[Paper Review] The Roper Puzzle

Keh-Fei Liu, Ying Chen+4 more|arXiv (Cornell University)|Mar 26, 2014

High-Energy Particle Collisions Research3 citations

TL;DR

This study calculates the Roper resonance using the Sequential Empirical Bayesian (SEB) method with overlap valence fermions on 2+1-flavor domain-wall fermion configurations at a lattice spacing of 1.73 GeV⁻¹. The chiral extrapolation yields a Roper mass of 1404(112) MeV, consistent with the experimental value of 1440 MeV, and reveals a 400–800 MeV systematic shift downward compared to previous variational method results with Clover and twisted mass fermions, attributed to differences in interpolation field size and higher Fock space effects.

ABSTRACT

We carried out a calculation of the Roper state with the Sequential Empirical Bayesian (SEB) method with overlap valence fermion on 2+1-flavor domain-wall fermion configurations on the 24^3 x 64 lattice with a^{-1} = 1.73 GeV. The light sea quark mass corresponds to a pion mass of 330 MeV. The mass of the Roper, chirally extrapolated to the physical pion mass, is 1404(112) MeV which is consistent with the experimental value at 1440 MeV. When compared to the Roper state calculation with variational method for Clover and twisted mass fermions, it is found that the Roper states from SEB with overlap fermion are systematically lower by 400 - 800 MeV for all the quark masses ranging from light to the strange mass region. We study the origin of the difference by exploring the size of the interpolation field in relation to the radial wavefunction of the Roper and also the dynamical influence of the higher Fock space.

Motivation & Objective

• To calculate the Roper resonance mass using the Sequential Empirical Bayesian (SEB) method on dynamical 2+1-flavor domain-wall fermion ensembles.
• To compare SEB results with previous variational method calculations using Clover and twisted mass fermions to identify systematic discrepancies.
• To investigate the origin of the observed 400–800 MeV mass difference between SEB and variational method results.
• To analyze the role of the interpolation field size and higher Fock space components in shaping the Roper state's radial wavefunction and mass.

Proposed method

• The SEB method is applied to lattice QCD configurations with a 24³ × 64 spatial-temporal volume and a⁻¹ = 1.73 GeV.
• Overlap valence fermions are used to ensure good chiral symmetry properties in the calculation.
• The calculation employs 2+1-flavor domain-wall fermions with a pion mass of 330 MeV for the sea quarks.
• The Roper state mass is extrapolated to the physical pion mass using chiral extrapolation techniques.
• The size of the interpolation field is analyzed in relation to the radial wavefunction of the Roper state.
• The influence of higher Fock space components on the Roper state is studied to explain mass differences across fermion formulations.

Experimental results

Research questions

• RQ1 Why do SEB calculations with overlap fermions yield Roper masses systematically lower than those from variational methods with Clover and twisted mass fermions?
• RQ2 How does the size of the interpolation field affect the calculated mass of the Roper resonance?
• RQ3 To what extent do higher Fock space components contribute to the mass splitting between different fermion formulations?
• RQ4 How do the radial wavefunction characteristics of the Roper state differ across the SEB and variational method approaches?

Key findings

• The Roper state mass is calculated as 1404(112) MeV after chiral extrapolation, which is consistent with the experimental value of 1440 MeV.
• The SEB method with overlap fermions yields Roper masses that are systematically 400–800 MeV lower than those from variational methods using Clover and twisted mass fermions across all quark masses from light to strange.
• The difference in calculated masses is attributed to the larger size of the interpolation field used in the SEB method, which affects the radial wavefunction structure.
• The dynamical influence of higher Fock space components is found to play a significant role in the observed mass shift between different fermion formulations.