Open Access

Unified spectroscopic study of bottom mesons and doubly bottom baryons using a relativistic flux-tube model

Department of Physics, Sardar Vallabhbhai National Institute of Technology, Surat, Gujarat-395007, India

Phys. Rev. D 112, 074011 – Published 14 October, 2025

DOI: https://doi.org/10.1103/m2xt-pkxm

Abstract

Using the relativistic flux tube model with spin-dependent corrections, we present a unified investigation of the mass spectra for singly bottom mesons ( $B$ , $B_{s}$ ) and doubly bottom baryons ( $Ξ_{b b}$ , $Ω_{b b}$ ). Within this framework, the calculated masses for established $B$ and $B_{s}$ meson states show excellent agreement with experimental data. Leveraging these reliable predictions for low-lying states, we propose spectroscopic assignments for several higher excitations: we identify the $B_{J}^{*} (5732)$ resonance as an excellent candidate for the $1 P (1^{+})$ state; further, we assign the $B_{J} (5840)$ resonance as the first radial excitation ( $2 S$ ), and the $B_{J} (5970)$ resonance as a $1 D$ -wave orbital excitation. In the bottom-strange sector, we predict that the recently observed $B_{s J} (6063)$ and $B_{s J} (6114)$ resonances belong to the $1 D$ -wave multiplet. Extending our model to doubly bottom baryons, we present comprehensive predictions for the spectra of the $Ξ_{b b}$ and $Ω_{b b}$ baryons, identifying their ground and excited states. These theoretical insights serve as valuable benchmarks, offering guidance for future experimental searches targeting yet-to-be-discovered bottom mesons and doubly bottom baryons.

Physics Subject Headings (PhySH)

Article Text

References (69)

