Spectrum of Light- and Heavy-Baryons

Abstract

A symmetry-preserving truncation of the strong-interaction bound-state equations is used to calculate the spectrum of ground-state J = 1/2 + , 3/2 + (qq q )-baryons, where q, q , q ∈ {u, d, s, c, b}, their first positive-parity excitations and parity partners. Using two parameters, a description of the known spectrum of 39 such states is obtained, with a mean-absolute-relativedifference between calculation and experiment of 3.6(2.7)%. From this foundation, the framework is subsequently used to predict the masses of 90 states not yet seen empirically.Keywords Poincaré-covariant Faddeev equation · baryon spectrum · light and heavy quarks · Dyson-Schwinger equations · emergence of mass 1 IntroductionThe Faddeev equation was introduced almost sixty years ago [1]. It treats the quantum mechanical problem of three-bodies interacting via pairwise potentials by reducing it to a sum of three terms, each of which describes a solvable scattering problem in distinct two-body subsystems. The Faddeev formulation of that three-body problem has a unique solution.An analogous approach to the three-valence-quark (baryon) bound-state problem in quantum chromodynamics (QCD) was explained in Refs. [2][3][4][5][6]. In this case, owing to dynamical mass generation, expressed most simply in QCD's one-body Schwinger functions in the gauge [7][8][9][10][11][12][13][14][15][16][17][18] and matter sectors [19][20][21][22][23][24], and the importance of symmetries [25][26][27], one requires a Poincaré-covariant quantum field theory generalisation of the Faddeev equation. Like the Bethe-Salpeter equation for mesons, it is natural to consider such a Faddeev equation as one of the tower of QCD's Dyson-Schwinger equations (DSEs) [28], which are being used to develop a systematic, symmetry-preserving, continuum approach to the strong-interaction bound-state problem [29][30][31][32][33][34].The Poincaré-covariant Faddeev equation for baryons is typically treated in a quark-diquark approximation, where the diquark correlations are nonpointlike and dynamical [35]. This amounts to a simplified treatment of the scattering problem in the two-body subchannels (as explained, e.g. in Ref. [36], Sec. II.A.2), which is founded on an observation that the same interaction which describes

Masses of ground-state mesons and baryons, including those with heavy quarks

“…This compares well with the fully-covariant three-body calculation described in Ref. [33], for which the analogous difference is 5.2(2.8)%. Of course, that study is more sophisticated: it did not use a quark-diquark approximation; instead, the Faddeev equations were solved in a fully-consistent RL truncation.…”

“…Moreover, the baryon spectra in Ref. [33] are ab initio predictions, whereas we used a parameter (g 2 in Eqs. (36), (38)) to readjust the scale of the J P = 1/2 + spectrum so that the proton mass matches experiment.…”

Triply charmed and bottom baryons in a constituent quark model

“…[16,32]. It should be mentioned that our predicted mass of Ω bbb (1 2 P 3/2 − ) is in good agreement with that predicted with Faddeev Equation [24]. Furthermore, our predicted mass splitting between Ω bbb (1 2 P 1/2 − ) and Ω bbb (1 2 P 3/2 − ), ∼ 6 MeV, is similar to the Lattice QCD prediction of ∼ 8 MeV in Ref.…”

“…The masses for the spin quartets Ω ccc (1 4 D J ) are predicted to be in the range of ∼ 5.35−5.42 GeV in present work, which [11] 4769(6) · · · Lattice QCD [12] 4789(6)(21) · · · Lattice QCD [13] 4761(52)(21)(6) · · · Lattice QCD [14] 4734(12)(11)(9) · · · Lattice QCD [9] 4763(6) · · · Lattice QCD [15] · · · 14371 ± 4 ± 11 NRCQM [16] 4965 14834 NRCQM [17] 4798 14396 NRCQM [18] 4763 14371 NRCQM [19] 4801 ± 5 14373 ± 25 QCD Sum Rule [20] 4670 ± 150 13280 ± 100 QCD Sum Rule [21] 4720 ± 120 14300 ± 200 QCD Sum Rule [22] 4990 ± 140 14830 ± 100 Faddeev Equation [23] 4900 13800 Faddeev Equation [24] 4760 14370 Faddeev Equation [25] 4799 14244 Diquark Model [26] 4760 14370 Diquark Model [27] 4800 14370 Variational Method [45] 4799 14396 Variational Method [28] 4760 ± 60 14370 ± 80 Bag model [29] 4777 14276 Bag model [30] 4790 14300 RQM [31] 4803 14569 HCQM [32] 4806 14496 HCQM [33] 4812 ± 85 14566 ± 122 Regge Theory [34] 4834 +82 −81 · · · Regge Theory [35] · · · 14788 ± 80 NRQCD [36] 4900(250) 14700(300) Bathe-Salpeter Equation [37] 4773 · · · RGPEP [38] 4797 14346 is compatible with the predictions from Lattice QCD [9] and NRCQM [17]. From Table VIII, it is found that the mass order for the spin quartets predicted in the literature is very different, in this work we predict a normal order, i.e.,…”

“…5142 5162 14773 14779 Lattice QCD [9] 5120(9) 5124(13) · · · · · · Lattice QCD [15] · · · · · · 14706.3 ± 9.8 ± 18.4 14714 ± 9.5 ± 18.2 NRCQM [16] 5155 5160 14975 14976 NRCQM [17] 5129 5129 14688 14688 QCD Sum Rule [21] · · · 4900 ± 100 · · · 14900 ± 200 QCD Sum Rule [22] · · · 5110 ± 150 · · · 14950 ± 110 Faddeev Equation [24] · · · 5027 · · · 14771 Bag model [30] 5140 · · · 14660 · · · HCQM [32] 5002 4982 14941 14935 Regge theory [34] · · · 5073 +109 −107 · · · · · · Regge theory [35] · · · · · · · · · 15055 ± 101 Bathe-Salpeter Equation [37] 5019 5014 · · · · · · There are two 2S -wave Ω ccc /Ω bbb states with J P = 1/2 + and J P = 3/2 + according to the quark model classification (see Table II). For a comparison, our predicted masses of the 2S -wave Ω ccc and Ω bbb states together with those of other theoretical predictions have been listed in Table VIII.…”