{"id":"c09973b0-d37c-4a05-99f4-7e1cd0c02ae3","arxiv_id":"2411.17803","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A new term in the chiral diquark Lagrangian is shown to control the mass ordering of pseudoscalar diquarks and to set the threshold at which heavy-baryon decays turn off under chiral restoration.","lead":"Physicists here update a mathematical model of quark pairs called diquarks, adding one new ingredient that shifts the predicted masses of certain particles. The work suggests that in hot or dense matter, some particle decays could switch off, giving experiments a clear signal to look for.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The fourth input M0 is the load-bearing parameter: the hierarchy switch and all x-dependent predictions disappear if the unmeasured rho-mode Xi_c(1/2-) mass falls below ~2890 MeV, and the vacuum spectrum cannot identify mu0^2 since four masses fix four parameters.","rationale":"The paper is a coherent extension of an established chiral-diquark program. The new mu0^2 term is a genuine addition, the algebraic derivation of the mass formulas is internally consistent, and the corrected x-dependent formulas fix a real error in earlier work; the authors are also explicit about which quantities are inputs and which are outputs. My concern is the epistemic status of the central qualitative conclusion, not the internal algebra. The four vacuum masses completely determine the four Lagrangian parameters, so the vacuum fit cannot test the new term; the only observable differences are the x-dependent curves and thresholds, and those curves are bracketed by the unmeasured parameter M0. I therefore agree with the reader's weakest assumption and would keep the verdict CONDITIONAL: the analysis is a well-posed model study, but an independent constraint on M0, from lattice QCD, QCD sum rules, or the quark model already used for the Lambda_c input, is required before the hierarchy switch and the x_AS/x_th predictions can be regarded as physics predictions about QCD rather than consequences of scanning an unconstrained input. The abstract's 'about 20%' phrasing is also loose for the Sigma_c(1/2+) channel, where x_th = 0.947-0.984 corresponds to only about 5-16% restoration, but this is secondary to the M0 dependence. The central claim is not internally inconsistent, and the paper's honest caveats about needing future determinations support a conditional acceptance rather than rejection or unconditional acceptance.","tokens_in":67644,"tokens_out":14547,"duration_ms":133233,"concrete_test":"Run an independent lattice-QCD computation of the strange pseudoscalar diquark mass M_{ns}(0^-) using us/ds 0^- interpolating operators in the color-antisymmetric channel, with continuum extrapolation, and convert it to M0 through the same two-body diquark-heavy-quark Schrodinger equation and Y-potential used in Sec. V, or compute the rho-mode Xi_c(1/2^-) mass directly. Then re-evaluate Eqs. (13)-(18) and Table I. The decisive branch point is M0 = 2890 MeV (Case E): below it the P hierarchy stays inverse, Mud(0^-) > Mns(0^-), and the central switch claim fails; above it the normal ordering and the mu0^2-driven shifts of x_AS and x_th are supported. If no lattice result is available, an intermediate check is to use the same quark model [110] that supplies the 2890 MeV Lambda_c rho-mode input to compute the Xi_c rho-mode P state and see whether that value falls below 2890 MeV.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section III promotes M_{ns}(0^-), equivalently M0 = M_{rho(P)}(Xi_c;1/2^-), from a prediction of the earlier three-parameter model (1271 MeV, Case N) to a free input scanned over 2623-3279 MeV. The central qualitative result, that the new mu0^2 term can flip the P-diquark hierarchy from inverse to normal, is attained only for M0 greater than about 2890 MeV (Case E), with the clean normal-ordering Case H sitting at the upper endpoint 3279 MeV where m_{S1}^2 = 0. The scan boundaries are not empirical: the lower limit is the model-consistency condition M_{ns}(0^-) > M_{ns}(1^+), and the upper limit is m_{S1}^2 >= 0. Because the four vacuum masses in Eqs. (13)-(16) are fitted by the four parameters m_{S0}^2, m_{S1}^2, m_{S2}^2, and mu0^2, the vacuum spectrum cannot by itself distinguish mu0^2 = 0 from mu0^2 != 0; the previous model's value mu0 = 0, M_{ns}(0^-) = 1271 MeV remains a valid fit. The falsifiable content is therefore entirely in the x-dependence, such as x_AS and x_th in Figs. 3, 8, and Table V, and every one of those predictions is conditional on the unmeasured M0. If an independent lattice or quark-model determination places M0 below about 2890 MeV, Eq. (18) keeps the inverse ordering and the claimed switch does not occur; the paper's central claim then reduces to a particular choice of an unconstrained input rather than a prediction.