Roper State from Overlap Fermions

Understand

The Roper state is extracted with valence overlap fermions on a $2+1$-flavor domain-wall fermion lattice (spacing $a = 0.114$ fm and $m_{\pi} = 330$ MeV) using both the Sequential Empirical Bayes (SEB) method and the variational method.

• The results are consistent, provided that a large smearing-size interpolation operator is included in the variational calculation to have better overlap with the lowest radial excitation.
• Similar calculations carried out for an anisotropic clover lattice with similar parameters find the Roper $\approx 280$ MeV higher than that of the overlap fermion.
• The fact that the prediction of the Roper state by overlap fermions is consistently lower than those of clover fermions, chirally improved fermions, and twisted-mass fermions over a wide range of pion masses has been dubbed a "Roper puzzle." To understand the origin of this difference, we study the hairpin $Z$-diagram in the isovector scalar meson ($a_0$) correlator in the quenched approximation.