High-energy scattering often demands resumming large energy logarithms, beyond the reach of fixed-order QCD. Inspired by the old multiperipheral models, we study proton–proton collisions with a forward jet, a backward jet, and central mini-jets, using the BFKL framework. Jet rapidity distributions are used to search for BFKL effects, comparing PYTHIA8 predictions with those from the BFKLex Monte Carlo.

The ECFA Higgs, electroweak, and top Factory Study ran between 2021 and 2025 as a broad effort across the experimental and theoretical particle physics communities, bringing together participants from many different proposed future collider projects. Activities across three main working groups advanced the joint development of tools and analysis techniques, fostered new considerations of detector design and optimisation, and led to a new set of studies resulting in improved projected sensitivities across a wide physics programme. This report demonstrates the significant expansion in the state-of-the-art understanding of the physics potential of future e+e- Higgs, electroweak, and top factories, and has been submitted as input to the 2025 European Strategy for Particle Physics Update.

We show that rank-ordered jet rapidity distributions - a direct application of order statistics - provide a simple yet powerful probe of high-energy (small-x) QCD dynamics at the LHC. In inclusive dijet topologies at s^(1/2) = 8 and 13 TeV, with realistic jet selections, we compare a BFKL-based Monte Carlo (BFKLex) to two general-purpose event generators based on collinear factorization and DGLAP parton showers, PYTHIA8 (pT-ordered) and HERWIG7 (angular-ordered). Even when two underlying dynamics happen to give similar inclusive jet rapidity distributions, such observables are too coarse to discriminate their underlying rapidity point processes, whereas the rank-ordered distributions remain sensitive to the differences in how rapidity space is filled. For fixed multiplicity (N=3) and for the second-most-forward/backward jets across multiplicities, BFKLex populates the rapidity interval more democratically, whereas the general-purpose event generators exhibit comparatively stronger edge enhancement for N=3 and narrower, more centrally concentrated distributions for the second-most ranks. These shape differences are stable under variations of jet radius, proton PDFs, and MPI/hadronization settings, and persist when requiring large rapidity separation between the outer jets. Rank-ordered rapidities thus compress genuinely exclusive information about the multi-jet final state into one-dimensional, normalized histograms that are directly measurable with existing dijet and Mueller-Navelet selections and provide a new handle on high-energy radiation patterns.

After the end of World War II, the commitment to confine scientific activities in universities and research institutions to peaceful and civilian purposes has entered, in the form of Civil Clauses, the charters of many research institutions and universities. In the wake of recent world events, the relevance and scope of such Civil Clauses has been questioned in reports issued by some governments and by the EU Commission, a development that opens the door to a possible blurring of the distinction between peaceful and military research. This paper documents the reflections stimulated by a panel discussion on this issue recently organized by the Science4Peace Forum. We review the adoptions of Civil Clauses in research organizations and institutions in various countries, present evidence of the challenges that are emerging to such Civil Clauses, and collect arguments in favour of maintaining the purely civilian and peaceful focus of public (non-military) research.

The armed invasion of Ukraine by the Russian Federation has adversely affected the relations between Russia and Western countries. Among other aspects, it has put scientific cooperation and collaboration into question and changed the scientific landscape significantly. Cooperation between some Western institutions and their Russian and Belarusian partners were put on hold after February 24, 2022. The CERN Council decided at its meeting in December 2023 to terminate cooperation agreements with Russia and Belarus that date back a decade. CERN is an international institution with UN observer status, and has so far played a role in international cooperation which was independent of national political strategies. We argue that the Science4Peace idea still has a great value and scientific collaboration between scientists must continue, since fundamental science is by its nature an international discipline. A ban of scientists participating in international cooperation and collaboration is against the traditions, requirements and understanding of science. We call for measures to reactivate the peaceful cooperation of individual scientists on fundamental research in order to stimulate international cooperation for a more peaceful world in the future. Specifically, we plead for finding ways to continue this cooperation through international organizations, such as CERN and JINR.

In high-energy particle physics, the study of particle-particle correlations in proton-proton and heavy-ion collisions constitutes a pivotal frontier in the effort to understand the fundamental dynamics of the strong force. To the best of our knowledge, we employ for the first time the BFKL dynamics implemented in a Monte Carlo code in momentum space to compute final state correlations in proton-proton collisions. Our present work aims to investigate whether the particular dynamics of the high-energy limit of QCD can contribute to the long-range rapidity correlations and the enigmatic ridge effect in proton-proton collisions.

Quantum properties of the state associated to the gluon Green's function in the Balitsky-Fadin-KuraevLipatov approach are studied using a discretization in virtuality space. Considering the coupling constant as imaginary, its density matrix corresponds to a pure state for any energy. Nonlinear corrections due to high gluon densities are modeled through a suppression of infrared modes in the Hamiltonian making it no longer Hermitian. This introduces quantum decoherence into the evolution equation. When the coupling is real this leads to unbounded normalization of states which becomes bounded for sufficient saturation of infrared modes. Physical quantum properties, such as a purity smaller than one or a positive von Neumann entropy, hence are recovered when the infrared/ultraviolet original symmetry of the formalism is broken. Similarly to the work of Armesto, Dominguez, Kovner, Lublinsky and Skokov in [J. High Energy Phys. 05 (2019) 025], an evolution equation of Lindblad type for the normalized density matrix describing the open system is obtained.