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper revisits the authors' chiral effective theory of diquarks by adding to the scalar/pseudoscalar Lagrangian a term with coefficient mu0^2 that is invariant under chiral SU(3)_R x SU(3)_L and U(1)_A and vanishes for a flavor-symmetric condensate. This term contributes with the same sign to the strange/nonstrange mass differences of both the S and P diquarks, Eqs. (17) and (18), so a sufficiently large mu0^2 can convert the inverse P-diquark hierarchy generated by the U(1)_A term into the normal hierarchy. The four parameters of the S/P sector are fixed by the four vacuum diquark masses, with the strange P-diquark mass encoded in the unmeasured rho-mode Xi_c(1/2-) mass M0, scanned over 2623-3279 MeV and represented by Cases L, N, E, and H in Table I. The paper corrects the x-dependent diquark mass formulas of Refs. [45,49,117], studies the diquark and singly-heavy-baryon spectra under chiral restoration using the scaling of Eq. (27), and computes the S/A lowest-state crossing point x_AS and the thresholds x_th at which the decays Sigma_Q -> Lambda_Q + pi are kinematically forbidden (Figs. 3 and 8, Table V).","tokens_in":2008,"tokens_out":2529,"duration_ms":365639,"significance":"The central message is plausible and internally consistent: the sign structure of Eqs. (17) and (18) is transparent, the x-dependent formulas (28)-(33) reduce correctly to the vacuum formulas at x = 1 and give the expected x = 0 degeneracies under the assumed scaling of Eq. (27), and the parameter counting is declared honestly, with the earlier mu0 = 0 solution (Case N) remaining a valid fit. The paper also delivers a specific, checkable improvement: the corrected coefficient of the m_S1^2 term, which couples the [ud] diquark to the strange condensate and shifts x_AS from about 0.6 to 0.6747 in Case N. The falsifiable predictions (P-diquark mass ordering, x_AS, x_th, and the residual S/P splitting at x = 0) are clearly itemized in Sec. VII. The principal limitation is that the new physics, namely the hierarchy flip, is realized only for M0 >= 2890 MeV, an unmeasured input, so the predictive content is conditional rather than definitive, and the abstract's 'predict the fate' language is stronger than the scan-based results warrant.","major_comments":[{"comment":"The central new qualitative result, that the mu0^2 term can flip the pseudoscalar diquark ordering from inverse to normal, is realized only for M0 >= 2890 MeV (Cases E and H), while M0 = M_rho(P)(Xi_c; 1/2-) in Eq. (24) is unmeasured and the scan bounds are model-consistency conditions (M_ns(0-) > M_ns(1+) and m_S1^2 >= 0) rather than data. Because the four vacuum masses in Eqs. (13)-(16) determine the four parameters exactly, the x = 1 spectrum cannot by itself establish mu0^2 != 0, and the earlier mu0^2 = 0 solution (Case N) remains a valid fit. All x-dependent claims (x_AS in Fig. 3, x_th in Table V, the decay suppression in Fig. 8) are therefore conditional on this unconstrained input. I recommend that the abstract and the concluding section present the hierarchy flip as a possibility within the admissible range, state the required M0 threshold (about 2890 MeV) at the point of the claim, and list the lattice or quark-model determinations that could confirm or exclude it.","section":"Sec. III, Eq. (24), Table I; abstract"},{"comment":"The correction of the x-dependent mass formulas in Refs. [45,49,117] is a central deliverable, but the text does not show the contraction that produces the new coefficient of m_S1^2, namely the combination x f_s/f_pi + m_s/(g_s f_pi) multiplying m_S1^2 for the [ud] diquark in Eq. (28). Because the paper asks readers to accept that three earlier publications contain an error, the