Periodic Reporting for period 1 - EFT4jets (An Effective Field Theory for Non-Global Observables at Hadron Colliders)
Reporting period: 2023-05-01 to 2025-10-31
In light of intriguing hints for the existence of heavy new particles from low-energy precision measurements, which strategy should one take to fully exploit the discovery potential of the CERN Large Hadron Collider (LHC)? Signals of new physics might be hiding in the LHC data, but we are limited in our ability to discover them due to present theoretical uncertainties. Jet processes at the LHC are the most interesting observables probing the underlying short-distance dynamics. New and powerful methods are required to obtain full control over the subtle quantum corrections affecting these processes, both in the Standard Model and in extensions featuring new particles. The EFT4jets proposal focusses on two of the most daunting challenges faced in theoretical collider physics: a rigorous field-theoretic understanding of the parametrically leading contributions to jet rates from so-called super-leading and non-global logarithms, and a quantitative understanding of the phenomenon of factorization violation, which threatens to jeopardize theoretical calculations of jet processes. This will for the first time provide a rigorous theoretical control over all logarithmically enhanced corrections to jet cross sections, give a generalized notion of factorization and enable more accurate calculations than ever before, thus boosting the LHC discovery potential for new phenomena. Detailed predictions will be obtained for important benchmark processes, including the production of Higgs, W or Z bosons in association with jets, and the di-jet production process.
During the first two years of the project, all goals and milestones outlined in the proposal have been accomplished. The main achievements on the four subprojects are summarized as follows.
I: Resummation of SLLs for arbitrary jet processes
In a paper published in JHEP 12 (2023) 116, we have presented a detailed derivation of the factorization formula for non-global observables at hadron colliders and performed the resummation of super-leading logarithms (SLLs) to all orders of perturbation theory and for arbitrary jet processes. The extension of the formalism to processes with massive final-state partons has been worked out and the results are being prepared for publication. In a paper published in JHEP 08 (2024) 035, we have developed an elegant formalism accomplishing the resummation of SLLs in renormalization-group (RG) improved perturbation theory in terms of a twofold scale integral, which can be evaluated numerically. With this advance, we have been able to include an important source of subleading logarithmic effects.
For project I, we have been able to complete also many of the tasks originally planned for years 3-5 of the project. In two papers published in JHEP 10 (2023) 075 and JHEP 02 (2024) 109, we have accomplished the construction of a color basis which closes under repeated applications of the collinear emission operator and the Glauber operator. In RG-improved perturbation theory, the contributions of higher-order terms in the Glauber series (i.e. terms involving multiple insertions of the Glauber operator) can be computed numerically by performing multiple scale integrals. In a paper published in JHEP 08 (2024) 036, we have reported on the remarkable observation that the Glauber series can be resumed to all orders in the large-Nc approximation. Armed with these results, we have studied the impact of higher-order terms in the Glauber series for all 2-to-2 partonic scattering processes.
II: Systematic study of single-logarithmic corrections
The resummation of non-global logarithms (NGLs) arising from multiple gluon emissions in jet processes has been extended by my collaboration partner Thomas Becher (Univ. Bern) from electron-positron colliders to the case of hadron colliders. However, this approach does not yet account for SLLs or other effects of Glauber phases. In years 3-5 of this project, we will study the combined effects of SLLs and NGLs by incorporating multiple real-gluon emissions in our formalism of SLLs and the Glauber series. Preliminary work on the case of two emission has already started.
III: Factorization violation and generalized factorization theorems
In a paper published in Phys. Rev. Lett. 134 (2025) 061901, we have performed the first detailed study of the structure of the low-energy functions in the factorization theorem for non-global observables at hadron colliders up to three-loop order in perturbation theory. This work has been based on a method-of-regions analysis in QCD as well as calculations using soft-collinear effective theory (SCET) including Glauber gluons. The presence of Glauber gluons breaks color coherence and soft-collinear factorization, thus invalidating the simple structure of other SCET-based factorization theorems. At the same time, it is well known that collinear factorization is broken in space-like collinear splittings. It was widely believed that collinear factorization breaking would imply a violation of PDF factorization starting at three-loop order in perturbation theory. In our paper, we have proved the opposite: through a “miraculous” conspiracy of collinear factorization violation at the high scale Q and soft-collinear factorization breaking at the low jet-veto scale Q0, PDF factorization is restored in the low-energy theory below Q0. This is a discovery of great importance, since PDF factorization is the basis for all calculations of LHC cross sections. A detailed publication presenting the results of our research on this topic is currently being prepared for submission.
IV: Phenomenological analyses of benchmark processes
In a paper published in JHEP 01 (2025) 171, we have performed the first phenomenological analysis of the gaps-between-jets cross section at the LHC, which has been measured by the ATLAS collaboration. We find that the impact of SLLs on this physical cross section is significant, enhancing the cross section by typically 5-10% depending on kinematic cuts. Work on other phenomenological cross sections is currently ongoing.