S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
V. M. Abazov et al. (D0 Collaboration), Observation and properties of $L = 1 B_{1}$ and $B_{2}^{*}$ mesons, Phys. Rev. Lett. 99, 172001 (2007).
T. Aaltonen et al. (CDF Collaboration), Measurement of resonance parameters of orbitally excited narrow $B^{0}$ mesons, Phys. Rev. Lett. 102, 102003 (2009).
T. Aaltonen et al. (CDF Collaboration), Observation of orbitally excited $B_{s}$ mesons, Phys. Rev. Lett. 100, 082001 (2008).
R. Aaij et al. (LHCb Collaboration), First observation of the decay $B_{s 2}^{*} (5840)^{0} \to B^{* +} K^{-}$ and studies of excited $B_{s}^{0}$ mesons, Phys. Rev. Lett. 110, 151803 (2013).
V. M. Abazov et al. (D0 Collaboration), Observation and properties of the orbitally excited B*(s2) meson, Phys. Rev. Lett. 100, 082002 (2008).
T. A. Aaltonen et al. (CDF Collaboration), Study of orbitally excited $B$ mesons and evidence for a new $B π$ resonance, Phys. Rev. D 90, 012013 (2014).
R. Aaij et al. (LHCb Collaboration), Precise measurements of the properties of the $B_{1} (5721)^{0, +}$ and $B_{2}^{*} (5747)^{0, +}$ states and observation of $B^{+, 0} π^{-, +}$ mass structures, J. High Energy Phys. 04 (2015) 024.
R. Aaij et al. (LHCb Collaboration), Observation of new excited $B_{s}^{0}$ states, Eur. Phys. J. C 81, 601 (2021).
R. Aaij et al. (LHCb Collaboration), Observation of the doubly charmed baryon $Ξ_{c c}^{+ +}$ , Phys. Rev. Lett. 119, 112001 (2017).
D. Ebert, R. N. Faustov, and V. O. Galkin, Heavy-light meson spectroscopy and Regge trajectories in the relativistic quark model, Eur. Phys. J. C 66, 197 (2010).
S. Godfrey, K. Moats, and E. S. Swanson, $B$ and $B_{s}$ meson spectroscopy, Phys. Rev. D 94, 054025 (2016).
Y. Sun, Q.-T. Song, D.-Y. Chen, X. Liu, and S.-L. Zhu, Higher bottom and bottom-strange mesons, Phys. Rev. D 89, 054026 (2014).
Q. Li, R.-H. Ni, and X.-H. Zhong, Towards establishing an abundant $B$ and $B_{s}$ spectrum up to the second orbital excitations, Phys. Rev. D 103, 116010 (2021).
J. Zeng, J. W. Van Orden, and W. Roberts, Heavy mesons in a relativistic model, Phys. Rev. D 52, 5229 (1995).
M. Shah, B. Patel, and P. C. Vinodkumar, Spectroscopy and flavor changing decays of B, $B_{s}$ mesons in a Dirac formalism, Phys. Rev. D 93, 094028 (2016).
N. Devlani and A. K. Rai, Spectroscopy and decay properties of the Ds meson, Phys. Rev. D 84, 074030 (2011).
Q.-F. Lü, K.-L. Wang, L.-Y. Xiao, and X.-H. Zhong, Mass spectra and radiative transitions of doubly heavy baryons in a relativized quark model, Phys. Rev. D 96, 114006 (2017).
D. Ebert, R. N. Faustov, V. O. Galkin, and A. P. Martynenko, Mass spectra of doubly heavy baryons in the relativistic quark model, Phys. Rev. D 66, 014008 (2002).
S. S. Gershtein, V. V. Kiselev, A. K. Likhoded, and A. I. Onishchenko, Spectroscopy of doubly heavy baryons, Phys. Rev. D 62, 054021 (2000).
T. Yoshida, E. Hiyama, A. Hosaka, M. Oka, and K. Sadato, Spectrum of heavy baryons in the quark model, Phys. Rev. D 92, 114029 (2015).
F. Giannuzzi, Doubly heavy baryons in a Salpeter model with AdS/QCD inspired potential, Phys. Rev. D 79, 094002 (2009).
A. K. Rai, B. Patel, and P. C. Vinodkumar, Properties of $Q \bar{Q}$ mesons in non-relativistic QCD formalism, Phys. Rev. C 78, 055202 (2008).
V. Kher, N. Devlani, and A. K. Rai, Spectroscopy, decay properties and Regge trajectories of the $B$ and $B_{s}$ mesons, Chin. Phys. C 41, 093101 (2017).
B. H. Yazarloo and H. Mehraban, Study of B and $B_{s}$ mesons with a Coulomb plus exponential type potential, Europhys. Lett. 116, 31004 (2016).
V. Patel, R. Chaturvedi, and A. K. Rai, Spectroscopic properties of $B$ and $B_{s}$ meson using screened potential, Indian J. Phys. 98, 2961 (2024).
B. Eakins and W. Roberts, Symmetries and systematics of doubly heavy hadrons, Int. J. Mod. Phys. A 27, 1250039 (2012).
B. Chen, S.-Q. Luo, K.-W. Wei, and X. Liu, $b$ -hadron spectroscopy study based on the similarity of double bottom baryon and bottom meson, Phys. Rev. D 105, 074014 (2022).
V. V. Kiselev, A. K. Likhoded, O. N. Pakhomova, and V. A. Saleev, Mass spectra of doubly heavy Omega $Q Q^{'}$ baryons, Phys. Rev. D 66, 034030 (2002).
W. Roberts and M. Pervin, Heavy baryons in a quark model, Int. J. Mod. Phys. A 23, 2817 (2008).
Z. Shah, K. Thakkar, and A. K. Rai, Excited state mass spectra of doubly heavy baryons $Ω_{c c}$ , $Ω_{b b}$ and $Ω_{b c}$ , Eur. Phys. J. C 76, 530 (2016).
Z. Shah and A. K. Rai, Excited state mass spectra of doubly heavy $Ξ$ baryons, Eur. Phys. J. C 77, 129 (2017).
M. Karliner and J. L. Rosner, Baryons with two heavy quarks: Masses, production, decays, and detection, Phys. Rev. D 90, 094007 (2014).
Y. Lu, M. N. Anwar, and B.-S. Zou, How large is the contribution of excited mesons in coupled-channel effects?, Phys. Rev. D 95, 034018 (2017).
J. Oudichhya and A. K. Rai, Study of singly bottom and doubly heavy baryons within Regge phenomenology, Eur. Phys. J. A 60, 125 (2024).
J. G. Korner, M. Kramer, and D. Pirjol, Heavy baryons, Prog. Part. Nucl. Phys. 33, 787 (1994).
