Nucleon Sigma Terms with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> Flavors of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>a</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>-Improved Wilson Fermions
Andria Agadjanov, Dalibor Djukanovic, Georg von Hippel, Harvey B. Meyer, Konstantin Ottnad, Hartmut Wittig
Abstract
We present a lattice-QCD based analysis of the nucleon sigma terms using gauge ensembles with ${N}_{f}=2+1$ flavors of $\mathcal{O}(a)$-improved Wilson fermions, with a complete error budget concerning excited-state contaminations, the chiral interpolation as well as finite-size and lattice spacing effects. We compute the sigma terms determined directly from the matrix elements of the scalar currents. The chiral interpolation is based on SU(3) baryon chiral perturbation theory using the extended on-mass shell renormalization scheme. For the pion nucleon sigma term, we obtain ${\ensuremath{\sigma}}_{\ensuremath{\pi}N}=(43.7\ifmmode\pm\else\textpm\fi{}3.6)\text{ }\text{ }\mathrm{MeV}$, where the error includes our estimate of the aforementioned systematics. The tension with extractions based on dispersion theory persists at the $2.4\text{\ensuremath{-}}\ensuremath{\sigma}$ level. For the strange sigma term, we obtain a nonzero value, ${\ensuremath{\sigma}}_{s}=(28.6\ifmmode\pm\else\textpm\fi{}9.3)\text{ }\text{ }\mathrm{MeV}$.