REVIEW
Chiral Lagrangians for Radiative Decays of Heavy Hadrons
High Energy Physics - Phenomenology · Submitted 21 Sep 1992 · 15 references
Pith's verdict: The electromagnetic extension of the Cheng–Yan heavy-hadron chiral Lagrangian is the real contribution; the D*0 → D0γ branching ratio is the one clean test, and the D*+ total-width 'consistency' claim is softer than the text implies.
T0 · AI review
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Referee report
The paper
The paper claims
Heavy-quark symmetry reduces the magnetic sector of heavy-hadron radiative decays to one meson and two baryon couplings.
The reading
What carries the argument
The machinery is the electromagnetic chiral Lagrangian for heavy hadrons, built by gauging the strong chiral Lagrangian and adding gauge-invariant anomalous magnetic moment operators. Heavy quark spin symmetry acts on the magnetic operators through interpolating fields for a heavy quark plus a light antiquark or light diquark, forcing the meson relation $d''=-2d$ and the baryon relations $a_3=-(sqrt{3}/2)a_1$, $a_5=-(3/2)a_1$, $a_4=sqrt{3}a_2$, and $a_6=0$. The nonrelativistic quark model then fixes $d$, $a_1$, and $a_2$ from the light-quark magnetic moments, with an added charm-quark magnetic term because $m_c$ is not taken to infinity.
Extended reading notes
Core claim
The central claim is that the electromagnetic interactions of heavy hadrons split into a minimal-coupling piece obtained by gauging the strong chiral Lagrangian and a magnetic piece whose independent couplings are fixed by heavy quark spin symmetry. In the meson sector the magnetic Lagrangian has one heavy-quark-independent constant $d$, and the spin-symmetry relation $d''=-2d$ holds; in the baryon sector six anomalous couplings collapse to two, $a_1$ and $a_2$, with $a_3=-(sqrt{3}/2)a_1$, $a_5=-(3/2)a_1$, $a_4=sqrt{3}a_2$, and $a_6=0$. The quark model then evaluates $d$, $a_1$, and $a_2$ from light-quark magnetic moments, while the charm quark's magnetic moment is added explicitly. With these inputs the paper predicts radiative widths for $D^*to Dgamma$, $B^*to Bgamma$, $Xi'_cto Xi_cgamma$, $Sigma_cto Lambda_cgamma$, and $Sigma_cto Lambda_cpi gamma$, and, combined with prior strong widths, total widths and branching ratios for $D^*$ and $Sigma_c$.
Load-bearing premise
The numerical predictions assume that fixed constituent quark masses ($m_u=338$ MeV, $m_d=322$ MeV, $m_s=510$ MeV, $m_c=1.6$ GeV) and the imported axial coupling $g_A^{ud}=0.75$ give the magnetic couplings and strong widths accurately enough, with no uncertainty propagated.
Editorial extensions
If this is right
- The $D^*$ branching ratios in Table I should match CLEO II: the paper reports $mathrm{Br}(D^{*+}to D^+gamma)=1.5%$ against the measured $1.1pm1.4pm1.6%$, and $mathrm{Br}(D^{*0}to D^0gamma)=33.3%$ against $36.4pm2.3pm3.3%$.
- The predicted total widths $Gamma_{mathrm{tot}}(D^{*+})=141$ keV, $Gamma_{mathrm{tot}}(D^{*0})=102$ keV, and $Gamma_{mathrm{tot}}(D_s^{*+})=0.3$ keV provide targets for precision width measurements; the $D^{*+}$ value is close to the ACCMOR upper limit of 131 keV.
- $Sigma_c^+toLambda_c^+gamma$ is predicted at 93 keV, giving $mathrm{Br}(Sigma_c^+toLambda_c^+gamma)=3.8%$ when combined with $Gamma(Sigma_c^+toLambda_c^+pi^0)=2.43$ MeV and a total $Sigma_c^+$ width of 2.54 MeV.
