Higgs production in bottom quark annihilation: Transverse momentum distribution at $\mathrm{NNLO}+\mathrm{NNLL}$

We present the inclusive transverse momentum distribution for Higgs bosons produced in bottom quark annihilation at the LHC. The results are obtained in the five-flavor scheme. The soft and collinear terms at small $p_T$ are resummed through NNLL accuracy and matched to the NNLO transverse momentum distribution at large $p_T$. We find that the theoretical uncertainty, derived from a variation of the unphysical scales entering the calculation, is significantly reduced with respect to lower orders.

Figure 1

Transverse momentum spectrum at NLO (blue, dashed line) and at $\mathrm{NLO}+\mathrm{NLL}$ (red, solid line) for (a) $Q=M/2$ and (b) $Q=M/4$. (Here and in the following plots, $m_H=M$ is the Higgs mass.)

Figure 2

(a) Transverse momentum spectrum at NNLO (blue, dashed line) and at $\mathrm{NNLO}+\mathrm{NNLL}$ (red, solid line) for the central scales; (b) only the $b\overline{b}$ channel for that quantity.

Figure 3

Resummed-matched $p_T$ distribution at $\mathrm{NLO}+\mathrm{NLL}$ (blue, dashed line) and $\mathrm{NNLO}+\mathrm{NNLL}$ (red, solid line). Lines are the central scale choices; bands are uncertainties due to ${\mu }_{\mathrm{F}},{\mu }_{\mathrm{R}}$ variation.

Figure 4

Resummed-matched $p_T$ distribution at $\mathrm{NLO}+\mathrm{NLL}$ (blue, dashed line) and $\mathrm{NNLO}+\mathrm{NNLL}$ (red, solid line). Lines are the central scale choices; bands are the uncertainty due to $Q$ variation.

Figure 5

Resummed-matched $p_T$ distribution at $\mathrm{NLO}+\mathrm{NLL}$ (blue, dashed line) and $\mathrm{NNLO}+\mathrm{NNLL}$ (red, solid line). Lines are the central scale choices; bands are the uncertainty due to variation of all scales.

Figure 6

Transverse momentum spectrum using $Q_0=M/4$ (red, solid line) and $Q_0=M/2$ (blue, dashed line) as the central resummation scale. The bands indicate the theoretical uncertainty of the prediction as in Fig. 5. (a) $\mathrm{NNLO}+\mathrm{NNLL}$; (b) $\mathrm{NLO}+\mathrm{NLL}$.

Figure 7

Resummed-matched $p_T$ distribution at (a) $\mathrm{NLO}+\mathrm{NLL}$ and (b) $\mathrm{NNLO}+\mathrm{NNLL}$ for MSTW2008 (blue, dotted line), NNPDF2.3 (red, solid line) and CT10 (black, dash-dotted line). Lines are the central curves; bands are $\mathrm{PDF}+{\alpha }_s$ uncertainties at 68% C.L.

Figure 8

Relative uncertainties (68% C.L.) for the MSTW2008 PDF set of the resummed-matched $p_T$ distribution at $\mathrm{NLO}+\mathrm{NLL}$ (blue, dashed line) and $\mathrm{NNLO}+\mathrm{NNLL}$ (red, solid line).

Figure 9

Relative uncertainties (68% C.L.) for the NNPDF2.3 PDF set of the resummed-matched $p_T$ distribution at $\mathrm{NLO}+\mathrm{NLL}$ (blue, dashed line) and $\mathrm{NNLO}+\mathrm{NNLL}$ (red, solid line).

Figure 10

Relative uncertainties (68% C.L.) for the CT10 PDF set of the resummed-matched $p_T$ distribution at $\mathrm{NLO}+\mathrm{NLL}$ (blue, dashed line) and $\mathrm{NNLO}+\mathrm{NNLL}$ (red, solid line).

Figure 11

A sample of Feynman diagrams for $b\overline{b}\to H$ contributing to the NNLO cross section at $p_T=0$. (a) LO, (b) one loop and (c) two loop.

