Bottom-charmed meson states in inverse problem of QCD

TL;DR

This paper introduces an inverse matrix QCD sum rules approach to analyze the bottom-charmed meson spectrum, enabling direct spectral density reconstruction with improved stability and reduced uncertainties, aligning well with experimental data.

Contribution

The study develops a novel inverse matrix QCD sum rules method for heavy meson spectroscopy, avoiding phenomenological assumptions and enhancing numerical stability.

Findings

Masses and decay constants match experimental data

Method shows improved numerical stability

Results are consistent with other theoretical approaches

Abstract

We present a comprehensive analysis of the bottom-charmed ($B_c$) meson spectrum within the inverse matrix QCD sum rules formalism. In this framework, conventional QCD sum rules are recast as an inverse problem, allowing for the direct reconstruction of hadronic spectral densities from first principles without invoking phenomenological continuum parametrizations or quark-hadron duality assumptions. We compute the masses and decay constants of conventional $B_c$ mesons with quantum numbers $J^P = 0^-$, $1^-$, $0^+$, and $1^+$. The obtained results are in close agreement with available experimental measurements and are consistent with predictions from various theoretical and phenomenological approaches. The inverse matrix formulation exhibits improved numerical stability and reduced systematic uncertainties relative to standard implementations, highlighting its suitability for precision spectroscopy of heavy quarkonium systems.