- $Xi_c'^+toXi_c^+gamma$ and $Xi_c'^0toXi_c^0gamma$ are predicted at 16 keV and 0.3 keV; if the $Xi_c'-Xi_c$ mass splitting is about 100 MeV, these radiative widths are effectively the total widths of the $Xi_c'$ states.
- The pion-photon decays $Sigma_c^+toLambda_c^+pi^0gamma$ and $Sigma_c^0toLambda_c^+pi^-gamma$ isolate different pieces of the Lagrangian: the charged-pion mode tests the contact term from gauging, while the neutral-pion mode tests the chiral structure of the magnetic Lagrangian.
Reading between the lines
- If the three-coupling reduction is correct, then once bottom-baryon masses are measured the same formulas give parameter-free radiative widths for $Sigma_b$, $Xi_b'$, and $Omega_b$, so the first observation of such a photon line becomes a direct symmetry test.
- The destructive interference of the charm magnetic moment in $D^{*+}$ and $D_s^{*+}$ suggests that a precise $Gamma(D^{*+})$ significantly above 141 keV, or a $D^{*+}to D^+gamma$ branching ratio well above about 2%, would point to missing $1/m_c$ corrections or a larger effective charm moment.
- The $Sigma_ctoLambda_cpi gamma$ amplitudes separate a contact term from a magnetic pole term; measuring the pion energy spectrum or photon angular distribution could distinguish them even with modest statistics, which the paper leaves for future work.
- Because the same quark-model magnetic moments feed the baryon and meson sectors, a discrepancy in one sector, such as the $Xi_c'^0$ width, would constrain the light-quark mass ratios $alpha=m_u/m_d$ and $beta=m_u/m_s$ used for SU(3) breaking.
Original abstract
The radiative decays of heavy mesons and heavy baryons are studied in a formalism which incorporates both the heavy quark symmetry and the chiral symmetry. The chiral Lagrangians for the electromagnetic interactions of heavy hadrons consist of two pieces: one from gauging electromagnetically the strong-interaction chiral Lagrangian, and the other from the anomalous magnetic moment interactions of the heavy baryons and mesons. Due to the heavy quark spin symmetry, the latter contains only one independent coupling constant in the meson sector and two in the baryon sector. These coupling constants only depend on the light quarks and can be calculated in the nonrelativistic quark model. However, the charm quark is not heavy enough and the contribution from its magnetic moment must be included. Applications to the radiative decays $D^\ast \rightarrow D \gamma~,~B^\ast \rightarrow B \gamma~,~ \Xi^\prime_c \rightarrow \Xi_c \gamma~, \Sigma_c \rightarrow \Lambda_c \gamma$ and $\Sigma_c \rightarrow \Lambda_c \pi \gamma$ are given. Together with our previous results on the strong decay rates of $D^\ast \rightarrow D \pi$ and $\Sigma_c \rightarrow \Lambda_c \pi$, predictions are obtained for the total widths and branching ratios of $D^\ast$ and $\Sigma_c$. The decays $\Sigma^+_c \rightarrow \Lambda^+_c \pi^0 \gamma $ and $\Sigma^0_c \rightarrow \Lambda^+_c \pi^- \gamma $ are discussed to illustrate the important roles played by both the heavy quark symmetry and the chiral symmetry.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
