Nucleon strange quark content from two-flavor lattice QCD with exact chiral symmetry

TL;DR

This work computes the nucleon strange quark content through a direct evaluation of the disconnected strange-loop contribution using two-flavor lattice QCD with exact chiral symmetry (overlap fermions). By employing all-to-all propagators and low-mode averaging, the authors control statistical noise and avoid operator-mixing artifacts that plagued Wilson-type formulations, obtaining $f_{T_s}=0.032(8)(22)$ and $y\approx0.050(12)(34)$ after chiral extrapolation. The results are consistent with previous indirect (Feynman-Hellmann) estimates and demonstrate the essential role of exact chiral symmetry in reliable determinations of disconnected contributions. The study also outlines how to extend this approach to $2+1$ flavor QCD and to other baryon observables involving disconnected loops, highlighting methodological advances for precision hadron structure calculations.

Abstract

Strange quark content of the nucleon is calculated in dynamical lattice QCD employing the overlap fermion formulation. For this quantity, exact chiral symmetry guaranteed by the Ginsparg-Wilson relation is crucial to avoid large contamination due to a possible operator mixing with $\bar{u}u+\bar{d}d$. Gauge configurations are generated with two dynamical flavors on a 16^3 x 32 lattice at a lattice spacing a \simeq 0.12fm. We directly calculate the relevant three-point function on the lattice including a disconnected strange quark loop utilizing the techniques of all-to-all quark propagator and low-mode averaging. Our result f_{T_s} = 0.032(8)(22), is in good agreement with our previous indirect estimate using the Feynman-Hellmann theorem.

Figures (18)

• Figure 1: Disconnected three-point function relevant to $\left\langle N|\bar{s}s|N\right\rangle$. Lines show quark propagators that are dressed by virtual gluons and sea quarks in QCD. The connected three lines correspond to the nucleon propagation and the disconnected loop arises from the strange scalar operator $\bar{s}s$.
• Figure 2: Effective mass $M_N(\Delta t)$ from the nucleon two-point function $C_{2\rm pt}$ at $m_{ud}=0.050$. The local operator is used for both source and sink. Circles show the result of the conventional point source, while squares (triangles) are obtained by averaging the $C_{2\rm pt}^{lll}$ ($C_{2\rm pt}^{lll}+C_{2\rm pt}^{llh}+C_{2\rm pt}^{lhl}+C_{2\rm pt}^{hll}$) contributions. Circles and triangles are slightly shifted in the horizontal direction for clarity.
• Figure 3: Effective mass $M_N(\Delta t)$ from $C_{2\rm pt}$ with an exponentially smeared source at $m_{ud}=0.050$. The symbols are the same as in Fig. \ref{['Fig:mN_lcl_m050']}.
• Figure 4: Comparison of $M_N(\Delta t)$ obtained with different numbers of source locations for LMA. Circles are those without LMA. Results averaged over the time slices are shown by squares. We obtain down- and up-triangles by further averaging over 8 and 16 spatial sites at each time slice, respectively. In the plot, $N_{\rm src}$ represents the number of the source locations.
• Figure 5: Effective mass $M_N(\Delta t)$ with the Gaussian smeared source and sink at $m_{ud}=0.050$. Circle are without LMA; triangles are obtained by averaging $C_{2\rm pt}^{lll}$ over 16 spatial sites at each time slice.