Light vector mesons in the nuclear medium

The light vector mesons ($\rho$,$\omega$, and $\varphi$) were produced in deuterium, carbon, titanium, and iron targets in a search for possible in-medium modifications to the properties of the $\rho$ meson at normal nuclear densities and zero temperature. The vector mesons were detected with the CEBAF Large Acceptance Spectrometer (CLAS) via their decays to $e^{+}{e}^{-}$. The rare leptonic decay was chosen to reduce final-state interactions. A combinatorial background was subtracted from the invariant mass spectra using a well-established event-mixing technique. The $\rho$-meson mass spectrum was extracted after the $\omega$ and $\varphi$ signals were removed in a nearly model-independent way. Comparisons were made between the $\rho$ mass spectra from the heavy targets ($A>2$) with the mass spectrum extracted from the deuterium target. With respect to the $\rho$-meson mass, we obtain a small shift compatible with zero. Also, we measure widths consistent with standard nuclear many-body effects such as collisional broadening and Fermi motion.

Figure 1

Reconstructed $e^{+}{e}^{-}$ vertex position along the beam direction $z$. The position of $z=0$ corresponds to the center of the CLAS detector.

Figure 2

Deposited energy in the EC vs momentum for positively charged particles.

Figure 3

Same as Fig. 2, but for negatively charged particles.

Figure 4

Invariant mass of $p{\pi }^{-}$ from the reaction $\gamma p\to p{\pi }^{-}{K}^{+}$. The shaded region is the cut to select the Λ events.

Figure 5

$e^{+}{e}^{-}$ invariant mass spectrum summed over all targets (a) before applying any cuts to pair candidates, (b) after vertex position and timing cuts, and (c) after the vertex position, timing, lepton momenta, and different-sector cuts. The overlaid histogram in (b) shows events with the $e^{-}$ and $e^{+}$ detected in the same sector of CLAS.

Figure 6

Feynman diagrams for the Bethe-Heitler processes. An incoming photon with four-momentum $k$ produces a lepton pair. The negative and positive leptons have four-momentum $p_{-}$ and $p_{+}$. The initial and final momenta of the nucleon are denoted $p_i$ and $p_f$. The four-momentum exchanged between the nucleon and one of the leptons is denoted by $q$.

Figure 7

Feynman diagrams of the Dalitz decays of two ${\pi }^0$'s. The combination of an electron and a positron from separate decays (dashed oval) could lead to an $e^{+}{e}^{-}$ background.

Figure 8

Comparison of the $e^{+}{e}^{-}$ invariant mass spectrum from mixing leptons from different events to the shapes of the mass spectra from $e^{-}{e}^{-}$ (squares) and $e^{+}{e}^{+}$ (triangles) events. The distributions have been manually scaled to the approximately same height.

Figure 9

Normalized combinatorial background (blue) for individual targets compared with data (black) for targets (a) ${}^2\mathrm{H}$, (b) C, and (c) Fe-Ti.

Figure 10

CLAS acceptance as a function of the $e^{+}{e}^{-}$ invariant mass for C targets at different $z$ locations in CLAS. The individual targets are located at $z=-12.0$ cm (a), −7.0 cm (b), 2.0 cm (c), and 3.0 cm (d). The results are shown for the $\rho$ channel and summed over all photon energies.

Figure 11

Result of the fits to the $e^{+}{e}^{-}$ invariant mass spectrum obtained for the (a) ${}^2\mathrm{H}$, (b) C, and (c) Fe-Ti data. The curves are Monte Carlo calculations by the BUU model [49, 50] for various vector-meson decay channels.

Figure 12

Individual Breit-Wigner/${\mu }^3$ fits to the $\rho$ mass spectra for (a) ${}^2\mathrm{H}$, (b) C, and (c) Fe-Ti.

Figure 13

Fits to the $\rho$ mass spectrum for the deuterium data using a Breit-Wigner (dashed) and a Breit-Wigner/${\mu }^3$ function (solid).

Figure 14

Ratios of the $e^{+}{e}^{-}$ invariant mass for C to ${}^2\mathrm{H}$. The ratios were obtained from the simulations without (a) and with (b) the mass shift predicted by Ref. [2] and from the data (c). The number of simulated events is five times more than the current data. The slope of a simple linear fit shown on each plot is used to investigate the sensitivity of the current data to a mass shift (shown in Fig. 16).

Figure 15

Same as Fig. 14, but for Fe-Ti to ${}^2\mathrm{H}$.

Figure 16

Slope (1/GeV) of the linear fit to the ratio of the $\rho$ mass distributions in the Fe-Ti data as a function of the mass shift parameter α. The prediction of the Hatsuda and Lee model [2] (blue) and the KEK result [31] (red) are compared with the Jefferson Lab data within $\pm 1\sigma$ (shaded green box).

Figure 17

Shift parameter α, with the errors given horizontally, from the slope analysis with the Fe-Ti and ${}^2\mathrm{H}$ data (circle). Also shown is a comparison with the KEK result [31] (square) and the prediction of Hatsuda and Lee model [2] (triangle). For the KEK result, the error is smaller than the symbol.

Figure 18

Result of a simultaneous fit to the $\rho$ mass spectra for (a) ${}^2\mathrm{H}$, (b) C, and (c) the ratio of $\mathrm{C}/$${}^2\mathrm{H}$.

Figure 19

Result of a simultaneous fit to the $\rho$ mass spectra for (a) ${}^2\mathrm{H}$, (b) Fe-Ti, and (c) the ratio of Fe-Ti/${}^2\mathrm{H}$.