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Two-Loop Quarkonium Hamiltonian in Nonannihilation Channel.

Go Mishima1, Yukinari Sumino1, Hiromasa Takaura2

  • 1Department of Physics, <a href="https://ror.org/01dq60k83">Tohoku University</a>, Sendai 980-8578, Japan.

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Researchers computed the two-loop heavy quarkonium Hamiltonian using potential-nonrelativistic-QCD. This is a key step towards the N^{4}LO Hamiltonian in the weak coupling regime.

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Area of Science:

  • High Energy Physics
  • Quantum Chromodynamics
  • Effective Field Theory

Background:

  • Heavy quarkonium systems are crucial for testing Quantum Chromodynamics (QCD).
  • Potential-nonrelativistic-QCD (pNRQCD) is an effective field theory used to study these systems.
  • Calculating higher-order corrections to the Hamiltonian is essential for precise predictions.

Purpose of the Study:

  • To calculate the two-loop heavy quarkonium Hamiltonian in the nonannihilation channel within pNRQCD.
  • To establish the first non-trivial step towards determining the N^{4}LO Hamiltonian in the weak coupling regime.

Main Methods:

  • Employed the β expansion to manage large computations.
  • Utilized differential equations for master integrals.
  • Adopted a single-step matching procedure, differing from conventional two-step approaches.

Main Results:

  • Successfully calculated the two-loop heavy quarkonium Hamiltonian in the specified channel.
  • Demonstrated a systematic method for handling complex calculations in pNRQCD.

Conclusions:

  • The two-loop calculation is a significant advancement in the perturbative expansion of the heavy quarkonium Hamiltonian.
  • The employed methods provide a robust framework for future higher-order calculations in pNRQCD.