The strange quark condensate in the nucleon in 2+1 flavor QCD

TL;DR

The method is to evaluate quark-line disconnected correlations on the MILC lattice ensembles, which include the effects of dynamical light and strange quarks.

Abstract

We calculate the "strange quark content of the nucleon", <N| s s_bar |N>, which is important for interpreting the results of some dark matter detection experiments. The method is to evaluate quark-line disconnected correlations on the MILC lattice ensembles, which include the effects of dynamical strange quarks. After continuum and chiral extrapolations, the result is <N |s s_bar |N> = 0.69 +- 0.07(statistical) +- 0.09(systematic), in the modified minimal subtraction scheme (2 GeV), or for the renormalization scheme invariant form, m_s partial{M_N}/partial{m_s} = 59(6)(8) MeV.

Figures (2)

• Figure 1: The nucleon correlator and the derivative of this correlator with respect to $m_s$ for the ensemble with $am_l=0.0093$ and $am_s=0.031$ (first panel). For the derivative, the squares are points where the derivative is negative, and crosses are points where it is positive. The vertical lines show the range used in fitting the correlator. The second panel shows ${\frac{\partial M_N}{\partial m_s}}$ for three ensembles with $a\approx 0.9$fm as a function of the minimum distance used in the fitting, and the third panel shows the fitted nucleon mass itself versus $D_{min}$. The error bars labelled "10%" in the second and third panels show the size of the ten percent systematic error estimate from excited state contamination.
• Figure 2: The derivative ${\frac{\partial M_N}{\partial m_s}}$ on the various ensembles. As discussed above, the data have been adjusted to the correct strange quark mass, and the quark mass converted to the $\overline{\mathrm{MS}}({\rm 2\ GeV})$ regularization. In the horizontal axis, $r_1$ is a hadronic length scale, approximately $0.31$ fm. In these plots the symbol size is proportional to the number of lattices in the ensemble, with the largest symbol corresponding to about 4500 lattices. In each panel, the cross at $m_l r_1 \approx 0.05$ ($m_l \approx 0.4 m_s$) also shows the value of the nearby point before adjusting the strange quark mass. The line on each panel is the continuum and chiral fit in Eq. \ref{['fitform']} evaluated at the corresponding lattice spacing, and the error bar at the left is the error on the combined fit to all the data.