We discuss the factorization of scattering processes near partonic threshold at next-to-leading power (NLP) in the threshold variable 1-z, with z ≡ q^2/ŝ. We review the general structure of power-suppressed contributions both in Soft-Collinear Effective Theory (SCET) and in a direct QCD approach, and discuss the definition of NLP jet functions as gauge-invariant operator matrix elements in QCD. As a controlled check of the resulting factorization formula, we verify it explicitly at one and two loops for the massive electromagnetic form factor in the limit m^2 ≪ s, using the method of regions. We conclude by outlining the two challenges that remain for a systematic resummation of NLP logarithms: the treatment of endpoint divergences in SCET convolutions, and the extension of jet functions to radiative processes capable of describing an arbitrary number of soft-gluon emissions – the latter being the last missing ingredient for exponentiation, given that the purely soft sector is already understood in terms of generalised webs via the replica trick.

We investigate the factorization properties of the massive fermion form factor in QED, to next-to-leading power in the fermion mass, and up to two-loop order. For this purpose we define new jet functions that have multiple connections to the hard part as operator matrix elements, and compute them to second order in the coupling. We test our factorization formula using these new jet functions in a region-based analysis and find that factorization indeed holds. We address a number of subtle aspects such as rapidity regulators and external line corrections, and we find an interesting sequence of relations among the jet functions.

The European Strategy for Particle Physics (ESPP) reflects the vision and presents concrete plans of the European particle physics community for advancing human knowledge in fundamental physics. The ESPP is updated every five-to-six years through a community-driven process. It commences with the submission of specific proposals and other input from the community at large, outlining projects envisioned for the near-, mid-, and long-term future. All submitted contributions are evaluated by the Physics Preparatory Group (PPG), and a preliminary analysis is presented at a Symposium meant to foster a broad community discussion on the scientific value and feasibility of the various ideas proposed. The outcomes of the analysis and the deliberations at the Symposium are synthesized in the current Briefing Book, which provides an important input in the deliberations of the Strategy recommendations by the European Strategy Group (ESG).

We investigate the origin of next-to-leading power corrections to the event shapes thrust and $c$-parameter, at next-to-leading order. For both event shapes we trace the origin of such terms in the exact calculation, and compare with a recent approach involving the eikonal approximation and momentum shifts that follow from the Low-Burnett-Kroll-Del Duca theorem. We assess the differences both analytically and numerically. For the $c$-parameter both exact and approximate results are expressed in terms of elliptic integrals, but near the elastic limit it exhibits patterns similar to the thrust results.

We report on updated precision predictions for total cross sections of coloured super- symmetric particle production at the LHC with a centre-of-mass energy of ,/S = 13.6 TeV, computed with the modern PDF4LHC21 set. The cross sections are calculated at an approximated NNLO accuracy in QCD and contain corrections from the threshold resummation of soft-gluon emission up to NNLL accuracy as well as Coulomb-gluon contributions including bound-state terms. The corrections are found to increase the cross sections and reduce the theoretical uncertainty as compared to the best available fixed-order calculations. These predictions constitute the state-of-the-art calculations and update the existing results for ,/S = 13 TeV. We make our new results publicly available in the version 2.0 update to the code package NNLL-FAST.

We perform an analysis of the one- and two-loop massive quark form factor in QED in a region expansion, up to next-to-leading power in the quark mass. This yields an extensive set of regional integrals, categorized into three topologies, against which factorization theorems at next-to-leading power could be tested. Our analysis reveals a number of subtle aspects involving rapidity regulators, as well as additional regions that manifest themselves only beyond one loop, at the level of single diagrams, but which cancel in the form factor.

For the event shapes thrust and c-parameter at next-to-leading order, we examine the origins of next-to-leading power corrections. We track down the origin of these factors for each shape of the event and compare our findings with a recent method that makes use of the eikonal approximation and momentum changes derived from the Low-Burnett-Kroll-Del Duca theorem. We do an analytical and numerical analysis of the differences. Both precise and approximate findings are described in terms of elliptic integrals for the c-parameter; yet, it exhibits patterns that are similar to those observed in the thrust results near the elastic limit.

