Momentum dependence of the $\phi$-meson nuclear transparency

The production of $\phi$ mesons in proton collisions with C, Cu, Ag, and Au targets has been studied via the $\phi \to K^{+}{K}^{-}$ decay at an incident beam energy of 2.83 GeV using the ANKE detector system at COSY. For the first time, the momentum dependence of the nuclear transparency ratio, the in-medium $\phi$ width, and the differential cross section for $\phi$-meson production at forward angles have been determined for these targets over the momentum range of 0.6–1.6 GeV/$c$. There are indications of a significant momentum dependence in the value of the extracted $\phi$ width, which corresponds to an effective $\phi N$ absorption cross section in the range of 14–21 mb.

Figure 1

Invariant mass distributions of $K^{+}{K}^{-}$ pairs produced in $p$C and $p$Au collisions in the $\phi$ momentum bins: (a) $0.600$–$0.825$, (b) $0.825$–$0.950$, (c) $0.950$–$1.075$, (d) $1.075$–$1.200$, (e) $1.200$–$1.325$, and (f) $1.325$–$1.600$ GeV/$c$. Fits to the uncorrected experimental data in terms of an expected $\phi$ shape and a physical background are shown by the solid lines. The dashed lines are third-order polynomial parametrizations of the backgrounds in the region of the $\phi$ peak.

Figure 2

Momentum dependence of the transparency ratio $R$, normalized to carbon, for Cu, Ag, and Au targets.

Figure 3

The transparency ratio $R$ for the nuclear combinations (a) Cu/C, (b) Ag/C, and (c) Au/C as functions of the $\phi$ laboratory momentum. The experimental data, shown in red, are connected with lines to guide the eye. The predictions of the three theoretical approaches are shown for model 1 (left), model 2 (center), model 3 (right). For the rest of the notations, see the text.

Figure 4

(a) In-medium width of the $\phi$ meson in the nuclear rest frame at saturation density ${\rho }_0$ as a function of the $\phi$ momentum. The points have been evaluated by comparing the data of Fig. 2 with the results of the three model calculations shown in Fig. 3 (model 1–solid squares, model 2–solid circles and model 3–open triangles). Also shown are the results from the other experiments noted [13, 15, 16]. The solid line represents the ${\Gamma }_{\phi }$ calculated on the basis of the predicted $\phi$ self-energy in nuclear matter [12]. (b) The $\phi N$ absorption cross section. In the case of model 3, this is the parameter that is directly determined from the comparison with experiment, whereas for models 1 and 2 it is deduced from the in-medium $\phi$ widths within the low-density approximation. The SPring-8 [15] and JLab [16] values of the cross section are also shown.

Figure 5

Inclusive double-differential cross sections for $\phi$ production at small angles, ${\theta }_{\phi }<8^{\circ }$, in the collisions of 2.83 GeV protons with C, Cu, Ag, and Au targets as functions of the $\phi$ laboratory momentum (solid squares). The errors shown are those from Table  added in quadrature. The experimental data are compared with the predictions of model 2 (dashed lines) and model 3 (solid lines) using, respectively, the central values of the $\phi$ width and effective $\phi N$ absorption cross section shown in Fig. 4.