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The S-wave topped meson

Jun-Hao Zhang, Shuo Yang, Bing-Dong Wan

TL;DR

This paper investigates whether S-wave topped mesons containing a single top quark, namely $t\bar{q}$, $t\bar{c}$, and $t\bar{b}$, can exist as bound or near-threshold states despite the top quark’s rapid weak decay. Using the Bethe-Salpeter equation under the instantaneous approximation with a lattice-inspired potential combining a linear confining term $V_S$ and a short-range vector term $V_V$, the authors compute the mass spectrum up to the $n=4$ radial excitations. The results show masses very close to the top-quark mass, with the 1S $t\bar{b}$ state around $177.84$ GeV (about $5.08$ GeV heavier than $m_t$) and the 1S $t\bar{c}$ state around $174.66$ GeV (about $1.90$ GeV heavier), while $^1S_0$ and $^3S_1$ are degenerate within numerical accuracy. They also discuss production and decay mechanisms at the LHC, noting the extreme suppression of toplike bound-state formation but outlining characteristic signatures such as a resonance near $m_t$ with a high-$p_T$ $W$ and multiple jets, which could be explored at high-luminosity colliders. Overall, the work provides a theoretical framework and concrete predictions for a novel class of heavy-light bound states that probe QCD dynamics at the electroweak scale.

Abstract

Inspired by the recent observation of the near-threshold enhancement in top-quark pair production by CMS and ATLAS, we investigate the mass spectrum of S-wave topped meson which containing a single top quark, i.e., $t\bar{q}$, $t\bar{c}$, and $t\bar{b}$, in the framework of Bethe-Salpeter formalism. These states are expected to exhibit significantly enhanced lifetimes and correspondingly narrower decay widths compared to toponium, primarily because only a single top quark participates in the weak decay process. The numerical results indicate that the masses of topped mesons are close to the top-quark mass. For the $t\bar{b}$ states, the $1S$ state is approximately 5.08~GeV heavier than the top quark, while the $2S$, $3S$, and $4S$ states are about 5.37~GeV, 5.57~GeV, and 5.74~GeV heavier, respectively. For the $t\bar{c}$ states, the corresponding mass differences are 1.90~GeV, 2.23~GeV, 2.45~GeV, and 2.60~GeV. The possible production and decay properties are also analyzed, which could be measured in LHC experiments.

The S-wave topped meson

TL;DR

This paper investigates whether S-wave topped mesons containing a single top quark, namely , , and , can exist as bound or near-threshold states despite the top quark’s rapid weak decay. Using the Bethe-Salpeter equation under the instantaneous approximation with a lattice-inspired potential combining a linear confining term and a short-range vector term , the authors compute the mass spectrum up to the radial excitations. The results show masses very close to the top-quark mass, with the 1S state around GeV (about GeV heavier than ) and the 1S state around GeV (about GeV heavier), while and are degenerate within numerical accuracy. They also discuss production and decay mechanisms at the LHC, noting the extreme suppression of toplike bound-state formation but outlining characteristic signatures such as a resonance near with a high- and multiple jets, which could be explored at high-luminosity colliders. Overall, the work provides a theoretical framework and concrete predictions for a novel class of heavy-light bound states that probe QCD dynamics at the electroweak scale.

Abstract

Inspired by the recent observation of the near-threshold enhancement in top-quark pair production by CMS and ATLAS, we investigate the mass spectrum of S-wave topped meson which containing a single top quark, i.e., , , and , in the framework of Bethe-Salpeter formalism. These states are expected to exhibit significantly enhanced lifetimes and correspondingly narrower decay widths compared to toponium, primarily because only a single top quark participates in the weak decay process. The numerical results indicate that the masses of topped mesons are close to the top-quark mass. For the states, the state is approximately 5.08~GeV heavier than the top quark, while the , , and states are about 5.37~GeV, 5.57~GeV, and 5.74~GeV heavier, respectively. For the states, the corresponding mass differences are 1.90~GeV, 2.23~GeV, 2.45~GeV, and 2.60~GeV. The possible production and decay properties are also analyzed, which could be measured in LHC experiments.
Paper Structure (6 sections, 31 equations, 5 figures, 1 table)

This paper contains 6 sections, 31 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Bethe-Salpeter Equation
  3. Numerical evaluation
  4. Possible Production and Decay Modes of Topped Mesons
  5. Summary
  6. The BS wave functions for $^1S_0$ states

Figures (5)

  • Figure 1: The BS wave functions for $^1S_0$$t\bar{b}$ states, blue line for 1S state, orange line for 2S state, green line for 3S state, and red line for 4S state.
  • Figure 2: The BS wave functions for $^1S_0$$t\bar{c}$ states, blue line for 1S state, orange line for 2S state, green line for 3S state, and red line for 4S state.
  • Figure 3: The BS wave functions for $^1S_0$$t\bar{s}$ states, blue line for 1S state, orange line for 2S state, green line for 3S state, and red line for 4S state.
  • Figure 4: The BS wave functions for $^1S_0$$t\bar{d}$ states, blue line for 1S state, orange line for 2S state, green line for 3S state, and red line for 4S state.
  • Figure 5: The BS wave functions for $^1S_0$$t\bar{u}$ states, blue line for 1S state, orange line for 2S state, green line for 3S state, and red line for 4S state.