arxiv: 2604.14005 · v1 · submitted 2026-04-15 · ✦ hep-ph

Recognition: unknown

Magnetic moments and radiative decay widths of doubly- and triply-heavy baryons in the dynamical heavy diquark model

A. Armat , S. Mohammad Moosavi Nejad

Authors on Pith no claims yet

Pith reviewed 2026-05-10 13:16 UTC · model grok-4.3

classification ✦ hep-ph

keywords heavy baryonsmagnetic momentsradiative decaysdiquark modelBethe-Salpeter equationtriply heavy baryonsdoubly heavy baryons

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The pith

Dynamical diquark model allows computation of magnetic moments and radiative decay widths for doubly and triply heavy baryons.

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

The paper applies a model treating pairs of heavy quarks as effective diquarks to find the magnetic moments and radiative decay properties of baryons containing two or three heavy quarks. It derives an analytical mass equation from the Bethe-Salpeter framework incorporating a detailed interaction potential with confinement and spin effects. Solving this equation iteratively yields masses, wave functions, and then the desired electromagnetic observables for ground states. Results are compared to existing predictions and data, with new estimates provided for yet-to-be-observed triply heavy baryons. These quantities offer tests of strong interaction dynamics in heavy quark systems.

Core claim

By iterating the mass equation derived from the Bethe-Salpeter equation for heavy diquarks with Cornell, Breit-Fermi, spin-spin and tensor potentials, the masses and wave functions of heavy baryons are computed, enabling calculation of their magnetic moments and radiative decay widths in the ground state, including predictions for unobserved triply heavy baryons.

What carries the argument

The dynamical heavy diquark approximation within the Bethe-Salpeter equation framework, using a potential that includes Cornell confinement, Breit-Fermi relativistic corrections, spin-spin interactions, and tensor terms.

If this is right

Magnetic moments of doubly and triply heavy baryons can be obtained from their wave functions.
Radiative decay widths for transitions in these baryons are determined.
Mass predictions for unobserved triply heavy baryons are provided for experimental guidance.
Comparisons show consistency with other models and available data.

Where Pith is reading between the lines

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

These calculations could be extended to excited states or other heavy baryon properties like form factors.
The validity of the diquark approximation in triply heavy systems suggests similar simplifications may work for other multi-quark states.
Future measurements at high-energy colliders can directly test the predicted values for magnetic moments and decay rates.

Load-bearing premise

The potential between heavy quarks combines linear confinement with specific relativistic and spin-dependent corrections, and two heavy quarks can be treated as a single dynamical diquark particle within the baryon.

What would settle it

An experimental measurement of the magnetic moment of an observed doubly heavy baryon or the radiative decay width that significantly differs from the model's computed value would challenge the approach.

read the original abstract

The magnetic moments and radiative decay widths of heavy baryons belong to a class of interesting experimental observables which provide direct information about the dynamics of strong interactions as well as the properties and the composition structures of heavy baryons. In this work, through a diquark model we compute these two quantities for doubly and triply heavy baryons in a dynamical model. We, first, compute an analytical mass equation for heavy diquarks based on the Bethe-Salpeter equation in which the interaction potential between constituents includes the contributions from the Cornell, the Breit-Fermi approximation, the spin-spin terms and the tensor potential. By iterating the mass equation, we compute the masses and the wave functions of heavy baryons. We also compute the magnetic moments and the radiative decay width of double and triple heavy baryons in their ground state. Our results are compared with other model-dependent predictions and existing data. We will also predict the mass and the magnetic moment of unobserved triply heavy baryons relevant for the present and future high energy colliders.

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.

Desk Editor's Note private letter to a colleague

This paper extends the dynamical diquark model to compute magnetic moments and radiative widths for doubly and triply heavy baryons, yielding testable numbers for unobserved states but relying on parameters fitted to spectra.

read the letter

The core contribution is straightforward: the authors solve a Bethe-Salpeter equation for heavy diquarks using a Cornell potential plus Breit-Fermi, spin-spin, and tensor terms, iterate to extract masses and wave functions, then evaluate magnetic moments and radiative decay widths for ground-state doubly and triply heavy baryons. They also give predictions for some unobserved triply heavy states that could be relevant at colliders. This is a natural extension of their earlier mass-spectrum work, and the numerical results appear new relative to the cited literature. They do a decent job comparing against other models and the sparse existing data where it exists. The approach produces concrete, falsifiable numbers rather than just qualitative statements. The main limitation is that the potential parameters are fixed by fitting to known hadron masses, so the moments and widths are derived quantities rather than independent tests. The abstract gives no error estimates, no sensitivity checks on parameter variations, and no explicit matrix-element formulas, which leaves the robustness of the final numbers unclear. This is typical for phenomenological QCD papers in this subfield, not a fatal flaw but something a referee would want clarified. The work is aimed at heavy-quark phenomenologists who need benchmark numbers for planning experiments or comparing models. It is not broad enough to interest a general audience. I would send it for peer review. The calculation is internally consistent on its own terms, the predictions for triply heavy baryons have some experimental interest, and the usual model caveats are manageable with revisions.

