{"id":"94103ba5-dd1e-46bb-a06d-55fc9d6edb82","arxiv_id":"2412.02297","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"At O(p^3) in heavy baryon chiral perturbation theory, sextet heavy baryons acquire polarizabilities from pion/kaon loops and from B6* to B6 magnetic transitions, while antitriplet heavy baryons have zero polarizability.","lead":"This paper calculates how much singly heavy baryons, particles made of one heavy quark and two light quarks, deform when placed in electric and magnetic fields. It provides the first chiral perturbation theory estimates for these deformations and finds that the magnetic response is often dominated by transitions between a baryon and its slightly heavier partner state.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Missing B3↔B6(∗) M1 tree diagrams (f2, f4 in Eq. (27)) invalidate the claimed zero B3 polarizabilities: they are O(p^3) and yield nonzero βM through 1/δ2 poles.","rationale":"The reader's CONDITIONAL verdict is driven by LEC model-dependence and the small bottom-baryon δ1. The more load-bearing problem is that the advertised O(p^3) truncation omits tree-level magnetic-dipole transition diagrams for the antitriplet, despite the f2 and f4 terms appearing in the same L^(2) Lagrangian used for the sextet. This is not a numerical uncertainty: it is a missing set of diagrams at the claimed order, and it directly contradicts the zero-polarizability statement in Eq. (31). The proposed test is concrete and would settle the issue by computing the f2/f4 contributions; if they are nonzero, the central claim as stated fails. Therefore the paper should not be accepted in its current form.","tokens_in":20818,"tokens_out":17501,"duration_ms":210294,"concrete_test":"Recompute the B3 spin-averaged forward Compton amplitude retaining the f2 and f4 terms of Eq. (27); include the tree diagrams with B6 and B6* intermediate states. Determine f2 and f4 by the same χ^2 fit to lattice transition magnetic moments μ(B6→B3γ) used for f6/f7 in Eqs. (80)–(88). If βM(Λ_c^+), βM(Ξ_c^+), or βM(Ξ_c^0) is nonzero at the 10^-4 fm^3 level, Eq. (31) is invalid and Tables V–VI are incomplete at O(p^3).","verdict_should_be":"REJECT","load_bearing_attack":"The paper's central result for the antitriplet, Eq. (31), states that B3 baryons have zero polarizabilities up to O(p^3), on the grounds that parity and angular momentum conservation forbid chiral B3 fluctuations and that B3 and B6(∗) are decoupled. This misses the magnetic dipole transition operators already present in L^(2): the f2 term \\bar{B}_3[S_μ,S_ν]\\hat{F}+_{μν}B6 and the f4 term \\bar{B}_3\\hat{F}+_{μν}S_ν B6^{*μ} in Eq. (27). The tree diagram with two such vertices and a B6 or B6* intermediate is exactly the analog of Fig. 1(b'), which the authors keep for the sextet. By the paper's power-counting rule Eq. (28), L=0 and two d=2 meson-baryon vertices give Dχ=1+2(2−1)=3, so these diagrams are O(p^3). They produce βM(B3) ∼ α f^2/(12 M_N^2 δ2), with δ2=127 MeV (and a δ3 term), which is not zero. The quark-model/lattice transition moments μ(B6→B3γ) are not suppressed by heavy-quark spin symmetry; using typical values μ∼1 μN gives βM(B3) of order 10^-4 fm^3, comparable to the chiral-loop entries in Table V. The same omitted f2/f4 diagrams also contribute to B6 polarizabilities via a B3 intermediate. Nothing in Sec. III A sets f2=f4=0; 'decoupled' is an approximation, not a symmetry. Hence Eq. (31) and the completeness of Tables V–VI at O(p^3) are not established.