QCD sum rule study of topped mesons within heavy quark effective theory

TL;DR

This work pioneers a nonperturbative QCD analysis of hadronic systems containing a single top quark by applying QCD sum rules within the heavy quark effective theory framework to topped mesons. Interpolating currents for ground-state $t\bar{q}$ states are constructed, and leading-order sum rules yield a residual mass $\overline{\Lambda}\approx 0.55\,\mathrm{GeV}$ and decay constant $f\approx 0.22\,\mathrm{GeV}^{3/2}$ within a stable Borel window. Including $O(1/m_t)$ corrections, matrix elements $K$ and $\Sigma$ are determined, leading to a mass prediction for the vector topped meson $m_{T_s^*}\approx 173.12^{+0.31}_{-0.30}\,\mathrm{GeV}$ when using the pole mass, with substantial scheme-dependent uncertainties. The results are exploratory and serve to guide future theoretical refinement and motivate experimental searches for these novel heavy-hadron states, while highlighting the sensitivity to heavy-quark mass schemes and continuum modeling.

Abstract

Motivated by the recent CMS observation of a near-threshold enhancement in top quark pair production, we investigate a novel class of hadronic systems containing a single top quark: the topped mesons ($t\bar{q}$, with $\bar q = \bar u, \bar d, \bar s$). In contrast to the extensively studied toponium ($t\bar{t}$) system, analyzed primarily within perturbative QCD, topped mesons offer a complementary nonperturbative probe of QCD dynamics in the heavy quark limit. These states are expected to exhibit longer lifetimes and narrower decay widths than toponium, as only a single top quark undergoes weak decay. We employ QCD sum rules within the framework of heavy quark effective theory to study the structure and mass spectrum of ground-state topped mesons. Our analysis predicts masses near 173.1 GeV, approximately 0.5-0.6 GeV above the top quark pole mass. Compared with singly topped baryons ($tqq$, with $q = u, d, s$) studied concurrently in [arXiv:2507.05895], topped mesons have a simpler quark composition and more favorable decay channels (a topped meson is anticipated to decay weakly into a $Υ$ meson and a charmed meson), enhancing their potential for both theoretical analysis and experimental discovery.

Figures (3)

• Figure 1: Dependence of (a) the convergence parameter (CVG), defined in Eq. (\ref{['eq_convergence']}), and (b) the pole contribution (PC), defined in Eq. (\ref{['eq:pole']}), for the interpolating current $J_\mu(x)$. The Borel window $0.61~\mathrm{GeV} < T < 0.94~\mathrm{GeV}$ is indicated by the gray-shaded region. Dashed, solid, and dotted curves correspond to $\omega_c = 1.65$, $1.85$, and $2.05~\mathrm{GeV}$, respectively.
• Figure 2: Variations of (a) the residual mass $\overline{\Lambda}$ and (b) the decay constant $f$ with respect to the Borel mass $T$ for the interpolating current $J_\mu(x)$. The Borel window $0.61~\mathrm{GeV} < T < 0.94~\mathrm{GeV}$ is indicated by the gray-shaded region. Dashed, solid, and dotted curves correspond to $\omega_c = 1.65$, $1.85$, and $2.05~\mathrm{GeV}$, respectively.
• Figure 3: Dependence of (a) the kinetic matrix element $K$ and (b) the chromomagnetic matrix element $\Sigma$ on the Borel mass $T$, calculated using the interpolating current $J_\mu(x)$. The Borel window $0.61~\mathrm{GeV} < T < 0.94~\mathrm{GeV}$ is indicated by the gray-shaded region. Dashed, solid, and dotted curves correspond to continuum thresholds $\omega_c = 1.65$, $1.85$, and $2.05~\mathrm{GeV}$, respectively.