abstract

The Roper resonance was discovered in L. David Roper’s Ph.D. thesis research at MIT with Prof. Bernard T. Feld as advisor, with the extensive computing done at Livermore Radiation Laboratory with Dr. Michael J. Moravcsik and programmer Robert M. Wright. The basic coding was taken from the nucleon–nucleon coding of Dr. Richard A. Arndt. Despite the fact of a negative scattering length, which had led to thinking that there would be no \(P_{11}\) resonance, the computer code and large amount of data at that time insisted that the resonance existed. This article discusses some features, including the serendipity, of the discovery and of the unusual Roper resonance.

abstract

The Roper resonance (\(P_{11}(1440)\) or \(N_{\scriptstyle \frac {1}{2}}^{\scriptstyle +}(1440))\) has been and continues to be the subject of experimental studies at both hadronic and electromagnetic facilities. This year, we celebrate and honor its discoverer, L. David Roper, on the occasion of his \(90^{\rm th}\) birthday. Recent studies and publications have emphasized the role of electromagnetic beams in studying the properties of the Roper resonance. In this article, we review the role of early experiments using hadronic beams that were sparked by the discovery of the “Roper”, and also motivated and encouraged the design and construction of the early meson factories such as LAMPF (Los Alamos Meson Physics Facility), TRIUMF (TRI University Meson Facility), PSI (Paul Scherrer Institute, formerly SIN), and INR (Institute for Nuclear Research).

abstract

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

The properties of the Roper resonance \(N(1440)\nicefrac {1}{2}^+\) are reviewed. Quark models have long struggled to reproduce its mass relative to its negative-parity partner \(N(1535)\nicefrac {1}{2}^-\). This discrepancy motivated interpretations of the Roper as a dynamically generated meson–baryon state. Including its isospin partners \({\mit \Delta }(1600)\nicefrac {3}{2}^+\) and \({\mit \Delta }(1700)\nicefrac {3}{2}^-\) further accentuates the tension between quark-model predictions and experiment. Recent developments based on AdS/QCD and functional methods achieve much improved agreement, identifying the Roper as an ordinary three-quark excitation. Electroproduction experiments at Jefferson Lab have now resolved this long-standing question, revealing the Roper as a \(qqq\) core dressed by a substantial meson cloud. The Roper resonance belongs to a family of four \(N^\ast \) states with \(J^P=\nicefrac {1}{2}^+\); the highest-mass member, \(N(2100)\nicefrac {1}{2}^+\), likely represents a Roper-like excitation in the fourth shell.

abstract

The \(N(1440)1/2^+\) nucleon resonance, first identified in 1964 by Roper and collaborators in analyses of \(\pi N\) hadroproduction data, has continued to provide pivotal insights that serve to advance our understanding of nucleon excited states. In this contribution, we present results from studies of the structure of the Roper resonance based on exclusive \(\pi N\) and \(\pi ^+\pi ^-p\) electroproduction data measured with the CLAS detector at Jefferson Lab. These analyses have revealed the Roper resonance as a complex interplay between an inner core of three dressed quarks and an external meson–baryon cloud. Analyses of the CLAS results on the evolution of the Roper resonance electroexcitation amplitudes with photon virtuality \(Q^2\), within the framework of the Continuum Schwinger Method, have conclusively demonstrated the capability to gain insight into the strong interaction dynamics responsible for generating more than 98% of hadron mass. Further extension of such studies to higher \(Q^2\), through experiments currently underway with the CLAS12 detector and in the future with a potential CEBAF energy upgrade to 22 GeV, offers the only foreseeable opportunity to explore the full range of distances where the dominant portion of hadron mass and resonance structure emerge.

abstract

Few baryon resonances have generated as much discussion, even controversy, as the first positive parity excited state with nucleon quantum numbers. We re-examine the issue using insight gained from lattice QCD, complemented by Hamiltonian effective field theory. In doing so, we also examine the distinction between a state that can be naturally described as a quark model state and one that is dynamically generated.

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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

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

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

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.

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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

The problem of ordering of radial versus 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

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

The theory of nuclear excitations involving nucleon resonances is revisited and significantly extended to asymmetric nuclear matter and higher \(P\)- and \(S\)-wave \(N^*\) resonances. Excited states are described as superpositions of particle–hole configurations including \(NN^{'-1}\) and \(N^*N^{-1}\) configurations. The configuration mixing is taken into account on the one-loop level by solving the generalized \(N^*\)RPA Dyson equation. The underlying coupled channels formalism is derived and the response functions are discussed. Applications of the approach are illustrated for charge-exchange modes of asymmetric nuclear matter and finite nuclei. The spectral gross structures of corresponding excitations in finite nuclei are investigated in the local density approximation. Applications of the approach to resonance studies by high-energy heavy-ion reactions are recapitulated.

abstract

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

Recent work on using density-dependent \({\mit \Lambda }\)-nuclear optical potentials in calculations of \({\mit \Lambda }\)-hypernuclear binding energies is reviewed. It is found that all known \({\mit \Lambda }\) binding energies in the mass range of \(16 \leq A \leq 208\) are well fitted in terms of two interaction parameters: one, attractive, for the spin-averaged \({\mit \Lambda } N\) interaction, and another one, repulsive, for the \({\mit \Lambda } NN\) interaction. The \({\mit \Lambda } N\) interaction term by itself overbinds \({\mit \Lambda }\) hypernuclei, in quantitative agreement with recent findings obtained in EFT and Femtoscopy studies. The strength of the \({\mit \Lambda } NN\) interaction term is compatible with values required to resolve the hyperon puzzle.

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We discuss in rather general terms the properties of space-like baryon transition form factors. In particular, we argue why these are necessarily complex-valued, what can be deduced from the respective phase motion, and why dealing with real-valued transition form factors in general leads to misleading results. For illustration, the transition form factors for the Roper resonance as derived in the Jülich–Bonn–Washington framework are discussed.

abstract

The long-standing debate over whether the complete set of observables in pseudo-scalar meson photoproduction consists of eight or merely four elements continues to persist. From the perspective of amplitude analysis, it is argued that all eight observables are necessary to completely determine the others. On the other hand, proponents of partial-wave analysis, working with theoretically precise data of infinite accuracy, claim that only four observables are needed. However, this claim is not acceptable from an experimental viewpoint, as all data in the real world contain some uncertainty. This paper illustrates that the controversy is artificial and is due to additional mathematical assumptions used in partial-wave analysis. Our research advances this discussion by moving from exact synthetic numerical data to also synthetic, but more realistic data in partial-wave analysis and shows that the claimed reduction in observables is unjustified. Consequently, the final conclusion is that the complete set of observables in pseudo-scalar meson photoproduction, whether using amplitude analysis or partial-wave analysis with practical data, must consist of eight observables.

abstract

This article proposes a universal mass equation (UME) for the baryon and meson equal-quantum excited states sets that have three or more known states in the set and have no more than one missing state. The conjecture is made that accurately measured masses using Breit–Wigner PDG2024 data at fixed \(J^P\) for all equal-quantum baryon excited-states sets (including LHCb exotic \(P_{c\bar {c}s}^+\)) and at fixed \(J^{PC}\) for all equal-quantum meson excited-states sets (including \(s\bar {s}\), \(s\bar {c}\), \(c\bar {c}\), \(c\bar {b}\), and \(b\bar {b}\)) are related by the logarithm function used here; at least for the mass range of currently known excited states. Our study examines the relationship between the ground-state masses and the logarithmic slopes, and finds an approximately inverse relationship. We discuss the measurability of overlapping states. We make an estimate of fundamental properties of the QCD potential.