Baryon spectroscopy

Eberhard Klempt and Jean-Marc Richard

Rev. Mod. Phys. 82, 1095 – Published 8 April 2010

Abstract

About 120 baryons and baryon resonances are known, from the abundant nucleon with $u$ and $d$ light-quark constituents up to the $Ξ_{b}^{-} = (b s d)$ , which contains one quark of each generation and to the recently discovered $Ω_{b}^{-} = (b s s)$ . In spite of this impressively large number of states, the underlying mechanisms leading to the excitation spectrum are not yet understood. Heavy-quark baryons suffer from a lack of known spin parities. In the light-quark sector, quark-model calculations have met with considerable success in explaining the low-mass excitations spectrum but some important aspects such as the mass degeneracy of positive-parity and negative-parity baryon excitations remain unclear. At high masses, above $1.8 GeV$ , quark models predict a very high density of resonances per mass interval which is not yet observed. In this review, issues are identified discriminating between different views of the resonance spectrum; prospects are discussed on how open questions in baryon spectroscopy may find answers from photoproduction and electroproduction experiments which are presently carried out in various laboratories.

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DOI:https://doi.org/10.1103/RevModPhys.82.1095

Authors & Affiliations

Eberhard Klempt^*

Helmholtz-Institut für Strahlen- und Kernphysik der Rheinischen Friedrich-Wilhelms Universität, Nußallee 14-16, D-53115 Bonn, Germany

Jean-Marc Richard^†

Laboratoire de Physique Subatomique et Cosmologie, Université Joseph Fourier-CNRS-IN2P3-INPG, Grenoble, France, and Institut de Physique Nucléaire de Lyon, Université de Lyon, CNRS-IN2P3-Université Claude Bernard, 4, rue Enrico Fermi, F-69622 Villeurbanne, France

^*klempt@hiskp.uni-bonn.de
^†j-m.richard@ipnl.in2p3.fr

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Vol. 82, Iss. 2 — April - June 2010