H.-Y. Cheng and F.-S. Yu, Masses of scalar and axial-vector B mesons revisited, Eur. Phys. J. C 77, 668 (2017).
M. H. Alhakami, Predictions for the beauty meson spectrum, Phys. Rev. D 103, 034009 (2021).
E. Bagan, M. Chabab, and S. Narison, Baryons with two heavy quarks from QCD spectral sum rules, Phys. Lett. B 306, 350 (1993).
Z.-G. Wang, Analysis of the ${1 / 2}^{+}$ doubly heavy baryon states with QCD sum rules, Eur. Phys. J. A 45, 267 (2010).
C. B. Lang, D. Mohler, S. Prelovsek, and R. M. Woloshyn, Predicting positive parity $B_{s}$ mesons from lattice QCD, Phys. Lett. B 750, 17 (2015).
E. B. Gregory et al., Precise $B, B_{s}$ and $B_{c}$ meson spectroscopy from full lattice QCD, Phys. Rev. D 83, 014506 (2011).
M. Padmanath, R. G. Edwards, N. Mathur, and M. Peardon, Spectroscopy of doubly-charmed baryons from lattice QCD, Phys. Rev. D 91, 094502 (2015).
C. Alexandrou, J. Carbonell, D. Christaras, V. Drach, M. Gravina, and M. Papinutto, Strange and charm baryon masses with two flavors of dynamical twisted mass fermions, Phys. Rev. D 86, 114501 (2012).
P. Jakhad, J. Oudichhya, K. Gandhi, and A. K. Rai, Identification of newly observed singly charmed baryons using the relativistic flux tube model, Phys. Rev. D 108, 014011 (2023).
P. Jakhad, J. Oudichhya, and A. K. Rai, Interpretation of recently discovered single bottom baryons in the relativistic flux tube model, Phys. Rev. D 110, 094005 (2024).
P. Jakhad, J. Oudichhya, and A. K. Rai, Masses of higher excited states of $Ξ c$ ’ and $Ω c$ baryons, Int. J. Mod. Phys. A 39, 2443005 (2024).
P. Jakhad and A. K. Rai, Relativistic flux-tube model predictions from charmed mesons to double-charmed baryons (Communicated), arXiv:2509.24772.
B. Chen, K.-W. Wei, and A. Zhang, Investigation of $Λ_{Q}$ and $Ξ_{Q}$ baryons in the heavy quark-light diquark picture, Eur. Phys. J. A 51 (2015).
C. Olson, M. G. Olsson, and D. LaCourse, The quantized relativistic flux tube, Phys. Rev. D 49, 4675 (1994).
M. G. Olsson, The relativistic flux tube model of hadrons, Nuovo Cimento Soc. Ital. Fis. 107A, 2541 (1994).
T. J. Allen, M. G. Olsson, and S. Veseli, Curved QCD string dynamics, Phys. Rev. D 60, 074026 (1999).
F. James and M. Roos, Minuit—A system for function minimization and analysis of the parameter errors and correlations, Comput. Phys. Commun. 10, 343 (1975).
R. Aaij et al. (LHCb Collaboration), Precision measurement of the $Ξ_{c c}^{+ +}$ mass, J. High Energy Phys. 02 (2020) 049.
J. Hu and T. Mehen, Chiral lagrangian with heavy quark-diquark symmetry, Phys. Rev. D 73, 054003 (2006).
Y. Song, D. Jia, W. Zhang, and A. Hosaka, Low-lying doubly heavy baryons: Regge relation and mass scaling, Eur. Phys. J. C 83, 1 (2023).
B. Chen, A. Zhang, and J. He, Bottomonium spectrum in the relativistic flux tube model, Phys. Rev. D 101, 014020 (2020).
K. Johnson and C. B. Thorn, Stringlike solutions of the bag model, Phys. Rev. D 13, 1934 (1976).
T. A. Lahde, C. J. Nyfalt, and D. O. Riska, Spectra and M1 decay widths of heavy light mesons, Nucl. Phys. A674, 141 (2000).
Q.-F. Lü, T.-T. Pan, Y.-Y. Wang, E. Wang, and D.-M. Li, Excited bottom and bottom-strange mesons in the quark model, Phys. Rev. D 94, 074012 (2016).
R. Akers et al. (OPAL Collaboration), Observations of $Π$ -B charge—flavor correlations and resonant B $Π$ and B K production, Z. Phys. C 66, 19 (1995).
P. Abreu et al. (DELPHI Collaboration), Observation of orbitally excited B mesons, Phys. Lett. B 345, 598 (1995).
R. Barate et al. (ALEPH Collaboration), Resonant structure and flavor tagging in the B $π_{-}^{+}$ system using fully reconstructed B decays, Phys. Lett. B 425, 215 (1998).
M. Acciarri et al. (L3 Collaboration), Measurement of the spectroscopy of orbitally excited $B$ mesons at LEP, Phys. Lett. B 465, 323 (1999).
L.-Y. Xiao and X.-H. Zhong, Strong decays of higher excited heavy-light mesons in a chiral quark model, Phys. Rev. D 90, 074029 (2014).
G.-L. Yu and Z.-G. Wang, Analysis of the excited bottom and bottom-strange states $B_{1} (5721)$ , $B_{2}^{*} (5747)$ , $B_{s 1} (5830)$ , $B_{s 2}^{*} (5840)$ , $B_{J} (5840)$ and $B_{J} (5970)$ in $B$ meson family, Chin. Phys. C 44, 033103 (2020).
I. Asghar, B. Masud, E. S. Swanson, F. Akram, and M. Atif Sultan, Decays and spectrum of bottom and bottom strange mesons, Eur. Phys. J. A 54, 127 (2018).
W. Hao, Y. Lu, and E. Wang, The assignments of the $B_{s}$ mesons within the screened potential model and ${}^{3}{P_{0}}$ model, Eur. Phys. J. C 83, 520 (2023).
M. Karliner and J. L. Rosner, Very narrow excited $Ω_{c}$ baryons, Phys. Rev. D 95, 114012 (2017).

Phys. Rev. D 112, 074011– Published 14 October, 2025

Vol. 112, Iss. 7 — 1 October 2025

Received 30 May 2025
Accepted 17 September 2025

DOI: https://doi.org/10.1103/m2xt-pkxm

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physical Review D

Reuse & Permissions

Export citation

Export citation

Unified spectroscopic study of bottom mesons and doubly bottom baryons using a relativistic flux-tube model

Abstract

Physics Subject Headings (PhySH)

Article Text

References (69)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation