[Paper Review] Excited-state spectroscopy of singly, doubly and triply-charmed baryons from lattice QCD

M. Padmanath, Robert G. Edwards+2 more|arXiv (Cornell University)|Nov 19, 2013

Quantum Chromodynamics and Particle Interactions4 references22 citations

TL;DR

This lattice QCD study computes the ground and excited states of singly, doubly, and triply charmed baryons using dynamical fermions and a large basis of symmetry-respecting operators. It reveals that low-lying states closely match SU(6) ⊗ O(3) symmetry predictions, with well-defined spins up to 7/2, and identifies potential hybrid states via strong overlaps with field-strength tensor operators.

ABSTRACT

We present the ground and excited state spectra of singly, doubly and triply-charmed baryons by using dynamical lattice QCD. A large set of baryonic operators that respect the symmetries of the lattice and are obtained after subduction from their continuum analogues are utilized. These operators transform as irreducible representations of SU(3)$_F$ symmetry for flavour, SU(4) symmetry for Dirac spins of quarks and O(3) symmetry for orbital angular momenta. Using novel computational techniques correlation functions of these operators are generated and the variational method is exploited to extract excited states. The lattice spectra that we obtain have baryonic states with well-defined total spins up to 7/2 and the low lying states remarkably resemble the expectations of quantum numbers from SU(6)$\otimes$O(3) symmetry.

Motivation & Objective

• To compute the complete spectra of singly, doubly, and triply charmed baryons using first-principles lattice QCD.
• To extract excited states with well-defined total spins up to 7/2 using variational methods.
• To test the validity of SU(6) ⊗ O(3) symmetry predictions for heavy baryon spectroscopy.
• To identify potential hybrid baryon states through overlaps with operators containing the field strength tensor.
• To provide model-independent inputs for future experimental searches at BES-III, LHCb, and PANDA.

Proposed method

• Utilized dynamical anisotropic lattice QCD configurations with Nf=2+1 flavors and a temporal spacing of 5.67 GeV⁻¹.
• Constructed a large basis of baryonic interpolating operators via derivative-based formalism, including non-local and two-derivative operators.
• Subduced continuum operators to irreducible representations of lattice symmetries (SU(3)F, SU(4)spin, O(3)orbital).
• Computed N×N correlation matrices from these operators and solved the generalized eigenvalue problem to extract energy levels.
• Used eigenvectors and overlap factors to identify spin quantum numbers and assign states to non-relativistic or hybrid character.
• Applied spectral decomposition and principal correlator fitting to extract masses and decay constants from Euclidean correlation functions.

Experimental results

Research questions

• RQ1 Do the low-lying spectra of singly, doubly, and triply charmed baryons exhibit quantum numbers consistent with SU(6) ⊗ O(3) symmetry?
• RQ2 Can lattice QCD resolve excited baryon states with total spin up to 7/2 in heavy baryons?
• RQ3 Which states show significant overlap with operators containing the field strength tensor, indicating possible hybrid structure?
• RQ4 How do the computed spectra compare with potential model predictions and experimental observations?
• RQ5 To what extent do systematic uncertainties such as chiral extrapolation and unphysical pion mass affect the results?

Key findings

• The low-lying spectra of triply charmed baryons show excellent agreement with SU(6) ⊗ O(3) symmetry predictions, with states in non-relativistic bands matching theoretical expectations.
• Excited states with total spin up to 7/2 were successfully extracted, confirming the method's capability for high-spin baryons.
• States with strong overlaps onto operators containing the field strength tensor (marked with thick borders in Figure 1) are identified as potential hybrid baryons.
• For doubly charmed baryons (Ωcc and Ξcc), the number of low-lying states in non-relativistic bands matches SU(6) ⊗ O(3) expectations, as seen in Figure 2.
• Preliminary results for singly charmed baryons (Λc, Σc, Ξc, Ωc) also show consistent quantum number assignments, with spectra subtracted by mD or mDs to reduce charm quark mass dependence.
• The overlap factors confirm that states inside pink ellipses in Figures 1–3 have strong coupling to non-relativistic operators, indicating good overlap with standard quark-model states.