Figure 12

A sample of Feynman diagrams for $b\overline{b}\to H$ contributing to the NNLO cross section at $p_T>0$. (a-b) single-real, (c-e) double-real, (f) mixed real-virtual.

Figure 13

Resummed-matched $p_T$ distribution at $\mathrm{NLO}+\mathrm{NLL}$ (blue, dashed line) and $\mathrm{NNLO}+\mathrm{NNLL}$ (red, solid line). Lines are central scale choices; bands are uncertainties due to ${\mu }_{\mathrm{F}},{\mu }_{\mathrm{R}}$ variation. (Same as Fig. 3, but for $\sqrt{s}=13\mathrm{T}\mathrm{e}\mathrm{V}$.)

Figure 14

Resummed-matched $p_T$ distribution at $\mathrm{NLO}+\mathrm{NLL}$ (blue, dashed line) and $\mathrm{NNLO}+\mathrm{NNLL}$ (red, solid line). Lines are central scale choices; bands are uncertainties due to $Q$ variation. (Same as Fig. 4, but for $\sqrt{s}=13\mathrm{T}\mathrm{e}\mathrm{V}$.)

Figure 15

Resummed-matched $p_T$ distribution at $\mathrm{NLO}+\mathrm{NLL}$ (blue, dashed line) and $\mathrm{NNLO}+\mathrm{NNLL}$ (red, solid line). Lines are central scale choices; bands are uncertainties due to variation of all scales. (Same as Fig. 5, but for $\sqrt{s}=13\mathrm{T}\mathrm{e}\mathrm{V}$.)

Figure 16

(a) Transverse momentum spectrum at NNLO (blue, dashed line) and at $\mathrm{NNLO}+\mathrm{NNLL}$ (red, solid line) for the central scales; (b) the $b\overline{b}$ channel for that quantity. (Same as Fig. 2, but for $Q_0=M/2$.)

Figure 17

Resummed-matched $p_T$ distribution at $\mathrm{NLO}+\mathrm{NLL}$ (blue, dashed line) and $\mathrm{NNLO}+\mathrm{NNLL}$ (red, solid line). Lines are central scale choices; bands are uncertainties due to ${\mu }_{\mathrm{F}},{\mu }_{\mathrm{R}}$ variation. (Same as Fig. 3, but for $Q_0=M/2$.)

Figure 18

Resummed-matched $p_T$ distribution at $\mathrm{NLO}+\mathrm{NLL}$ (blue, dashed line) and $\mathrm{NNLO}+\mathrm{NNLL}$ (red, solid line). Lines are central scale choices; bands are uncertainties due to $Q$ variation. (Same as Fig. 4, but for $Q_0=M/2$.)

Figure 19

Resummed-matched $p_T$ distribution at $\mathrm{NLO}+\mathrm{NLL}$ (blue, dashed line) and $\mathrm{NNLO}+\mathrm{NNLL}$ (red, solid line). Lines are central scale choices; bands are uncertainties due to variation of all scales. (Same as Fig. 5, but for $Q_0=M/2$.)

Figure 20

Resummed-matched $p_T$ distribution at $\mathrm{NLO}+\mathrm{NLL}$ (blue, dashed line) and $\mathrm{NNLO}+\mathrm{NNLL}$ (red, solid line). Lines are central scale choices; bands are uncertainties due to ${\mu }_{\mathrm{F}},{\mu }_{\mathrm{R}}$ variation. (Same as Fig. 13, but for $Q_0=M/2$.)

Figure 21

Resummed-matched $p_T$ distribution at $\mathrm{NLO}+\mathrm{NLL}$ (blue, dashed line) and $\mathrm{NNLO}+\mathrm{NNLL}$ (red, solid line). Lines are central scale choices; bands are uncertainties due to $Q$ variation. (Same as Fig. 14, but for $Q_0=M/2$.)

Figure 22

Resummed-matched $p_T$ distribution at $\mathrm{NLO}+\mathrm{NLL}$ (blue, dashed line) and $\mathrm{NNLO}+\mathrm{NNLL}$ (red, solid line). Lines are central scale choices; bands are uncertainties due to variation of all scales. (Same as Fig. 15, but for $Q_0=M/2$.)