Soft Pomeron in light of the LHC correlated data

The LHC has released precise measurements of elastic proton-proton scattering that provide a unique constraint on the asymptotic behavior of the scattering amplitude at high energies. Recent reanalyses of part of these data indicate that the central values of some forward quantities would be different than initially observed. We introduce correlation information between the original and the reanalyzed data sets in a way suitable for a global fitting analysis of all data. The careful treatment of correlated errors leads to much less stringent limits on the $\rho$ uncertainty and sets up the stage for describing the forward data using a scattering amplitude dominated by only crossing-even terms. In the light of these correlated data, we determine the parameters of the soft Pomeron from the Regge theory. We use Born-level and eikonalized amplitudes. In the Born-level case, we estimate the contribution of the double Pomeron exchange, while in the latter case we investigate the role of the eikonalization in both the one- and two-channel models. The role of the proton-Pomeron vertex form and of the nearest $t$-channel singularity in the Pomeron trajectory receives particular attention. We discuss the implications of our results and present predictions for the total cross section and the $\rho$ parameter in proton-proton collisions at LHC and cosmic ray energies.

Figure 1

Set of correlated data used in our global fitting analyses. The inner error bars are the original (published) uncertainties and the outer error bars are the uncertainties after introducing correlation information. The squares, circles, and triangles correspond, respectively, to the energies of 7, 8, and 13 TeV. The solid symbols represent the TOTEM data, while the open ones represent the ATLAS results.

Figure 2

Total cross section [(a) and (b)] and ratio of the real to imaginary part of the forward scattering amplitude [(c) and (d)] for $pp$ (•) and $\overline{p}p$ (∘) channels. The solid line shows the results obtained using the BI or BII or $\mathrm{BI}+\mathbb{P}\mathbb{P}$ models, while the dashed line shows the results obtained using the BIII model. Also shown the predictions for cosmic ray energies.

Figure 3

Total cross section [(a) and (b)] and ratio of the real to imaginary part of the forward scattering amplitude [(c) and (d)] for $pp$ (•) and $\overline{p}p$ (∘) channels. The solid, dashed, and dotted lines show the results obtained using the OI, OII, and OIII models, respectively. Also shown the predictions for cosmic ray energies.

Figure 4

Total cross section [(a) and (b)] and ratio of the real to imaginary part of the forward scattering amplitude [(c) and (d)] for $pp$ (•) and $\overline{p}p$ (∘) channels. The solid, dashed, and dotted lines show the results obtained using the TI, TII, and TIII models, respectively. Also shown the predictions for cosmic ray energies.

Figure 5

Total cross section [part (a)] and ratio of the real to imaginary part of the forward scattering amplitude [part (b)] for $pp$ (•) channel. The solid, dashed, and dotted lines show the results obtained using the BIII, OIII, and TIII models, respectively. Also shown the predictions for cosmic ray energies.

Figure 6

The elastic differential cross section for $pp$ (•) channel. In parts (a)–(c), we show the curves of $d{\sigma }^{pp}/dt$ for the Born level, one- and two-channel eikonal models, respectively. A comparison among the differential cross sections from the models BIII (solid), OIII (dashed), and TIII (dotted) is shown in part (d).