In-medium $\omega$ mass from the $\gamma$+Nb $\to$ ${\pi }^0\gamma$+$X$ reaction

Data on the photoproduction of $\omega$ mesons on nuclei have been reanalyzed in a search for in-medium modifications. The data were taken with the crystal barrel (CB)/two-arm photon spectrometer (TAPS) detector system at the ELectron Stretcher Anlage (ELSA) accelerator facility in Bonn. First results from the analysis of the data set were published by Trnka et al. [Phys. Rev. Lett. 94, 192303 (2005)], claiming a lowering of the $\omega$ mass in the nuclear medium by 14$\%$ at normal nuclear matter density. The extracted $\omega$ line shape was found to be sensitive to the background subtraction. For this reason a reanalysis of the same data set has been initiated, and a new method has been developed to reduce the background and to determine the shape and absolute magnitude of the background directly from the data. Details of the reanalysis and of the background determination are described. The $\omega$ signal on the Nb target, extracted in the reanalysis, does not show a deviation from the corresponding line shape on a ${\mathrm{LH}}_2$ target, measured as reference. The earlier claim of an in-medium mass shift is thus not confirmed. The sensitivity of the $\omega$ line shape to different in-medium modification scenarios is discussed.

Figure 1

Left: CB/TAPS setup. The tagged photons impinge on the nuclear target in the center of the CB detector. The TAPS detector at a distance of 1.18 m from the target serves as a forward wall of the crystal barrel. The combined detector system provides photon detection capability over almost the full solid angle. Charged particles leaving the target are identified in the inner scintillating-fiber detector and in the plastic scintillators in front of each Ba$F_2$ crystal in TAPS. Right: Detector acceptance for the $p{\pi }^0\gamma$ final state as a function of the invariant mass and momentum of the ${\pi }^0\gamma$ pair for incident photon energies of 900–2200 MeV.

Figure 2

(a) Invariant mass of two $\gamma$’s (${\pi }^0\to \gamma \gamma$ and $\eta \to \gamma \gamma$) as a function of the momentum of the 2$\gamma$ pair for the Nb target. The vertical lines show the slices for the projections on the $y$ axis. (b) The peak positions of the ${\pi }^0$ and $\eta$ invariant masses in eight slices of the momentum. The horizontal lines show the tolerance of $\pm$2.5 MeV of the ${\pi }^0$ mass ($135$ MeV/$c^2$) and of $\pm$7 MeV of the $\eta$ mass ($547$ MeV/$c^2$). (c) The ${\pi }^0$ invariant mass for low and high momenta. (d) The $\eta$ invariant mass for low and high momenta.

Figure 3

(a) ${\pi }^0$ and (b) $\eta$ invariant mass distributions reconstructed from the ${\pi }^0(\eta )\to \gamma \gamma$ decay for the ${\mathrm{LH}}_2$, C, and Nb targets after background subtraction.

Figure 4

TAPS-tagger coincidence time spectra (a) without and (b) with requiring the hit in TAPS to be due to a photon (no response in plastic scintillator in front of TAPS). The shaded areas represent the applied cuts. The peaks reside on a uniformly distributed background stemming from random coincidences.

Figure 5

Left: Experimental data for the reaction $\gamma \mathrm{Nb}\to Xp3\gamma$: the invariant mass of two photons (all three $\gamma \gamma$ combinations) vs the ${\pi }^0\gamma$ invariant mass. On the $x$ axis, only one value is plotted per event for the 3$\gamma$ combination with the best ${\pi }^0$. Right: Monte Carlo simulation: corresponding plot for the reaction $\gamma p\to p{\pi }^0\eta$. Only those events are plotted where one proton and three photons are registered.

Figure 6

(a) Invariant mass of two $\gamma$’s; $y$ projection of Fig. 5 left for a cut of $M({\pi }^0\gamma$) between 570 and 630 MeV. The shaded areas show the cuts for sideband subtraction. (b) The $M({\pi }^0\gamma$) invariant mass distribution for the ${\pi }^0$ peak (black) and left (blue) and right (red) from the peak position as shown in (a). (c) The ${\pi }^0\gamma$ invariant mass in the ${\pi }^0$ peak (black) and the sum of the $M({\pi }^0\gamma$) projections left and right from the peak. The solid curve is a fit to the summed background spectrum. (d) The ${\pi }^0\gamma$ invariant mass distribution after sideband subtraction (solid histogram) compared with the spectrum without sideband subtraction (dashed histogram). All spectra refer to the Nb target.

Figure 7

Left: Experimental data for the reaction $\gamma \mathrm{Nb}\to Xp4\gamma$: after omitting one of the photons, the invariant mass of two photons is plotted vs the ${\pi }^0\gamma$ invariant mass. On the $x$ axis, only one value is plotted per event for the 3$\gamma$ combination with the best ${\pi }^0$. Right: The ${\pi }^0\gamma$ invariant mass in the ${\pi }^0$ peak (black) and the sum of the $M({\pi }^0\gamma$) projections left and right from the peak. The solid curve is a fit to the summed background spectrum.

Figure 8

(a) ${\pi }^0\gamma$ signal (solid curve) and background spectrum (dotted curve) for the C target deduced from events with four neutral and one charged hit. (b) Correction function derived from the carbon data. The dashed curve shows the mass dependence of this correction expected from a simulation of the 2${\pi }^0$ channel. (c) The ${\pi }^0\gamma$ signal spectrum and the corrected and normalized background spectrum for the Nb target. The solid curve represents a fit to the background distribution. (d) Ratio of the ${\pi }^0\gamma$ spectrum to the background spectrum for the Nb target generated from events with four neutral and one charged hit.

Figure 9

(a) $\omega$ signal for the Nb target from this analysis (solid points) compared with the $\omega$ signal published in Ref. [8] (dashed). For the comparison of the line shapes, the latter data have been scaled down by factor of 3.3 to match the intensity of the signal in the current analysis where more restrictive cuts have been applied. The spectra are without cut on the pion kinetic energy. (b) Fit to the $\omega$ signal published in Ref. [8] using the function given by Eq. (5). (c) Fit to the $\omega$ signal obtained in this analysis using the same function. The fit to the signal from Ref. [8] is included for comparison as the red dashed line.

Figure 10

(a) $\omega$ signal for ${\pi }^0\gamma$ momenta below 500 MeV/$c$ and kinetic energy $T_{{\pi }^0}>$ 150 MeV (Nb target). The solid curve represents a fit with the function of Eq. (5). (b) $\omega$ signal for a ${\mathrm{LH}}_2$ target, and (c) $\omega$ signal from MC simulation.

Figure 11

$\omega$ signal for the Nb target from this analysis (solid points) in comparison to the $\omega$ line shape measured on a ${\mathrm{LH}}_2$ target (dashed curve) and to a GiBUU simulation [24] (solid curve) assuming a mass shift of $-$16$\%$ at normal nuclear matter density.