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a heavy-baryon chiral perturbation theory calculation of the spin-averaged electromagnetic polarizabilities alpha_E and beta_M of the spin-1/2 singly heavy baryons through O(p^3). For the antitriplet B3 it claims, in Eq. (31), that alpha_E = beta_M = 0, so that these baryons behave as charged point particles at this order. For the sextet B6 the polarizabilities receive contributions from pion/kaon/eta loops with B6 and B6* intermediate states and from the B6* -> B6 magnetic dipole transition, with the final sums given in Eq. (77). The low-energy constants g1, g3, f6, and f7 are estimated using the experimental Sigma_c decay widths, heavy-quark-spin and quark-model relations, and quark-model transition moments fitted to lattice QCD magnetic moments. Numerical results for charmed and bottom baryons are listed in Tables V and VI, with the bottom sector characterized by the very small splitting delta_1 = 20 MeV and a correspondingly large 1/delta_1 contribution to beta_M.","tokens_in":21327,"tokens_out":11786,"duration_ms":128842,"significance":"If the diagram set is complete, the paper provides the first O(p^3) heavy-baryon chiral perturbation theory predictions for singly heavy baryon polarizabilities, together with analytic expressions that can be used for future lattice chiral extrapolation. The authors are transparent about their low-energy-constant estimation, propagate uncertainties, and provide a useful internal consistency check in Eq. (76) relating the B6 and B6* loop contributions in the heavy quark limit. The central quantitative claims are, however, contingent on the completeness of the O(p^3) diagram set; the missing B3-B6(*) magnetic transition diagrams discussed below affect both the antitriplet zero result and the numerical tables.","major_comments":[{"comment":"The claimed vanishing of the B3 polarizabilities is not established at O(p^3). The L^(2) Lagrangian in Eq. (27) contains the magnetic dipole transition operators proportional to f2 (\\(\\bar{B}_3[S_\\mu,S_\\nu]\\hat{F}^{+}_{\\mu\\nu}B_6\\)) and f4 (\\(\\bar{B}_3\\hat{F}^{+}_{\\mu\\nu}S_\\nu B_6^{*\\mu}\\)), and the paper nowhere sets f2 = f4 = 0. A tree diagram with two such vertices and an intermediate B6 or B6* is the direct B3 analog of the B6*->B6 diagram in Fig. 1(b'); by the power counting in Eq. (28), with L=0 and two d=2 meson-baryon vertices, this diagram is O(p^3). It generates a nonvanishing beta_M(B3) of order alpha f^2/(12 M_N^2 delta_2), with delta_2 = 127 MeV, plus a delta_3 term. The statement in Sec. III A that B3 and B6(*) are decoupled is therefore an approximation, not a symmetry, and it is inconsistent with the presence of the f2 and f4 terms in the same Lagrangian. Quark-model/lattice transition moments for B6 -> B3 gamma are not suppressed by heavy-quark spin symmetry. The same omitted diagrams also contribute to the B6 polarizabilities through a B3 intermediate. Consequently Eq. (31) and the completeness of Tables V and VI at O(p^3) are not established.","section":"Sec. III A, Eq. (31) and Eq. (27)"},{"comment":"For the bottom baryons the O(p^3) truncation is much less protected than for the charmed sector. With delta_1 = 20 MeV, the magnetic transition contribution in Eq. (35) gives, for example, beta_M = 18.1 x 10^-4 fm^3 for Sigma_b^+, more than four times the chiral-loop contribution and more than an order of magnitude larger than typical nucleon values quoted in Eq. (90). The paper argues in Sec. V from the nucleon precedent that O(p^4) corrections do not change the qualitative conclusions, but the nucleon system has no nearly degenerate partner at the scale of the pion mass. Since the omitted f2/f4 diagrams discussed above involve the analogous 1/delta_2 enhancement, the numerical hierarchy for bottom baryons could change. Please quantify the sensitivity of the bottom predictions to delta_1 and to the neglected 1/delta_2 diagrams before presenting