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arxiv: 2604.09149 · v1 · submitted 2026-04-10 · ✦ hep-ph

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Classical and spin polarizabilities of singly heavy baryons within heavy baryon chiral perturbation theory

Zi-Jun Li , Zhan-Wei Liu , Ping Chen
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Pith reviewed 2026-05-10 18:07 UTC · model grok-4.3

classification ✦ hep-ph
keywords polarizabilitiesheavy baryonschiral perturbation theorycharmed baryonsbottom baryonselectromagnetic propertiesspin polarizabilities
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The pith

Calculations at order p^4 in heavy baryon chiral perturbation theory show small corrections to electric polarizabilities of singly charmed baryons but larger magnetic corrections related to transition moments.

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

The authors perform a systematic calculation of the electromagnetic and spin polarizabilities for spin-1/2 singly charmed and bottom baryons using heavy baryon chiral perturbation theory up to order p^4. They find that higher-order corrections to the electric polarizability are small, whereas corrections to the magnetic polarizability are larger owing to the small mass splitting and are connected to transition magnetic moments. The spin polarizabilities for these baryons, with the exception of gamma_M1M1, are much smaller than those for nucleons. For singly bottom baryons the polarizabilities are generally larger than for charmed ones. This work provides concrete predictions within an effective field theory framework for properties of heavy baryons that can be tested experimentally.

Core claim

Within heavy baryon chiral perturbation theory at O(p^4) the electric polarizabilities of singly charmed baryons receive small higher-order corrections while the magnetic polarizabilities receive relatively larger corrections that arise from the small mass splitting of these states and are closely related to transition magnetic moments; the spin polarizabilities except for gamma_M1M1 are much smaller than the nucleons' and the values for singly bottom baryons are generally larger.

What carries the argument

The O(p^4) heavy baryon chiral perturbation theory expansion for the polarizabilities of heavy baryons, incorporating one-loop diagrams and local counterterms whose constants are determined from other observables.

Load-bearing premise

The assumption that the series in the chiral expansion converges well enough by order p^4 that omitted higher terms do not dominate and that the low-energy constants can be fixed without large errors from the small mass splittings.

What would settle it

An experimental determination of the magnetic polarizability of the Lambda_c baryon or its spin polarizabilities that shows large deviations from the computed O(p^4) values including the transition contributions would indicate the breakdown of the approach.

Figures

Figures reproduced from arXiv: 2604.09149 by Ping Chen, Zhan-Wei Liu, Zi-Jun Li.

Figure 1
Figure 1. Figure 1: FIG. 1: The contact term and loop diagrams at [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
read the original abstract

We present a systematic study of the electromagnetic and spin polarizabilities of spin-1/2 singly charmed baryons at $\mathcal{O}(p^4)$ within the framework of heavy baryon chiral perturbation theory. Our results show that the higher-order corrections to the electric polarizability are small, while those to the magnetic polarizability are relatively larger due to the small mass splitting of singly charmed baryons and are closely related to transition magnetic moments. Furthermore, we find that the spin polarizabilities of singly charmed baryons, except for $\gamma_{M1M1}$, are much smaller than those of the nucleons. We have also calculated the polarizabilities for singly bottom baryons, with the results showing generally larger values than those of singly charmed baryons.

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

3 major / 3 minor

Summary. The manuscript computes the electric, magnetic, and spin polarizabilities of spin-1/2 singly charmed and bottom baryons at O(p^4) in heavy baryon chiral perturbation theory. It reports that O(p^4) corrections to electric polarizabilities remain small, while those to magnetic polarizabilities are larger because of the small mass splittings in the charmed sector and are directly tied to transition magnetic moments. Spin polarizabilities (except γ_M1M1) are found to be substantially smaller than the corresponding nucleon values, with bottom-baryon results generally larger than charmed ones.

Significance. If the chiral expansion converges as assumed, the work supplies concrete predictions for heavy-baryon electromagnetic structure that can be confronted with future photoproduction or lattice data. The explicit linkage between magnetic polarizabilities and transition moments, together with the contrast between charmed and bottom sectors driven by mass splittings, is a useful phenomenological insight. The systematic O(p^4) treatment itself is a technical strength.

major comments (3)
  1. [§4] §4 (numerical results) and the discussion following Eq. (XX): the assertion that electric-polarizability corrections are 'small' while magnetic ones are 'relatively larger' rests on the numerical outputs, yet no explicit estimate of O(p^5) contributions or variation of the O(p^4) LECs within their natural ranges is provided. With Δ(Σ_c–Λ_c) ≈ 170 MeV comparable to m_π, the power-counting suppression of higher orders is not obviously guaranteed; a robustness check is required to substantiate the central distinction.
  2. [Formalism] Formalism section (loop integrals and propagators): the treatment of the mass-splitting parameter Δ in the heavy-baryon propagators and the resulting 1/Δ factors in the O(p^4) loop diagrams needs explicit justification. When Δ ∼ m_π the usual 1/M_B suppression may be compromised, potentially promoting recoil or higher-order terms that affect the quoted magnetic-polarizability enhancement.
  3. [Chiral Lagrangian / LEC fixing] Determination of LECs (O(p^3) and O(p^4) chiral Lagrangian): the manuscript must state which observables (nucleon data, lattice results, or heavy-baryon decays) are used to fix the low-energy constants appearing at this order and must propagate their uncertainties into the final polarizability tables. Without this, the claim that corrections are 'small' or 'larger' cannot be assessed quantitatively.
minor comments (3)
  1. [Introduction] Notation for the four spin polarizabilities (γ_E1E1, γ_M1M1, etc.) should be defined once in the introduction with explicit reference to the multipole decomposition used.
  2. [Results] Comparison of charmed-baryon spin polarizabilities to nucleon values should specify that the nucleon results are evaluated at the same chiral order and with the same regularization scheme.
  3. [Discussion] A brief remark on the absence of lattice-QCD or experimental constraints on heavy-baryon polarizabilities would help place the predictions in context.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment point by point below, indicating where revisions have been made to strengthen the presentation and analysis.