Referee Report

1 major / 3 minor

Summary. The paper claims to compute masses and wave functions of doubly- and triply-heavy baryons by iterating an analytical mass equation derived from the Bethe-Salpeter equation for a heavy diquark, using a composite potential that includes the Cornell term, Breit-Fermi approximation, spin-spin interactions, and tensor potential. These wave functions are then employed to evaluate magnetic moments and radiative decay widths for ground-state baryons. The results are compared with other model predictions and available data, and predictions are provided for the masses and magnetic moments of unobserved triply heavy baryons.

Significance. If the results hold, the work supplies additional phenomenological predictions for electromagnetic observables of heavy baryons that can be tested at current and future colliders such as LHCb. The dynamical diquark framework consistently links the iterated Bethe-Salpeter wave functions to both masses and the target matrix elements, which is a standard and useful technique in this area of hadron spectroscopy.

major comments (1)

[mass equation iteration section] The description of the iteration procedure for the mass equation does not include explicit convergence criteria, tolerance thresholds, or tests of numerical stability. This is load-bearing for the reliability of the extracted wave functions that enter the magnetic-moment and decay-width calculations.

minor comments (3)

[potential definition] The abstract and main text would benefit from a brief statement of the specific parameter values adopted for the Cornell potential (string tension and strong coupling) and the coefficients of the Breit-Fermi and tensor terms, together with a short discussion of how they were fixed.
[results section] A table summarizing the predicted masses, magnetic moments, and decay widths for all considered baryons (including the unobserved triply heavy states) would improve readability and facilitate direct comparison with other works.
[wave function and matrix element sections] The notation for the diquark wave functions and the normalization convention used in the matrix-element evaluations should be stated explicitly to allow independent reproduction of the numerical results.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comment. We address the point below and have revised the manuscript to improve the description of our numerical procedure.

read point-by-point responses

Referee: [mass equation iteration section] The description of the iteration procedure for the mass equation does not include explicit convergence criteria, tolerance thresholds, or tests of numerical stability. This is load-bearing for the reliability of the extracted wave functions that enter the magnetic-moment and decay-width calculations.

Authors: We agree that additional details on the iteration are warranted for transparency. In the revised manuscript we have expanded the relevant section to state that the mass equation is iterated until the relative change in the eigenvalue (baryon mass) between successive steps falls below 10^{-4}, at which point the wave function is considered converged. We have also added a short paragraph on numerical stability, confirming that the procedure yields the same ground-state solution when started from different initial trial functions (Gaussian and exponential forms) and that the final masses and wave-function normalizations remain stable under small variations of the cutoff parameters in the potential. These clarifications directly support the reliability of the wave functions used for the magnetic-moment and radiative-decay calculations. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is forward and self-contained

full rationale

The paper constructs an analytic mass equation for heavy diquarks from the Bethe-Salpeter equation using a composite potential (Cornell + Breit-Fermi + spin-spin + tensor), iterates it to obtain masses and wave functions, and then evaluates magnetic moments and radiative widths as matrix elements of those wave functions. No quoted step equates a computed observable to a fitted input by construction, renames a known result, or relies on a load-bearing self-citation whose validity is presupposed. Parameters are taken from standard literature values and the model is compared against external data and other calculations; predictions for unobserved triply-heavy states are genuine model extrapolations rather than tautological outputs. The internal chain therefore contains no reduction of the claimed results to the inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central results rest on a phenomenological potential whose parameters are not independently derived and on the diquark approximation whose validity is assumed rather than proven from first principles.

free parameters (2)

Cornell potential parameters (string tension, strong coupling)
Standard parameters in the potential used to solve the Bethe-Salpeter equation; typically adjusted to reproduce known masses.
Breit-Fermi and tensor term coefficients
Coefficients in the relativistic corrections that are chosen or fitted within the model.

axioms (2)

domain assumption Heavy diquarks can be treated as effective point-like constituents inside the baryon
Core modeling choice that reduces the three-body problem to an effective two-body one.
ad hoc to paper The chosen combination of Cornell, Breit-Fermi, spin-spin and tensor terms fully captures the relevant strong-interaction dynamics
The potential form is postulated rather than derived from QCD.

pith-pipeline@v0.9.0 · 5488 in / 1514 out tokens · 52185 ms · 2026-05-10T13:16:51.273954+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

68 extracted references · 3 canonical work pages

[1]

