Bottom-charmed meson states in inverse problem of QCD

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.

Figures (5)

• Figure 1: Integration contour $C$ employed in the complex $s$-plane. The contour comprises a circular arc $C_R$ of radius $R$ together with segments $C_{\text{cut}}$ that run parallel to and enclose the branch cut situated along the positive real axis.
• Figure 2: s dependence of the ground state solution $\Delta \rho_0(s, \Lambda)$ for $\Lambda = 4.5 \ \text{GeV}^2$ of $B_c(0^+)$ meson.
• Figure 3: s dependence of the ground state solution $\Delta \rho_0(s, \Lambda)$ for $\Lambda = 3.5 \ \text{GeV}^2$ of $B_c(0^-)$ meson.
• Figure 4: s dependence of the ground state solution $\Delta \rho_0(s, \Lambda)$ for $\Lambda = 5.5 \ \text{GeV}^2$ of $B_c(1^-)$ meson.
• Figure 5: s dependence of the ground state solution $\Delta \rho_0(s, \Lambda)$ for $\Lambda = 6.5 \ \text{GeV}^2$ of $B_c(1^+)$ meson.