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Figure 1
(Color online) Mass gap from the respective ground states to the lowest excitation with $J^{P} = 5 ∕ 2^{+}$ .Reuse & Permissions
Figure 2
Excitation spectrum of $Λ$ , $Λ_{c}^{+}$ , and $Ξ_{c}$ . Between $Λ_{3 ∕ 2^{-}} (1690)$ and $Λ_{5 ∕ 2^{+}} (1690)$ there are two further states which are omitted for clarity. The quantum number assignments of $Λ_{c}$ and $Ξ_{c}$ follow 40, those with question marks are our tentative assignments. The $Λ_{c} (2880)$ marked ?? is suggested to have $J^{P} = 5 ∕ 2^{+}$ . From 7.Reuse & Permissions
Figure 3
The $Λ_{c}^{+} π^{+} π^{-}$ invariant mass distribution after a cut on the $Λ_{c}^{+}$ (reconstructed from five decay modes) and using side bins (dashed line). From 27.Reuse & Permissions
Figure 4
Invariant mass distribution for $D^{0} p$ candidates at BABAR. Also shown are the contributions from $D^{0}$ sidebands (gray) and wrong-sign combinations (open dots). From 72.Reuse & Permissions
Figure 5
The yield of $Λ_{c} {(2880)}^{+} \to Σ_{c} {(2455)}^{0} π^{+}$ and $Σ_{c} {(2455)}^{+ +} π^{-}$ decays as a function of the helicity angle. The fits correspond to $Λ_{c} {(2880)}^{+}$ spin hypotheses $j = 1 ∕ 2$ (dotted line), $3 ∕ 2$ (dashed curve), and $5 ∕ 2$ (solid curve), respectively. From 7.Reuse & Permissions
Figure 6
Mass difference spectrum $M (Λ_{c}^{+} π^{0}) - M (Λ_{c}^{+})$ from CLEO. The solid line fit is to a third-order polynomial background shape and two $P$ -wave Breit-Wigner functions smeared by Gaussian resolution functions for the two signal shapes. The dashed line shows the background function. From 39.Reuse & Permissions
Figure 7
The $Ξ_{c}$ and $Ξ_{c}^{'}$ . Upper panel: (a) Summed invariant mass distributions for $Ξ^{-} π^{+} π^{+}$ and $Ξ^{0} π^{+} π^{0}$ combinations with $x_{p} > 0.5$ and 0.6, respectively, and (b) for $Ξ^{-} π^{+}$ , $Ξ^{-} π^{+} π^{0}$ , $Ω^{-} K^{+}$ , and $Ξ^{0} π^{+} π^{-}$ combinations. Lower panel: Invariant mass difference $Δ M (Ξ_{c} γ - Ξ_{c})$ distributions for $Ξ_{c}^{+} γ$ and $Ξ_{c}^{0} γ$ , where contributions from the different $Ξ_{c}$ decay modes have been summed in each case. From 309.Reuse & Permissions
Figure 8
(Color online) $Ξ_{c}$ spectroscopy. (a) $M (Λ_{c}^{+} K^{-} π^{+})$ and (b) $M (Λ_{c}^{+} K_{S}^{0} π^{-})$ distribution at BELLE (164). (c) The $Λ_{c}^{+} K^{-} π^{+}$ invariant mass distribution for $M (Λ_{c}^{+} π^{+})$ consistent with the $Σ_{c} (2455)$ and (d) with the $Σ_{c} (2520)$ , measured at BABAR (68, 73).Reuse & Permissions
Figure 9
(Color online) The invariant mass distributions of $Ω_{c}^{0} γ$ candidates, with $Ω_{c}^{0}$ reconstructed in various decay modes. The $M_{Ω_{c}^{0} γ}$ mass is corrected for the difference between the reconstructed $Ω_{c}^{0}$ mass and the nominal value $M_{Ω_{c}^{0}}^{PDG}$ . The shaded histograms represent the mass distribution expected from the mass sideband of $Ω_{c}^{* 0}$ . From 70.Reuse & Permissions
Figure 10
(Color online) The invariant mass distributions for the $Λ_{b}^{0} π^{+}$ (top) and $Λ_{b}^{0} π^{-}$ (bottom) combinations at CDF. From 1.Reuse & Permissions
Figure 11
(Color online) The invariant mass distributions of the $J ∕ ψ Ξ^{-}$ combinations at DØ (top) (5) and CDF (bottom) (2).Reuse & Permissions
Figure 12
(Color online) The search for the $Ω_{b}^{-}$ . Top: DØ data. The $M (Ω_{b}^{-})$ distribution of the $Ω_{b}^{-}$ candidates after all selection criteria. The dotted curve is an unbinned likelihood fit to the model of a constant background plus a Gaussian signal. From 6. Bottom: CDF data. $J ∕ Ψ Ω^{-}$ mass distribution. From 3.Reuse & Permissions
Figure 13
(Color online) The total and elastic cross sections for $π^{\pm}$ scattering off protons. From http://pdg.lbl.gov/current/xsect/, courtesy of the COMPAS group, IHEP, Protvino.Reuse & Permissions
Figure 14
(Color online) Differential cross section for several different center-of-mass energies. Solid and dashed curves correspond to different SAID (http://gwdac.phys.gwu.edu/ solutions).Reuse & Permissions
Figure 15