The radiative decays of heavy mesons and heavy baryons are studied in a formalism which incorporates both the heavy quark symmetry and the chiral symmetry. The chiral Lagrangians for the electromagnetic interactions of heavy hadrons consist of two pieces: one from gauging electromagnetically the strong-interaction chiral Lagrangian, and the other from the anomalous magnetic moment interactions of the heavy baryons and mesons. Due to the heavy quark spin symmetry, the latter contains only one independent coupling constant in the meson sector and two in the baryon sector. These coupling constants only depend on the light quarks and can be calculated in the nonrelativistic quark model. However, the charm quark is not heavy enough and the contribution from its magnetic moment must be included. Applications to the radiative decays $D^\ast \rightarrow D \gamma~,~B^\ast \rightarrow B \gamma~,~ \Xi^\prime_c \rightarrow \Xi_c \gamma~, \Sigma_c \rightarrow \Lambda_c \gamma$ and $\Sigma_c \rightarrow \Lambda_c \pi \gamma$ are given. Together with our previous results on the strong decay rates of $D^\ast \rightarrow D \pi$ and $\Sigma_c \rightarrow \Lambda_c \pi$, predictions are obtained for the total widths and branching ratios of $D^\ast$ and $\Sigma_c$. The decays $\Sigma^+_c \rightarrow \Lambda^+_c \pi^0 \gamma $ and $\Sigma^0_c \rightarrow \Lambda^+_c \pi^- \gamma $ are discussed to illustrate the important roles played by both the heavy quark symmetry and the chiral symmetry.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The radiative decays of heavy mesons and heavy baryons are studied in a formalism which incorporates both the heavy quark symmetry and the chiral symmetry. | contribution 0.94 | 0.86 | 0.08 | asserted 1.00 |
| s1 | The chiral Lagrangians for the electromagnetic interactions of heavy hadrons consist of two pieces: one from gauging electromagnetically the strong-interaction chiral Lagrangian, and the other from the anomalous magnetic moment interactions of the heavy baryons and mesons. | method 0.51 | 0.71 | 0.11 | asserted 1.00 |
| s2 | Due to the heavy quark spin symmetry, the latter contains only one independent coupling constant in the meson sector and two in the baryon sector. | result 0.56 | 0.62 | 0.09 | asserted 1.00 |
| s3 | These coupling constants only depend on the light quarks and can be calculated in the nonrelativistic quark model. | method 0.42 | 0.43 | 0.07 | asserted 1.00 |
| s4 | However, the charm quark is not heavy enough and the contribution from its magnetic moment must be included. | limitation 0.86 | 0.43 | 0.06 | asserted 1.00 |
| s5 | Applications to the radiative decays $D^\ast \rightarrow D \gamma~,~B^\ast \rightarrow B \gamma~,~ \Xi^\prime_c \rightarrow \Xi_c \gamma~, \Sigma_c \rightarrow \Lambda_c \gamma$ and $\Sigma_c \rightarrow \Lambda_c \pi \gamma$ are given. | contribution 0.97 | 0.90 | 0.09 | asserted 0.99 |
| s6 | Together with our previous results on the strong decay rates of $D^\ast \rightarrow D \pi$ and $\Sigma_c \rightarrow \Lambda_c \pi$, predictions are obtained for the total widths and branching ratios of $D^\ast$ and $\Sigma_c$. | result 0.92 | 0.90 | 0.25 | asserted 1.00 |
| s7 | The decays $\Sigma^+_c \rightarrow \Lambda^+_c \pi^0 \gamma $ and $\Sigma^0_c \rightarrow \Lambda^+_c \pi^- \gamma $ are discussed to illustrate the important roles played by both the heavy quark symmetry and the chiral symmetry. | interpretation 0.49 | 0.83 | 0.15 | asserted 0.99 |
What was examined, and what was not
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- P abstract
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References
How the literature uses it
39 arXiv papers cite this in 47 sentences
Papers citing it · 20 sentences without a confident label
Uses its method or tool 14 papers
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To calculate the diagrams shown in Fig. [ref], the effective Lagrangian approach is adopted, where we use the following Lagrangians constructed in heavy quark limit [ref] : [equation] where $ℬ_αβ^∗=∂_αB_β^∗-∂_βB_α^∗$.
