Nuclear modification of forward $D$ production in pPb collisions at the LHC

We study nuclear modification factors for single $D$ meson and semileptonic decay lepton $l$ ($=e,\mu$) production in minimum bias proton-nucleus (p$A$) collisions at the LHC in the color-glass-condensate (CGC) framework at leading order in strong coupling. In our numerical computations, transverse momentum ($k_\perp$) dependent multi-point Wilson line correlators are employed for describing target nucleus for p$A$ and proton for pp. The projectile proton is treated with unintegrated gluon distribution function, which is also $k_\perp$-dependent. The rapidity evolutions of these functions in the small Bjorken $x$ region are taken into account by solving running coupling Balitsky-Kovchegov (BK) equation at leading logarithmic accuracy. For simplicity, we employ Kartvelishvili's type fragmentation function and a simple model for lepton energy distribution from seileptonic decay, respectively, to compute differential cross sections for $D$ and $l$ production. The gluon saturation scale inside the heavy nucleus is enhanced and dependent on $x$, which we take into account by replacing the initial saturation scale in the BK equation with a larger value for the heavy nucleus. We show that the saturation effect leads to perceptible nuclear suppression of $D$ production at forward rapidity. Our numerical results predict similar nuclear suppressions in p$A$ collisions for forward $l$ production at lower transverse momentum $p_\perp<2\;{\rm GeV}$. Numerical tables on the nuclear modifications of $D$ and $l$ are listed in this note.