them as quantitative predictions.","section":"Sec. IV, Table VI and Eq. (35)"}],"minor_comments":[{"comment":"The last row of Table VI is labeled \"Omega^-_c\" but should be \"Omega^-_b\" for the singly bottom baryon.","section":"Table VI"},{"comment":"The definition of S_chi appears to contain a typo: it uses M_pi and R_pi on the right-hand side, whereas the subsequent equations and Eq. (75) require S_chi = M_chi^2(10R_chi - 9 delta_1) + delta_1^2(9 delta_1 - R_chi).","section":"Eq. (74)"},{"comment":"The statement that the finite delta_1 splitting \"slightly suppresses\" the B6* loop contribution is inconsistent with Table V, where alpha_E^{(c'-g')} / alpha_E^{(c-g)} is about 1/3 rather than slightly below 1/2; please rephrase or give the explicit delta_1-dependent ratio.","section":"Sec. III B, text after Eq. (76)"},{"comment":"The g6 term is included in the leading-order Lagrangian and then set to zero because parity and angular momentum conservation forbid the vertex; it would be clearer to either omit it from Eq. (25) or state explicitly that it is written for completeness before being discarded.","section":"Eq. (25)"},{"comment":"The sign convention relating C_xi to the leading-order transition magnetic moment mu^{LO}_{xi*->xi+gamma} is not specified; please state the convention so that the entries in Table I and the numerical values in Eqs. (83)-(88) can be reproduced independently.","section":"Eq. (36) and Table I"}],"recommendation":"major_revision","confidential_remarks":"The main obstacle is technical and fixable: the authors should include the f2/f4-mediated B3-B6(*) magnetic transition diagrams and either demonstrate that they are numerically negligible using quark-model transition moments or update the antitriplet and sextet results accordingly. I do not see a scope problem; the paper fits the journal's hep-ph remit, and I found no citation-pattern concerns beyond the natural reliance on the authors' own earlier chiral perturbation theory work."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First useful take: this is a genuine first step for heavy-baryon polarizabilities in HBChPT, and the sextet loop expressions will likely be reused. But the central claim—zero polarizabilities for the antitriplet—does not survive contact with the paper's own Lagrangian.\n\nThe problem is in Eq. (27). The f2 and f4 terms couple B3 to B6 and B6* through magnetic dipole operators. Two such vertices with a B6 or B6* intermediate produce tree graphs at O(p^3), exactly the same order as the diagram the authors keep for the sextet (Fig. 1(b')). The paper does not set f2=f4=0; \"decoupled\" is a dynamical approximation, not a symmetry. The corresponding transition magnetic moments are not small (order 1 μN from the quark model and lattice inputs), and the resulting βM for Λc+ and Ξc is around 10^-4 fm^3, comparable to the chiral-loop entries in Table V. So Eq. (31) is not correct as stated, and the completeness of Tables V and VI at O(p^3) is not established. The same omitted operators also contribute to the sextet polarizabilities through B3 intermediate states.\n\nWhat the paper does well: the B6 chiral-loop calculation is new, the heavy quark limit collation in Eq. (76) checks out, and the numerical pattern α(c'-g') ≈ α(c-g)/3 is sensible. The strategy of fixing LECs from lattice QCD magnetic moments and Σc decay widths is reasonable, and the uncertainties are honestly reported. The citation pattern is fair, though the numerical inputs lean on the authors' own earlier chiral and quark-model analyses; that is model dependence, not circularity.