Toward NNLL threshold resummation for hadron pair production in hadronic collisions

We investigate QCD threshold resummation effects beyond the next-to-leading logarithmic (NLL) order for the process $H_1{H}_2\to h_1{h}_{2}X$ at high invariant mass of the produced hadron pair. We take into account the color structure of the underlying partonic hard-scattering cross sections and determine the relevant hard and soft matrices in color space that contribute to the resummed cross section at next-to-next-to-leading logarithmic (NNLL) accuracy. We present numerical results for fixed-target and collider regimes. We find a significant improvement compared to previous results at NLL accuracy. In particular, the scale dependence of the resummed cross section is greatly reduced. Use of the most recent set of fragmentation functions also helps in improving the comparison with the experimental data. Our calculation provides a step towards a systematic NNLL extension of threshold resummation also for other hadronic processes, in particular for jet production.

Figure 1

Diagrams relevant for the calculation of the NLO soft matrix $S^{(1)}$. The blobs represent a Born amplitude and the letters are color indices.

Figure 2

Comparison of NLO (dashed), NLL resummed (dot-dashed), and NNLL resummed (solid) calculations of the cross section for $pp\to {\pi }^0{\pi }^{0}X$ to the NA24 data [21], for two different choices of the renormalization and factorization scales, ${\mu }_R={\mu }_F=M$ (upper lines) and ${\mu }_R={\mu }_F=2M$ (lower lines). The crosses display the NLO $\mathcal{O}({\alpha }_s)$ expansion of the resummed cross section.

Figure 3

Comparison of the scale dependence of the NLL resummed (dot-dashed) and the NNLL resummed (solid) cross sections for NA24 kinematics. We choose a pion pair invariant mass of $M=5.125\mathrm{GeV}$ and show the variation of the cross sections as a function of $\mu /M$, where ${\mu }_R={\mu }_F=\mu$.

Figure 4

Same as Fig. 2, but for $pp$ collisions at $\sqrt{S}=62.4\mathrm{GeV}$. The data are from CCOR [24].

Figure 5

Dihadron production at RHIC at a center-of-mass energy of $\sqrt{S}=200\mathrm{GeV}$. The full NLO result (dashed) is shown in comparison to the NLO expansion of the resummed result (crosses). The solid line shows the NNLL resummed cross section. As before, we use the scales ${\mu }_R={\mu }_F=M$ and ${\mu }_R={\mu }_F=2M$.