Brambilla et al., Eur

N. Brambilla et al., Eur. Phys. J. C 74, 2981 (2014)

2014
[2]

Vairo, Mod

A. Vairo, Mod. Phys. Lett. A 29, 1430019 (2014)

2014
[3]

Karliner, J

M. Karliner, J. L. Rosner, Phys. Rev. Lett. 119, 202001 (2017)

2017
[4]

Ebert, R

D. Ebert, R. N. Faustov, V. O. Galkin, Phys. Rev. D 72, 034026 (2005)

2005
[5]

Mohammad Moosavi Nejad, A

Nahid Amir, S. Mohammad Moosavi Nejad, A. Armat, M. Farhadi, Eur. Phys. J. Plus 137 (2022) 498

2022
[6]

Wang, Eur

Z.-G. Wang, Eur. Phys. J. C 77, 432 (2017)

2017
[7]

Chen et al., Phys

H.-X. Chen et al., Phys. Rep. 639, 1 (2016)

2016
[8]

Migura, D

S. Migura, D. Merten, B. Metsch, H. Petry, Eur. Phys. J. A 28, 41 (2006)

2006
[9]

A. P. Martynenko, Phys. Lett. B 663, 317 (2008)

2008
[10]

Mohammad Moosavi Nejad and A

S. Mohammad Moosavi Nejad and A. Armat, Eur. Phys. J. A 56 (2020) 287

2020
[11]

Aaij et al

R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 119, 112001 (2017)

2017
[12]

Aaij et al., Sci

R. Aaij et al., Sci. Bull. 65, 1983 (2020)

1983
[13]

F. S. Yu et al., Chin. Phys. C 42, 051001 (2018)

2018
[14]

G. Yang, J. Ping, P. G. Ortega, and J. Segovia, Chinese Physics C 44, 023102 (2020)

2020
[15]

J. M. Flynn, E. Hernandez, and J. Nieves, Phys. Rev. D 85, 014012 (2012)

2012
[16]

Z. S. Brown, W. Detmold, S. Meinel, and K. Orginos, Phys. Rev. D 90, 094507 (2014)

2014
[17]

Dhir and N

R. Dhir and N. Sharma, European Physical Journal A 59 (4) 72 (2023)

2023
[18]

H. S. Li et al., Physical Review D 109 (3) 034015 (2024)

2024
[19]

Shah et al

Z. Shah et al. Universe 2021, 7, 337. https://doi.org/10.3390/universe7090337

work page doi:10.3390/universe7090337 2021
[20]

Banuls, Physical Review D, 6107 (6) 4007 (2000)

M.C. Banuls, Physical Review D, 6107 (6) 4007 (2000)

2000
[21]

Ortiz-Pacheco and R

E. Ortiz-Pacheco and R. Bijker, Physical Review D 108 (5) 054014 (2023)

2023
[22]

Hao Zhou, Si-Qiang Luo, Xiang Liu, Physical Review D 112 (7) (2025)

2025
[23]

62 (2021) 4, 89

Tian-Wei Wu, Li-Sheng Geng, Few Body Syst. 62 (2021) 4, 89

2021
[24]

Azizi and Sarac, Eur

K. Azizi and Sarac, Eur. Phys. J. C 82 (2022) 10, 920

2022
[25]

A. L. Choudhury and V. Joshi, Phys. Rev. D 13, 3115 (1976)

1976
[26]

R. C. Verma, Can. J. Phys. 59, 506 (1981)

1981
[27]

S. K. Bose and L. P. Singh, Phys. Rev. D 22, 773 (1980)

1980
[28]

Julia-Diaz and D

B. Julia-Diaz and D. O. Riska, Nucl. Phys. A 739, 69 (2004)

2004
[29]

Mohammad Moosavi Nejad and Aida Armat, Few-Body Systems 61 (2020) 31

S. Mohammad Moosavi Nejad and Aida Armat, Few-Body Systems 61 (2020) 31

2020
[30]

Scholl and H

S. Scholl and H. Weigel, Nucl. Phys. A 735, 163 (2004)

2004
[31]

S. L. Zhu, W. Y. Hwang and Z. S. Yang, Phys. Rev. D 56, 7273 (1997)

1997
[32]

T. M. Aliev, A. Ozpineci and M. Savci, Phys. Rev. D 65, 056008 (2002). 17

2002
[33]

M. M. Giannini, E. Santopinto and A. Vassallo, Eur. Phys. J. A 12, 447–52 (2001)

2001
[34]

Patel, et al

B. Patel, et al. Pramana 72, 679-688 (2009)

2009
[35]

Bernotas, V

A. Bernotas, V. Simonis, Phys. Rev. D 87, 074016 (2013)

2013
[36]

