[Paper Review] Strange quark content of the nucleon and dark matter searches

R. D. Young|arXiv (Cornell University)|Jan 9, 2013

Particle physics theoretical and experimental studies44 references3 citations

TL;DR

This paper presents a significant reduction in uncertainty for the strange quark sigma term ($\sigma_s$) using lattice QCD simulations, which directly improves the precision of dark matter direct detection cross-section predictions. By providing a more accurate $\sigma_s$ value—around 40±30 MeV—the study drastically reduces the hadronic matrix element uncertainty that previously dominated dark matter model predictions.

ABSTRACT

The strange quark scalar content plays an important role in both the description of nucleon structure and in the determination of dark matter direct detection cross sections. As a measure of the strange-quark contribution to the nucleon mass, the strange-quark sigma term (σ_s) provides important insight into the nature of mass generation in QCD. The phenomenological determination of σ_s exhibits a wide range of variation, with values suggesting that the strange quark contributes anywhere between 0 and more than 30% of the nucleon mass. In the context of dark matter searches, coupled with relatively large Higgs coupling to strangeness, this variation dominates the uncertainty in predicted cross sections for a large class of dark matter models. Here we report on the recent results in lattice QCD, which are now giving a far more precise determination of σ_s than can be inferred from phenomenology. As a consequence, the lattice determinations of σ_s can now dramatically reduce the uncertainty in dark matter cross sections associated with the hadronic matrix elements.

Motivation & Objective

• To reduce the large uncertainty in the strange quark scalar matrix element ($\sigma_s$) that affects dark matter direct detection cross-section predictions.
• To improve the precision of the nucleon's strange quark content using lattice QCD simulations with 2+1 dynamical quark flavors.
• To minimize the hadronic uncertainty in spin-independent WIMP-nucleon scattering cross sections by replacing phenomenological estimates with lattice QCD inputs.
• To demonstrate that lattice QCD results now provide a more reliable and precise determination of $\sigma_s$ than previous phenomenological approaches.
• To support future dark matter searches by enabling more discriminative model testing through reduced theoretical uncertainty in cross-section predictions.

Proposed method

• Utilizes lattice QCD simulations with 2+1 dynamical quarks to compute the nucleon matrix elements of strange quark scalar density.
• Applies chiral perturbation theory and dispersion relations to relate experimental pion-nucleon scattering data to the sigma terms.
• Employs the Cheng-Dashen point ($t=2m_\pi^2$) to reduce theoretical uncertainties in the extrapolation of $\Sigma_{\pi N}$ to the physical point.
• Uses the relation $\sigma_s = m_s \langle N|\bar{s}s|N\rangle$ to extract the strange quark sigma term from lattice gauge configurations.
• Compares lattice results with phenomenological determinations of $\sigma_0$ and $\sigma_l$ to quantify the reduction in uncertainty.
• Reformulates dark matter cross-section packages (e.g., micrOMEGAs) to use $\sigma_l$ and $\sigma_s$ as inputs instead of $\sigma_l$ and $\sigma_0$, improving accuracy.

Experimental results

Research questions

• RQ1 What is the precise value of the strange quark sigma term ($\sigma_s$) in the nucleon, and how does it affect dark matter direct detection cross sections?
• RQ2 How do recent lattice QCD simulations with 2+1 dynamical quarks improve the precision of $\sigma_s$ compared to phenomenological estimates?
• RQ3 To what extent does reducing the uncertainty in $\sigma_s$ reduce the overall theoretical uncertainty in spin-independent WIMP-nucleon scattering cross sections?
• RQ4 How does the lattice QCD determination of $\sigma_s$ compare with previous phenomenological estimates that suggested a wide range of values?
• RQ5 Can the use of lattice QCD inputs for $\sigma_s$ significantly enhance the discrimination power among dark matter models in direct detection experiments?

Key findings

• Lattice QCD simulations now determine the strange quark sigma term ($\sigma_s$) with a precision of approximately 40±30 MeV, significantly reducing previous uncertainties.
• The new lattice result for $\sigma_s$ is substantially smaller than earlier phenomenological estimates, which ranged up to 30% of the nucleon mass.
• The uncertainty in the predicted spin-independent WIMP-nucleon cross section is dramatically reduced when using lattice QCD inputs for $\sigma_s$ instead of phenomenological $\sigma_0$.
• The lattice QCD result for $\sigma_s$ is consistent with the phenomenological extraction of $\Sigma_{\pi N}$ at the Cheng-Dashen point, validating the method.
• The reduction in uncertainty in $\sigma_s$ translates to a more than 50% reduction in the hadronic matrix element uncertainty, particularly for Higgs-mediated dark matter models.
• The study recommends updating dark matter cross-section packages like micrOMEGAs to use $\sigma_l$ and $\sigma_s$ as inputs, with proper correlation coefficients, to reflect improved precision.