Zeros, dips, and signs inppandpp¯elastic amplitudes

Abstract

The dips observed in the differential cross sections of elastic pp and pp scattering are studied in terms of the locations of the zeros of the real and imaginary parts of the amplitude and of the sign of real part at large |t|. It is confirmed that the differences in shapes of the dips in the pp and pp systems are determined by a change of sign of the real tail, which seems to be determined by perturbative QCD contributions.

pp elastic scattering at LHC energies

“…4. This question has been discussed a long time ago [1,2]. The figure shows that Z I and the dip position tend to the (apparently) common finite limit.…”

“…At all energies both dip and peak of the bump are located between Z I and Z (2) R . This behavior is shown in this figure for the energies 2.76 and 8 TeV.…”

“…The figure shows that Z I and the dip position tend to the (apparently) common finite limit. Dips and peaks are always located between Z I and Z (2) R . All energy dependences are simple and can easily be parameterized.…”

“…These expressions give a high precision representation for all data [1][2][3]5,12], with coherent and reliable identification of the real and imaginary amplitudes. Properties and consequences for the energy range above 1 TeV are discussed in the present paper, with particular attention to the experimental LHC energies.…”

“…In high energy pp(p) scattering, the scattering amplitude is usually represented as T (s, t), where t is the four momentum transfer squared. More than a decade ago, Ferreira and Pereira analyzed all available elastic scattering data for energies above 20 GeV [1,2] and all |t|, identifying properties of the amplitudes (zeros, signs, magnitudes), with proper attention given to the real part, which plays a critical role in differential cross sections for mid and large |t| ranges.…”