The Pion-Nucleon sigma-Term with Dynamical Wilson Fermions

TL;DR

This study performs a full QCD lattice calculation with $n_f=2$ dynamical Wilson fermions to quantify the pion-nucleon sigma-term and the strange-quark content of the nucleon. By applying multiple ratio methods (Global Summation, Plateau Density, Plateau Accumulation) and using stochastic estimators for quark loops, the authors extract both connected and disconnected scalar-density amplitudes, obtaining $\sigma_{\pi N} = 18(5)$ MeV and $y = 0.59(13)$, with the former being notably small due to unquenching effects on light-quark masses. The work highlights the importance of sea quarks in shaping nucleon scalar structure and demonstrates that improved analysis (PAM) is essential for reliable disconnected signals. It also stresses the need for continuum scaling and $n_f \geq 3$ studies to fully constrain these quantities and to clarify the phenomenological implications for chiral dynamics and strangeness content of the nucleon.

Abstract

We calculate connected and disconnected contributions to the flavour singlet scalar density amplitude of the nucleon in a full QCD lattice simulation with $n_f=2$ dynamical Wilson fermions at $β=5.6$ on a $16^3 \times 32$ lattice. We find that both contributions are of similar size at the light quark mass. We arrive at the estimate $σ_{πN} = 18(5)$MeV. Its smallness is directly related to the apparent decrease of $u$, $d$ quark masses when unquenching QCD lattice simulations. The $y$ parameter can be estimated from a semi-quenched analysis, in which there are no strange quarks in the sea, the result being $y=0.59(13)$.}

Figures (7)

• Figure 1: Connected (a) and disconnected (b) contributions to the scalar density amplitude of a nucleon. Please note that all quark lines, including the quark loop, are connected by infinitely many gluon lines and virtual quark loops.
• Figure 2: Summation method: The raw data $R_u$ and $R_d$ for the connected amplitudes $C_{u,d}$ at our sea quark masses. The fits (range and value) are indicated by solid lines.
• Figure 3: Plateau method: The raw data $R_u$ and $R_d$ for the connected amplitudes $C_{u,d}$ at our sea quark masses. The fits (range and value) are indicated by solid lines.
• Figure 4: Summation method: The raw data $R_q$ for the disconnected amplitudes $D_q$ at our sea quark masses. The fits (range and value) are indicated by solid lines.
• Figure 5: PAM with $\Delta {t_0}=\Delta t=1$: The raw data $R_q$ for the disconnected amplitudes $D_q$ at our sea quark masses. The fits (range and value) are indicated by solid lines.