[Paper Review] Hadronic Interactions

Takeshi Yamazaki|arXiv (Cornell University)|Mar 30, 2015

Quantum Chromodynamics and Particle Interactions12 citations

TL;DR

This paper reviews recent lattice QCD studies of hadronic interactions, focusing on scattering, decay, and light nuclei using L"uscher's method and the HALQCD approach. It highlights key discrepancies in two-nucleon bound state predictions between the two methods, despite agreement in simpler channels like I=2 two-pion scattering, and discusses systematic uncertainties affecting both techniques in the context of nuclear binding energy calculations at unphysically large pion masses.

ABSTRACT

Understanding hadronic interactions is crucial for investigating the properties of unstable hadrons, since measuring physical quantities for unstable hadrons including the resonance mass and decay width requires simultaneous calculations of final scattering states. Recent studies of hadronic scatterings and decays are reviewed from this point of view. The nuceon-nucleon and multi-nucleon interactions are very important to understand the formation of nucleus from the first principle of QCD. These interactions have been studied mainly by two methods, due originally to Lüscher and to HALQCD. The results obtained from the two methods are compared in three channels, $I=2$ two-pion, H-dibaryon, and two-nucleon channels. So far the results from the two methods for the two-nucleon channels are different even at the level of the presence or absence of bound states. We then discuss possible uncertainties in each method. Recent results on the binding energy for helium nuclei are also reviewed.

Motivation & Objective

• To compare results from L"uscher's method and the HALQCD method for hadronic interactions in the context of scattering and bound state formation.
• To investigate systematic uncertainties affecting the prediction of two-nucleon bound states in lattice QCD calculations.
• To assess the consistency of lattice QCD results for light nuclei binding energies with experimental values, particularly at unphysically large pion masses.
• To evaluate the reliability of scattering phase shifts and resonance parameters extracted from finite-volume energy spectra.
• To explore the implications of discrepancies in two-nucleon channel results for the first-principles derivation of nuclear forces from QCD.

Proposed method

• Uses L"uscher's finite-volume formula to extract scattering phase shifts from energy levels of two-particle states in lattice QCD simulations.
• Applies the HALQCD method to compute the potential between hadrons via the Nambu-Bethe-Salpeter wave function in finite volume.
• Employs chiral perturbation theory (ChPT) for chiral extrapolation of scattering lengths to the physical point.
• Analyzes the energy dependence of two-particle states in moving frames to extract phase shifts and resonance parameters.
• Uses the L"uscher formula in the infinite-volume limit to extract scattering lengths and binding energies from finite-volume energy levels.
• Compares results from both methods across three channels: I=2 two-pion, H-dibaryon, and two-nucleon systems.

Experimental results

Research questions

• RQ1 Do L"uscher's method and the HALQCD method yield consistent predictions for the existence of bound states in the two-nucleon channel?
• RQ2 What are the dominant systematic uncertainties affecting the results from L"uscher's method and the HALQCD method in two-nucleon systems?
• RQ3 How do lattice QCD calculations of light nuclei binding energies compare with experimental values, especially at unphysically large pion masses?
• RQ4 To what extent do the results for the I=2 two-pion scattering length agree with chiral perturbation theory and experiment?
• RQ5 What explains the discrepancy in the H-dibaryon binding energy predictions between the two methods in the large pion mass region?

Key findings

• In the I=2 two-pion channel, results from L"uscher's method and the HALQCD method agree numerically, confirming consistency in a simple, non-resonant system.
• For the H-dibaryon, both methods conclude that it exists as a bound state only at pion masses larger than the physical value, though the binding energy differs quantitatively.
• In the two-nucleon channel, L"uscher's method finds a bound state, while the HALQCD method does not, indicating a fundamental discrepancy between the two approaches.
• The binding energy of 4He in lattice QCD is roughly consistent with experiment at mπ ≈ 300 MeV, but the 3He binding energy is overestimated by a factor of three.
• Systematic uncertainties in L"uscher's method include contamination from higher excited states, finite lattice spacing, and quark mass effects.
• In the HALQCD method, uncertainties in the short-distance potential and the use of the Nambu-Bethe-Salpeter wave function may explain the absence of a bound state in the two-nucleon channel.