Charge and matter radial distributions of heavy-light mesons calculated on a lattice

For a heavy-light meson with a static heavy quark, we can explore the light quark distribution. The charge and matter radial distributions of these heavy-light mesons are measured on a ${16}^3\times 24$ lattice at $\beta =5.7\mathrm{}$ and a hopping parameter corresponding to a light quark mass about that of the strange quark. Both distributions can be well fitted up to 4 lattice spacings $\left(r\approx 0.7\mathrm{fm}\right)$ with the exponential form $w_i^2\mathrm{}\left(r\right),$ where $w_i\mathrm{}\left(r\right)\mathrm{}$ $=\mathrm{A}\mathrm{}\exp \left(-{r/r}_i\right).\mathrm{}$ For the charge (c) and matter (m) distributions $r_c\approx 0.32\left(2\right)\mathrm{}\mathrm{fm}$ and $r_m\approx 0.24\left(2\right)\mathrm{}\mathrm{fm}.$ We also discuss the normalization of the total charge and matter integrated over all space, finding 1.30(5) and 0.4(1), respectively.