Anomalous radiative transitions between $h_b(nP)$ and $\eta_b(mS)$ and hadronic loop effect · radiative transitions between $h_b(nP)$ and $η_b(mS)$ · 0.99
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Considering the heavy-quark symmetry and chiral symmetry, the relevant effective Lagrangians can be constructed as [ref] , [equation] with $𝒟^(*)=(D^(*)0,D^(*)+,D_s^(*)+)$, $𝒟_1=(D_1(2420)^0,$ $D_1(2420)^+, D_s1(2536)^+)$ and $A↔∂^μB=A(∂^μB)-(∂^μA) B$.
Hidden Charm Decays of $Y(4626)$ in a $D_{s}^{*+}D_{s1}(2536)^{-}$ Molecular Frame · Effective Lagrangians · 0.97
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According to the heavy quark limit and chiral symmetry, the interactions of the light pesudoscalar, vector and scalar mesons with the S-wave heavy flavor mesons were constructed as [ref] [equation] where the multiplet fields are expressed as $H_a^(Q)=1+v/2[𝒫^*_aμγ^μ-𝒫_aγ_5]$, $H^(Q̅)=[P_a^*μγ_μ-P_aγ_5] 1-v/2$, $H̅=γ_0H^†γ_0$ with $v=(1,0)$, $𝒫^(*)T =(D^(*)0,D^(*)+,D_s^(*)+)$ or $(B^(*)-,B̅^(*)0,B̅_s^(*)0)$, $𝒫^(*)T =(D̅^(*)0,D^(*)-,D_s^(*)-)$ or $(B^(*)+,B^(*)0,B_s^(*)0)$, which satisfy the normalization relations $⟨0|𝒫|Qq̅(0^-)⟩=⟨0|𝒫|Q̅q(0^-)⟩=√(M_𝒫)$ and $⟨0|𝒫^*_μ|Qq̅(1^-)⟩=⟨0|𝒫^*_μ|Q̅q(1^-)⟩=ϵ_μ√(M_𝒫^*)$.
Hadronic molecules with both open charm and bottom · The effective potential of $B_c$-like molecules · 0.91
Uses its data or values 2 papers
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[ref] [equation] where the coupling constants $g_Σ_bNB̅=5.7$, $g_Σ_bNB̅^*=3.7$, and $g_Σ_b^*NB̅^*=6.9$ are obtained from Ref. [ref] .
Investigating the Molecular Nature of $\Lambda_b(6146)$ and $\Lambda_b(6152)$ via Strong Decays and Predicting Their Heavy-Quark Symmetry Partners · Theoretical formulism · 0.91
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The coupling constants between light vector mesons and bottom mesons are [equation] where the gauge coupling $β=0.9$, $λ=0.56 GeV^-1$, and $g_V=m_ρ/f_π$ with pion decay constant $f_π=132$ MeV [ref] .
Explaining the anomalous $\Upsilon(5S)\to \chi_{bJ}\omega$ decays through the hadronic loop effect · Introduction · 0.83
Cites it as background 8 papers
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The evaluation of this matrix element was discussed in Refs. [ref] .
Testing the hypothesis of vector X17 boson by D meson, Charmonium, and $\phi$ meson decays · Introduction · 0.85
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Radiative decays of ground state heavy flavored baryons have been studied within Heavy Hadron Chiral Perturbation Theory (HHCPT) [ref] –an approach which combines Heavy Quark (HQ) symmetry with the chiral symmetry in the light sector–, employing light-cone QCD sum-rules [ref] , supplementing Heavy Quark symmetry with a SU$(2N_f)×$O(3) symmetry in the light diquark system [ref] , or implementing also dynamical effects for the internal quark structure of the hadrons within the relativistic three-quark model (RTQM) [ref] or other non-relativistic quark models [ref] .
Radiative decays of dynamically generated charmed baryons · Introduction · 0.94
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Both neutral and charged transitions of $Ξ_c γ→Ξ'_c$ have been previously studied using QCD sum rules [ref] , heavy hadron chiral perturbation theory [ref] , quark model [ref] and bag model [ref] .
$\Xi_c \gamma \rightarrow\Xi^\prime_c$ transition in lattice QCD · Results And Discussion · 0.96
Discussion
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