Super-Leading Logarithms in Top-Quark Pair Production at Hadron Colliders

TL;DR

This work extends the resummation of super-leading logarithms to hadron-hadron processes with massive final states by deriving the massive-final-state hard-function anomalous dimension and uncovering a new Coulomb-phase source of SLLs. It shows how soft, Coulomb, and Glauber interactions combine to produce a tower of SLLs at leading logarithmic accuracy for 2→M processes, and provides both fixed-coupling and RG-improved resummation formalisms. The formalism is then applied to top-quark pair production, where Coulomb SLLs appear only in the gluon-initiated channel and require Sommerfeld resummation near threshold to account for the $eta o 0$ behavior. Numerical results indicate that Coulomb and Glauber SLLs can be comparable near moderate top-quark velocities, with larger impact from Glauber effects at higher hard scales; the framework also sets the stage for Coulomb resummation in lepton colliders and for extensions to other heavy colored final states. Overall, the paper provides a first quantitative treatment of Coulomb-induced SLLs in massive final states and a practical pathway to their systematic resummation in hadronic observables.

Abstract

To date, the appearance and resummation of "super-leading" logarithms in hadron-hadron collisions has been studied only for massless parton states. We extend the formalism to include an arbitrary number of massive final states. We derive the corresponding anomalous dimension and identify an additional Coulomb phase that gives rise to a new source of super-leading logarithms. We then perform a systematic leading-logarithmic resummation of these contributions for $2\to M$ processes. Finally, we analyze the numerical impact in partonic scattering processes for $t\bar{t}$ production, including a treatment of the Sommerfeld enhancement observed near threshold.

Figures (3)

• Figure 1: Dependence on $\beta$ of the Coulomb-SLL contributions to the differential cross section of $gg\to t\bar{t}$, normalized to the Born cross section. The jet-veto scale is set to $Q_0 =20GeV$, with the pseudorapidity of the top quark chosen as $\eta=2$. The gray line indicates the single Coulomb insertion, while the blue line additionally includes the double Coulomb insertion. The red line shows the effect of resumming the Coulomb insertions.
• Figure 2: SLL contribution to the differential cross section, normalized to the Born cross section. On the left side we show only the Coulomb-SLL contributions, while in the right the known Glauber SLLs are shown in addition. These plots also include the resummation of an arbitrary even number of Coulomb insertions to correctly treat the Sommerfeld enhancement close to threshold (see Section \ref{['subsec:Sommerfeld_resummation']}). The jet-veto scale is fixed to $Q_0 = 20\,\mathrm{GeV}$, while the pseudorapidities of the top quarks are restricted to lie outside the veto region marked in gray.
• Figure 3: $Q_0$ dependence of the Coulomb SLLs. The shaded band indicates the scale variation $Q_0/2 \leq \mu_s \leq 2Q_0$ as an estimate of the perturbative uncertainties.