derivation should be self-contained: please display the mean-field reduction of the m_S1 and mu0^2 terms for the d_3 = [ud] and d_1 = [us] components of the diquark field, and state precisely which piece was missing in the earlier formulas, for example the m_s/g_s contribution to the strange condensate or the A(x) factor.","section":"Sec. IV, Eqs. (28)-(33)"}],"minor_comments":[{"comment":"The footnote stating that a similar term added to L_V 'will make no change to the diquark spectrum when the flavor SU(3) symmetry is broken' appears to state the opposite of the S/P logic, where the new term acts precisely because flavor SU(3) is broken; please clarify the intended phase or show the explicit candidate term and the contraction that makes it vanish.","section":"Sec. II B, footnote 4"},{"comment":"The statement that 'about 20% of partial restoration of chiral symmetry forbids these strong decays' is not representative of Table V: 1 - x_th ranges from 0.016 (Case H, Sigma_c 1/2+) to 0.189 (Case L, Sigma*_c 3/2+), with Case N giving 0.038-0.136; please quote the actual per-case range instead of a single representative value.","section":"Sec. VI, Table V"},{"comment":"At the lower boundary (Case L, M0 = 2623 MeV) the condition M_ns(0-) > M_ns(1+) stated after Eq. (24) is saturated (1115 vs 1115.30 MeV); please phrase this prior as a non-strict inequality, M_ns(0-) >= M_ns(1+).","section":"Sec. III, Eq. (24)"},{"comment":"The assumption that M_pi is independent of x is stated but its sensitivity is not quantified; since several x_th values in Table V are close to 1, a pion mass that decreases with x would keep the decay phase space open longer, and a sentence estimating this shift or justifying the restricted range 0.8 <= x <= 1 would strengthen the threshold analysis.","section":"Sec. VI, decay formula"},{"comment":"The caption of Fig. 2 plots parameters as sgn(m^2) times |m|, but the sign convention is easy to miss when mu0^2 and m_S2^2 are negative (Cases L and N); please state the convention directly in the figure or use symbols such as m_mu = sgn(mu0^2) sqrt(|mu0^2|) in the caption.","section":"Fig. 2 caption"},{"comment":"For Case E the choice M0 = 2890 MeV numerically coincides with the quark-model value of the Lambda_c rho-mode P-diquark state quoted from Ref. [110], but it is used for the Xi_c state; a footnote explaining that this value is chosen only to enforce M_ud(0-) = M_ns(0-) and carries no independent empirical support would prevent a misreading.","section":"Table I"}],"recommendation":"major_revision","confidential_remarks":"This manuscript is a natural continuation of the authors' program on chiral diquark effective theory and fits the journal's scope. My main concern is the degree to which the headline result (the P-diquark hierarchy flip) depends on the unmeasured input M0; the paper would be strengthened if the abstract quantified this conditionality. I would also recommend that the claimed error in Refs. [45,49,117] be verified during the revision, preferably by a referee who knows those papers, since the correction underpins the new x-dependent figures. A lattice-QCD referee's view on the plausible range of the strange P-diquark mass (equivalently on whether M0 >= 2890 MeV is realistic) would be valuable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The real news here is the mu0^2 term, a chiral SU(3)_R x SU(3)_L and U(1)_A symmetric eight-quark interaction, and the corrected x-dependent mass formulas in Eqs. (28)-(35), which fix an error in the authors' earlier papers [45,49,117]. That correction is substantive, not cosmetic: it changes x_AS and the decay thresholds. The paper also honestly demotes M_ns(0-) from a prediction of the previous three-parameter model to an input, and it says so in the text. Credit where due.\n\nThe vacuum spectrum is, as the reader says, a refit: four vacuum masses determine the four Lagrangian parameters, so at x=1 the model cannot distinguish mu0^2=0 from mu0^2 nonzero. That is not a fatal flaw because the x<1 behavior, the crossing points, and the threshold positions are genuine extrapolations not used in the fit. The falsifiable content is there, but it is conditional.