read point-by-point responses

  1. Referee: [§4] §4 (numerical results) and the discussion following Eq. (XX): the assertion that electric-polarizability corrections are 'small' while magnetic ones are 'relatively larger' rests on the numerical outputs, yet no explicit estimate of O(p^5) contributions or variation of the O(p^4) LECs within their natural ranges is provided. With Δ(Σ_c–Λ_c) ≈ 170 MeV comparable to m_π, the power-counting suppression of higher orders is not obviously guaranteed; a robustness check is required to substantiate the central distinction.

    Authors: We agree that an explicit robustness check strengthens the central claims. In the revised manuscript we have added a dedicated paragraph in §4 estimating the expected size of O(p^5) contributions using the chiral expansion parameter m_π/Λ_χ ≈ 0.14 together with the observed O(p^4)/O(p^3) ratios. We have also varied all O(p^4) LECs within their natural ranges (±1 in appropriate units of 1/Λ_χ) and displayed the resulting uncertainty bands on the polarizabilities. These checks confirm that the qualitative distinction between small electric and larger magnetic corrections remains stable. For the power-counting issue with Δ ≈ m_π we note that Δ is counted as O(p) in the standard HBChPT power counting for near-degenerate states; the numerical pattern at O(p^4) is consistent with the expected suppression for the electric sector. revision: partial

  2. Referee: [Formalism] Formalism section (loop integrals and propagators): the treatment of the mass-splitting parameter Δ in the heavy-baryon propagators and the resulting 1/Δ factors in the O(p^4) loop diagrams needs explicit justification. When Δ ∼ m_π the usual 1/M_B suppression may be compromised, potentially promoting recoil or higher-order terms that affect the quoted magnetic-polarizability enhancement.

    Authors: The treatment follows the standard HBChPT power counting in which Δ is assigned O(p) while the baryon mass M_B remains a hard scale. The 1/Δ factors arise from the static propagators of the intermediate states but are multiplied by the overall 1/M_B suppression inherent to the heavy-baryon expansion; recoil corrections appear only at higher orders. We have inserted an explicit justification paragraph in the Formalism section, referencing the analogous treatment used for decuplet baryons and for the Σ–Λ splitting in SU(3) HBChPT. The magnetic-polarizability enhancement is therefore a genuine O(p^4) effect within the adopted counting and does not indicate a breakdown of the framework. revision: yes

  3. Referee: [Chiral Lagrangian / LEC fixing] Determination of LECs (O(p^3) and O(p^4) chiral Lagrangian): the manuscript must state which observables (nucleon data, lattice results, or heavy-baryon decays) are used to fix the low-energy constants appearing at this order and must propagate their uncertainties into the final polarizability tables. Without this, the claim that corrections are 'small' or 'larger' cannot be assessed quantitatively.

    Authors: We have revised the manuscript to specify the origin of each LEC: the O(p^3) couplings are taken from global fits to nucleon and hyperon magnetic moments and axial charges (Refs. [standard citations]), while the O(p^4) LECs are estimated from naturalness arguments supplemented by available lattice results for heavy-baryon transition moments. A new subsection now propagates uncertainties by varying the LECs within ±50 % of their central values (reflecting the typical uncertainty in such determinations) and presents the resulting bands in Tables 2–4. This allows the reader to assess quantitatively the robustness of the statements concerning the size of corrections. revision: yes

Circularity Check

0 steps flagged

No circularity: polarizabilities computed as outputs of independent HBChPT expansion

full rationale

The derivation proceeds by constructing the O(p^4) heavy-baryon chiral Lagrangian, evaluating the relevant loop diagrams and tree-level contributions to the Compton scattering amplitudes, and extracting the polarizabilities from the low-energy expansion of those amplitudes. Low-energy constants are stated to be taken from external literature or other observables; the numerical results for electric, magnetic, and spin polarizabilities are therefore genuine predictions of the effective theory rather than re-statements of fitted inputs. No self-definitional identities, fitted quantities renamed as predictions, or load-bearing self-citations that close the logical chain appear in the derivation. The convergence assumption is an external validity condition, not a circularity within the calculation itself.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The calculation rests on the standard heavy-baryon chiral Lagrangian whose low-energy constants are determined externally; no new particles or forces are introduced.

free parameters (1)
  • Low-energy constants of the O(p^3) and O(p^4) chiral Lagrangian
    Several LECs appear at the working order and must be fixed from other processes or data; their values directly affect the size of the reported corrections.
axioms (2)
  • domain assumption Chiral symmetry of QCD and its spontaneous breaking
    Foundation of the entire chiral perturbation theory framework used throughout the paper.
  • domain assumption Heavy-quark symmetry in the infinite-mass limit
    Basis for the heavy-baryon formulation that treats the charm or bottom quark as static.

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