Drell-Yan process with jet vetoes: breaking of generalized factorization

TL;DR

This work tests the validity of factorization for Drell–Yan–like processes under stringent jet vetoes by constructing a scalar-quark toy model. It shows that standard factorization fails due to spectator-spectator Glauber exchanges, and that generalized factorization, which decouples the two collinear sectors, cannot hold either because a nonzero leading-power spin asymmetry arises from Glauber interactions. The authors compute the sole nonvanishing two-Glauber cut diagram at order αs^2, finding an infrared-finite, nonzero contribution to the doubly differential beam thrust spin asymmetry, thereby proving factorization breaking. The results imply that entanglement between the two collinear sectors is necessary for proper resummation of jet-veto logarithms and suggest revisions to the factorization framework for beam-thrust-type observables in hadron collisions.

Abstract

Resummation of hadron collision cross sections, when the measurement imposes a hierarchy of scales, relies on factorization. Cancellation of Glauber / Coulomb gluons is a necessary condition for factorization. For Drell-Yan-like processes, the known proofs of cancellation of Glauber gluons are not applicable when jet vetoes are introduced, via jet algorithms or event shape variables such as the beam thrust. A priori, this does not rule out the possibility that an unknown new cancellation mechanism exists, or the possibility that a generalized factorization formalism is correct. To resolve the questions, we construct a direct counter-example in QCD with scalar quarks, contradicting any form of factorization in which the two collinear sectors are decoupled from each other. In the counter-example, decoupling of the two collinear sectors implies zero dependence of the beam thrust distribution on the longitudinal spin of the incoming hadrons, but we find a non-zero spin asymmetry at leading power due to Glauber gluons exchanged between spectators. We discuss implications for resumming large logarithms from jet vetoes.

Figures (5)

• Figure 1: The leading-order Feynman diagram for $\gamma + \gamma \rightarrow \Phi + X$ in the model theory. Here $X = \phi + \phi^*$.
• Figure 2: The one-Glauber exchange diagram in the model field theory.
• Figure 3: Example cut diagrams, each with only one gluon attached to the spectator line on the lower half of the graph, while more than one gluons may attach to the upper spectator line.
• Figure 4: Two Glauber gluons exchanged on the same side of the cut, in the model field theory.
• Figure 5: The cut diagram with one Glauber gluon exchanged on either side of the cut, i.e. the square of Fig. \ref{['fig:spectator']}.