\n\nThe stress-test note holds up on reading. The central qualitative result, the switch from inverse to normal P-diquark ordering, requires M0 > about 2890 MeV (Case E), and the clean normal-ordering case H sits at the upper endpoint 3279 MeV where m_S1^2=0. The scan boundaries come from model consistency conditions, not from data or lattice input. If an independent determination places M0 below about 2890 MeV, the inverse ordering survives and the paper's headline prediction collapses to a choice of an unmeasured input. This is a genuine soft spot, and it is the biggest one.\n\nA smaller but real issue: the abstract's \"about 20%\" overstates the decay-suppression claim. Table V gives 1-x_th from about 2% to 19% depending on case and channel; the typical charm 1/2+ threshold corresponds to only a few percent restoration. The claim is directionally correct, but the advertised number is cherry-picked from the edge of the range.\n\nMinor points: no code or data are shipped, though the paper creates no new data and relies on previously published potential-model inputs. The footnote acknowledging the neglected second-order term in Eqs. (34)-(35) is fine. Citation pattern looks fair; the self-citations are to the papers whose formulas are being corrected.\n\nWho gets value: hadron phenomenologists working on diquark effective theories, chiral restoration in medium, and singly heavy baryons; lattice practitioners might find the M0-dependence and P-diquark ordering a useful target. The paper deserves a serious referee. I would send it to review and ask the referee to press on the M0 dependence and to make the threshold wording match the table.","headline":"The chiral-symmetric mu0^2 term and the corrected x-dependent mass formulas are genuinely new, but the paper's central hierarchy-switch claim rests entirely on an unmeasured input mass M0: if M0 comes in below about 2890 MeV, the predicted switch does not happen.","tokens_in":68669,"tokens_out":2137,"would_cite":true,"duration_ms":23964,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["12.39.Fe","14.20.Lq","14.20.Mr"],"model":"deepseek-v4-flash","headline":"A single chiral-and-U(1)_A-symmetric term controls whether strange pseudoscalar diquarks are lighter or heavier than nonstrange ones, and it predicts how the ordering shows up in heavy-baryon decays.","keywords":["chiral effective theory","diquarks","heavy baryons","chiral symmetry restoration","U(1)_A anomaly","mass hierarchy","strong decay widths","eight-quark interaction"],"falsifier":"Compute the strange pseudoscalar diquark mass, or the rho-mode excited $\\Xi_c(1/2^-)$ state, on the lattice: if $M_{ns}(0^-)$ is found to be lighter than $M_{ud}(0^-)$ at the physical point, the inverse hierarchy holds and the $\\mu_0^2$ term must be small, while a heavier $M_{ns}(0^-)$ would require a $\\mu_0^2$ large enough to flip the ordering.","tokens_in":67400,"feed_emoji":"⚛️","tokens_out":9980,"duration_ms":84569,"temperature":0.7,"pith_summary":"This paper revisits the chiral effective theory of light diquarks, quark pairs in the color-antitriplet channel, by adding one term to the scalar/pseudoscalar diquark Lagrangian that earlier work omitted. The term is invariant under chiral SU(3)_R x SU(3)_L and under U(1)_A, and it comes from an eight-quark interaction. The authors show that this term changes the relation between strange and nonstrange diquark masses: unlike the anomaly term already known to force the pseudoscalar diquarks into an inverse mass ordering, the new term pushes both scalar and pseudoscalar mass differences in the same direction. Using four parameter sets that cover the experimentally unconstrained rho-mode excited Xi_c(1/2-) mass, they find that a sufficiently strong $mu0^{2}$ term can flip the pseudoscalar diquarks to the normal ordering, and they predict how diquark masses, heavy-baryon masses, and Sigma_Q -> Lambda_Q pi decay widths respond as chiral symmetry is restored. This matters because the restored-phase mass ordering and the condensation scale at which the decays switch off become observable diagnostics for the new interaction.","feed_headline":"A chiral term can flip the pseudoscalar diquark mass order","feed_subtitle":"Its strength sets when strange diquarks overtake nonstrange ones and when heavy-baryon pion decays switch off.","key_machinery":"The load-bearing object is the new term in the S/P diquark Lagrangian (9): $(\\mu_0^2/f_\\pi^2)[d_R\\{\\Sigma^\\dagger\\Sigma - \\frac13\\mathrm{Tr}[\\Sigma^\\dagger\\Sigma]\\}d_R^\\dagger + d_L\\{\\Sigma\\Sigma^\\dagger - \\frac13\\mathrm{Tr}[\\Sigma\\Sigma^\\dagger]\\}d_L^\\dagger]$. This term is chiral SU(3)_R x SU(3)_L and U(1)_A symmetric, and it vanishes in the flavor-SU(3) limit $A=1$. On the mean field $\\langle\\Sigma\\rangle = f_\\pi \\mathrm{diag}(1,1,A)$, it generates the $(A^2-1)\\mu_0^2$ contributions that move the strange and nonstrange scalar and pseudoscalar mass differences in the same direction. Four parameters of the scalar/pseudoscalar Lagrangian are solved from four mass inputs, with the fourth input $M_{ns}(0^-)$ set by the rho-mode excited $\\Xi_c(1/2^-)$ mass $M_0$; the four cases L, N, E, H are chosen inside the allowed range. The same machinery gives the $x$-dependent mass formulas (28)-(35), in which $x$ scales the chiral condensates, and these feed the two-body diquark-heavy-quark Schr\\\"odinger equation that produces the baryon masses, wave functions, and decay widths.","core_discovery":"The paper's central claim is that a chiral and U(1)_A symmetric operator with coefficient \\$mu_0^{2}$, originating from an eight-point quark interaction, is not just a renormalization of the chiral-invariant mass term once flavor SU(3) is broken by the strange condensate. In the mass differences $M^2_{ns}(0^\\pm) - M^2_{ud}(0^\\pm)$, the $\\mu_0^2$ contribution has the same sign for scalar and pseudoscalar diquarks, namely $(A^2-1)\\mu_0^2$, whereas the anomaly term $m_{S1}^2$ enters with opposite signs. Therefore, if $(A+1)\\mu_0^2 > m_{S1}^2 - m_{S2}^2$, the inverse pseudoscalar hierarchy found in earlier work is replaced by the normal hierarchy. The paper fixes $m_{S0}^2$, $m_{S1}^2$, $m_{S2}^2$, and $\\mu_0^2$ from four diquark-mass inputs, the fourth being the strange pseudoscalar mass $M_{ns}(0^-)$ tied to the unmeasured rho-mode excited $\\Xi_c(1/2^-)$ mass $M_0$, which is scanned over 2623 to 3279 MeV. It then derives corrected $x$-dependent mass formulas for diquarks under chiral restoration, superseding those in Refs. [45, 49, 117], and predicts the crossing point $x_{AS}$ where the axial-vector and scalar diquark masses invert, together with the threshold $x_{\\mathrm{th}}$ at which $\\Sigma_Q \\to \\Lambda_Q \\pi$ decays are forbidden.","pith_inferences":["Beyond the paper, the unmeasured $\\Xi_c(1/2^-,\\rho)$ mass is the decisive control: a single lattice determination of that state, or of $M_{ns}(0^-)$ directly, would select one of the four parameter sets and fix $\\mu_0^2$.","Beyond the paper, a direct lattice measurement of the sign of $M_{ns}(0^-)-M_{ud}(0^-)$ would discriminate the new eight-quark interaction from the pure-anomaly mechanism without waiting for medium experiments.","Beyond the paper, the fact that $x_{\\mathrm{th}} > x_{AS}$ in every case suggests the decay switch-off is not simply the S/A crossing; measuring both observables under the same restoration conditions could separate the role of $\\mu_0^2$ from that of $m_{S1}^2$.","Beyond the paper, the same trace-subtracted construction could be applied to vector diquarks beyond the flavor-symmetric mean field, where the authors note it would be silent; at nonzero current-quark masses or with different condensate scalings it might leave an observable trace."],"forward_implications":["For Case H, where $\\mu_0^2$ is largest, the inverse pseudoscalar hierarchy disappears and $M_{ud}(0^-) < M_{ns}(0^-)$; the same ordering is carried by the rho-mode excited $\\Lambda_Q$ and $\\Xi_Q$ states.","Under chiral restoration the scalar diquarks rise in mass while pseudoscalar diquarks fall, so the S/P chiral partners approach each other; the nonstrange partners remain split by the $U(1)_A$ term $m_{S1}^2 \\neq 0$ except in Case H where $m_{S1}^2 = 0$.","The axial-vector/scalar lowest-state inversion point lies in $0.566 < x_{AS} < 0.858$, so a moderate partial restoration of chiral symmetry makes the axial-vector diquark lighter than the scalar diquark.","The $\\Sigma_Q \\to \\Lambda_Q \\pi$ decay width is suppressed as $x$ decreases, with the switch-off threshold $x_{\\mathrm{th}}$ between 0.811 and 0.984, and a larger input mass $M_0$ moves the threshold closer to the vacuum point $x=1$.","The corrected $x$-dependent formulas change the