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arXiv · 1511.07382

The size of the pion from full lattice QCD with physical $u$, $d$, $s$ and $c$ quarks

J. Koponen·F. Bursa·C. T. H. Davies·R. J. Dowdall·G. P. Lepage
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Abstract

We present the first calculation of the electromagnetic form factor of the $π$ meson at physical light quark masses. We use configurations generated by the MILC collaboration including the effect of $u$, $d$, $s$ and $c$ sea quarks with the Highly Improved Staggered Quark formalism. We work at three values of the lattice spacing on large volumes and with $u$/$d$ quark masses going down to the physical value. We study scalar and vector form factors for a range in space-like $q^2$ from 0.0 to -0.1 $\mathrm{GeV}^2$ and from their shape we extract mean square radii. Our vector form factor agrees well with experiment and we find $\langle r^2 \rangle_V = 0.403(18)(6) \,\mathrm{fm}^2$. For the scalar form factor we include quark-line disconnected contributions which have a significant impact on the radius. We give the first results for SU(3) flavour-singlet and octet scalar mean square radii, obtaining: $\langle r^2 \rangle_S^{\mathrm{singlet}} = 0.506(38)(53) \mathrm{fm}^2$ and $\langle r^2 \rangle_S^{\mathrm{octet}} = 0.431(38)(46) \mathrm{fm}^2$. We discuss the comparison with expectations from chiral perturbation theory.

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J. Koponen, F. Bursa, C. T. H. Davies, R. J. Dowdall, G. P. Lepage. 2015-11-23. The size of the pion from full lattice QCD with physical $u$, $d$, $s$ and $c$ quarks. https://doi.org/10.1103/physrevd.93.054503

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