The Roper resonance and kin

TL;DR

The paper surveys the Roper resonance and the longstanding mass puzzle, weighing conventional three-quark excitations against dynamically generated meson–baryon scenarios. It integrates insights from AdS/QCD, functional methods, and Lattice QCD to support a picture in which the Roper is a three-quark core dressed by a substantial meson cloud, a view corroborated by electroproduction data that reveal a Q^2-dependent transition structure separating core and cloud contributions. Extending the discussion to higher positive-parity nucleon excitations, the work shows a systematic pattern in the second excitation shell and considers the nature of N(2100) as a potential fourth-shell state or hybrid. Together, these findings provide a coherent, QCD-rooted framework for understanding nucleon resonance structure across distance scales and offer stringent tests for baryon spectroscopy models.

Abstract

The properties of the Roper resonance N(1440) are reviewed. Quark models have long struggled to reproduce its mass relative to its negative-parity partner N(1535). This discrepancy motivated interpretations of the Roper as a dynamically generated meson-baryon state. Including its isospin partners Delta(1600) and Delta(1700) 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* states with JP = 1/2+; the highest-mass member, N(2100), likely represents a Roper-like excitation in the fourth shell.

Figures (9)

• Figure 1: Breit--Wigner masses from all entries in the RPP ParticleDataGroup:2024cfk. The box widths give the uncertainty, the height is inverse proportional to the uncertainty. The data are from Refs. Arndt:2006bfBatinic:2010zzCutkosky:1980rhHunt:2018wqzHohler:1979yrPenner:2002maSarantsev:2025likShrestha:2012epCBELSATAPS:2015kka (low mass) and Arndt:2006bfShklyar:2012jsVrana:1999nt (high-mass). See text for a discussion.
• Figure 2: Comparison of calculated masses of spin-$1/2$ nucleon and spin-$3/2$$\Delta$ resonances with RPP values (shown by boxes). The models are characterized by their interaction: One-gluon exchange (OGE) Capstick:1986ter, Goldstone-boson exchange (GBE) Glozman:1997ag, instanton-induced interactions (I.I.I.) without Loring:2001kx or with additional Goldstone-boson exchange Ronniger:2012xp, the hypercentral constituent-quark model (HQM) Giannini:2001kb, diquark (DQ) models Santopinto:2004hwSantopinto:2014opa, the algebraic model (AM) Bijker:1994yr, a holographic model Brodsky:2014yha, an empirical mass formula (MF) Burkert:2025coj, and functional methods (FM) Eichmann:2016hgl The three latter models are compared to the pole masses.
• Figure 3: Kinematics of $\pi^+$ electroproduction off protons in the laboratory system.
• Figure 4: Magnetic transition multipole $M_{1-}$ of the proton to Roper resonance transition versus W. The red lines represent the imaginary part of $M_{1-}$, the blue lines the real part, using two different analysis techniques; left: $Q^2=0$, right: $Q^2=2$ GeV$^2$.
• Figure 5: Left: The $\gamma^\ast p\to N(1440)$ helicity transition amplitude $A_{1/2}$. Right: $S_{1/2}$. Both amplitudes in units of $10^{-3}$ GeV$^{-1/2}$. The solid red curves are from a light-front relativistic quark model Aznauryan:2012ec and the black dashed curves are DSE results Segovia:2015hra. The green triangles and the blue full circles markers are data from the CLAS collaboration CLAS:2012wxwCLAS:2009cesMokeev:2023zhq. The red cicle at the very small $Q^2$ value is from Stajner:2017fmh. See also text for details.