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arxiv: 2604.13205 · v1 · submitted 2026-04-14 · ✦ hep-lat · hep-ph

Recognition: unknown

Heavy baryons with relativistic quarks

Archana Radhakrishnan, Debsubhra Chakraborty, Nilmani Mathur

Pith reviewed 2026-05-10 13:24 UTC · model grok-4.3

classification ✦ hep-lat hep-ph
keywords lattice QCDheavy baryonsrelativistic quarksbottom quarkscharm baryonsHISQphysical pointspin 3/2 baryons
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The pith

Lattice QCD calculations treat bottom quarks fully relativistically to determine ground-state energies of heavy baryons with charm and bottom quarks.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper conducts a lattice QCD investigation of heavy baryons that include charm and bottom quarks by treating all valence quarks relativistically. It uses physical-point Nf=2+1+1 HISQ ensembles to find the energies of spin-3/2+ states for singly, doubly, and triply heavy combinations. A reader would care because this removes the need for non-relativistic approximations for the bottom quark, which have been common in prior work. The calculations cover both charmed and bottom baryons, marking the first such fully relativistic approach for bottom quarks.

Core claim

The central claim is that ground-state energies of spin-3/2+ heavy baryons containing charm and bottom quarks can be computed using fully relativistic valence quarks on Nf=2+1+1 HISQ ensembles at the physical point, and this represents the first investigation of heavy baryons using fully relativistic bottom quarks.

What carries the argument

The fully relativistic treatment of bottom quarks within lattice QCD using the HISQ action on physical-point ensembles, which enables direct computation of baryon energies without effective heavy-quark approximations.

If this is right

  • Ground-state energies are provided for singly-heavy, doubly-heavy, and triply-heavy charmed and bottom baryons in the spin-3/2+ channel.
  • The method demonstrates the feasibility of including bottom quarks on the same relativistic footing as lighter quarks in baryon calculations.
  • Results can serve as benchmarks for other theoretical approaches to heavy baryon spectroscopy.
  • Extension to other quantum numbers and excited states becomes possible with the same setup.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the relativistic treatment works well, it could be applied to compute properties like decay rates or magnetic moments of these baryons in future lattice studies.
  • This approach might help resolve discrepancies in heavy baryon masses between different lattice methods that use different quark treatments.
  • Similar fully relativistic treatments could be tested for even heavier systems or for tetraquark states involving bottom quarks.

Load-bearing premise

That discretization effects and lattice artifacts stay under control for fully relativistic bottom quarks on the HISQ ensembles at the physical point.

What would settle it

Observation of large dependence of the computed energies on the lattice spacing or significant mismatch with experimental masses for well-known states like the Xi_c or Omega_b would falsify the reliability of the approach.

Figures

Figures reproduced from arXiv: 2604.13205 by Archana Radhakrishnan, Debsubhra Chakraborty, Nilmani Mathur.

Figure 1
Figure 1. Figure 1: Dispersion relation of 𝜂𝑏 (top) and Υ (bottom). The ground state energy 𝑎𝐸0 ( ®𝑝) in lattice units is plotted against the lattice momentum squared parameter Í 𝑖 sin 𝜋𝑛𝑖 𝑁 2 . The red line represents a fit to the data with a 1𝜎 error band, yielding slope parameters 𝑐 = 1.00379±0.00011 (𝜂𝑏) and 𝑐 = 1.00369±0.00073 (Υ). A fitted value of 𝑐 ≈ 1 demonstrates the successful tuning of the bare bottom quark mass,… view at source ↗
Figure 2
Figure 2. Figure 2: Summary of the ground-state masses for the charmed Ω baryon family (Ω, Ω∗ 𝑐 , Ω∗ 𝑐𝑐, Ω𝑐𝑐𝑐). Our fully relativistic HISQ results are shown as red circles. Experimental values from the PDG are denoted by gray horizontal bands. Previous lattice QCD determinations utilizing various fermion actions are included for comparison. 14.36 14.38 Meinel 10 Brown 14 Mathur 02 Mathur 18 Mathur 22 This work 10.5 11.0 Ω ∗ … view at source ↗
Figure 3
Figure 3. Figure 3: Summary of the ground-state masses for the bottom and mixed bottom-charm Ω baryon family (Ω∗ 𝑏 , Ω∗ 𝑐𝑏, Ω∗ 𝑐𝑐𝑏, Ω∗ 𝑏𝑏, Ω∗ 𝑐𝑏𝑏, Ω𝑏𝑏𝑏). Our fully relativistic HISQ results (red circles) are compared against previous non-relativistic (NRQCD) calculations by Brown et al.(2014), Mathur et al.(2002,2018 and 2022), showing excellent consistency across the entire heavy quark mass range. 6 [PITH_FULL_IMAGE:figures… view at source ↗
Figure 4
Figure 4. Figure 4: Effective-mass plateaus, 𝑀eff(𝑡), for the ground state of spin-3/2 Ω𝑏𝑏𝑏 baryon evaluated using two independent staggered interpolating operators with distinct point-split taste constructions. The orange curve indicates the ground-state masses extracted via multi-exponential fits, with shaded bands representing 1𝜎 statistical uncertainties. The green band denotes the selected fit window for constant fit. Th… view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of the Ω𝑏𝑏𝑏 (3/2 + ) ground-state mass extracted from this work with previous lattice determinations. The red marker and the horizontal band represents our fully relativistic measurement using the HISQ action, with the width indicating the 1𝜎 statistical uncertainty. Systematic uncertainties, including electromagnetic corrections, are not currently included in this calculation, although we expec… view at source ↗
read the original abstract

