Precise Predictions for Dijet Production at the LHC

We present the calculation of dijet production, doubly differential in dijet mass $m_{jj}$ and rapidity difference $|y^{*}|$, at leading color in all partonic channels at next-to-next-to-leading order (NNLO) in perturbative QCD. We consider the long-standing problems associated with scale choice for dijet production at next-to-leading order (NLO) and investigate the impact of including the NNLO contribution. We find that the NNLO theory provides reliable predictions, even when using scale choices that display pathological behavior at NLO. We choose the dijet invariant mass as the theoretical scale on the grounds of perturbative convergence and residual scale variation and compare the predictions to the ATLAS 7 TeV $4.5{\mathrm{fb}}^{-1}$ data.

Figure 1

Ratio of theory predictions to data for $0.0<|y^{*}|<0.5$ (left) and $1.5<|y^{*}|<2.0$ (right) for the scale choices $\mu =m_{jj}$ (top) and $\mu =⟨p_T⟩$ (bottom) at LO (green), NLO (blue), and NNLO (red). Scale bands represent the variation of the cross section by varying the scales independently by factors of 2 and 0.5.

Figure 2

The dijet cross section as a function of invariant mass $m_{jj}$ for the six bins of $|y^{*}|$, compared to ATLAS 7 TeV $4.5{\mathrm{fb}}^{-1}$ data.

Figure 3

NLO/LO (blue), NNLO/NLO (red), and NNLO/LO (purple) $K$-factors double differential in $m_{jj}$ and $|y^{*}|$. Bands represent the scale variation of the numerator. NNLO PDFs are used for all predictions.

Figure 4

The NLO (blue) and NNLO (red) theory predictions and ATLAS data normalized to the NLO central value. The bands represent the variation of the theoretical scales in the numerator by factors of 0.5 and 2. Electroweak effects are implemented as a multiplicative factor and are shown separately as the green dashed line.

Figure 5

The cross section evaluated in three bins as a function of ${\mu }_R/m_{jj}$: $370<m_{jj}<440\mathrm{GeV}$, $0.0<|y^{*}|<0.5$ (left); $850<m_{jj}<950\mathrm{GeV}$, $1.5<|y^{*}|<2.0$ (center); $2120<m_{jj}<2550\mathrm{GeV}$, $2.5<|y^{*}|<3.0$ (right). The variation of the cross section, for fixed ${\mu }_F/m_{jj}$, from the central value is shown as solid lines, computed from the renormalization group equation, for LO (green), NLO (blue), and NNLO (red). The thickness of the bands shows the variation due to the factorization scale, with boundaries given by ${\mu }_F/m_{jj}=0.5$ (dashed) and ${\mu }_F/m_{jj}=2.0$ (dotted). The points show the nnlojet result evaluated at ${\mu }_R/m_{jj}={\mu }_F/m_{jj}=\{0.5,1,2\}$.