Next-to-leading-logarithmic power corrections for $N$-jettiness subtraction in color-singlet production

We present a detailed derivation of the power corrections to the factorization theorem for the 0-jettiness event shape variable $\mathcal{T}$. Our calculation is performed directly in QCD without using the formalism of effective field theory. We analytically calculate the next-to-leading logarithmic power corrections for small $\mathcal{T}$ at next-to-leading order in the strong coupling constant, extending previous computations which obtained only the leading-logarithmic power corrections. We address a discrepancy in the literature between results for the leading-logarithmic power corrections to a particular definition of 0-jettiness. We present a numerical study of the power corrections in the context of their application to the $N$-jettiness subtraction method for higher-order calculations, using gluon-fusion Higgs production as an example. The inclusion of the next-to-leading-logarithmic power corrections further improves the numerical efficiency of the approach beyond the improvement obtained from the leading-logarithmic power corrections.

Figure 1

Deviations of the NLO coefficient obtained using $N$-jettiness subtraction as a function of ${\mathcal{T}}^{\mathrm{cut}}$ from the dipole-subtraction result for three different cases: no power corrections included, only the leading-logarithmic (LL) power corrections included, and the full NLL power corrections included.

Figure 2

Study of the differing definitions of the LL power corrections in the hadronic $\mathcal{T}$ case between this work and Ref. [32] (labeled 1710.03227 according to its arXiv number).

Figure 3

Comparison of the leptonic and hadronic $\mathcal{T}$ deviations from dipole subtraction for the total cross section (left panel) and forward rapidity region (right panel). No power corrections are included.

Figure 4

Comparison of the leptonic and hadronic $\mathcal{T}$ deviations from dipole subtraction for the total cross section (left panel) and forward rapidity region (right panel). The full $\mathcal{O}(\mathcal{T})$ power corrections are included.

Figure 5

Deviations of the $qg+gq$ NLO coefficient obtained using $N$-jettiness subtraction as a function of ${\mathcal{T}}^{\mathrm{cut}}$ from the dipole-subtraction result for three different cases: no power corrections included, only the leading-logarithmic (LL) power corrections included, and the full NLL power corrections included.

Figure 6

Deviations of the $q\overline{q}$ NLO coefficient obtained using $N$-jettiness subtraction as a function of ${\mathcal{T}}^{\mathrm{cut}}$ from the dipole-subtraction result for three different cases: no power corrections included and the full NLL power corrections included.