluated within the MSTW, CTEQ and ABKM schemes. In the insert, shown in percentage are the deviations within a given scheme and the CTEQ and ABKM central values when the cross sections are normalized to the MSTW centralvalue.

Left: the PDF+$\Delta^{\rm exp}\alpha_s$ uncertainties in the MSTW scheme and the PDF uncertainties in the ABKM schemes on the $gg \to H$ cross section at the Tevatron as a function of $M_H$. Right: the PDF+$\Delta^{\rm exp}\alpha_s +\Delta^{\rm th}\alpha_s$ uncertainties in the MSTW scheme using the new set--up and the PDF+$\Delta^{\rm exp}\alpha_s$+$\Delta^{\rm th}\alpha_s$ error in the ABKM scheme using our naive procedure. In the inserts, shown are the same but withthe cross sections normalized to the MSTW central cross section.

Left: the PDF+$\Delta^{\rm exp}\alpha_s$ uncertainties in the MSTW scheme and the PDF uncertainties in the ABKM schemes on the $gg \to H$ cross section at the Tevatron as a function of $M_H$. Right: the PDF+$\Delta^{\rm exp}\alpha_s +\Delta^{\rm th}\alpha_s$ uncertainties in the MSTW scheme using the new set--up and the PDF+$\Delta^{\rm exp}\alpha_s$+$\Delta^{\rm th}\alpha_s$ error in the ABKM scheme using our naive procedure. In the inserts, shown are the same but withthe cross sections normalized to the MSTW central cross section.

Left: the scale dependence of $\sigma(p \bar p \to WH)$ at NLO for variations $M_{HV}/{\kappa} \le \mu_R, \mu_F \le \kappa M_{HV}$ with $\kappa=2,3$ and 4, compared to the NNLO value; in the insert, shown are the variations in percentage and where the NNLO cross section is normalized to the NLO one. Right: the scale dependence of $\sigma( p\bar p \to WH)$ at NNLO for a variation in the domains $M_{HV}/2 \le \mu_R= \mu_F \le 2 M_{HV}$; the relativedeviations from the central value are shown in the insert.

Left: the scale dependence of $\sigma(p \bar p \to WH)$ at NLO for variations $M_{HV}/{\kappa} \le \mu_R, \mu_F \le \kappa M_{HV}$ with $\kappa=2,3$ and 4, compared to the NNLO value; in the insert, shown are the variations in percentage and where the NNLO cross section is normalized to the NLO one. Right: the scale dependence of $\sigma( p\bar p \to WH)$ at NNLO for a variation in the domains $M_{HV}/2 \le \mu_R= \mu_F \le 2 M_{HV}$; the relativedeviations from the central value are shown in the insert.

The central values and the PDF uncertainties in the cross section $\sigma( p \bar p \to WH)$ at the Tevatron when evaluated within the MSTW, CTEQ and ABKM schemes. In the insert, the relative deviations from thecentral MSTW value are shown.

Left: the PDF uncertainties in the MSTW and ABKM schemes when the additional experimental errors on $\alpha_s$ is included in MSTW as discussed in the text; in the insert, the relative deviations from the central MSTW value are shown. Right: the same as in a) but when the theoretical error on$\alpha_s$ is added in both the MSTW and ABKM cases.

Left: the PDF uncertainties in the MSTW and ABKM schemes when the additional experimental errors on $\alpha_s$ is included in MSTW as discussed in the text; in the insert, the relative deviations from the central MSTW value are shown. Right: the same as in a) but when the theoretical error on$\alpha_s$ is added in both the MSTW and ABKM cases.

The production cross section $\sigma(gg\to H)$ at NNLO at the Tevatron with the uncertainty band when all the errors are added using our procedure (last columns of Table 2). It is compared to $\sigma(gg \to H)$ at NNLL when the scale and PDF errors given in Ref.~\cite{ggH-FG} are added in quadrature. In the insert the relative deviations are shown whenthe central values are normalized to $\sigma^{\rm NNLO+EW}$.

The production cross section $\sigma(p \bar p \to WH)$ and $\sigma(p \bar p \to ZH)$ at NNLO in QCD and electroweak NLO at the Tevatron evaluated with the MSTW set of PDFs, together with the uncertainty bands when all the theoretical errors are added. In the insert, the relative deviationsfrom the central MSTW value are shown in the case of $\sigma(p\bar p \to WH)$.