We present a lattice QCD study of heavy baryons containing charm and bottom quarks, with particular emphasis on the relativistic treatment of all valence quarks. We use $N_f=2+1+1$ HISQ ensembles at the physical point to compute ground-state energies of spin-$3/2^+$ baryons, including singly-, doubly-, and triply-heavy charmed and bottom baryons. This work represents the first investigation of heavy baryons using fully relativistic bottom quarks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript reports a lattice QCD study of ground-state energies for spin-3/2^+ heavy baryons (singly, doubly, and triply heavy with charm and bottom quarks) using fully relativistic valence quarks on N_f=2+1+1 HISQ ensembles at the physical point. It claims to be the first investigation employing fully relativistic bottom quarks.

Significance. If discretization effects are shown to be under control, the results would provide valuable first-principles masses for heavy baryons without non-relativistic approximations for the bottom sector, offering benchmarks for effective theories and experimental comparisons in a regime where relativistic effects matter.

major comments (1)
  1. The central novelty and reliability claims depend on demonstrating that HISQ discretization errors remain under control for bottom quarks (where am_b is typically O(1) on the a≈0.06–0.12 fm ensembles). The manuscript must supply quantitative evidence—such as continuum extrapolations, comparisons to known masses, or explicit artifact estimates—in the results or methods sections showing these effects do not exceed the quoted uncertainties.
minor comments (1)
  1. The abstract supplies no error budgets, fitting details, or cross-checks against known masses; adding a concise statement on these would improve clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful review and constructive feedback on our manuscript. We address the major comment below.

read point-by-point responses

  1. Referee: The central novelty and reliability claims depend on demonstrating that HISQ discretization errors remain under control for bottom quarks (where am_b is typically O(1) on the a≈0.06–0.12 fm ensembles). The manuscript must supply quantitative evidence—such as continuum extrapolations, comparisons to known masses, or explicit artifact estimates—in the results or methods sections showing these effects do not exceed the quoted uncertainties.

    Authors: We agree that explicit demonstration of control over discretization effects is essential to support the reliability claims for the bottom sector. The current manuscript discusses the use of the HISQ action on multiple spacings (a≈0.06–0.12 fm) and its general suitability for heavy quarks but does not include dedicated quantitative estimates or comparisons in the results section. In the revised version we will add a dedicated subsection (in Methods or Results) providing explicit artifact estimates based on the known O(a^2) improvement of HISQ, comparisons of our singly-heavy bottom baryon masses to experimental values (e.g., Ξ_b^* and Ω_b), and a statement that residual effects lie within the quoted uncertainties. A full continuum extrapolation is not feasible with the present ensembles and will be noted as future work. revision: yes

Circularity Check

0 steps flagged

No circularity: direct numerical lattice QCD computation from external ensembles

full rationale

The paper reports a standard lattice QCD calculation of heavy baryon ground-state energies on pre-existing N_f=2+1+1 HISQ ensembles at the physical point. The central result is obtained by computing two-point correlation functions from the QCD action, extracting energies via fits, and presenting the numerical values. No derivation step reduces a claimed prediction to a fitted parameter by construction, no self-citation chain is load-bearing for the main claim, and the novelty statement (first use of fully relativistic bottom quarks) follows directly from the choice of action and ensembles rather than from any tautological redefinition. The computation is self-contained against external benchmarks and does not rely on internal re-labeling of inputs as outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The calculation rests on standard lattice QCD assumptions and the availability of pre-generated physical-point HISQ ensembles; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Lattice QCD on HISQ ensembles at the physical point accurately reproduces continuum QCD for the quantities studied.
    Invoked by the choice of ensembles and the claim of physical-point results.

pith-pipeline@v0.9.0 · 5365 in / 1099 out tokens · 55903 ms · 2026-05-10T13:24:24.979217+00:00 · methodology

discussion (0)

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Reference graph

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