The production of the doubly charmed baryon in deeply inelastic $ep$ scattering at the Large Hadron Electron Collider

In this paper, we carry out a detailed study on the production of the doubly charmed baryon in deeply inelastic $ep$ scattering (DIS) for $Q^2in[2, 100]~textrm{GeV}^2$, at the Large Hadron Electron Collider (LHeC) with $E_e=60(140)$ GeV and $E_p=7000$ GeV. To exclude the contributions from the diffractive productions and the $b$ hadron decays, we impose the kinematic cuts $0.3<z<0.9$, and $p_{t,textrm{baryon}}^{star2}>1~textrm{GeV}^2$ in the center-of-mass (CM) frame of $gamma^{*}p$. Based on the designed LHeC luminosity, by detecting the decay channel $Xi^{+}_{cc}(Xi^{++}_{cc}) to Lambda_c^{+}$ with the subsequent decay $Lambda_c^{+} to pK^{-}pi^{+}$, we predict that about 1880 (2700) $Xi^{+}_{cc}$ events and 3750 (5400) $Xi^{++}_{cc}$ events can be accumulated per year, which signifies the prospect of observing them via the DIS at the forthcoming LHeC. In addition, we also predict the distributions of a rich variety of physical observables in the laboratory frame and the $gamma^{*}p$ CM frame, including $Q^2$, $p_t^{2}$, $Y$(rapidity), $p_t^{star2}$, $Y^{star}$, $W$, and $z$ distributions, respectively, which can provide helpful references for studying the doubly charmed baryon. In conclusion, we think that in addition to the LHC, the LHeC is also a helpful platform for studying the properties of the doubly charmed baryon.