Patrick Hager

We propose a novel factorization theorem for N -jettiness at hadron colliders, which incorporates coherence-violating effects induced by Glauber gluons and several new momentum modes. Their interplay generates coherence-violating logarithms starting at four-loop ( N ≥ 1 ) or five-loop order ( N = 0 ). We calculate the anomalous dimensions required for the resummation of coherence-violating logarithms and establish a general framework for the systematic treatment of coherence violation. Our findings imply that most existing factorization formulas for global LHC observables must be revised.

A bstract: For light and massless scalar fields, cosmological correlation functions suffer from infrared divergences and secular logarithms. Soft de Sitter Effective Theory (SdSET) has been proposed by Cohen and Green as the effective description of the non-trivial dynamics of long-wavelength modes k _phys < H in de Sitter space, which is responsible for the infrared and late-time logarithms, and as a systematic extension of the stochastic approach. In this article, we construct SdSET in dimensional regularisation, including an initial-condition functional. We demonstrate by examples that renormalisation and matching works as for flat-space effective field theories. Adopting massless κϕ ⁴ theory as the UV theory, we match the tree-level trispectrum and six-point function, and the one-loop power spectrum to SdSET, verifying explicitly that SdSET is the appropriate effective field theory for the quantum dynamics of superhorizon modes.

A bstract: The consistency of collinear factorization violation with PDF factorization has been an outstanding challenge and subject of considerable debate. In this work we demonstrate their compatibility using a factorization theorem for non-global jet observables. Our analysis relies on consistency relations derived from renormalization conditions in effective field theory. We verify these relations through an explicit computation at three-loop order and show that the double-logarithmic evolution sourcing the super-leading logarithms reduces to single-logarithmic DGLAP running below the lowest perturbative scale. The crucial ingredient reconciling the two evolutions is a perturbative Glauber contribution to the low-energy matrix elements which breaks soft-collinear factorization at the cross section level but restores PDF factorization.

The consistency of collinear factorization violation with PDF factorization has been an outstanding challenge and subject of considerable debate. In this work we demonstrate their compatibility using a factorization theorem for non-global jet observables. Our analysis relies on consistency relations derived from renormalization conditions in effective field theory. We verify these relations through an explicit computation at three-loop order and show that the double-logarithmic evolution sourcing the super-leading logarithms reduces to single-logarithmic DGLAP running below the lowest perturbative scale. The crucial ingredient reconciling the two evolutions is a perturbative Glauber contribution to the low-energy matrix elements which breaks soft-collinear factorization at the cross section level but restores PDF factorization.

We analyze the low-energy dynamics of gap-between-jets cross sections at hadron colliders, for which phase factors in the hard amplitudes spoil collinear cancellations and lead to double (“super-leading”) logarithmic behavior. Based on a method-of-regions analysis, we identify three-loop contributions from perturbative active-active Glauber-gluon exchanges with the right structure to render the cross section consistent with PDF factorization below the gap veto scale. The Glauber contributions we identify are unambiguously defined without regulators beyond dimensional regularization.

A bstract: A new strategy is presented for systematically treating super-leading logarithmic contributions including higher-order Glauber exchanges for non-global LHC observables in renormalization-group (RG) improved perturbation theory. This represents an important improvement over previous approaches, as it allows for the consistent inclusion of the scale dependence of the strong coupling, thereby providing more reliable estimates of the scale uncertainties in theoretical predictions. The key idea is to rearrange the relevant RG evolution operator in such a way that all double-logarithmic corrections are exponentiated from the outset. This forms the starting point for the first resummation of super-leading logarithms at leading order in RG-improved perturbation theory for arbitrary 2 → M scattering processes. Moreover, the asymptotic scaling of subleading logarithmic corrections from higher-order Glauber exchanges is determined, demonstrating their parametric suppression.

A bstract: The Glauber series for non-global jet observables at hadron colliders simultaneously includes the super-leading logarithms alongside an arbitrary number of Glauber phases. Building on the formalism of [1], it is shown that the leading terms in this series for large N _c can be resummed in closed form in renormalization-group improved perturbation theory. This remarkable observation suggests that large- N _c methods might also be helpful to study other aspects of non-global logarithms at hadron colliders, and to combine our analytic results with amplitude-level parton showers.