Toward NNLL threshold resummation for hadron pair production in hadronic collisions

Abstract

We investigate QCD threshold resummation effects beyond the next-to-leading logarithmic (NLL) order for the process H 1 H 2 → 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.

Toward NNLL Resummation for Single- and Di-Hadron Production in Hadronic Collisions

“…The evaluation of the integrals in Eq. (3.2) up to NNLL accuracy can be found in [9]. In addition, we obtain a trace structure Tr{HS † N SS N } in color space [2,10] that is associated with large-angle soft emission which is sensitive to the color state of the hard scattering.…”

“…The relevant coefficients up to NNLL accuracy can be found in [1,9,14,15,16,17,18,19,20]. The evaluation of the integrals in Eq.…”

“…The functions ξ R,F are related to the scale dependence of the resummed cross section but they do not contain threshold logarithms, see [9] for more details. For every external parton in the hardscattering, we need to take into account a "jet function" ∆ N i (i = a, b, c, d) which exponentiates logarithms that arise due to soft-collinear gluon emissions [4,12,13].…”

“…5. The results reported in this paper are taken from [9], to which we refer the reader for further details.…”

Soft evolution of multi-jet final states

“…All-order analytical calculations have been performed recently for an increasing number of jet-substructure observables, including jet masses [71][72][73][74], other jet shapes [75][76][77][78][79], sub-jet multiplicity [80] and grooming algorithms [81][82][83]. Recently, there has also been substantial progress towards achieving NNLL accuracy in threshold resummation for dijet production [84,85].…”