(Color online) Pion-nucleon scattering: (a) $s$ -channel exchange, (b) $t$ -channel exchange, and (c) $u$ -channel exchange.Reuse & Permissions
Figure 16
(Color online) The $γ p \to n π^{+}$ differential cross section as a function of $- t$ for $E_{γ} = 5.53 GeV$ (476). The data are from 42, 43 and 524.Reuse & Permissions
Figure 17
Definition of polarization variables. From 35.Reuse & Permissions
Figure 18
Fit to the $I = \frac{1}{2} Re (T_{π N, π N})$ and $Im (T_{π N, π N})$ of SAID (http://gwdac.phys.gwu.edu/).Reuse & Permissions
Figure 19
Total cross section for $π^{-} p \to n η$ , $K^{-} p \to Λ η$ , and $γ p \to p η$ . The later cross section is scaled by a factor of 137. From 443.Reuse & Permissions
Figure 20
The total cross sections as functions of the equivalent total energy $\sqrt{s_{eq}}$ , defined as the standard $s$ for pions and as $\sqrt{s_{eq}} \equiv \sqrt{s} - (m_{s} - m_{d})$ for incident kaons (424). Circles: $σ_{tot} (π^{-} p \to π^{0} π^{0} n)$ . Triangles: $σ_{tot} (K^{-} p \to π^{0} π^{0} Λ)$ . Crosses: $σ_{tot} (K^{-} p \to π^{0} π^{0} Σ^{0})$ .Reuse & Permissions
Figure 21
Dalitz plots of $M_{n π}^{2}$ vs $M_{p π}^{2}$ for $J ∕ ψ \to p π^{-} \bar{n}$ and $p π^{-}$ invariant mass spectrum. From 362.Reuse & Permissions
Figure 22
Total photoabsorption cross section and exclusive cross sections for single-meson and multimeson production. (a) Total, $p π^{0}$ , $p η$ , $p η^{'}$ ; (b) total, $Λ K^{+}$ , $Σ^{0} K^{+}$ , $Σ^{+} K^{0}$ ; (c) $p ρ$ , $p ω$ , $p ϕ$ , $Λ K^{* +}$ , $Σ^{+} K^{* 0}$ , $Σ^{0} K^{* +}$ ; (d) $p π^{+} π^{-}$ , $p π^{0} π^{0}$ , $p π^{0} η$ , $p π^{+} π^{-} π^{0}$ , $p K^{+} K^{-}$ .Reuse & Permissions
Figure 23
Separate helicity state total cross sections $σ_{3 ∕ 2}$ and $σ_{1 ∕ 2}$ of the proton (14, 15, 17; 212).Reuse & Permissions
Figure 24
Differential cross sections for $γ p \to p π^{0}$ . The solid line represents the BnGa, the dashed line the SAID (SM05), and the dotted line the MAID model.Reuse & Permissions
Figure 25
(Color online) Photon asymmetry $Σ$ in the $Δ$ resonance region for $γ p \to p π^{0}$ . The solid line is the MAID model. From 112.Reuse & Permissions
Figure 26
$G_{M}^{*}$ normalized by the dipole factor $G_{D} = {[1 + Q^{2} ∕ 0.71 {(GeV ∕ c)}^{2}]}^{- 1}$ .Reuse & Permissions
Figure 27
(Color online) Differential cross sections for the reaction $γ p \to p η$ from CBELSA (105) and CLAS (206) for different invariant masses and fit results (417). The dashed line represents the $S_{11}$ , the dash-dot-dotted line the $D_{13}$ , and the dash-dotted line the meson-exchange contribution; their sum is given as solid line.Reuse & Permissions
Figure 28
Differential cross sections for $γ p \to K^{+} Λ$ . The solid curves represent a Bonn-Gatchina fit. From 130.Reuse & Permissions
Figure 29
Angular distributions of the beam recoil observable $O_{z}$ (372). Data are compared with predictions of the Bonn-Gatchina (solid line, private communication from the GRAAL Collaboration) and the Regge-plus-resonance model of 172.Reuse & Permissions
Figure 30
(Color online) Contributions to $ω$ photoproduction. (a) The handbag diagram for hard photoproduction and electroproduction. The large blob represents the generalized parton distribution of the nucleon. At lower energies, processes (b), (c), (d) are more appropriate to describe the reaction. (b) Natural parity $t$ -channel exchange and (c) $t$ -channel exchange via the pion trajectory. (d) $s$ -channel intermediate resonance excitation. The same diagrams contribute to $ρ$ production while $ϕ$ are produced dominantly via (b). For $K^{*}$ production, a kaon trajectory is exchanged, the outgoing $N^{'}$ is replaced by a hyperon. (d), (e) Baryon pole in the $s$ and $u$ channel.Reuse & Permissions
Figure 31
The total cross section for $ω$ photoproduction (101) and decomposition into partial waves by 471.Reuse & Permissions
Figure 32