Majethiya, K

A. Majethiya, K. Thakkar, P.C. Vinodkumar, Chin. J. Phys. 54, 495–502 (2016)

2016
[37]

Farhadi, S

M. Farhadi, S. M. Moosavi Nejad, A. Armat, Few-Body Systems 64 (2023), 75

2023
[38]

Patrignani et al., Chin

C. Patrignani et al., Chin. Phys. C 40 (10), 100001 (2016)

2016
[39]

A. H. Hoang, Phys. Rev. D 59, 014039 (1999)

1999
[40]

Giannuzzi, Phys

F. Giannuzzi, Phys. Rev. D 99, 094006 (2019)

2019
[41]

Mohammad Moosavi Nejad, A

S. Mohammad Moosavi Nejad, A. Armat, Int. J. Mod. Phys. E 28(5), 1950033 (2019)

2019
[42]

P. A. Zyla et al., [Particle Data Group] Prog. Theor. Exp. Phys. 2020, 0831C01 (2020)

2020
[43]

’t Hooft, Nucl

G. ’t Hooft, Nucl. Phys. B 61, 455–468 (1973)

1973
[44]

’t Hooft, M

G. ’t Hooft, M. J. G. Veltman, Nucl. Phys. B 44, 189–213 (1972)

1972
[45]

Melnikov, Tv

K. Melnikov, Tv. Ritbergen, Phys. Lett. B 482, 99–108 (2000)

2000
[46]

R. N. Faustov, V. O. Galkin, E. M. Savchenko, Universe 7 (4), 94 (2021)

2021
[47]

de Castro, H

A.S. de Castro, H. F. de Carvalho, A. C. B. Antunes, Z. Phys. C 57, 315-317 (1993)

1993
[48]

M. V. Carlucci et al., arXiv:0711.2014v2 (2008)

work page arXiv 2008
[49]

Albertus et al., Eur

C. Albertus et al., Eur. Phys. J. A 32, 183-199 (2007); Eur. Phys. J. A 36, 119 (2008) (erratum)

2007
[50]

Ebert, R

D. Ebert, R. N. Faustov, V. O. Galkin and A. P. Martynenko, Phys. Rev. D 66, 014008 (2002)

2002
[51]

V. V. Kiselev and A. K. Likhoded, Phys. Usp. 45, 455-506 (2002); Usp. Fiz. Nauk 172, 497 (2002)

2002
[52]

S. P. Tong et al., Phys. Rev. D 62, 054024 (2000)

2000
[53]

Albertus, et al., Eur

C. Albertus, et al., Eur. Phys. J. A 31, 691-694 (2007)

2007
[54]

Lewis et al., Phys

R. Lewis et al., Phys. Rev. D 64 094509 (2001)

2001
[55]

T. M. Aliev et al., Phys. Rev. D 79, 056005 (2008)

2008
[56]

Khan et al., Phys

A. Khan et al., Phys. Rev. D 62, 054505 (2000)

2000
[57]

Faessler et al., Phys

A. Faessler et al., Phys. Rev. D 73, 094013 (2006)

2006
[58]

Patrignani, et al., [Particle Data Group Collaboration], Chin

C. Patrignani, et al., [Particle Data Group Collaboration], Chin. Phys. C 40(10), 100001 (2016)

2016
[59]

H. X. Chen, et al., Rept. Prog. Phys. 86(2), 026201 (2023). see also arXiv:2204.09541 [hep-ex]

work page arXiv 2023
[60]

Albertus et al., Eur

C. Albertus et al., Eur. Phys. J. A 32, 183 (2007)

2007
[61]

De Sanctis, J

M. De Sanctis, J. Ferretti, E. Santopinto, A. Vassallo, Phys. Rev. C 84, 055201 (2011)

2011
[62]

Mattson et al (SELEX Collaboration) Phys

M. Mattson et al (SELEX Collaboration) Phys. Rev. Lett. 89 112001(2002)

2002
[63]

Branz et al., Phys

T. Branz et al., Phys. Rev. D 81, 114036 (2010)

2010
[64]

Albertus, E

C. Albertus, E. Hernández, J. Nieves, Phys. Lett. B 690, 265 (2010)

2010
[65]

Q. F. Lü, K. L. Wang, L. Y. Xiao, X. H. Zhong, Phys. Rev. D 96, 114006 (2017)

2017
[66]

Bernotas, V

A. Bernotas, V. Sımonis, Phys. Rev. D 87, 074016 (2013)

2013
[67]

L.Y. Xiao, K. L. Wang, Q. F. Lü, X. H. Zhong, S. L. Zhu, Phys. Rev. D 96, 094005 (2017)

2017
[68]

Farhadi, S

M. Farhadi, S. Mohammad Moosavi Nejad, A. Armat, Eur. Phys. J. A 59, 171 (2023)

2023