The strange and light quark contributions to the nucleon mass from Lattice QCD

TL;DR

This paper addresses how quark masses contribute to the nucleon mass by computing the scalar matrix elements $<N|qbar q|N>$ for light and strange quarks using lattice QCD with $n_f=2$ sea quarks and Wilson-clover fermions. It carefully treats connected and disconnected contributions and includes flavour mixing in renormalization, employing a chiral-extrapolation strategy anchored in the sea-quark dependence of the nucleon mass. The key findings are that renormalized light-quark content drives the bulk of the nucleon mass while the strangeness contribution is small, yielding $σ_{πN}^{phys}≈38$ MeV and $σ_s≈12$ MeV with $f_{T_s}≈0.012$, and a high-$f_{T_G}$ gluonic fraction $≈0.95$, with an upper limit $y<0.14$. These results constrain the Higgs-nucleon coupling and beyond-Standard-Model scenarios, though they remain to be refined by continuum extrapolation and inclusion of dynamical strange quarks to fully control systematic effects.

Abstract

We determine the strangeness and light quark fractions of the nucleon mass by computing the quark line connected and disconnected contributions to the matrix elements m_q <N|qbar q|N> in lattice QCD, using the non-perturbatively improved Sheikholeslami-Wohlert Wilson Fermionic action. We simulate n_F=2 mass degenerate sea quarks with a pion mass of about 285 MeV and a lattice spacing a approx 0.073 fm. The renormalization of the matrix elements involves mixing between contributions from different quark flavours. The pion-nucleon sigma-term is extrapolated to physical quark masses exploiting the sea quark mass dependence of the nucleon mass. We obtain the renormalized values σ_{πN} = 38(12) MeV at the physical point and f_{T_s}=σ_s/m_N= 0.012(14)^{+10}_{-3} for the strangeness contribution at our larger than physical sea quark mass.

Figures (7)

• Figure 1: Quark line connected (top) and disconnected (bottom) three-point functions. We have omitted the relative minus sign between the diagrams. Note that for scalar matrix elements, the vacuum expectation value of the current insertion needs to be subtracted ($\bar{q}q\mapsto\bar{q}q-\langle\bar{q}q\rangle$), see Eq. (\ref{['eq:rati']}).
• Figure 2: Dependence of $R^{\mathrm{dis}}$ on $t_{\mathrm{f}}$ for smeared-smeared (SS) and smeared-point (SP) two-point functions, together with the fit result.
• Figure 3: Determination of the slope $Z_m^s/Z_m^{ns}=1+\alpha_{\mathrm{Z}}$, see Eqs. (\ref{['eq:1']}) and (\ref{['eq:2']}).
• Figure 4: The unrenormalized mass fraction $f_{T_q}^{\mathrm{lat}}$, as a function of the current pseudoscalar mass on the $L=32a$ lattices, at the smallest valence mass $m_{\mathrm{PS}}\approx 285$ MeV.
• Figure 5: Eq. (\ref{['eq:rati']}), partially summed up to a maximum spatial distance from the source $x_{\max}$, see Eq. (\ref{['eq:partial']}).