On the prompt contribution to the atmospheric neutrino flux

The prompt contribution to the atmospheric neutrino flux is analyzed. We demonstrate that the corresponding theoretical uncertainties related to perturbative treatment of charm production, notably, the ones stemming from the low- and high-$x$ behavior of parton distribution functions, can be conveniently studied at the level of charm quark production. Additionally, we discuss the nonperturbative contribution to the prompt neutrino flux, related to the intrinsic charm content of the proton and analyze its main features.

Figure 1

Energy dependence of the CR spectrum-weighted moment of $c$-quark production spectrum $Z_{p\text{-air}}^c(E,\gamma )$ for proton-air interactions, calculated using $\gamma =3$ and employing gluon PDFs from CT14nlo_NF3 (solid), ABMP16_3_nlo (dashed), and NNPDF31_nlo_pch_as_0118_nf_3 (dash-dotted) PDF sets.

Figure 2

Left: $x$ dependence of the gluon PDF $g_p(x,Q)$, for $Q=2\mathrm{GeV}$, for the considered PDF sets; the meaning of the lines is the same as in Fig. 1. Right: the ratios of the gluon PDFs, for $Q=2\mathrm{GeV}$, from the ABMP16_3_nlo and NNPDF31_nlo_pch_as_0118_nf_3 sets to the one of the CT14nlo_NF3 PDF set—dashed and dash-dotted lines, respectively.

Figure 3

Distributions of the LC momentum fractions $x^{\pm }$ for, respectively, projectile (left) and target (right) gluons, $d{Z}_{p\text{-air}}^c/d{x}^{\pm }$, for $E=1\mathrm{PeV}$ and $\gamma =3$. The meaning of the lines is the same as in Fig. 1.

Figure 4

Energy dependence of the ratio of the CR spectrum-weighted moments $Z_{p\text{-air}}^c(E,\gamma )$, for $\gamma =3.3$ and $\gamma =3$. The meaning of the lines is the same as in Fig. 1.

Figure 5

Distributions of the LC momentum fractions $x^{\pm }$ for, respectively, projectile (left) and target (right) gluons, $d{Z}_{p\text{-air}}^c/d{x}^{\pm }$, for $E=1\mathrm{PeV}$, using gluon PDF from the CT14nlo_NF3 set. Solid lines correspond to $\gamma =3$ and dashed ones to $\gamma =3.3$.

Figure 6

CR spectrum-weighted moments of $c$-quark production spectrum $Z_{p\text{-air}}^c(E,\gamma )$, for $\gamma =3$, calculated using different combinations of the factorization and renormalization scales: $({\mu }_{\mathrm{F}},{\mu }_{\mathrm{R}})=(1,1)m_{{\perp }_c}$ (solid), $({\mu }_{\mathrm{F}},{\mu }_{\mathrm{R}})=(2,1)m_{{\perp }_c}$ (dashed), $({\mu }_{\mathrm{F}},{\mu }_{\mathrm{R}})=(1,2)m_{{\perp }_c}$ (dot-dashed), and $({\mu }_{\mathrm{F}},{\mu }_{\mathrm{R}})=(2,2)m_{{\perp }_c}$ (dotted). The graphs in the left, middle, and right panels are based on gluon PDFs from ABMP16_3_nlo, CT14nlo_NF3, and NNPDF31_nlo_pch_as_0118_nf_3 PDF sets, respectively.

Figure 7

Distribution of the constituent $c$-quark LC momentum fraction in the proton, for the BHPS model (solid line) and for the Regge ansatz (dashed line).