Computing the η and η′ Mesons in Lattice QCD

Abstract

It has been known for a long time that the large experimental singlet-octet mass gap in the pseudoscalar meson mass spectrum originates from the anomaly of the axial vector current, i.e. from nonperturbative effects and the nontrivial topological structure of the QCD vacuum. In the N colour → ∞ limit of the theory, this connection elucidates in the famous Witten-Veneziano relation between the η ′ -mass and the topological susceptibility of the quenched QCD vacuum. While lattice quantum chromodynamics (LQCD) has by now produced impressive high precision results on the flavour nonsinglet hadron spectrum, the determination of the pseudoscalar singlet mesons from direct correlator studies is markedly lagging behind, due to the computational complexity in handling observables that include OZI-rule violating diagrams, like the η ′ propagator. In this article we report on some recent progress in dealing with this numerical bottleneck problem.

Study of theηandη′mesons with improved staggered fermions

“…In unquenched lattice QCD calculations it is not clear how to start from unmixed states. It is possible to estimate the elements of the mixing matrix in quenched and partially quenched QCD [61,62]. We also note that the properties of the connected strange-strange pseudoscalar meson determined by the HPQCD collaboration [56] are also useful for developing a partially quenched mixing analysis [61].…”

Hadron Spectrum from Dynamical Lattice QCD Simulations

“…They are consistent with each other while the TEA has smaller statistical error. The value at physical point is different: M η ∼ 290 MeV with TEA [72,74] and ∼ 520 +125 −58 MeV with Z 2 [69]. Systematic study of chiral extrapolation with more data at smaller quark masses will clarify the difference of these data.…”

“…There have been a series of studies calculating the flavor singlet mass in unquenched simulations [69][70][71][72]19,73].…”

“…The data at lighter two crosses [19] (a = 0.1 fm) seems to be constant. Squares [69] are obtained with Z 2 noise method, while bursts [72,74] are obtained with truncated eigenvalue approximation (TEA) method from the same SESAM configuration [27] (symbols are slightly shifted horizontally to avoid overlapping). They are consistent with each other while the TEA has smaller statistical error.…”

Pseudoscalar Singlet Physics with Staggered Fermions

“…Hence flavor-singlet mesons present a rich proving ground for lattice simulations. To this end a number of simulations have been performed on the lattice using quenched Wilson [3], N f = 2 Wilson [4,5,6,7,8], and N f = 2 staggered fermion formulations [9,10].…”