I: Resummation of SLLs for arbitrary jet processes
In a paper published in JHEP 12 (2023) 116, we have presented a detailed derivation of the factorization formula for non-global observables at hadron colliders and performed the resummation of super-leading logarithms (SLLs) to all orders of perturbation theory and for arbitrary jet processes. The extension of the formalism to processes with massive final-state partons has been worked out and the results are being prepared for publication. In a paper published in JHEP 08 (2024) 035, we have developed an elegant formalism accomplishing the resummation of SLLs in renormalization-group (RG) improved perturbation theory in terms of a twofold scale integral, which can be evaluated numerically. With this advance, we have been able to include an important source of subleading logarithmic effects.
For project I, we have been able to complete also many of the tasks originally planned for years 3-5 of the project. In two papers published in JHEP 10 (2023) 075 and JHEP 02 (2024) 109, we have accomplished the construction of a color basis which closes under repeated applications of the collinear emission operator and the Glauber operator. In RG-improved perturbation theory, the contributions of higher-order terms in the Glauber series (i.e. terms involving multiple insertions of the Glauber operator) can be computed numerically by performing multiple scale integrals. In a paper published in JHEP 08 (2024) 036, we have reported on the remarkable observation that the Glauber series can be resumed to all orders in the large-Nc approximation. Armed with these results, we have studied the impact of higher-order terms in the Glauber series for all 2-to-2 partonic scattering processes.
II: Systematic study of single-logarithmic corrections
The resummation of non-global logarithms (NGLs) arising from multiple gluon emissions in jet processes has been extended by my collaboration partner Thomas Becher (Univ. Bern) from electron-positron colliders to the case of hadron colliders. However, this approach does not yet account for SLLs or other effects of Glauber phases. In years 3-5 of this project, we will study the combined effects of SLLs and NGLs by incorporating multiple real-gluon emissions in our formalism of SLLs and the Glauber series. Preliminary work on the case of two emission has already started.
III: Factorization violation and generalized factorization theorems
In a paper published in Phys. Rev. Lett. 134 (2025) 061901, we have performed the first detailed study of the structure of the low-energy functions in the factorization theorem for non-global observables at hadron colliders up to three-loop order in perturbation theory. This work has been based on a method-of-regions analysis in QCD as well as calculations using soft-collinear effective theory (SCET) including Glauber gluons. The presence of Glauber gluons breaks color coherence and soft-collinear factorization, thus invalidating the simple structure of other SCET-based factorization theorems. At the same time, it is well known that collinear factorization is broken in space-like collinear splittings. It was widely believed that collinear factorization breaking would imply a violation of PDF factorization starting at three-loop order in perturbation theory. In our paper, we have proved the opposite: through a “miraculous” conspiracy of collinear factorization violation at the high scale Q and soft-collinear factorization breaking at the low jet-veto scale Q0, PDF factorization is restored in the low-energy theory below Q0. This is a discovery of great importance, since PDF factorization is the basis for all calculations of LHC cross sections. A detailed publication presenting the results of our research on this topic is currently being prepared for submission.
IV: Phenomenological analyses of benchmark processes
In a paper published in JHEP 01 (2025) 171, we have performed the first phenomenological analysis of the gaps-between-jets cross section at the LHC, which has been measured by the ATLAS collaboration. We find that the impact of SLLs on this physical cross section is significant, enhancing the cross section by typically 5-10% depending on kinematic cuts. Work on other phenomenological cross sections is currently ongoing.
The five most significant achievements obtained during the first two years of the project were i) the proof that PDF factorization holds for non-global observables at hadron collider up to three-loop order in perturbation theory, ii) the derivation of the factorization theorem for non-global LHC observables in soft-collinear effective theory, iii) the discovery that super-leading logarithms can be resummed in closed form, to all orders of perturbation theory and for arbitrary jet processes, iv) the observation that the Glauber series can be resummed in closed form in the large-Nc approximation, and v) the discovery of a three-loop contribution to a hadron-collider cross section involving a genuine Glauber contribution.
Our discovery that PDF factorization holds for jet cross sections was an unexpected finding to several researchers in the field. In fact, PDF factorization had only been proved for the simplest LHC process, the Drell-Yan production of a colorless object in the final state (Collins, Soper, Sterman 1985). Our results pave the way to a proof of PDF factorization for a much wider class of observables.
Our discovery that PDF factorization holds for jet cross sections was an unexpected finding to several researchers in the field. In fact, PDF factorization had only been proved for the simplest LHC process, the Drell-Yan production of a colorless object in the final state (Collins, Soper, Sterman 1985). Our results pave the way to a proof of PDF factorization for a much wider class of observables.