Strange quark contributions to nucleon mass and spin from lattice QCD

TL;DR

The paper investigates how strange quarks contribute to the nucleon’s mass and spin using a 2+1-flavor mixed-action lattice QCD approach with domain-wall fermions. By computing disconnected strange-quark loops and nucleon two-point functions, the authors extract the scalar content $f_{T_s}$ and the strange spin contribution $\Delta s$, renormalizing to $\overline{MS}$ at 2 GeV and extrapolating to the physical pion mass. They find $f_{T_s}=0.046(11)$ and $\Delta s=-0.031(17)$, indicating modest but nonzero strange content; the results are supported by mild renormalization and carefully quantified systematic uncertainties. The findings constrain the strange-quark role in nucleon structure and have implications for dark matter coupling to nucleons and for the strange component of the nucleon spin, while showcasing the benefits of chiral-symmetry-preserving lattice formulations.

Abstract

Contributions of strange quarks to the mass and spin of the nucleon, characterized by the observables f_Ts and Delta s, respectively, are investigated within lattice QCD. The calculation employs a 2+1-flavor mixed-action lattice scheme, thus treating the strange quark degrees of freedom in dynamical fashion. Numerical results are obtained at three pion masses, m_pi = 495 MeV, 356 MeV, and 293 MeV, renormalized, and chirally extrapolated to the physical pion mass. The value extracted for Delta s at the physical pion mass in the MSbar scheme at a scale of 2 GeV is Delta s = -0.031(17), whereas the strange quark contribution to the nucleon mass amounts to f_Ts =0.046(11). In the employed mixed-action scheme, the nucleon valence quarks as well as the strange quarks entering the nucleon matrix elements which determine f_Ts and Delta s are realized as domain wall fermions, propagators of which are evaluated in MILC 2+1-flavor dynamical asqtad quark ensembles. The use of domain wall fermions leads to mild renormalization behavior which proves especially advantageous in the extraction of f_Ts.

Figures (5)

• Figure 1: Disconnected contribution to nucleon matrix elements. The nucleon propagates between a source at $t=0$ and a sink at $t=T$; the insertion of $\Gamma \equiv \Gamma^{obs}$ occurs at an intermediate time $t=\tau$.
• Figure 2: Setup of the lattice calculation. The nucleon source is located at lattice time $t=0$. An average over operator insertion times $\tau$ is performed in the range $\tau =3,\ldots ,7$; accordingly, stochastic sources are distributed over the bulk of the lattice in this entire time range. The temporal position $T$ of the nucleon sink is variable.
• Figure 3: Correlator ratio $R\{ f_{T_s } \}$, cf. (\ref{['corrfts']}), averaged over insertion time $\tau$ as described in section \ref{['setupsec']}, as a function of sink time $T$, for the three pion masses considered.
• Figure 4: Correlator ratio $R\{ \Delta s \}$, cf. (\ref{['corrds']}), averaged over insertion time $\tau$ as described in section \ref{['setupsec']}, as a function of sink time $T$, for the three pion masses considered.
• Figure 5: Pion mass dependence of the results for $m_s \langle N| \bar{s} s |N \rangle = m_N f_{T_s }$ and $\Delta s$. Filled circles represent renormalized lattice data; in the case of $\Delta s$, these are obtained by multiplying the $T=10$ values from Table \ref{['dsplat']} by the corresponding renormalization constants from Table \ref{['zatab']}, whereas $m_N f_{T_s }$ is obtained by multiplying the $T=10$ values from Table \ref{['ftsplat']} by the corresponding nucleon masses from Table \ref{['tabmilc']}. Open symbols show chiral extrapolations of the lattice data to the physical pion mass, cf. main text. Open circles represent the LO (constant) chiral extrapolations, whereas open squares represent the reduced NNLO extrapolations obtained by dropping the $\Delta$-resonance degrees of freedom, with the dashed lines showing the pion mass dependences of the central values in the latter case.