Sigma terms and strangeness content of the nucleon with $N_f=2+1+1$ twisted mass fermions

TL;DR

The paper investigates the nucleon's scalar quark content, important for dark matter direct detection, by directly computing light, strange, and charm contributions using N_f=2+1+1 twisted mass lattice QCD. It employs a variance-reduction technique for disconnected diagrams and a mixed-action setup to control renormalization, enabling precise determinations of the light and strange scalar contents. The results yield sigma_piN ≈ 151 MeV at m_PS ≈ 390 MeV and a small strange content with y_N ≈ 0.082, while the charm content remains statistically inaccessible, producing only a bound. This work demonstrates the practicality of twisted-mass lattice methods for nucleon matrix elements and provides a benchmark for future continuum and chiral extrapolations with explicit implications for WIMP-nucleon scattering predictions.

Abstract

We study the nucleon matrix elements of the quark scalar-density operator using maximally twisted mass fermions with dynamical light ($u$,$d$), strange and charm degrees of freedom. We demonstrate that in this setup the nucleon matrix elements of the light and strange quark densities can be obtained with good statistical accuracy, while for the charm quark counterpart only a bound can be provided. The present calculation which is performed at only one value of the lattice spacing and pion mass serves as a benchmark for a future more systematic computation of the scalar quark content of the nucleon.

Figures (8)

• Figure 1: The Higgs-boson exchange contribution to the WIMP-Nucleon low energy scattering process.
• Figure 2: Connected (left) and the disconnected (right) graphs arising from the Wick contractions of the 3-point function.
• Figure 3: Signal to noise ratio (SNR) of the quantity $R_{s}(\tau,\tau_{\rm op})$, see Eq. (\ref{['eq:ratio_def']}), for fixed values of $\tau/a=12$ and $\tau_{\rm op}/a=6$ as a function of $N_\xi$ and for different values of $N_{\rm src}$. The bare strange valence quark mass is $a\mu_s = 0.016$. The number of configurations used is $677$.
• Figure 4: Signal to noise ratio (SNR) of the quantity $R_{s}(12a,6a)$, see Eq. (\ref{['eq:ratio_def']}), for $N_\xi=12$ and $N_{\rm src}=4$ as a function of the number of gauge field configurations $N_{\rm{conf}}$, for the variance noise reduction technique used in this paper and the hopping parameter expansion technique. The dashed curves are drawn to guide the eye. The bare strange valence quark mass is the same as in Fig. \ref{['fig:scaling_R']}.
• Figure 5: Plot of the contributions $R_{\rm{disc.}}$ (blue triangle), $R_{\rm{conn.}}$ (black circles) and of their sum, $R_{l}$ (red diamonds) as function of $\tau_{op}$ at $\tau=12a$ for $a\mu_l=0.0055$ and $\beta=1.95$.