The pion-nucleon Sigma term is definitely large: results from a G.W.U. analysis of pion nucleon scattering data

TL;DR

The paper tackles the long-standing puzzle of the pion-nucleon sigma term $\Sigma$ by performing a comprehensive energy-dependent $\pi N$ partial-wave analysis up to 2.1 GeV constrained by dispersion relations and updated data, including PSI pionic-hydrogen measurements. It extracts subthreshold coefficients and evaluates $\Sigma$ via the Cheng-Dashen framework, finding $\Sigma = 79 \pm 7$ MeV (with $\Sigma_d = 67 \pm 6$ MeV) and a stable $g^2/4\pi = 13.69 \pm 0.07$. The result is robust against Coulomb corrections and database variations, but implies a relatively large nucleon strangeness content $y/2 \sim 0.23$, challenging the standard interpretation and motivating a re-examination of the $\Sigma$–strangeness connection in low-energy QCD.

Abstract

A new result for the pion nucleon Sigma term from a George Washington University/TRIUMF group analysis of pion nucleon data is presented. The value Sigma=79$\pm$7 MeV was obtained, compared to the canonical value 64$\pm$8 MeV found by Koch. The difference is explained simply by the PSI pionic hydrogen value for a(pi -p), the latest results for the $πNN$ coupling onstant, and a narrower Delta resonance. Many systematic effects have been investigated, including Coulomb corrections, and database changes, and our results are found to be robust. In the standard interpretation, our value of Sigma implies a nucleon strangeness fraction y/2~0.23. The implausibility of such a large strange component suggests that the relationship between Sigma and nucleon strangeness ought to be re-examined.

Figures (2)

• Figure 1: Determination of the $\pi NN$ coupling constant from the Hüper dispersion relation. The y-intercept gives the coupling $g^{2}/M$, and the left (right)-hand side of the figure is dominated by $\pi ^{-}p$ ($\pi ^{+}p)$ data. This technique is well suited to determine the coupling constant since most systematic effects ( e.g. Coulomb corrections) affect each side asymmetrically, "pivoting" the curves about the intercept, hence greatly reducing their effect on $g^2$.
• Figure 2: The amplitude $\overline{C}^{+}(0,t)$ (points) evaluated from fixed-t $C^{+}(\nu,t)$ dispersion relations. A fit (dashed line) yields the subthreshold coefficients in the table. The solid diagonal line is inferred from forward $C+$ and $E^+$ dispersion relations, and agrees perfectly with $\overline{d}_{00}$ and $\overline{d}_{01}$ in the table. The curvature terms ( $\overline{d}_{0i}, i\geq2$) imply $\Delta_{D}>$11 MeV, consistent with the canonical result 12$\pm$1 MeV from Ref. glls88. The amplitude is very small as expected at $t=m_{\pi}^2$ ("Adler point"). The overall consistency tends to support our result for the sigma term, $\Sigma\sim79\pm7$ MeV.