Can the hyperfine mass splitting formula in heavy quarkonia be applied to the $B_c$ system?

Abstract

The mass relation $M_{0^{+}}+3M_{1^{+\prime }}+5M_{2^{+}}=9M_{1^{+}}$ miraculously holds for the $P$-wave charmonium $(c\bar{c})$ and bottomonium $(b\bar{b})$ systems with soaring precision. The origin of such relation can be addressed from Quark Models, and have been confirmed experimentally in a limited number of cases. In this connection, we propose $M_{0^{+}}+5M_{2^{+}}=3(M_{1^{+\prime }}+M_{1^{+}})$ as an extension to the $P$-wave $B_c$ case. In order to test its applicability, we employ a variety of Quark Model predictions for the $B_c$ mass spectrum. Our numerical analysis confirms such formula is accurate up to very small deviations.

arXiv comment3 pages, no figures

References in corpus (29)

• Properties of heavy quarkonia and B_c mesons in the relativistic quark model
• Mesons with Beauty and Charm: Spectroscopy
• Observation of the B_c Meson in p-bar p Collisions at sqrt{s} = 1.8 TeV
• Algebraic models of hadron structure: I. Nonstrange baryons
• Spectroscopy of B_c Mesons in the Relativized Quark Model
• $B_c$ spectroscopy
• Algebraic Models of Hadron Structure II. Strange Baryons
• First observation of the P-wave spin-singlet bottomonium states h_b(1P) and h_b(2P)
• Precise predictions of charmed-bottom hadrons from lattice QCD
• Observation of two excited B${}_{\mathrm{c}}^{+}$ states and measurement of the B${}_{\mathrm{c}}^{+}$(2S) mass in pp collisions at $\sqrt{s}=$ 13 TeV
• Phenomenological prediction of the properties of the B_{C} system
• Masses of ground-state mesons and baryons, including those with heavy quarks
• Spectra of heavy mesons in the Bethe-Salpeter approach
• Masses of Light and Heavy Mesons and Baryons: A Unified Picture
• Precision Measurement of the Mass of the h_c(1P1) State of Charmonium
• Observation of an excited $B_c^{+}$ state
• Rigourous QCD Evaluation of Spectrum and Other Properties of Heavy Quarkonium Systems; II Bottomium with n=2, l=0,1
• Bc spectroscopy in a quantum-chromodynamic potential model
• The excited bottom-charmed mesons in a nonrelativistic quark model
• Mass-dependence of pseudoscalar meson elastic form factors
• Spectroscopy of ${\mathbf{B}}_{\mathbf{c}}$ mesons and the possibility of finding exotic ${\mathbf{B}}_{\mathbf{c}}$-like structures
• Effects of a dressed quark-gluon vertex in vector heavy-light mesons and theory average of B(c)* meson mass
• $B_c$ Meson Spectrum Via Dyson-Schwinger Equation and Bethe-Salpeter Equation Approach
• Effective Field Theory and Heavy Quark Physics
• P-wave heavy quarkonium spectrum with next-to-next-to-next-to-leading logarithmic accuracy
• Quarkonium $h$ States As Arbiters of Exoticity
• Excited $B_c$ States via Continuum QCD
• $P-$state Positronium for Precision Physics: an Ultrafine Splitting at ${\alpha }^6$
• Heavy-Quark Hybrid Mass Splittings: Hyperfine and "Ultrafine"

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