arXiv subjects

Michel Stillger

Publications and source records attributed to Michel Stillger.

9 recordsLinked to original sources

arXiv2026

On the universality of soft emission beyond the next-to-soft order

The Low-Burnett-Kroll theorem (extended to non-abelian gauge theory) states that the tree-level emission amplitude of a soft gauge boson from an arbitrary hard process can be expressed in terms of the non-radiative amplitude including the next-to-soft term. Reformulating the soft theorem in the framework of an on-shell effective theory leads to a natural gauge-invariant split into an external and internal emission process to any order in the soft expansion. In this framework, we derive a compact expression for the all-order external emission amplitude expressed in terms of the non-radiative amplitude, and express the local emission amplitude through a single gauge-invariant operator at every order beyond the next-to-soft one. For scalar QCD, we compare the number of Lorentz- and $SU(3)$-invariant amplitudes for the radiative and non-radiative hard process with an arbitrary number of scalar quarks and antiquarks.

hep-ph↗

arXiv2026

One-loop matching of QCD currents to power-suppressed two-jet operators

We compute the matching of QCD quark-antiquark currents onto the set of the two-particle and three-particle two-jet operators in soft-collinear effective theory (SCET) at next-to-leading order (NLO) in the perturbative QCD series, including for the first time operators up to second order in the power expansion in the transverse momentum over energy. These results contribute to the ongoing programme of computing power corrections and summing power-suppressed logarithmically enhanced terms for event shapes in the two-jet region and deep-inelastic scattering in the Bjorken-$x\to 1$ limit. The three-particle operators depend on the partonic momentum fractions of two partons moving into the same direction. When one of the momentum fractions approaches zero, the coefficient functions are shown to satisfy endpoint factorization relations, which allow for a consistent cancellation of endpoint singularities among various terms in the complete factorization formula for power corrections.

hep-ph↗

arXiv2024

Super-Leading Logarithms in $pp\to2$ Jets

Jet observables at hadron colliders feature ''super-leading'' logarithms, double-logarithmic corrections resulting from a breakdown of color coherence due to complex phases in hard-scattering amplitudes. While these effects only arise in high orders of perturbation theory and are suppressed in the large-$N_c$ limit, they formally constitute leading logarithmic corrections to the cross sections. We present the first analysis of the corresponding contributions to a hadronic cross section, including all partonic channels and interference effects. Interestingly, some interference terms in partonic $q\bar q\to q\bar q$ scattering are only linearly suppressed in $1/N_c$. Our results for the $pp\to 2$ jets gap-between-jets cross section demonstrate the numerical importance of super-leading logarithms for small values of the veto scale $Q_0$, showing that these contributions should be accounted for in precision studies of such observables.

hep-ph↗

arXiv2024

Resummation of Glauber Phases in Non-Global LHC Observables for Large $N_c$

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 arXiv:2405.05305, 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.

hep-ph↗

arXiv2024

Renormalization-Group Improved Resummation of Super-Leading Logarithms

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 $2\to M$ scattering processes. Moreover, the asymptotic scaling of subleading logarithmic corrections from higher-order Glauber exchanges is determined, demonstrating their parametric suppression.

hep-ph↗

arXiv2023

Glauber Phases in Non-Global LHC Observables: Resummation for Gluon-Initiated Processes

The resummation of the ''Glauber series'' in non-global LHC observables is extended to processes with gluons in the initial state. This series simultaneously incorporates large double-logarithmic corrections, the so-called ''super-leading logarithms'', together with higher-order exchanges of pairs of Glauber gluons associated with the large numerical factor $(iπ)^2$. On a technical level, the main part of this work is devoted to the systematic reduction of the appearing color traces and construction of basis structures, which consist of thirteen elements for $gg$ and eleven elements for $qg$ scattering. Numerical estimates for wide-angle gap-between-jet cross sections at the parton level show that, in particular for $gg$ scattering at relatively small vetoes $Q_0$, the contribution involving four Glauber exchanges gives a sizeable correction and should not be neglected.

hep-ph↗

arXiv2023

Glauber Phases in Non-Global LHC Observables: Resummation for Quark-Initiated Processes

It has been known for many years that jet cross sections at hadron colliders exhibit double-logarithmic corrections starting at four-loop order, arising from two soft Glauber-gluon interactions between the two colliding partons. The resummation of these "super-leading logarithms" has been achieved only recently by means of a renormalization-group treatment in soft-collinear effective theory. We generalize this result and, within the same framework and for quark-initiated processes, resum the double logarithms arising in the presence of an arbitrary number of Glauber-gluon exchanges. For typical choices of parameters, the higher-order Glauber terms give rise to corrections which are expected to be numerically of the same magnitude as the super-leading logarithms. However, we find that the Glauber series for jet cross sections is dominated by the two-Glauber contribution, if the colliding partons are quarks or anti-quarks.

hep-ph↗

arXiv2023

Factorization of Non-Global LHC Observables and Resummation of Super-Leading Logarithms

We present a systematic formalism based on a factorization theorem in soft-collinear effective theory to describe non-global observables at hadron colliders, such as gap-between-jets cross sections. The cross sections are factorized into convolutions of hard functions, capturing the dependence on the partonic center-of-mass energy $\sqrt{\hat s}$, and low-energy matrix elements, which are sensitive to the low scale $Q_0\ll\sqrt{\hat s}$ characteristic of the veto imposed on energetic emissions into the gap between the jets. The scale evolution of both objects is governed by a renormalization-group equation, which we derive at one-loop order. By solving the evolution equation for the hard functions for arbitrary $2\to M$ jet processes in the leading logarithmic approximation, we accomplish for the first time the all-order resummation of the so-called "super-leading logarithms" discovered in 2006, thereby solving an old problem of quantum field theory. We study the numerical size of the corresponding effects for different partonic scattering processes and explain why they are sizable for $pp\to 2\,\text{jets}$ processes, but suppressed in $H/Z$ and $H/Z$+jet production. The super-leading logarithms are given by an alternating series, whose individual terms can be much larger than the resummed result, even in very high orders of the loop expansion. Resummation is therefore essential to control these effects. We find that the asymptotic fall-off of the resummed series is much weaker than for standard Sudakov form factors.

hep-ph↗

arXiv2022

Impact of unphysical meson decays on the parameter fixing in the three-flavour Nambu-Jona-Lasinio model for different regularisation methods

We investigate the influence of the allowed unphysical meson decay into a quark-antiquark pair of the three flavour Nambu--Jona-Lasinio (NJL) model on its parameter fixing. This decay manifests in a non-vanishing imaginary part of the corresponding meson propagator and its polarisation loop, respectively. In order to handle the emerging divergent integrals, we focus on the Pauli-Villars, three- and four momentum cutoff regularisation method. Here, we fix the parameters to certain observables, which are effected by the non-vanishing imaginary part. The resulting parameter-sets for each regularisation scheme are compared to each other with and without taking the imaginary part of the polarisation loop into account.

hep-ph↗