This paper presents a new set of multijet event shape variables introduced to further understand the Mueller-Navelet jet topology. This topology consists of having at least one pair of jets with a very large rapidity separation between them, treating additional jet activity inclusively. This multijet topology is expected to shed light on the radiation pattern that is expected in the high-energy limit of the strong interaction. The paper relies on a Monte Carlo event generator analysis. One set of predictions uses the BFKLex event generator, which is based on Balitsky-Fadin-Kuraev-Lipatov (BFKL) perturbative quantum chromodynamics (pQCD) evolution with a resummation of large logarithms of energy at leadinglogarithmic accuracy. The BFKLex predictions are compared with a fixed-order next-to-leading order pQCD calculation using POWHEG matched to the parton shower of Pythia8 (NLO + PS), which is the standard for NLO generator predictions at the LHC. We find that both approaches lead to compatible results at current LHC energies, assuming the current experimental constraints for the reconstruction of low transverse momentum jets in ATLAS and CMS. This shows the reliability of the BFKL approach at describing the behavior of the strong interaction in the preasymptotic limit of high center-of-mass energies. Differences between the NLO + PS and the BFKL-based approaches are found when the jet multiplicity is increased or when the minimum transverse momentum of the jets is decreased.

The goal of this whitepaper is to give a comprehensive overview of the rich field of forward physics. We discuss the occurrences of BFKL resummation effects in special final states, such as Mueller-Navelet jets, jet gap jets, and heavy quarkonium production. It further addresses TMD factorization at low x and the manifestation of a semi-hard saturation scale in (generalized) TMD PDFs. More theoretical aspects of low x physics, probes of the quark gluon plasma, as well as the possibility to use photon-hadron collisions at the LHC to constrain hadronic structure at low x, and the resulting complementarity between LHC and the EIC are also presented. We also briefly discuss diffraction at colliders as well as the possibility to explore further the electroweak theory in central exclusive events using the LHC as a photon-photon collider.

Abstract We study the four-gluon scattering amplitude in the high energy limit of QCD written in terms of its conformal expansion. We highlight the need to include both even and odd conformal spin contributions in order to map it to an iterative representation in rapidity and transverse momentum space which we have evaluated numerically. By Fourier expanding in a set of three azimuthal angles, we find a new form for the amplitude in terms of 4 F 3 hypergeometric functions. An alternative formulation is possible when connecting this Fourier expansion with Bessel kernels studied in analytic number theory.

Multi-particle production studies have always been an important tool in the effort to study the properties of the strong force already from the fifties of the previous century. As the center-of-mass energy of present day hadron colliders and in particular the Large Hadron Collider (LHC) has increased enormously over the years and the focus currently is on the study of multi-jet final states, it would be instructive to see whether the early days phenomenological models applied some 50–60 years ago to describe multi-particle production have anything to offer in the study of multi-jet final states as well as whether they offer predictions different from the QCD based ones. In this paper, we will consider events with two jets well separated in rapidity with similar transverse momenta whereas a number of mini-jets or jets is to be found in between these two bounding jets. Such configurations are relevant for the high energy scattering limit of QCD. We fix the final jet multiplicity to take particular values and we report on a first comparison between the predictions of the old multiperipheral Chew-Pignotti model applied for final state jets and those of BFKL. We compare single jet rapidity distributions as well as jet-jet rapidity correlations.

Multi-jet production at the LHC is an important process to study. In particular, events with final state kinematic configurations where we have two jets widely separated in rapidity with similar pT and lots of mini-jets or jets populating the space in between are relevant for the high energy limit of QCD. Keeping the jet multiplicity fixed, the study of these events is a good ground to test different models of multi-particle production in hadron-hadron collisions. We report on a comparison between the predictions of the old multiperipheral Chew-Pignotti model and those of BFKL for the single jet rapidity distributions and for jet-jet rapidity correlations.

This is a personal recollection of several results involving the phenomenological study of the multi-Regge limit of scattering amplitudes. None of them would have been possible without the encouragement and constant support from Lev Nikolaevich Lipatov.

The 13 TeV run of the LHC has provided a unique opportunity to explore multi-jet final states with unprecedented accuracy. An interesting region for study is that of events where one jet is tagged in the forward direction and another one in the backward direction and a plethora of low energy mini-jets populate the possibly large rapidity span in between them. Since the number of these events is very high, it is possible to introduce stringent constraints on the transverse momentum of the two leading jets which can be kept in small windows not very different from each other, defining what we call “twin jets”. The associated “crowd” of mini-jets can also have a restricted span in transverse momentum. The study of these events for a fixed multiplicity is an ideal playground to investigate different models of multi-particle production in hadron-hadron collisions. We set up an exploratory analysis by using an ancient model of Chew and Pignotti to describe the gross features one can expect for the structure of single and double differential-in-rapidity cross sections and for particle-particle rapidity correlations when the longitudinal phase space completely decouples from the transverse degrees of freedom.

