Measurement of the differential cross section $d\sigma /dt$ in elastic $p\overline{p}$ scattering at $\sqrt{s}\mathbf{=}1.96\mathrm{TeV}$

We present a measurement of the elastic differential cross section $d\sigma (p\overline{p}\to p\overline{p})/dt$ as a function of the four-momentum-transfer squared $t$. The data sample corresponds to an integrated luminosity of $\approx 31{\mathrm{nb}}^{-1}$ collected with the D0 detector using dedicated Tevatron $p\overline{p}$ Collider operating conditions at $\sqrt{s}=1.96\mathrm{TeV}$ and covers the range $0.26<|t|<1.2{\mathrm{GeV}}^2$. For $|t|<0.6{\mathrm{GeV}}^2$, $d\sigma /dt$ is described by an exponential function of the form $A{e}^{-b|t|}$ with a slope parameter $b=16.86\pm 0.10(\mathrm{stat})\pm 0.20(\mathrm{syst}){\mathrm{GeV}}^{-2}$. A change in slope is observed at $|t|\approx 0.6{\mathrm{GeV}}^2$, followed by a more gradual $|t|$ dependence with increasing values of $|t|$.

Figure 1

Schematic view of the Roman pot stations (${\mathrm{A}}_1$, ${\mathrm{A}}_2$, ${\mathrm{P}}_1$, ${\mathrm{P}}_2$) comprising the forward proton detector as described in the text (not drawn to scale). The dipole spectrometer is not shown. The letters U, D, I, O make reference to the up, down, inner, and outer detectors, respectively.

Figure 2

Schematic view of the design of one FPD scintillating fiber detector. U, ${\mathrm{U}}^{\prime }$, V, ${\mathrm{V}}^{\prime }$, X, and ${\mathrm{X}}^{\prime }$ are the scintillating fiber layers. The local detector $x$, $y$ coordinates are indicated by the arrows. The scintillating fibers are indicated by the green stripes.

Figure 3

Schematic view of part of the U and ${\mathrm{U}}^{\prime }$ fiber layers with the definitions of wide and fine fiber segments. Similar definitions are used for the X, ${\mathrm{X}}^{\prime }$ and V, ${\mathrm{V}}^{\prime }$ fiber layers.

Figure 4

Comparison of detector $y$ coordinates in the spectrometers (a) ${\mathrm{P}}_{\mathrm{U}}$ and (b) ${\mathrm{P}}_{\mathrm{D}}$.

Figure 5

The correlation plots $y_p$ vs $y_{\overline{p}}$ for the first detectors in the spectrometers ($y$ coordinates measured in the local coordinate system shown in Fig. 6) for ${\mathrm{A}}_{\mathrm{U}}{\mathrm{P}}_{\mathrm{D}}$ and ${\mathrm{A}}_{\mathrm{D}}{\mathrm{P}}_{\mathrm{U}}$. Plots (a) and (d) show the correlations without any timing requirement; (b) and (e) correspond to hits with a coincident tag in the corresponding scintillator early time windows; (c) and (f) show events with no hits within the early time window (most of the hits in this case are in the in-time window). The dashed lines correspond to the fiducial requirements applied.

Figure 6

Detector positions with respect to beam center (dashed lines) for the data set corresponding to the closest pot insertion to the beam. The arrows indicate the local coordinate system in each detector.

Figure 7

Size of the IP determined by the reconstruction of the primary vertex from nonelastic triggers (black points) fitted with a Gaussian function (solid line). (a) $x$ distribution of the IP. (b) $y$ distribution of the IP. (c) $z$ distribution of the IP.

Figure 8

Difference in the reconstructed $|t|$ between $p$ and $\overline{p}$ vertical spectrometers. The MC (solid line) expected distribution is compared to data (solid points). (a) ${\mathrm{A}}_{\mathrm{U}}{\mathrm{P}}_{\mathrm{D}}$ combination. (b) ${\mathrm{A}}_{\mathrm{D}}{\mathrm{P}}_{\mathrm{U}}$ combination. The number of entries in each distribution is normalized to unity.

Figure 9

Comparison of MC (solid line) and data (black points) for the coordinate difference $y_p\mathrm{\text{−}}{y}_{\overline{p}}$ for the elastic configuration ${\mathrm{A}}_{1,\mathrm{U}}{\mathrm{P}}_1\mathrm{D}$ for the data set with detectors closer to the beam.

Figure 10

Azimuthal acceptance of the FPD in data, after fiducial cuts, for the closest detector position of the ${\mathrm{A}}_{\mathrm{U}}{\mathrm{P}}_{\mathrm{D}}$ elastic combination. The points correspond to MC, the solid line corresponds to the calculation of the $\varphi$ acceptance from the detector positions and the fiducial area.

Figure 11

The measured $d\sigma /dt$ differential cross section. The normalization uncertainty of 14.4% is not shown. The uncertainties are obtained by adding in quadrature statistical and systematic uncertainties. The predictions of Bourrely et al. ([25]) and Deile et al. ([26]) are compared to the data.

Figure 12

The $d\sigma /dt$ differential cross section measured by the D0 Collaboration and compared to the CDF and E710 measurements at $\sqrt{s}=1.8\mathrm{TeV}$, and to the UA4 measurement at $\sqrt{s}=0.546\mathrm{TeV}$ (scaled by a factor of 100). A normalization uncertainty of 14.4% on the D0 measurement is not shown.