Hyperon sigma terms for 2+1 quark flavours

TL;DR

The paper tackles the problem of determining the light and strange sigma terms for the baryon octet using 2+1 flavour lattice QCD. It introduces a constant-$\bar m$ path combined with an SU(3) flavour symmetry breaking expansion to constrain hadron-mass gradients and avoids relying on chiral perturbation theory. By connecting mass derivatives to scalar matrix elements via the Feynman-Hellmann theorem and carefully treating renormalisation mixing for Wilson/clover fermions, the authors derive RG-invariant relations that yield $\sigma_l^{(H)}$ and $\sigma_s^{(H)}$ in terms of gradient coefficients $c_H$ and $M_0'(m_0)$ and the mass ratio $r$. Their results, notably $\sigma_l^{(N)*} = 31(3)(4)$ MeV and $\sigma_s^{(N)*} = 71(34)(59)$ MeV, support a relatively small light-quark sigma contribution and a moderately large strange sigma term, with systematic uncertainties explored via curvature analyses. The work provides a framework for precise sigma-term determinations with minimal reliance on chiral expansions, with implications for hadron structure and dark-matter cross-section constraints.

Abstract

QCD lattice simulations determine hadron masses as functions of the quark masses. From the gradients of these masses and using the Feynman-Hellmann theorem the hadron sigma terms can then be determined. We use here a novel approach of keeping the singlet quark mass constant in our simulations which upon using an SU(3) flavour symmetry breaking expansion gives highly constrained (i.e. few parameter) fits for hadron masses in a multiplet. This is a highly advantageous procedure for determining the hadron mass gradient as it avoids the use of delicate chiral perturbation theory. We illustrate the procedure here by estimating the light and strange sigma terms for the baryon octet.

Figures (9)

• Figure 1: $M_H/ X_N$ ($H = N$, $\Lambda$, $\Sigma$, $\Xi$) against $M_\pi^2/X_\pi^2$ for an initial point ("sym. pt.") on the flavour symmetric line given by $\kappa_0 = 0.12090$, left panel, and $\kappa_0 = 0.12092$, right panel. The $32^3\times 64$ lattices are filled circles, while the $24^3\times 48$ lattices are open triangles. Also shown is the combined fit of eq. (\ref{['mNoXN_mps2oXpi2']}) (the dashed lines) to the $32^3\times 64$ lattice data. The fit results are the open circles, while the experimental points are the (red) stars. $l$ and $s$ denote the light and strange quark content of the hadron.
• Figure 2: The left panel shows the nucleon mass, $aM_N$, versus $1/\kappa_l$, (for the $\overline{m} = \hbox{const.}$ points, green diamonds with $\kappa_0 = 0.12090$) and versus $1/\kappa_0$ (for the flavour symmetric points, "sym. pts.", maroon squares). The common flavour symmetric points are denoted by red circles. The $24^3\times 48$ volume results are open symbols together with a dashed line for the (linear) fit, while the $32^3\times 64$ volume results are filled symbols and solid lines. Similarly the right panel shows the nucleon mass $aM_N$, versus $(aM_\pi)^2$ (same notation as for the left panel).
• Figure 3: $X_N(\overline{m}) / X_N(m_0)$ versus $X_\pi^2(\overline{m}) / X_\pi^2(m_0)$ along the flavour symmetric line, together with the linear fit from eq. (\ref{['XNoXN_Xpi2oXpi2']}).
• Figure 4: $(2M_K^2-M_\pi^2)/X_N^2$ versus $M_\pi^2 / X_N^2$ for $\kappa_0 = 0.12090$ (left panel) and $\kappa_0 = 0.12092$ (right panel). The $32^3\times 64$ volume results are given by the filled symbols, while the $24^3\times 48$ volume results are shown using empty triangles. The fit is given in eq. (\ref{['const_mbar_fit']}). Experimental points are denoted by (red) stars.
• Figure 5: Left panel: $M_H/X_N$ for $H = N$, $\Lambda$, $\Sigma$, $\Xi$ against $a\delta m_l$ for initial point on the flavour symmetric line given by $\kappa_0 = 0.12090$ together with the previous linear fit (dashed lines) and quadratic fit (solid lines). Other notation as in Fig. \ref{['mpsO2omNOpmSigOpmXiOo32_mNOomNOpmSigOpmXiOo3_32x64_lin']}. Right panel: $X_N(\overline{m}) / X_N(m_0)$ versus $X_\pi^2(\overline{m}) / X_\pi^2(m_0)$ along the flavour symmetric line, together with a linear fit from eq. (\ref{['XNoXN_Xpi2oXpi2']}) (dashed line) and a quadratic fit (solid line).