Fourth Generation Bound States

TL;DR

This paper studies the spectrum and properties of bound states formed by hypothetical heavy fourth-generation quarks, including effects of strong Yukawa couplings, relativistic corrections, and Higgs interactions.

Contribution

It provides a detailed analysis of the spectrum, wave functions, and binding energies of fourth-generation quark bound states, incorporating perturbative, relativistic, and Higgs effects.

Findings

Bound states exist for certain heavy quark masses.

Color singlet states always form bound states, influenced by Higgs couplings.

Lightest quark masses for bound states are identified.

Abstract

We investigate the spectrum and wave functions of {\bar q}'q' bound states for heavy fourth generation quarks (q') that have a very small mixing with the three observed generations of standard model quarks. Such bound states come with different color, spin and flavor quantum numbers. Since the fourth generation Yukawa coupling, \lambda_{q'}, is large we include all perturbative corrections to the potential between the heavy quark and antiquark of order \lambda_{q'}^2N_c/16\pi^2 where N_c is the number of colors, as well as relativistic corrections suppressed by (v/c)^2. We find that the lightest fourth generation quark masses for which a bound state exists for color octet states. For the the color singlet states, which always have a bound state, we analyze the influence that the Higgs couplings have on the size and binding energy of the bound states.