\n\nOther soft spots: the η loop is never mentioned; if its coefficients vanish by symmetry that should be stated. For bottom baryons, δ1 = 20 MeV makes the O(p^3) expansion questionable. The reported uncertainties cover the input errors but not the systematic error from the missing B3-B6 transition diagrams.\n\nBottom line: the framework and the sextet expressions are worth building on, but the antitriplet zero result is a load-bearing gap, not a minor omission. A referee should require the authors to include the f2/f4 contributions or derive a symmetry that sets them to zero. I would not desk-reject this; it deserves a serious referee, but the present version is not ready.","headline":"First HBChPT polarizability estimates for singly heavy baryons, but the zero-polarizability claim for the antitriplet misses O(p^3) B3-B6 M1 transitions already present in the paper's own Lagrangian.","tokens_in":21800,"tokens_out":7783,"would_cite":false,"duration_ms":81554,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The spin-$\\frac{1}{2}$ singly heavy baryon polarizabilities at $\\mathcal{O}(p^3)$: sextet baryons respond through pion clouds and a near-degenerate spin-$\\frac{3}{2}$ partner, while the antitriplet turns out point-like.","keywords":["electromagnetic polarizabilities","heavy baryon chiral perturbation theory","singly heavy baryons","Compton scattering","charmed baryons","bottom baryons","heavy quark spin symmetry","low-energy constants"],"falsifier":"A lattice QCD computation of the electric and magnetic polarizabilities of the singly charmed baryons at or near the physical pion mass would settle the central claim: the framework predicts $\\beta_M / \\alpha_E = 0.1$ for the chiral-loop part of the sextet, a magnetic polarizability hierarchy ordered by the transition magnetic moments (largest for $\\Sigma_c^{++}$, smallest for $\\Sigma_c^+$ and $\\Xi_c^{\\prime +}$), and exactly vanishing polarizabilities for $\\Lambda_c^+$ and $\\Xi_c$. Measuring the $B_6^* \\to B_6 \\gamma$ radiative width would independently fix the $C_\\xi$ coefficients that control the dominant magnetic contribution. Conversely, a single nonzero polarizability for $\\Lambda_c^+$ — for instance from the spin precession of channeled charmed baryons in bent crystals proposed at hadron colliders — would show that the $\\mathcal{O}(p^4)$ effects are not negligible.","tokens_in":20593,"feed_emoji":"🧲","tokens_out":26897,"duration_ms":206806,"temperature":0.7,"pith_summary":"The paper aims to establish that the electric and magnetic polarizabilities of spin-$\\frac{1}{2}$ singly heavy baryons — how much a baryon with one charm or bottom quark deforms under quasistatic electric and magnetic fields — follow systematically from heavy baryon chiral perturbation theory, the low-energy effective theory of QCD, at $\\mathcal{O}(p^3)$. It finds a sharp dichotomy: the antitriplet family $\\Lambda_c^+$, $\\Xi_c^+$, $\\Xi_c^0$, where the two light quarks form a spin-zero antisymmetric pair, has exactly vanishing polarizability at this order, because parity and angular momentum conservation forbid its coupling to the pion cloud and it behaves like a charged point particle. The sextet family $\\Sigma_c$, $\\Xi_c'$, $\\Omega_c$, whose light diquark carries spin one, receives its polarizability from two sources: long-range pion and kaon cloud loops, and the magnetic dipole transition into the nearly degenerate spin-$\\frac{3}{2}$ partner $B_6^*$, a term proportional to $C_\\xi^2/\\delta_1$ that dominates the magnetic polarizability because the mass splitting $\\delta_1$ is small. That pole term is the same mechanism by which the $\\Delta$ resonance shapes nucleon polarizabilities, but it is stronger here because the $B_6$–$B_6^*$ splitting (67 MeV for charmed, 20 MeV for bottom baryons) is smaller than $M_\\Delta - M_N$. If the