Approximate Hamiltonian for baryons in heavy-flavor QCD

Abstract

Aiming at relativistic description of gluons in hadrons, the renormalization group procedure for effective particles (RGPEP) is applied to baryons in QCD of heavy quarks. The baryon eigenvalue problem is posed using the Fock-space Hamiltonian operator obtained by solving the RGPEP equations up to second order in powers of the coupling constant. The eigenstate components that contain three quarks and two or more gluons are heuristically removed at the price of inserting a gluon-mass term in the component with one gluon. The resulting problem is reduced to the equivalent one for the component of three quarks and no gluons. Each of the three quark-quark interaction terms thus obtained consists of a spin-dependent Coulomb term and a spin-independent harmonic oscillator term. Quark masses are chosen to fit the lightest spin-one quarkonia masses most accurately. The resulting estimates for bbb and ccc states match estimates obtained in lattice QCD and in quark models. Masses of ccb and bbc states are also estimated. The corresponding wave functions are invariant with respect to boosts. In the ccb states, charm quarks tend to form diquarks. The accuracy of our approximate Hamiltonian can be estimated through comparison by including components with two gluons within the same method.

Triply heavy baryons in the constituent quark model *

“…The relativistic effects may have been (somehow) implemented in Refs [27,36]. The predicted states reported in [27] are 0.2 − 0.3 GeV higher than ours, and those reported by lattice-QCD [43]. Authors of Ref.…”

“…The mass of the same state is predicted by lattice-QCD to be 4.76 GeV, which compares reasonably well with ours. A similar level of agreement between lattice and our calculation is repeated for each ground state of the reported J P -channel in Table III. Lattice QCD [40] reports two almost degenerate states in each channel with quantum numbers J P = 1 This work 4798 5286 5376 5129 5129 5558 [21] 4812 ± 85 ----- [22] 4763 5317 5412 5132 5132 5637 [24] 4803 ----- [25] 4773 -5216 5109 5014 - [26] 4799 5243 5324 5094 5094 5494 [27] 4797 5309 5358 5103 5103 - [28] 4670 ± 150 ----- [29] 4990 ± 140 ---5110 ± 150 - [31] 4720 ± 120 ---4900 ± 100 - [33] 4760 ± 60 ----- [35] 4979 ± 271 ----- [36] 4760 5150 --5027 - [37] 5000 ----- [41] 4789 ± 6 ± 21 ----- [42] 4796 ± 8 ± 18 ----- [65] 4632 -4915 ± 283 4808 ± 176 -when coupling a D-wave component with either S = 1 2 or 3 2 . Table III shows the eigenstate of lowest mass, which corresponds to the coupling L ⊗ S = 2 ⊗ 3/2.…”

“…11569 [21] 11446 ± 99 11487 ± 101 ------[24] 11280 11287 ------[26] 11217 11251 11625 11643 11718 11524 11524 11598 [27] 11218 11218 11585 11585 11626 11438 11438 11601 [28] 10300 ± 100 10450 ± 110 ------ [29] 11500 ± 110 11490 ± 110 ---11620 ± 110 11620 ± 110 - [30] 11730…”

Triply charmed and bottom baryons in a constituent quark model

“…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.,…”

Computation of effective front form Hamiltonians for massive Abelian gauge theory

“…Results could suggest the structure of effective FF Hamiltonians needed to properly account for some non-perturbative effects of the theory. For examples of computing or guessing such terms, see [3,42,43] and references therein. It is also worth stressing that the Hamiltonians computed using the RGPEP are obtained without putting any restriction on the motion of field quanta and without making any non-relativistic approximation concerning their motion.…”