The intrinsic strangeness and charm of the nucleon using improved staggered fermions

TL;DR

Using MILC Asqtad and HISQ gauge configurations with improved staggered fermions, the paper computes the intrinsic strangeness $\langle N|\bar{s}s|N\rangle$ and intrinsic charm $\langle N|\bar{c}c|N\rangle$ of the nucleon. It introduces and validates an improved hybrid method that combines direct and Feynman-Hellman approaches to reduce statistical errors and control excited-state effects on large lattice ensembles. The Asqtad analysis yields $\langle N|\bar{s}s|N\rangle = 0.637(55)(74)$ after chiral and continuum extrapolations, while HISQ results give $\langle N|\bar{s}s|N\rangle = 0.44(8)(5)$ and $\langle N|\bar{c}c|N\rangle = 0.056(27)$, with the charm result compatible with perturbative expectations. The findings imply that dark matter scattering through Higgs-like exchange receives roughly comparable contributions from all heavy quark flavors, and the work demonstrates a robust, scalable methodology for scalar nucleon matrix elements on large, improved-staggered lattices.

Abstract

We calculate the intrinsic strangeness of the nucleon, <N|ss|N> - <0|ss|0>, using the MILC library of improved staggered gauge configurations using the Asqtad and HISQ actions. Additionally, we present a preliminary calculation of the intrinsic charm of the nucleon using the HISQ action with dynamical charm. The calculation is done with a method which incorporates features of both commonly-used methods, the direct evaluation of the three-point function and the application of the Feynman- Hellman theorem. We present an improvement on this method that further reduces the statistical error, and check the result from this hybrid method against the other two methods and find that they are consistent. The values for <N|ss|N> and <N|cc|N> found here, together with perturbative results for heavy quarks, show that dark matter scattering through Higgs-like exchange receives roughly equal contributions from all heavy quark flavors.

Figures (14)

• Figure 1: Feynman diagram of an incoming neutralino interacting with a sea strange quark loop in the proton, mediated by a Higgs boson. The overall interaction amplitude depends on the intrinsic strangeness of the nucleon which must be computed on the lattice.
• Figure 2: A history of calculations of the nucleon strangeness. The "natural scale", given by the perturbative QCD calculationKRYJEVSKI03 as discussed in \ref{['sec-pert']}, is shown as a vertical blue dashed line (color online). NELSON87FUKUGITA94DONG96SESAM98MICHAEL01BABICH08BALI08OHKI08JLQCD09JLQCD10ENGELHARDT2010DURR11HORSLEY11DINTER11OURPRLKRYJEVSKI03
• Figure 3: A schematic illustration of the strangeness of the nucleon: the presence of the valence quarks creates a "bubble" in the vacuum chiral condensate.
• Figure 4: A schematic depiction of the perturbative approach to ${\frac{\partial M_N}{\partial m_c}}$ taken by Shifman and Kryjevski at leading order, inspired by a similar presentation by Kryjevski in Ref. KRYJEVSKI03. Changing the mass of a heavy quark changes the scale at which it freezes out and thus affects the running of the coupling constant, affecting all low-mass scales equally.
• Figure 5: The correlation between nucleon propagators of length $5a$, $10a$, and $15a$ with the strange quark condensate as a function of the distance from the propagator source on one of the MILC $a=0.12$ fm ensembles. The source and sink location of the propagators are marked as green vertical lines (color online).