Mesons with beauty and charm: Spectroscopy

Abstract: We make a detailed study of the photoproduction mechanism of the doubly heavy flavored ${B}_{c}^{(*)}$ meson at the purposed Large Hadron Electron Collider (LHeC) within the framework of nonrelativistic QCD. In addition to the photoproduction mechanism via the gluon-induced channel $\ensuremath{\gamma}+g\ensuremath{\rightarrow}{B}_{c}^{(*)}+b+\overline{c}$, the extrinsic heavy quark mechanism via the two channels $\ensuremath{\gamma}+c\ensuremath{\rightarrow}{B}_{c}^{(*)}+b$ and $\ensuremath{\gamma}+\overline{b}\ensuremath{\rightarrow}{B}_{c}^{(*)}+\overline{c}$ has also been studied. Those two extrinsic channels are generally suppressed by the heavy quark distribution functions in the proton, which provide significant contributions in the low and intermediate ${p}_{T}$ region. A detailed comparison of those channels together with the theoretical uncertainties has been presented. By summing up all the mentioned photoproduction channels, we observe that about $(1.0{4}_{\ensuremath{-}0.53}^{+0.90})\ifmmode\times\else\texttimes\fi{}1{0}^{5}$ ${B}_{c}$ and $(4.8{6}_{\ensuremath{-}2.30}^{+3.72})\ifmmode\times\else\texttimes\fi{}1{0}^{5}$ ${B}_{c}^{*}$ events can be generated at the LHeC in one operation year with the proton-electron collision energy $\sqrt{S}=1.30\text{ }\text{ }\mathrm{TeV}$ and the luminosity $\mathcal{L}\ensuremath{\simeq}1{0}^{33}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$. Here the errors are for ${m}_{c}=1.50\ifmmode\pm\else\textpm\fi{}0.20$ and ${m}_{b}=4.9\ifmmode\pm\else\textpm\fi{}0.40\text{ }\text{ }\mathrm{GeV}$. Thus, in addition to the hadronic experiments, the LHeC shall provide another helpful platform for studying the ${B}_{c}^{(*)}$ meson properties, especially to test the extrinsic heavy quark mechanism.

TL;DR: The theory of atoms with one or two electrons is the simplest and most completely treated field of application of quantum mechanics as mentioned in this paper, and it is one of the simplest fields of application for quantum mechanics.