Precision Determination of the Small-$x$ Gluon from Charm Production at LHCb

The small-$x$ gluon in global fits of parton distributions is affected by large uncertainties from the lack of direct experimental constraints. In this Letter, we provide a precision determination of the small-$x$ gluon from the exploitation of forward charm production data provided by LHCb for three different center-of-mass (c.m.) energies: 5 TeV, 7 TeV, and 13 TeV. The LHCb measurements are included in the parton distribution function (PDF) fit by means of normalized distributions and cross-section ratios between data taken at different c.m. values, $R_{13/7}$ and $R_{13/5}$. We demonstrate that forward charm production leads to a reduction of the PDF uncertainties of the gluon down to $x\simeq {10}^{-6}$ by up to an order of magnitude, with implications for high-energy colliders, cosmic ray physics, and neutrino astronomy.

Figure 1

The $1\sigma$ relative PDF uncertainties for the small-$x$ gluon at $Q^2=4{\mathrm{GeV}}^2$ in nnpdf3.0 and in the subsequent fits when the LHCb charm data are included one at a time.

Figure 2

The NLO gluon in nnpdf3.0 and for various combinations of the included LHCb data, at $Q^2=4{\mathrm{GeV}}^2$.

Figure 3

Dependence of the small-$x$ gluon from the $N_5+N_7+N_{13}$ fits for variations in the input theory settings.

Figure 4

Same as Fig. 3 for the $N^7+R^{13/5}$ fits.

Figure 5

The structure function $F_L(x,Q^2)$ at $Q^2=3.5{\mathrm{GeV}}^2$, comparing the nnpdf3.0 predictions both with the results of this work and with the GRRT calculation.

Figure 6

The NLO charged-current neutrino-nucleus cross section as a function of the neutrino energy $E_{\nu }$, computed with nnpdf3.0 and with the results of this work.