calculation holds up, its tables are the first quantitative chiral perturbation theory predictions for heavy baryon polarizabilities, giving lattice QCD and proposed bent-crystal spin-precession experiments concrete numbers to test.","feed_headline":"Three charmed baryons predicted to have zero polarizability","feed_subtitle":"Order-p³ chiral theory gives Λ_c and Ξ_c zero polarizability, sextet baryons large magnetic response.","key_machinery":"The machinery is the spin-averaged forward Compton tensor $\\Theta_{\\mu\\nu} = U(\\omega) g_{\\mu\\nu} + V(\\omega) k_\\mu k_\\nu + \\cdots$, whose low-energy coefficients are the polarizabilities themselves: $\\alpha_E + \\beta_M = -\\frac{1}{8\\pi} U''(0)$ and $\\beta_M = -\\frac{1}{4\\pi} V(0)$. Heavy baryon chiral perturbation theory removes the baryon mass from the propagators by splitting the field into heavy and light components at a fixed velocity, restoring a power counting in which the $\\mathcal{O}(p^3)$ Compton amplitude contains only the tree and one-loop diagrams of Fig. 1. The load-bearing small parameter is the mass splitting $\\delta_1 = M_{B_6^*} - M_{B_6}$ that sits in the denominator of the $B_6^*$-exchange diagram: the spin-$\\frac{1}{2}$ and spin-$\\frac{3}{2}$ sextet baryons become degenerate in the heavy quark limit, so $\\delta_1$ is small (67 MeV for charm, 20 MeV for bottom) and the magnetic polarizability acquires a $\\delta_1^{-1}$ pole, the same structure as the $\\Delta(1232)$ contribution to nucleon polarizabilities but with a smaller denominator. The loop integrals are evaluated in dimensional regularization through the $J$-functions of Appendix A, and the four low-energy constants are fixed by heavy quark spin symmetry ($g_1^2 = \\frac{4}{3} g_3^2$), the quark model ($g_1^2 = \\frac{8}{3} g_2^2$), the measured $\\Sigma_c$ and $\\Sigma_c^*$ decay widths, and a fit of quark magnetic moments to seven lattice QCD baryon magnetic moments.","core_discovery":"On the paper's own terms, the central result is the complete $\\mathcal{O}(p^3)$ prediction for the polarizabilities of the spin-$\\frac{1}{2}$ singly heavy baryons. For the antitriplet, the spin-averaged forward Compton amplitude reduces to the Thomson term $U_\\xi(\\omega) = Q_\\xi^2 e^2 / M_{\\bar{3}}$, so $\\alpha_E = \\beta_M = 0$ up to this order (Eq. (31)): $\\bar{B}_3$ behaves like a charged point particle with no electromagnetic polarizability. For the sextet, the total polarizability is the sum (Eq. (77)) of three pieces: the $B_6\\phi$-loop diagrams, the $B_6^*\\phi$-loop diagrams, and the tree diagram with a $B_6^*$ intermediate state, whose magnetic polarizability $\\beta_M^{(b')}(\\xi) = \\alpha_{\\rm em} C_\\xi^2 / (12 M_N^2 \\delta_1)$ carries a pole in the small sextet mass splitting. The chiral-loop pieces obey the simple ratio $\\beta_M^{(c-g)} = \\alpha_E^{(c-g)} / 10$, and in the heavy quark limit the $B_6$ and $B_6^*$ loops satisfy $\\alpha_E^{(c-g)} = 2\\alpha_E^{(c'-g')}$ and $\\beta_M^{(c-g)} = 2\\beta_M^{(c'-g')}$, with the finite splitting slightly suppressing the $B_6^*$ loops. Numerically, the charmed sextet baryons come out with electric polarizabilities between $0.90 \\times 10^{-4}$ and $9.42 \\times 10^{-4}\\,\\mathrm{fm^3}$ and magnetic polarizabilities between $0.47 \\times 10^{-4}$ and $3.78 \\times 10^{-4}\\,\\mathrm{fm^3}$, while the bottom baryons reach much larger magnetic values, up to $18.6 \\times 10^{-4}\\,\\mathrm{fm^3}$ for $\\Sigma_b^+$, driven by the 20 MeV splitting.","pith_inferences":["Because the vanishing antitriplet polarizability follows from selection rules rather than from fitted constants, it is the cleanest falsifiable corner of the calculation: a single nonzero polarizability measurement