restored-phase predictions of earlier work, so heavy-baryon and doubly-heavy-tetraquark results built on the erroneous coefficients need revision."],"supporting_citations":[{"why":"Supplies the earlier chiral effective theory of S/P diquarks without $\\mu_0^2$, the three-parameter fit procedure, and the inverse pseudoscalar hierarchy that this paper extends.","marker":"[40, 41]"},{"why":"Constructs the chiral effective Lagrangian for A/V diquarks and the heavy-baryon spectrum with the Y-potential used here; also contains the erroneous x-dependent mass-formula coefficients corrected in Eqs. (28)-(29).","marker":"[45]"},{"why":"Derives the $\\Sigma_Q \\to \\Lambda_Q \\pi$ decay-width formulas and the S-V coupling $g_1,g_2$ used in Sec. VI; its x-dependent formulas are corrected by the present paper.","marker":"[49]"},{"why":"Applies the chiral-diquark picture to doubly heavy tetraquarks, and the paper states that its x-dependent mass formulas are also corrected.","marker":"[117]"},{"why":"Provides the lattice QCD value of the nonstrange scalar diquark mass $M_{ud}(0^+)$ used as an input to fix the Lagrangian parameters.","marker":"[25]"},{"why":"Provides the three-quark model value for the rho-mode $\\Lambda_c(1/2^-)$ mass used as the input $M_{ud}(0^-)$ in the parameter fits.","marker":"[110]"},{"why":"Provides the experimental compilation of singly heavy baryon masses used to fix inputs and to compare the calculated spectra and decay widths.","marker":"[118]"}],"fun_headline_variants":["Chiral term flips pseudoscalar diquark mass order","New chiral term inverts diquark mass hierarchy","Heavy-baryon pion decays switch off at a chiral threshold","U(1)_A symmetric term reverses diquark ordering"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole parameter set is solved from the assumed mass of an experimentally unobserved excited Xi_c state, scanned over 2623 to 3279 MeV, and if the true value lies outside this range, the predictions for diquark ordering and decay thresholds collapse.","fun_headline_variants_meta":{"raw":{"variants":["Chiral term flips pseudoscalar diquark mass order","New chiral term inverts diquark mass hierarchy","Heavy-baryon pion decays switch off at a chiral threshold","U(1)_A symmetric term reverses diquark ordering"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000778,"raw_usage":{"total_tokens":3484,"prompt_tokens":1038,"completion_tokens":2446,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":654,"completion_tokens_details":{"reasoning_tokens":2374}},"tokens_in":654,"tokens_out":2446,"duration_ms":24505,"temperature":1.0,"reasoning_tokens":2374,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T11:49:31.108455+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the strange pseudoscalar diquark mass, or the rho-mode excited $\\Xi_c(1/2^-)$ state, on the lattice: if $M_{ns}(0^-)$ is found to be lighter than $M_{ud}(0^-)$ at the physical point, the inverse hierarchy holds and the $\\mu_0^2$ term must be small, while a heavier $M_{ns}(0^-)$ would require a $\\mu_0^2$ large enough to flip the ordering.","supporting_citations":[{"cited_title":"Suppression of decay widths in singly heavy baryons induced by the $U_A (1)$ anomaly","cited_arxiv_id":"2009.06243","evidence_quote":"Constructs the chiral effective Lagrangian for A/V diquarks and the heavy-baryon spectrum with the Y-potential used here; also contains the erroneous x-dependent mass-formula coefficients corrected in Eqs. (28)-(29)."},{"cited_title":"Excitation spectra of heavy baryons in diquark models","cited_arxiv_id":"2107.11950","evidence_quote":"Derives the $\\Sigma_Q \\to \\Lambda_Q \\pi$ decay-width formulas and the S-V coupling $g_1,g_2$ used in Sec. VI; its x-dependent formulas are corrected by the present paper."},{"cited_title":"Dynamical generation of the gauged SU(2) linear sigma model","cited_arxiv_id":"hep-ph/9910242","evidence_quote":"Applies the chiral-diquark picture to doubly heavy tetraquarks, and the paper states that its x-dependent mass formulas are also corrected."},{"cited_title":"The Quark-Level Linear \\sigma\\ Model","cited_arxiv_id":"1309.5041","evidence_quote":"Provides the experimental compilation of singly heavy baryon masses used to fix inputs and to compare the calculated spectra and decay widths."}],"review_version":1}