Scale setting and the light baryon spectrum in Nf = 2 + 1 QCD with Wilson fermions

Abstract

A bstract We determine the light baryon spectrum on ensembles generated by the Coordinated Lattice Simulations (CLS) effort, employing N f = 2 + 1 flavours of non-perturbatively improved Wilson fermions. The hadron masses are interpolated and extrapolated within the quark mass plane, utilizing three distinct trajectories, two of which intersect close to the physical quark mass point and the third one approaching the SU(3) chiral limit. The results are extrapolated to the continuum limit, utilizing six different lattice spacings ranging from a ≈ 0 . 10 fm down to below 0.04 fm. The light pion mass varies from M π ≈ 429 MeV down to 127 MeV. In general, the spatial extent is kept larger than four times the inverse pion mass and larger than 2 . 3 fm, with additional small and large volume ensembles to investigate finite size effects. We determine the Wilson flow scales $$ \sqrt{t_{0,\textrm{ph}}}={0.1449}_{(9)}^{(7)}\textrm{fm} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msqrt><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>ph</mml:mi></mml:mrow></mml:msub></mml:msqrt><mml:mo>=</mml:mo><mml:msubsup><mml:mn>0.1449</mml:mn><mml:mfenced><mml:mn>9</mml:mn></mml:mfenced><mml:mfenced><mml:mn>7</mml:mn></mml:mfenced></mml:msubsup><mml:mi>fm</mml:mi></mml:math> [1] and $$ {t}_0^{\ast}\approx {t}_{0,\textrm{ph}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>t</mml:mi><mml:mn>0</mml:mn><mml:mo>∗</mml:mo></mml:msubsup><mml:mo>≈</mml:mo><mml:msub><mml:mi>t</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>ph</mml:mi></mml:mrow></mml:msub></mml:math> [2] from the octet cascade (Ξ baryon). Determining the light baryon spectrum in the continuum limit, we find the nucleon mass $$ {m}_N={941.7}_{(7.6)}^{(6.5)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>m</mml:mi><mml:mi>N</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:msubsup><mml:mn>941.7</mml:mn><mml:mfenced><mml:mn>7.6</mml:mn></mml:mfenced><mml:mfenced><mml:mn>6.5</mml:mn></mml:mfenced></mml:msubsup></mml:math> MeV and the other stable baryon masses to agree with their experimental values within sub-percent level uncertainties. Moreover, we determine SU(3) and SU(2) chiral perturbation theory low energy constants, including the octet and the Ω baryon sigma terms σ πN = 43 . 9(4 . 7) MeV, $$ {\sigma}_{\pi \Lambda}={28.2}_{(5.4)}^{(4.3)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi>π</mml:mi><mml:mi>Λ</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msubsup><mml:mn>28.2</mml:mn><mml:mfenced><mml:mn>5.4</mml:mn></mml:mfenced><mml:mfenced><mml:mn>4.3</mml:mn></mml:mfenced></mml:msubsup></mml:math> MeV, $$ {\sigma}_{\pi \Sigma}={25.9}_{(6.1)}^{(3.8)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi>π</mml:mi><mml:mi>Σ</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msubsup><mml:mn>25.9</mml:mn><mml:mfenced><mml:mn>6.1</mml:mn></mml:mfenced><mml:mfenced><mml:mn>3.8</mml:mn></mml:mfenced></mml:msubsup></mml:math> MeV, $$ {\sigma}_{\pi \Xi}={11.2}_{(6.4)}^{(4.5)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi>π</mml:mi><mml:mi>Ξ</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msubsup><mml:mn>11.2</mml:mn><mml:mfenced><mml:mn>6.4</mml:mn></mml:mfenced><mml:mfenced><mml:mn>4.5</mml:mn></mml:mfenced></mml:msubsup></mml:math> and $$ {\sigma}_{\pi \Omega}={6.9}_{(4.3)}^{(5.3)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>σ</mml:mi><mml:mrow><mml:mi>π</mml:mi><mml:mi>Ω</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msubsup><mml:mn>6.9</mml:mn><mml:mfenced><mml:mn>4.3</mml:mn></mml:mfenced><mml:mfenced><mml:mn>5.3</mml:mn></mml:mfenced></mml:msubsup></mml:math> MeV, as well as various parameters, renormalization factors and improvement coefficients that are relevant for simulations with our lattice action.