Top Quark Bound States in Finite and Holomorphic Quantum Field Theories
E. J. Thompson
TL;DR
The paper tackles the LHC-observed near-threshold enhancement in $t\bar{t}$ production and asks whether it can be explained within a finite, UV-complete nonlocal QFT framework. It develops a modified Bethe–Salpeter equation with exponential regulators, deriving a regulated Coulomb potential and solving a Schrödinger equation to predict binding-energy shifts and threshold rates governed by the kernel scale $\Lambda_{\mathrm{Ker}}$. It further introduces a holomorphic deformation of the QCD beta function, $\beta_h(\alpha_s) = -\beta_0\frac{\alpha_s^2}{4\pi}\left[1-\frac{\alpha_s}{\alpha_*}\right]$, solved via a Lambert $W$ function, which yields at most $\mathcal{O}(10\%)$ enhancement in threshold cross sections for plausible $\alpha_*$. A cross-quarkonium comparison clarifies that toponium is best viewed as a threshold resonance embedded in the continuum. With a benchmark choice $\Lambda_{\mathrm{QCD}}^{*}=2m_t$, the model reproduces the CMS excess magnitude around $8.8\pm1.3$ pb, demonstrating that minimal HUFT can account for the observed phenomenon and offering a novel avenue for precision tests of QCD and UV completion.
Abstract
We investigate the recently reported threshold enhancement in top-antitop production at the LHC in a finite, nonlocal, holomorphic quantum field theory framework. Our results demonstrate that the observed threshold excess can be consistently accommodated by a data-driven $Λ_{\mathrm{ker}}$ and small RG effects, while keeping global QCD tests intact. We quantify and contrast the key properties of the three heavyquark systems charmonium and bottomonium, highlighting the unique role of the top quark's decay width in shaping the phenomenology of toponium. Toponium emerges as a powerful laboratory for both infrared boundstate dynamics and ultraviolet completion effects, opening new avenues for precision tests of QCD.