Basis light-front quantization approach to $Λ$ and $Λ_c$ and their isospin triplet baryons

TL;DR

The paper addresses the nonperturbative structure of the hyperons $\Lambda$, $\Lambda_c$, and their isospin partners by solving the bound-state problem with Basis Light-Front Quantization (BLFQ) using an effective light-front Hamiltonian that includes confinement and one-gluon exchange. The mass spectrum, electromagnetic form factors, magnetic moments, charge and magnetic radii, and parton distribution functions are computed from the resulting light-front wave functions, with PDFs evolved to higher scales via NNLO DGLAP evolution. The results show baryon masses in the experimental range and EM observables in reasonable agreement with data and lattice QCD, while the PDFs reveal gluon and sea contributions generated through QCD evolution from a valence-only initial state. The work provides predictions for heavy-baryon moments and radii, demonstrates the utility of BLFQ LFWFs for a broad set of parton observables, and outlines future extensions to include higher Fock sectors for explicit gluon and sea dynamics.

Abstract

We obtain the masses, the electromagnetic properties, and the parton distribution functions (PDFs) of $Λ$, $Λ_c$, and their isospin triplet baryons, i.e, $Σ^0$, $Σ^+$, $Σ^-$ and $Σ_c^0$, $Σ_c^+$, $Σ_c^{++}$ from a light-front effective Hamiltonian in the leading Fock sector in the basis light-front quantization framework. The light-front wave functions of these baryons are given by the eigenstates of the effective Hamiltonian consisting of a three-dimensional confinement potential and a one-gluon exchange interaction with fixed coupling. The masses of these baryons in our approach are in the experimental range while isospin-dependent mass differences are too small. Meanwhile, the electromagnetic properties are in agreement with the available experimental data, the lattice QCD simulations, and the other theoretical calculations. We also present the gluon and the sea quark PDFs, which we generate dynamically from the QCD evolution of the valence quark distributions.

Figures (16)

• Figure 1: Flavor Dirac FFs of the $\Lambda$ baryon and its isospin states $(\Sigma^0,\Sigma^+,\Sigma^-)$. The red lines with red bands represent the light quark ($u$ and/or $d$) FFs, whereas the black lines with gray bands correspond to the strange quark ($s$) FFs. The bands reflect the $10\%$ uncertainty in the coupling constant $\alpha_s$.
• Figure 2: Flavor Pauli FFs of the $\Lambda$ baryon and its isospin states $(\Sigma^0,\Sigma^+,\Sigma^-)$. The red lines with red bands represent the light quark ($u$ and/or $d$) FFs, whereas the black lines with gray bands correspond to the strange quark ($s$) FFs. The bands reflect the $10\%$ uncertainty in the coupling constant $\alpha_s$.
• Figure 3: Comparison of the flavor FFs in $\Sigma^+$ and $\Sigma^-$ evaluated within BLFQ and the lattice QCD simulations Lin:2008mr. The red lines with red bands represent the light quark ($u$ and/or $d$) FFs, whereas the black lines with gray bands correspond to the strange quark ($s$) FFs. The black pionts are lattice QCD results. The bands reflect the $10\%$ uncertainty in the coupling constant $\alpha_s$.
• Figure 4: Flavor Dirac FFs of the $\Lambda_c$ baryon and its isospin states $(\Sigma^+_c,\Sigma^{++}_c,\Sigma^{0}_c)$. The red lines with red bands represent the light quark ($u$ and/or $d$) FFs, whereas the black lines with gray bands correspond to the charm quark ($c$) FFs. The bands reflect the $10\%$ uncertainty in the coupling constant $\alpha_s$.
• Figure 5: Flavor Pauli FFs of the $\Lambda_c$ baryon and its isospin states $(\Sigma^+_c,\Sigma^{++}_c,\Sigma^{0}_c)$. The red lines with red bands represent the light quark ($u$ and/or $d$) FFs, whereas the black lines with gray bands correspond to the charm quark ($c$) FFs. The bands reflect the $10\%$ uncertainty in the coupling constant $\alpha_s$.