Medium modifications of the $\rho$ meson in nuclear photoproduction

We extend our recent study of dilepton invariant-mass spectra from the decays of $\rho$ mesons produced by photon reactions off nuclei. We specifically focus on experimental spectra as recently measured by the CLAS Collaboration at the Thomas Jefferson National Accelerator Facility using carbon and iron nuclei. Building on our earlier work, we broaden our description to a larger set of observables to identify sensitivities to the medium effects predicted by microscopic calculations of the $\rho$ spectral function. We compute mass spectra for several target nuclei and study the spectral shape as a function of the three-momentum of the outgoing lepton pair. We also compute the so-called nuclear transparency ratio, which provides an alternative means (and thus consistency check) of estimating the $\rho$ width in the cold nuclear medium.

Figure 1

Probability distributions (normalized to 1) of the nuclear density at the $\rho$-meson decay points, ${\mathit{dP}}_{\mathrm{decay}}/d{\varrho }_N$: (a) using an input photon-energy spectrum as in CLAS for two different nuclei and (b) using a ${}^{238}\text{U}$ target for different photon energies. Vertical lines indicate the bins used for the histogram.

Figure 2

Excess mass spectra for (a) ${}^{12}\mathrm{C}$ and (b) ${}^{56}\mathrm{Fe}$ and (c, d) ratios of these spectra to the deuterium spectrum. (In the ratios, both numerator and denominator are normalized to the corresponding target-mass number, $A$.) The full calculation using explicit density distributions (solid lines) is compared to simplified calculations using a single average density.

Figure 3

Calculations for excess mass spectra off (a, b) ${}^{12}\mathrm{C}$ and (c, d) ${}^{56}\mathrm{Fe}$ targets compared to the CLAS data [15, 16] at JLab. The full calculations (solid lines) are decomposed by modifying different theoretical ingredients, by (i) switching off the baryon-resonance contributions in the elementary production amplitude (dash-dotted lines), (ii) switching off the in-medium widths of the baryon-resonance contributions in the elementary production amplitude (dashed lines), or (iii) replacing the in-medium electromagnetic correlator, $G_{\rho }$, with the vacuum one (dotted lines). (a, c) All spectra are (${\chi }^2$) normalized to the data, while (b, d) we keep the normalization of the full model also for the other scenarios.

Figure 4

Absolutely normalized cross sections for excess mass spectra for (a) several nuclei from carbon (uppermost curve) to uranium (lowest curve) and for (b) several fixed nuclear densities from $0.1{\varrho }_0$ (uppermost curve) to ${\varrho }_0$ (lowest curve).

Figure 5

Excess dilepton invariant-mass spectra for several nuclei. The full model (solid lines) is compared to the calculations using the vacuum $\rho$ propagator (scaled to the peak height of the full calculation by the indicated factors). Furthermore, absolutely normalized calculations are shown for in-medium and vacuum spectral functions applying the indicated momentum cuts to the spectra.

Figure 6

Nuclear transparency ratio, $T_A$, as a function of nuclear mass number, $A$. The full calculation is compared to results when switching off the medium effects on the baryon resonances in the production amplitude and when using the vacuum $\rho$ propagator in the electromagnetic correlator, $G_{\rho }$.

Figure 7

Same as Fig. 6 but in infinite nuclear matter as a function of density.

Figure 8

Transparency ratio as a function of the mass number $A$ for different photon energies.

Figure 9

Fit parameter $\beta$ used to describe the dependence of the transparency ratio on the photon energy.