Soft and collinear radiation in collider processes can be described in a universal way, that is independent of the underlying process. Recent years have seen a number of approaches for probing whether radiation beyond the leading soft approximation can also be systematically classified. In this paper, we study a formula that captures the leading next-to-soft QCD radiation affecting processes with both final- and initial-state partons, by shifting the momenta in the non-radiative squared amplitude. We first examine W+jet production, and show that a previously derived formula of this type indeed holds in the case in which massive colour singlet particles are present in the final state. Next, we develop a physical understanding of the momentum shifts, showing precisely how they disrupt the well-known angular ordering property of leading soft radiation.

We consider Drell-Yan production and QCD-induced diphoton production and compute their rapidity distributions up to next-to-leading power (NLP) in the threshold variable. We give results for rapidity distributions of the Drell-Yan process up to NNLO accuracy and show that a factorised structure occurs for the leading logarithms (LL) at NLP, generalising the result at leading power. For diphoton production, we generalise methods based on kinematical shifts to find the NLO cross section up to NLP for rapidity distributions. From the results for these two processes, we derive resummed cross sections at NLP LL accuracy that are double differential in the threshold variable and the rapidity variable, which generalise results for single differential resummed cross sections.

We compute non-perturbative contributions to the Adler function, the derivative of the vacuum polarization function in gauge theory, using resurgence methods and Borel-summed gauge field propagators. At 2-loop, to order $1/N_f$, we construct the full 2-parameter transseries and perform the sum over the non-perturbative sectors. We then introduce a convolution-based method to derive the transseries structure of product series, which can also be used to study higher orders in the expansion in $1/N_f$. We compute 3-loop planar diagrams, at order $1/N_f^2$, and for each diagram study the asymptotic behavior and resulting non-perturbative information in the transseries. A structure emerges that, from a resurgence point of view, is quite different from toy models hitherto studied. We study in particular the first and second non-perturbative sectors, their relation to UV and IR renormalons, and how their presence influences the perturbative expansions in neighbouring sectors. Finally, finding that many non-perturbative sectors have asymptotic series, we derive relations among all of them, thus providing an interesting new perspective on the alien lattice for the Adler function.

A bstract We compute non-perturbative contributions to the Adler function, the derivative of the vacuum polarization function in gauge theory, using resurgence methods and Borel-summed gauge field propagators. At 2-loop, to order 1 /N f , we construct the full 2-parameter transseries and perform the sum over the non-perturbative sectors. We then introduce a convolution-based method to derive the transseries structure of product series, which can also be used to study higher orders in the expansion in 1 /N f . We compute 3-loop planar diagrams, at order 1 / $$ {N}_f^2 $$ N f 2 , and for each diagram study the asymptotic behavior and resulting non-perturbative information in the transseries. A structure emerges that, from a resurgence point of view, is quite different from toy models hitherto studied. We study in particular the first and second non-perturbative sectors, their relation to UV and IR renormalons, and how their presence influences the perturbative expansions in neighbouring sectors. Finally, finding that many non-perturbative sectors have asymptotic series, we derive relations among all of them, thus providing an interesting new perspective on the alien lattice for the Adler function.

Abstract We compute non-perturbative contributions to the Adler function, the derivative of the vacuum polarization function in gauge theory, using resurgence methods and Borel-summed gauge field propagators. At 2-loop, to order 1/N f , we construct the full 2-parameter transseries and perform the sum over the non-perturbative sectors. We then introduce a convolution-based method to derive the transseries structure of product series, which can also be used to study higher orders in the expansion in 1/N f . We compute 3-loop planar diagrams, at order 1/ N f 2 $$ {N}_f^2 $$ , and for each diagram study the asymptotic behavior and resulting non-perturbative information in the transseries. A structure emerges that, from a resurgence point of view, is quite different from toy models hitherto studied. We study in particular the first and second non-perturbative sectors, their relation to UV and IR renormalons, and how their presence influences the perturbative expansions in neighbouring sectors. Finally, finding that many non-perturbative sectors have asymptotic series, we derive relations among all of them, thus providing an interesting new perspective on the alien lattice for the Adler function.

Flow Oriented Perturbation Theory (FOPT) is a novel approach to Feynman diagrams based on the coordinate (position) space description of Quantum Field Theories (QFT). FOPT offers interesting features regarding the computation of higher-loop Feynman amplitudes such as combinatorial and canonical Feynman rules, explicit infrared singularity factorization on a per-diagram level and the potential to have manifest cancellation of real and virtual singularities. In these proceedings we briefly summarize the derivation of FOPT and present its Feynman rules for covariant diagrams, S-matrix elements and cut diagrams in massless scalar QFT, supported by examples. We then discuss the extension of FOPT to massless fermion fields and indicate steps towards the treatment of massive lines in arbitrary dimensions.

We study next-to-leading-power (NLP) threshold corrections in colour-singlet production processes, with particular emphasis on Drell-Yan (DY) and single-Higgs production. We assess the quality of the partonic and hadronic threshold expansions for each process up to NNLO. We determine numerically the NLP leading-logarithmic (LL) resummed contribution in addition to the leading-power next-to-next-to-leading logarithmic (LP NNLL) resummed DY and Higgs cross sections, matched to NNLO. We find that the inclusion of NLP logarithms is numerically more relevant than increasing the precision to N$^3$LL at LP for these processes. We also perform an analytical and numerical comparison of LP NNLL + NLP LL resummation in soft-collinear effective theory and direct QCD, where we achieve excellent analytical and numerical agreement once the NLP LL terms are included in both formalisms. Our results underline the phenomenological importance of understanding the NLP structure of QCD cross sections.

Cross sections in perturbative QCD are plagued by large corrections from soft and collinear radiation. The most singular terms are known to be universal, which allows their resummation to all orders in the coupling. We have examined the structure of the next-to-singular contributions, which can originate from the emission of both soft quarks and gluons. We show that we can derive a next-to-soft amplitude for both types of emissions. The numerical impact of these contributions on the transverse momentum distribution of the single-photon production process are also discussed.

We assess and compare different methods for including leading threshold logarithms at next-to-leading-power in prompt photon production at hadron colliders, for both the direct and parton fragmentation mechanisms. We do this in addition to next-to-leading logarithmic threshold and joint resummation at leading power. We study the size of these effects and their scale variations for LHC kinematics. We find that the next-to-leading power effects have a noticeable effect on the photon transverse momentum distribution, typically of order $\mathcal{O}(10\%)$, depending on the method of inclusion. Our results indicate that next-to-leading power terms can reduce the scale dependence of the distribution considerably.

Large perturbative corrections, which appear in perturbative expressions for many QCD observables, either at small \(Q_T\) or at partonic threshold, can be organized by way of all order resummation. Joint resummation allows simultaneous resummation of threshold and recoil effects and its impact has been assessed upto leading log, next-to-leading log (NLL) and in some cases up to NNLL accuracy. We discuss another class of terms, called soft-collinear effects, which give rise to corrections of the form \(\frac{\ln ^jN}{N}\) and their impact on the joint resummed calculations of prompt photon production cross section.

We present recent results in an ongoing program to construct a resummation formalism for threshold logarithms at next-to-leading power (NLP) in the threshold expansion. We discuss a factorised expression for the Drell-Yan scattering amplitude, valid at NLP, which arises from the LowBurnett-Kroll-Del Duca theorem, and correctly reproduces all relevant logarithms at two loops for the abelian-like color structure. We then discuss methods to generalise this formalism to the full non-abelian theory, and propose a simple ansatz which succeeds in generating all non-abelian NLP logarithms at two loops, in terms of a small set of universal soft and collinear functions.

We present updated predictions for the cross sections for pair production of squarks and gluinos at the LHC Run II. First of all, we update the calculations based on NLO+NLL partonic cross sections by using the NNPDF3.0NLO global analysis. This study includes a full characterization of theoretical uncertainties from higher orders, PDFs and the strong coupling. Then we explore the implications for this calculation of the recent NNPDF3.0 PDFs with NLO+NLL threshold resummation. We find that the shift in the results induced by the threshold-improved PDFs is within the total theory uncertainty band of the calculation based on NLO PDFs. However, we also observe that the central values of the NLO+NLL cross sections are modified both in a qualitative and a quantitative way, illustrating the relevance and impact of using threshold-improved PDFs together with resummed partonic cross sections. The updated NLO+NLL cross sections based on NNPDF3.0NLO are publicly available in the NLL-fast format, and should be an important ingredient for the interpretation of the searches for supersymmetric particles at Run II.

There is ample evidence, dating as far back as Low's theorem, that the universality of soft emissions extends beyond leading power in the soft energy. This universality can, in principle, be exploited to generalise the formalism of threshold resummations beyond leading power in the threshold variable. In the past years, several phenomenological approaches have been partially successful in performing such a resummation. Here, we briefly review some recent developments which pave the way to a solution of this problem, at least for electroweak annihilation processes.