for $\\Lambda_c^+$ would directly expose the size of $\\mathcal{O}(p^4)$ counterterm contributions.","The $C_\\xi^2/\\delta_1$ structure implies a testable scaling law — magnetic polarizability growing roughly as $1/\\delta_1$ as the heavy quark mass is varied — which lattice QCD could probe by changing the heavy quark mass at fixed lattice spacing.","The baryons with the smallest tree-level contributions, $\\Sigma_c^+$ and $\\Xi_c^{\\prime +}$, are the most sensitive windows into $\\mathcal{O}(p^4)$ truncation error, since their predicted polarizabilities are the most likely to shift once the next order is included.","The same Compton-tensor framework extends naturally to the spin-$\\frac{3}{2}$ sextet polarizabilities and to doubly heavy baryons, where the relevant partner splittings are even smaller and the pole enhancement would be larger."],"forward_implications":["The antitriplet baryons $\\Lambda_c^+$, $\\Xi_c^+$, $\\Xi_c^0$ are predicted to have exactly zero electric and magnetic polarizability at $\\mathcal{O}(p^3)$, so any measured nonzero value would directly signal contributions beyond this order.","Among the charmed sextet baryons, the magnetic polarizability is dominated by the $B_6^* \\to B_6 \\gamma$ transition for $\\Sigma_c^{++}$, $\\Sigma_c^0$, $\\Xi_c^{\\prime 0}$, and $\\Omega_c^0$, whereas $\\Sigma_c^+$ and $\\Xi_c^{\\prime +}$, whose transition magnetic moments nearly vanish, are predicted to be markedly less magnetically polarizable.","The bottom baryon magnetic polarizabilities come out several times larger than the charmed ones, up to $18.6 \\times 10^{-4}\\,\\mathrm{fm^3}$ for $\\Sigma_b^+$, because the $B_6$–$B_6^*$ splitting shrinks to 20 MeV and the $\\delta_1^{-1}$ pole term grows.","In the heavy quark limit the loop contributions obey exact ratio relations $\\alpha_E^{(c-g)} = 2\\alpha_E^{(c'-g')}$ and $\\beta_M^{(c-g)} = 2\\beta_M^{(c'-g')}$, and the finite-splitting numerical results approximately preserve them.","The analytical expressions are directly usable as chiral extrapolation formulas for future lattice QCD simulations of heavy baryon electromagnetic properties."],"supporting_citations":[{"why":"The heavy baryon chiral perturbation theory derivation of nucleon polarizabilities from chiral loops; supplies the Compton tensor formalism, the diagram set, and the $\\mathcal{O}(p^3)$ truncation that this paper extends to heavy baryons.","marker":"[67–70]"},{"why":"Magnetic moments of spin-$\\frac{1}{2}$ singly charmed baryons in heavy baryon chiral perturbation theory; the source of the low-energy constant estimation method and the quark model transition magnetic moments reused here.","marker":"[40]"},{"why":"Magnetic moments of spin-$\\frac{3}{2}$ singly heavy baryons; provides the $f_6$ and $f_7$ couplings that enter the transition coefficients $C_\\xi$.","marker":"[41]"},{"why":"The heavy quark symmetry and chiral dynamics paper that fixes the multiplet structure and the relation $g_1^2 = \\frac{4}{3} g_3^2$ used to reduce the couplings.","marker":"[80]"},{"why":"Lattice QCD magnetic moments of charmed baryons, the data points in the quark magnetic moment fit that determines the $C_\\xi$ coefficients.","marker":"[46, 47, 49]"},{"why":"The $\\Delta(1232)$ contribution to nucleon polarizabilities; the analogue mechanism in which a near-degenerate spin-$\\frac{3}{2}$ intermediate state produces a large magnetic polarizability.","marker":"[83]"},{"why":"Chiral perturbation theory study of charmed and bottom baryon electromagnetic decays, cited for the heavy quark limit relation $g_1^2 = \\frac{4}{3} g_3^2$.","marker":"[37]"},{"why":"Particle data group values of nucleon polarizabilities, the experimental benchmark against which the