Analysis and implications of precision near-forward TOTEM data

Abstract

Very precise data on elastic proton-proton scattering at √ s = 7, 8 and 13 TeV have been obtained by the TOTEM group at LHC in the near-forward region (momentum transfers down to |t| = 6 × 10 −4 GeV 2 at √ s = 8 TeV and to |t| = 8 × 10 −4 GeV 2 at √ s = 13 TeV). The Coulomb-nuclear interference has been measured with sufficient accuracy for TOTEM to establish the falloff of the ρ parameter with increasing energy. The predictions from a previously studied model are shown to be in good agreement with the data and thus allow us to draw rather firm conclusions about the structure of the near-forward nuclear amplitude. We point out that due to a zero in the real part of the nuclear amplitude occurring at a very small momentum transfer-that can migrate into the Coulomb-nuclear interference (CNI) region at higher energies-much care is needed in extracting the numerical value of ρ for such energies. Thus, the true value of ρ would be higher than the TOTEM value for ρ found under the hypothesis that the real part of the elastic nuclear amplitude is devoid of such a zero in the CNI

The elastic differential pp cross-section at 13 TeV: an empirical model analysis

“…In a recent paper [5], we have presented results for the CNI region at 8 and 13 TeV from the empirical model described above. The basic observation following from this model and relevant to the study of the ρ parameter, is that besides the well-known diffraction dip due to a zero in the absorptive part of the amplitude, there is also a zero in the real part of the nuclear amplitude [19].…”

“…5, with the asymptotics as discussed above, we now define 4-sets of rotated amplitudes through the following substitution possibilities. For further details, see [5]. We have considered all four possibilities with the following four sets of nuclear amplitudes:…”

“…It was shown in [5] that both the real and imaginary parts of the nuclear amplitude are practically identical for A 2 and A 3 , but they are substantially different from A o and A 1 . Moreover, the predictions from the amplitudes A 2 and A 3 are in remarkable accord with the TOTEM data in the CNI region whereas those from A o and A 1 are decidedly inferior.…”

“…The value of the parameters follows the parametrization in Eqs. (5)(6)(7)(8)(9)(10). The result is shown in the left panel and indicates that, while the small −t behaviour is satisfactorily reproduced, the model fails both at the dip and beyond.…”

“…Thus, we now have data for the modulus (through the elastic differential cross-section) and the phase (through CNI) of the near forward nuclear amplitude. In a recent paper [5], we have analyzed the CNI region thoroughly pointing out certain subtleties involved in extracting a value of ρ. We shall elaborate upon it later in the present paper.…”