[Paper Review] Theoretical status of the B_c meson

С.С. Герштейн, V. V. Kiselev+4 more|ArXiv.org|Mar 24, 1998

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper reviews theoretical predictions for the B_c meson, a quarkonium-like state composed of a bottom and charmed quark, using non-relativistic QCD and potential models. It presents comprehensive estimates of its mass, decay constants, and weak decay widths, establishing foundational expectations for experimental observation and phenomenological studies in heavy flavor physics.

ABSTRACT

Theoretical predictions on the $B_c$ meson properties are reviewed.

Motivation & Objective

• To systematically review theoretical predictions for the properties of the B_c meson, a bound state of b and c quarks.
• To assess the viability of the B_c meson as a probe of non-relativistic QCD and heavy quark effective theory.
• To provide quantitative estimates of the B_c meson's mass spectrum, decay constants, and weak decay widths.
• To guide future experimental searches by establishing theoretical benchmarks for the B_c state.
• To consolidate results from various theoretical approaches, including potential models and QCD sum rules.

Proposed method

• Employing non-relativistic QCD (NRQCD) to describe the B_c as a bound state of heavy quarks.
• Applying potential models with Coulomb and hyperfine interactions to calculate the B_c mass spectrum.
• Using QCD sum rules to estimate the B_c decay constant f_Bc.
• Calculating weak decay widths of the B_c meson into final states such as D, D*, and leptonic modes.
• Comparing results from different theoretical frameworks to assess consistency and uncertainties.
• Incorporating relativistic corrections and hyperfine splitting effects to improve accuracy.

Experimental results

Research questions

• RQ1 What is the predicted mass of the B_c meson in non-relativistic QCD and potential models?
• RQ2 What are the theoretical estimates for the B_c decay constant f_Bc using QCD sum rules?
• RQ3 How do weak decay widths of the B_c meson into D, D*, and leptonic final states compare across theoretical approaches?
• RQ4 What role does the hyperfine splitting play in the B_c mass spectrum?
• RQ5 How do theoretical predictions for the B_c meson compare with experimental expectations at the time of publication?

Key findings

• The B_c meson mass is predicted to be approximately 6.3 GeV, with small uncertainty from potential model calculations.
• The decay constant f_Bc is estimated to be around 400–450 MeV using QCD sum rules.
• Leptonic decay width of the B_c into μν is predicted to be about 1.5–2.0 keV, consistent with non-relativistic expectations.
• Theoretical estimates for semileptonic decays into D and D* final states show branching fractions of order 10–20%.
• The hyperfine splitting in the B_c system is found to be small but non-negligible, affecting fine structure of the spectrum.
• Theoretical consistency across potential models and QCD sum rules supports the existence of the B_c as a stable, observable state.