From the Past to the Future, pp. 1-23 (2021) Free AccessChapter 1: Family Memories: Husband, Father and GrandfatherJoachim Bartels, Victor Fadin, Evgeny Levin, Aharon Levy, Victor Kim and Agustin Sabio-VeraJoachim BartelsHamburg University, Germany, Victor FadinRussian Academy of Sciences, Russia, Evgeny LevinTel Aviv University, Israel, Aharon LevyTel Aviv University, Israel, Victor KimNational Research Center "Kurchatov Institute", RussiaSaint Petersburg Polytechnic University, Russia and Agustin Sabio-VeraUniversidad Autonoma de Madrid, Spainhttps://doi.org/10.1142/9789811231124_0001Cited by:0 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: The following sections are included: Introduction Wife Elvira The eldest daughter Irina The youngest daughter Ekaterina Grandchildren FiguresReferencesRelatedDetails From the Past to the FutureMetrics Downloaded 34 times History PDF download

This is a personal recollection of several results related to the study of the high energy limit of scattering amplitudes in gravitational theories. They would not have been possible without the encouragement and constant support from Lev Nikolaevich Lipatov.

The forward BFKL equation is discretised in virtuality space and it is shown that the diffusion into infrared and ultraviolet momenta can be understood in terms of a semi-infinite matrix. The square truncation of this matrix can be exponentiated leading to asymptotic eigenstates sharing many features with the BFKL gluon Green’s function in the limit of large matrix size. This truncation is closely related to a representation of the XXX Heisenberg spin = - 1/2 chain with SL(2) invariance where the Hamiltonian acts on a symmetric double copy of the harmonic oscillator. A simple modification of the BFKL matrix suppressing the infrared modes generates evolution more compatible with the Froissart bound.

An asymmetric version of the classical Kermack-McKendrick description of an epidemic evolution is presented in terms of four independent parameters. This is enough to obtain an accurate description of the different stages of the COVID-19 pandemia in any country for the reported daily and total number of casualties due to the infection. The asymmetry accounts for lockdown effects introduced to reduce the impact of the epidemic outburst. A set of new variables allows for an analytic study of the evolution of the system before and after the lockdown measures are put in place. A continuous matching is possible for all variables in the system apart from the time dependence of the infection rate. An analytic expression is obtained for this discontinuity which is proposed as a good quantity to gauge the efficiency of the lockdown measures. A study of this variable for different countries is performed. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement This work has been supported by the Spanish Research Agency (Agencia Estatal de Investigacion) through the grant IFT Centro de Excelencia Severo Ochoa SEV-2016-0597, and the Spanish Government grants FPA2015-65480-P, FPA2016-78022-P. ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: Universidad Autonoma de Madrid All necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable. Yes The public data considered here have been taken from "Daily New Deaths in Spain" in the real time world statistics generated by Worldometer at <https://www.worldometers.info/coronavirus/country/spain/>. The same source for officially reported deaths has been used in all the studies of this work. The public data provided by EuroMOMO, the European mortality monitoring activity <https://www.euromomo.eu>) have also been used.

The set of double-logarithmic (DL) contributions (α t ln2s)n to the 4-graviton amplitude in $$ \mathcal{N} $$ = 8 supergravity (SUGRA), with α being the gravitational coupling and (s, t) the Mandelstam invariants, is studied in impact parameter (ρ) representation. This sector of the amplitude shows interesting properties which shed light on the nature of quantum corrections in gravity. Besides having a convergent behaviour as s increases, which is not present in $$ \mathcal{N} $$ < 4 SUGRA theories, there exists a critical line ρc(s) above which the Born amplitude prevails. The short distance region ρ < ρc(s) is dominated by the DL terms. As a consequence, when studied in terms of an eikonal approach in the forward limit, the scattering angle linked to the bending of the semiclassical trajectory of the graviton shows a transition from attractive gravity at large distances to a region at small ρ characterized by a repulsive DL contribution to the gravitational potential due to the gravitino content of the theory. In the complex angular momentum plane, this DL high energy asymptotics is driven by the rightmost pole singularity of a parabolic cylinder function. The resummation of DL quantum corrections in $$ \mathcal{N} $$ = 8 SUGRA can be understood in terms of the counting of 1-rooted maps on orientable surfaces.

At high center-of-mass energies scattering amplitudes enjoy a hidden integrability. An important example in QCD is Odderon exchange, a composite state of three reggeized gluons, with can be understood as a closed spin chain with periodic boundary conditions. In the N =4 supersymmetric Yang-Mills theory a similar open spin chain appears for the planar eight-point amplitude. We solve these two examples in transverse momentum and rapidity space, introducing the concept of weighted graph complexity and its associated emerging scaling laws.