Positronium Hydride an Tetron

• Author / Creator

  Leng, Bo

• Variational calculations of the ground state of positronium hydride are performed where the various
  expectation values including the inter-particle distances and the non-relativistic ground state energy.
  These calculations have been performed using wave function in Gaussian basis with the basis set of

  1. A good agreement with the corresponding values reported in the literature is found for different parameters. Later, we consider the interactions in a mesonic system, referred here to as ‘tetron’, consisting of two heavy quarks and two lighter antiquarks (which may still be heavy in the scale of QCD), i.e. generally QaQbqcqd, and study the existence of bound states below the threshold for decay into heavy meson pairs. At a small ratio of the lighter to heavier quark masses an expansion parameter arises for treatment of the binding in such systems. We find that in the limit where all the quarks and antiquarks are so heavy that a Coulomb-like approximation can be applied to the gluon exchange between all of them, such bound states arise when this parameter is below a certain critical value. We find the parametric dependence of the critical mass ratio on the number of colors Nc, and confirm this dependence by numerical calculations. In particular there are no stable tetrons when all constituents have the same mass. We discuss an application of a similar expansion in the large Nc limit to realistic systems where the antiquarks are light and their interactions are nonperturbative. In this case our findings are in agreement with the recent claims from a phenomenological analysis that a stable bbu  d tetron is likely to exist, unlike those where one or both bottom quarks are replaced by the charmed quark.

• Subjects / Keywords

  • Variational method
  • Positronium Hydride
  • Tetraquark

• Graduation date

  Spring 2020

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/r3-w832-9163

• License

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