Nuclear Drell-Yan effect in a covariant model

We investigate effects of a nuclear medium on antiquark distribution in nuclei by applying the results of a recently developed relativistically covariant self-consistent model for the pion and the isobar. We take into account Fermi motion, including Pauli blocking and binding effects on the nucleons and medium effects on the isobar and pion, leading to modest enhancement of the pion light-cone-momentum distribution in large nuclei. As a consequence, the Drell-Yan cross-sectional ratio with respect to the deuteron exceeds one only for small values of the light-cone momentum.

Figure 1

Pion distribution in the free proton: $f^{{\pi }^{0}N/N}\left(y\right)$ is shown by the solid line and $f^{{\pi }^{-}\Delta /N}\left(y\right)$ is shown by the dashed line.

Figure 2

The pion-cloud result for the $\overline{d}-\overline{u}$ asymmetry in free proton (solid line) compared to the difference of the proton $\overline{d}$ and $\overline{u}$ distributions (dot line) from the fit CT10 [17] and data points by the Fermilab E866/NuSea Collaboration [18]. The isobar contribution (dash-dotted line) is negative and much smaller than the nucleon term (dashed line). Used parameter values: ${\Lambda }_{\pi N}^{\left(\pi \right)}=0.95$GeV and ${\Lambda }_{\pi \Delta }^{\left(\pi \right)}=0.75$GeV.

Figure 3

Sum of the second, third, fourth, and fifth terms in Eq. (14) divided by the antiquark distribution of the free “isoscalar” nucleon. The solid line is for the pion parameter set (1) and the dashed line is for parameter set (2).

Figure 4

The ratio of $F_2\left(x\right)$ per nucleon for isospin symmetric nuclear medium with the following parameters: Fermi momentum $p_F=250$MeV, $\eta =0.97$, and deuteron. Pion contributions with parameter sets (1) and (2) are included in the results shown by solid and dash-dotted lines.

Figure 5

Types of diagrams contributing to the in-medium pion distribution with outgoing nucleon. The same types appear also with outgoing $\Delta$ baryon. The dashed line denotes the dressed pion propagator, while the solid and the double lines correspond to nucleon and $\delta$.

Figure 6

Nucleon contribution to the pion distribution [$f^{{\pi }^{0}N/A}\left(y\right)$] for the in-medium nucleon compared to the case of a free nucleon.

Figure 7

Isobar contribution to the pion distribution [$f^{{\pi }^{-}\Delta /A}\left(y\right)$] in the in-medium nucleon compared to the free nucleon. For both in-medium curves $M_{*}=0.89\text{GeV}$ and ${\Sigma }_N^v=0$.

Figure 8

Full pion distribution [$f^{\pi /A}\left(y\right)$] in the in-medium nucleon compared to the case of free “isoscalar” nucleon.

Figure 9

The ${\overline{u}}_p^{\text{(medium)}}/{\overline{u}}_p^{\text{(free)}}$ (solid lines) and ${\overline{d}}_p^{\text{(medium)}}/{\overline{d}}_p^{\text{(free)}}$ (dashed lines) ratios of antiquark distributions of an in-medium proton relative to the free proton for parameter sets (1) and (2).

Figure 10

The cross-section ratio (10) as a function of $x_2$ for fixed values of $x_1$. The used parameter values are $M_{*}=0.85\text{GeV},{\Sigma }_N^v=0.04\text{GeV},{\Sigma }_{\Delta }^s=-0.1\text{GeV},{\Sigma }_{\Delta }^v=0,g_{11}^{\prime }=0.8,g_{12}^{\prime }=0.3,\text{and}{g}_{22}^{\prime }=0.3$.

Figure 11

The same as Fig. 10 but with para-meter values $M_{*}=0.89\text{GeV},{\Sigma }_N^v=0,{\Sigma }_{\Delta }^s=-0.1\text{GeV},{\Sigma }_{\Delta }^v=0,g_{11}^{\prime }=1,g_{12}^{\prime }=0.4,\text{and}{g}_{22}^{\prime }=0.3$.

Figure 12

Experimental results from Ref. [8] compared to our calculation for different parameter values. Short dashed line: $M_{*}=0.89\text{GeV},{\Sigma }_N^v=0$; solid line: $M_{*}=0.85\text{GeV},{\Sigma }_N^v=0.05\text{GeV}$; and dash-dotted line: $M_{*}=0.8\text{GeV},{\Sigma }_N^v=0.09\text{GeV}$. For all three curves, ${\Sigma }_{\Delta }^s=-0.1\text{GeV},{\Sigma }_{\Delta }^v=0,g_{11}^{\prime }=1.0,g_{12}^{\prime }=0.4,\text{and}{g}_{22}^{\prime }=0.3$.