Electroproduction of $p π^{+} π^{-}$ after integration over the full dynamics. The cross sections are decomposed into the dominant isobar channels. The recent CLAS data (225) are shown by full symbols. Shadowed areas represent the systematical uncertainties. The solid lines correspond to an EBAC fit (JM06) to the six one-fold differential cross sections (406). The contributions from $π^{-} Δ^{+ +}$ , $π^{+} Δ^{0}$ channels are shown by dashed and dot-dashed lines and the contributions from direct $2 π$ production by dotted lines, respectively.Reuse & Permissions
Figure 33
Dalitz plot (Crystal Barrel at ELSA) for the reaction $γ p \to p π^{0} η$ for (a) $E_{γ} < 1.9 GeV$ and (b) $E_{γ} > 1.9 GeV$ . $Δ (1232)$ is seen in both Dalitz plots; $N (1535)$ is visible only for high photon energies even though the $N (1535) π$ production threshold $(\sim 1.0 GeV)$ is lower than the $Δ (1232) η$ production threshold $(\sim 1.2 GeV)$ .Reuse & Permissions
Figure 34
(Color online) Three-quark confinement in the string limit.Reuse & Permissions
Figure 35
(Color online) The light hadron spectrum of QCD. Horizontal lines and bands are the experimental values with their decay widths. The lattice results are shown by solid circles. Vertical error bars represent the combined statistical and systematic error estimates. $π$ , $K$ , and $Ξ$ masses input quantities.Reuse & Permissions
Figure 36
(Color online) Comparison of the excitation energy single-charm and single-beauty baryons above the $Λ_{c}$ ( $Λ_{b}$ mass). The quantum numbers are deduced from the quark model (512). For the $Ω_{b}$ both DØ (top) and CDF (bottom) results are shown as dotted lines.Reuse & Permissions
Figure 37
Mass difference between spin- $3 ∕ 2$ baryons ( $Δ$ , $Σ^{*}$ , $Σ_{c}^{*}$ , $Σ_{b}^{*}$ ) and spin- $1 ∕ 2$ baryons. In spin- $1 ∕ 2$ baryons, the light-light or a heavy-light-quark pair can have spin zero. The spin-0 diquark is indicated by $[q_{1} q_{2}]$ . The masses are drawn as a function of the inverse (constituent) quark mass.Reuse & Permissions
Figure 38
(Color online) Light baryon orbital spectrum for (a) $N^{*}$ and (b) $Δ^{*}$ . The lower dashed curves correspond to baryon states dual to spin- $1 ∕ 2$ modes in the bulk and the upper continuous curve to states dual to spin- $3 ∕ 2$ modes. From 192.Reuse & Permissions
Figure 39
Regge trajectory for $Δ^{*}$ resonances as a function of the leading intrinsic orbital angular momentum $L$ and the radial excitation quantum number $N$ (corresponding to $n_{1} + n_{2}$ in quark models) (336). The line represents a prediction based on AdS/QCD correspondence (soft wall) (231, 232). Resonances with $N = 0$ and 1 are listed above or below the trajectory. The mass predictions are 1.27, 1.64, 1.92, 2.20, 2.43, 2.64, $2.84 GeV$ for $L + N = 0, 1, \dots, 6$ , respectively.Reuse & Permissions
Figure 40
(Color online) Pair creation on a lattice, calculated for mesons. A sea quark-antiquark pair is created in the vacuum. At large distances, two-meson states are energetically preferred. For static quarks, the levels cross at some distance $R$ (with $a \approx 0.083 fm$ ), the string breaking introduces mixing of the energy levels defined by the potential $V (R)$ and the threshold $2 m (B)$ . From 400.Reuse & Permissions
Figure 41
Helicity amplitudes for the $γ^{*} p \to N (1440) P_{11}$ transition. The full circles are recent results from CLAS (80) and open boxes are results of an earlier analysis which included $2 π$ electroproduction data (81). The bands show the model uncertainties. The full triangle at $Q^{2} = 0$ is the PDG estimate (40). The thick curves correspond to quark models assuming that $N (1440) P_{11}$ is a first radial excitation of the $3 q$ ground state: (144) dashed and (79) solid. The thin dashed curves are obtained assuming that $N (1440) P_{11}$ is a gluonic baryon excitation ( $q^{3} G$ hybrid state) (363).Reuse & Permissions
Figure 42
Transverse (top) and longitudinal (bottom) helicity amplitudes for the $γ^{*} p \to N_{1 ∕ 2^{-}} (1535)$ transition. The data points are from CLAS (190). The value at the photon point is from 40. The lines represent calculations by 310.Reuse & Permissions

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