$\ensuremath{\pi}\mathrm{N}$ and strangeness sigma terms at the physical point with chiral fermions

$π N$ and strangeness sigma terms at the physical point with chiral fermions

Yi-Bo Yang, Andrei Alexandru, Terrence Draper, Jian Liang, and Keh-Fei Liu (χQCD Collaboration)

Phys. Rev. D 94, 054503 – Published 8 September 2016

Abstract

Lattice QCD calculations with chiral fermions of the $π N$ sigma term $σ_{π N}$ and strangeness sigma term $σ_{s N}$ including chiral interpolation with continuum and volume corrections are provided in this work, with the excited-state contaminations subtracted properly. We calculate the scalar matrix element for the light/strange quark directly and find $σ_{π N} = 45.9 (7.4) (2.8) MeV$ , with the disconnected insertion part contributing 20(12)(4)%, and $σ_{s N} = 40.2 (11.7) (3.5) MeV$ , which is somewhat smaller than $σ_{π N}$ . The ratio of the strange/light scalar matrix elements is $y = 0.09 (3) (1)$ .

Received 6 December 2015

DOI:https://doi.org/10.1103/PhysRevD.94.054503

Physics Subject Headings (PhySH)

Lattice QCD

Protons

Particles & Fields

Authors & Affiliations

Yi-Bo Yang¹, Andrei Alexandru², Terrence Draper¹, Jian Liang¹, and Keh-Fei Liu¹ (χQCD Collaboration)

¹Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky 40506, USA
²Department of Physics, The George Washington University, Washington, D.C. 20052, USA

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Vol. 94, Iss. 5 — 1 September 2016

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Figure 1
The light ( $m_{π} = 148 / 330 MeV$ in the upper/lower panel respectively) $g_{S, l}$ and strange quark loops $g_{S, s}$ , with the quark mass in the nucleon the same as that of the light quark loop, from the 48I lattice are plotted. High-mode contribution (H) and the sum of the high- and low-mode contributions ( $H + L$ ) to the DI part of the scalar matrix elements are shown separately. The contributions from the stochastic high-mode part of the quark loops are quite small and the results are dominated by the exact low-mode part of the quark loop, so that the LMA method is very effective.
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Figure 2
The ratio $R (t_{f}, t)$ , as a function of the separation $t_{f}$ (three curves for three separations) and the current position $t$ (the data points on the curves), for each of the light (upper panel) and strange (lower panel) scalar matrix elements in proton, $g_{S}$ , is plotted at $m_{π} = 148 MeV$ (on the 48I ensemble) which is close to the physical point. The green bands show the results extrapolated to infinite separation which correspond to the predictions of $g_{S}$ . The excited-state contaminations are obvious with the final uncertainties much larger than those for the finite separations.
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Figure 3
The ratio $R (t_{f}, t)$ , as a function of the sink-source separation $t_{f}$ (three curves for three separations) and the current position $t$ (the data points on the curves) for the light and strange matrix elements (left and right panels, respectively). The three sets of the panels from top to bottom show the cases for $m_{π} \sim 280 MeV$ on the 24I, 32I, and 48I ensembles, respectively. The green bands show the results extrapolated to infinite separation, which corresponds to the prediction of $g_{S}$ . The excited-state contaminations are obvious, and the final uncertainties are larger than those on the finite separations.
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Figure 4
The summary figures of the light/strange quark content at 18 quark masses on the three ensembles (24I, 32I, and 48I as defined in Table 1), as a function of the square of the pion mass. Both the lattice spacing and sea-quark mass dependence are mild. The curve in each figure shows the behavior in the infinite-volume and continuum limits without the partial quenching effect. In each case, the band of the total error is almost the same as that of the statistical error, and thus is barely visible.
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Figure 5
The results of $σ_{π N}$ and $f_{s}^{N}$ , from both phenomenology and lattice simulations. Numbers are from GLS [11], Pavan [13], Young et al. [2], Alarcon et al. [36, 52], Chen et al. [53], Shanahan et al. [3], Alvarez et al. [21], Lutz et al. [22], Ren et al. [23], Hoferichter et al. [14], JLQCD [15, 31, 37], QCDSF [26], ETMC [27, 28, 54], RQCD [29], BMWc [16, 20], MILC [34], QCDSF-UKQCD [17], Engelhardt et al. [38], Junnarkar et al. [35], and $χ QCD$ [1]. The narrow error bar for each data point is the statistical error, and the broad bar shows the total uncertainty. The physical proton mass 938 MeV is used to obtain $f_{s}^{N}$ in this work.
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Physical Review D

covering particles, fields, gravitation, and cosmology

$π N$ and strangeness sigma terms at the physical point with chiral fermions

Yi-Bo Yang, Andrei Alexandru, Terrence Draper, Jian Liang, and Keh-Fei Liu (χQCD Collaboration)

Phys. Rev. D 94, 054503 – Published 8 September 2016

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Physical Review D

covering particles, fields, gravitation, and cosmology

πN and strangeness sigma terms at the physical point with chiral fermions

Yi-Bo Yang, Andrei Alexandru, Terrence Draper, Jian Liang, and Keh-Fei Liu (χQCD Collaboration)

Phys. Rev. D 94, 054503 – Published 8 September 2016

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$π N$ and strangeness sigma terms at the physical point with chiral fermions