Odderon Exchange from Elastic Scattering Differences between $pp$ and $p\overline{p}$ Data at 1.96 TeV and from $pp$ Forward Scattering Measurements

We describe an analysis comparing the $p\overline{p}$ elastic cross section as measured by the D0 Collaboration at a center-of-mass energy of 1.96 TeV to that in $pp$ collisions as measured by the TOTEM Collaboration at 2.76, 7, 8, and 13 TeV using a model-independent approach. The TOTEM cross sections, extrapolated to a center-of-mass energy of $\sqrt{s}=1.96\mathrm{TeV}$, are compared with the D0 measurement in the region of the diffractive minimum and the second maximum of the $pp$ cross section. The two data sets disagree at the $3.4\sigma$ level and thus provide evidence for the $t$-channel exchange of a colorless, $C$-odd gluonic compound, also known as the odderon. We combine these results with a TOTEM analysis of the same $C$-odd exchange based on the total cross section and the ratio of the real to imaginary parts of the forward elastic strong interaction scattering amplitude in $pp$ scattering for which the significance is between $3.4\sigma$ and $4.6\sigma$. The combined significance is larger than $5\sigma$ and is interpreted as the first observation of the exchange of a colorless, $C$-odd gluonic compound.

Figure 1

The TOTEM measured $pp$ elastic cross sections as functions of $|t|$ at 2.76, 7, 8, and 13 TeV (filled circles), and the extrapolation (discussed in the text) to 1.96 TeV (empty circles). The lines show the double exponential fits to the data points (see text).

Figure 2

The ratio $R$ of the cross sections at the bump and dip as a function of $\sqrt{s}$ for $pp$ and $p\overline{p}$. The $pp$ data are fitted to the function noted in the legend.

Figure 3

(a) Schematic definition of the characteristic points in the TOTEM differential cross section data. $A$ represents the vertical distance between bump and dip. (b) and (c) Characteristic points in (b) $|t|$ and (c) $d\sigma /dt$ from TOTEM measurements at 2.76, 7, 8, and 13 TeV (circles) as a function of $\sqrt{s}$ extrapolated to Tevatron center-of-mass energy (stars). On (c), a multiplication factor indicated in parenthesis is applied in order to distinguish the different fits. Filled symbols are from measured points; open symbols are from extrapolations or definitions of the characteristic points.

Figure 4

Comparison between the D0 $p\overline{p}$ measurement at 1.96 TeV and the extrapolated TOTEM $pp$ cross section, rescaled to match the OP of the D0 measurement. The dashed lines show the $1\sigma$ uncertainty band on the extrapolated $pp$ cross section.