We provide an elementary pedagogical introduction to some basic concepts and techniques of soft (or Sudakov) resummation, specifically in QCD, paying particular attention to simple but useful tricks of the trade. We briefly review collinear (Altarelli–Parisi) and infrared (eikonal) factorization, cancellation of infrared singularities, and factorization of mass singularities. We recall basic concepts on renormalization group invariance and the solution of renormalization group equations. We then show how threshold resummation can be derived from a renormalization group argument following from the cancellation of infrared singularities. We discuss various equivalent forms of the resummed result, and we briefly present transverse momentum resummation. Abstract Published by the Jagiellonian University 2026 authors

Italy

S. Forte

G. Ridolfi

A Simple Introduction to Soft Resummation

The Roper resonance \(N^\ast (1440)\) was discovered by David Roper in 1964 through sophisticated partial-wave analyses of \(\pi N\) scattering data. However, the first direct observation of the Roper resonance peak in the \(\pi N\) invariant mass spectrum was only realized 40 years later from the charmonium decay \(J/\psi \to \bar pn\pi ^+ +\mathrm {c.c.}\) at the Beijing Electron–Positron Collider. Further observations of the Roper resonance production from various charmonium decays helped reveal its multiquark nature, with a large \(\sigma N\) component. Abstract Published by the Jagiellonian University 2026 authors

B.S. Zou

Roper Resonance \(N^\ast (1440)\) from Charmonium Decays

The first baryon resonance was discovered in the early 1950s. The Roper resonance joined the collection ten years later. Today, many baryon resonances are known and more are being discovered. As baryons, these states are the most fundamental three-body systems in Nature. They must all be understood, not just the isolated ground-state nucleon. This contribution sketches applications of continuum Schwinger function methods to the baryon resonance problem. Whilst spectroscopy is of value, particular emphasis is placed on resonance electroproduction because transition form factors extracted from electroproduction data provide a keen tool for revealing resonance structure. Abstract Published by the Jagiellonian University 2026 authors

China

P. Cheng

L. Liu

Y. Lu

C.D. Roberts

Insights into Nucleon Resonances via Continuum Schwinger Function Methods

Sixty years ago, the first excited state of a proton/neutron was “born”. During this time, we learned a lot about it, specifically, how unique this case is: a single resonance with two-pole positions on different Riemann sheets. Let me provide a brief history to remind the readers how development progressed. Sure, history is sometimes what never happened, described by those who were never there … Abstract Published by the Jagiellonian University 2026 authors

United States

I. Strakovsky

Anatomy of Roper Resonance

The second excitation of the nucleon, the Roper, has properties differentiated from other low-lying nucleon resonances. Their properties challenge our understanding of the structure of the baryons in terms of the degrees of freedom from QCD. In the present work, we discuss the properties of the Roper resonance and the nucleon to Roper electromagnetic transition, based on the quark degrees of freedom, that are expected to dominate for large square momentum transfer \(Q^2\). We also discuss the analytic structure of the transition amplitudes in the low-\(Q^2\) region, and how the contributions of baryon–meson states can help to describe the low- and intermediate-\(Q^2\) data, and the nature of the Roper. Abstract Published by the Jagiellonian University 2026 authors

South Korea

G. Ramalho

Nucleon to Roper Transition Amplitudes and Electromagnetic Form Factors

In honor of Dave Roper’s \(90^{\mathrm {th}}\) birthday, I present a pedagogical introduction to our modern understanding of unstable particles in Quantum Field Theory, based on the analytic structure of the propagator, with occasional remarks on the Roper resonance. I discuss the mass and decay rate of unstable particles, the Breit–Wigner resonance formulae and width, poles and branch cuts, and pole trajectories. Abstract Published by the Jagiellonian University 2026 authors

S. Willenbrock

Unstable Particles in Quantum Field Theory

Calculating the properties of baryon resonances from quantum chromodynamics requires evaluating the temporal correlations between hadronic operators using integrations over field configurations weighted by a phase associated with the action. By formulating quantum chromodynamics on a space-time lattice in imaginary time, such integrations can be carried out non-perturbatively using a Markov-chain Monte Carlo method with importance sampling. The energies of stationary states in the finite volume of the lattice can be extracted from the temporal correlations. A quantization condition involving the scattering \(K\)-matrix and a complicated “box matrix” also yields a finite-volume energy spectrum. By appropriately parametrizing the scattering \(K\)-matrix, the best-fit values of the \(K\)-matrix parameters are those that produce a finite-volume spectrum which most closely matches that obtained from the Monte Carlo computations. Results for the \({\mit \Delta }\) resonance are presented, and a study of scattering for energies near the \({\mit \Lambda }(1405)\) resonance is outlined, showing a two-pole structure. The prospects for applying this methodology to the Roper resonance are discussed. Abstract Published by the Jagiellonian University 2026 authors

C. Morningstar

Low-lying Baryon Resonances from Lattice QCD

In many reactions leading to excitations of the nucleon, the Roper resonance \(N^*(1440)\) can be sensed only very indirectly by complex partial-wave analyses. In nucleon–nucleon collisions the isoscalar single-pion production as well as specific two-pion production channels present the Roper excitation free of competing resonance processes at a mass of 1370 MeV and a width of 150 MeV. A detailed analysis points to the formation of \(N^*(1440)N\) dibaryonic systems during the nucleon–nucleon collision process similar to what is known from the \({\mit \Delta }(1232)N\) threshold. Abstract Published by the Jagiellonian University 2026 authors

Germany

H. Clement

The Roper Resonance \(N^*(1440)\) in Nucleon–Nucleon Collisions and the Issue of Dibaryons

The problem of ordering of radial &lt;span class="it"&gt;versus&lt;/span&gt; orbital excitations is reviewed. It is shown that the current quark models cannot explain the location of the Roper resonance which is slightly lower than the lowest negative-parity excitations. We also study some related spectral problems, such as the dependence of the energies on the quark masses, and the possibility of bound states in simple chromelectric models. Abstract Published by the Jagiellonian University 2026 authors

France

J.M. Richard

Level Order of Quark Systems: The Puzzle of the Roper Resonance, and Related Questions

Ever since its discovery in 1964, the nature of the \(N^\ast (1440)\) nucleon resonance has been a perpetual and one of the outstanding puzzles in hadronic physics. The Ljubljana group joined the global effort in the late 1990s, first from the theoretical viewpoint and later experimentally. This paper is a short overview of our attempts to understand this elusive resonance. Abstract Published by the Jagiellonian University 2026 authors