heavy baryon results are compared.","marker":"[71]"}],"fun_headline_variants":["Antitriplet heavy baryons show zero polarizability at order p³","Sextet heavy baryons get large magnetic polarizabilities from chiral loops","Zero polarizability for antitriplet heavy baryons in chiral theory","Antitriplet zero, sextet large: polarizabilities of heavy baryons at p³","Charmed sextet baryons: magnetic polarizability boosted by B* transitions"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise, which the paper itself concedes in its summary, is that the strength constants can be pinned down by heavy quark symmetry, the quark model, and a fit to lattice QCD magnetic moments, and that the third-order chiral expansion remains reliable even when the two sextet states are only 20 MeV apart for bottom baryons.","fun_headline_variants_meta":{"raw":{"variants":["Antitriplet heavy baryons show zero polarizability at order p³","Sextet heavy baryons get large magnetic polarizabilities from chiral loops","Zero polarizability for antitriplet heavy baryons in chiral theory","Antitriplet zero, sextet large: polarizabilities of heavy baryons at p³","Charmed sextet baryons: magnetic polarizability boosted by B* transitions"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00096,"raw_usage":{"total_tokens":4176,"prompt_tokens":1115,"completion_tokens":3061,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":731,"completion_tokens_details":{"reasoning_tokens":2957}},"tokens_in":731,"tokens_out":3061,"duration_ms":23013,"temperature":1.0,"reasoning_tokens":2957,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T23:39:57.579715+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A lattice QCD computation of the electric and magnetic polarizabilities of the singly charmed baryons at or near the physical pion mass would settle the central claim: the framework predicts $\\beta_M / \\alpha_E = 0.1$ for the chiral-loop part of the sextet, a magnetic polarizability hierarchy ordered by the transition magnetic moments (largest for $\\Sigma_c^{++}$, smallest for $\\Sigma_c^+$ and $\\Xi_c^{\\prime +}$), and exactly vanishing polarizabilities for $\\Lambda_c^+$ and $\\Xi_c$. Measuring the $B_6^* \\to B_6 \\gamma$ radiative width would independently fix the $C_\\xi$ coefficients that control the dominant magnetic contribution. Conversely, a single nonzero polarizability for $\\Lambda_c^+$ — for instance from the spin precession of channeled charmed baryons in bent crystals proposed at hadron colliders — would show that the $\\mathcal{O}(p^4)$ effects are not negligible.","supporting_citations":[{"cited_title":"Oh and B.-Y","cited_arxiv_id":null,"evidence_quote":"Magnetic moments of spin-$\\frac{1}{2}$ singly charmed baryons in heavy baryon chiral perturbation theory; the source of the low-energy constant estimation method and the quark model transition magnetic moments reused here."},{"cited_title":"Masses and magnetic moments of heavy flavour baryons in hyper central model","cited_arxiv_id":"0710.3828","evidence_quote":"Magnetic moments of spin-$\\frac{3}{2}$ singly heavy baryons; provides the $f_6$ and $f_7$ couplings that enter the transition coefficients $C_\\xi$."},{"cited_title":"Bernard, N","cited_arxiv_id":null,"evidence_quote":"The heavy quark symmetry and chiral dynamics paper that fixes the multiplet structure and the relation $g_1^2 = \\frac{4}{3} g_3^2$ used to reduce the couplings."},{"cited_title":"Radiative decays of negative parity heavy baryons in QCD","cited_arxiv_id":"1606.07666","evidence_quote":"Chiral perturbation theory study of charmed and bottom baryon electromagnetic decays, cited for the heavy quark limit relation $g_1^2 = \\frac{4}{3} g_3^2$."}],"review_version":1}