Black disk, maximal Odderon and unitarity

Abstract

We argue that the so-called maximal Odderon contribution breaks the 'black disk' behaviour of the asymptotic amplitude, since the cross section of the events with Large Rapidity Gaps grows faster than the total cross section. That is the 'maximal Odderon' is not consistent with unitarity.Recently the TOTEM collaboration at the LHC has published the results of the first measurements at √ s=13 TeV of the pp total cross section σ tot = 110.6 ± 3.4 mb [1] and of the ratio of the real-to-imaginary parts of the forward pp-amplitude, ρ =Re/Im= 0.10 ± 0.01 [2]. Since the latter value appears to be sufficiently smaller than that predicted by the conventional COMPETE parametrization (ρ = 0.13 − 0.14) [3], it may indicate either a slower increase of the total cross section at higher energies or a possible contribution of the odd-signature amplitude. (Note that within the COMPETE parametrization the odd-signature term is described by secondary Reggeons and dies out with energy.) Note that a C-odd amplitude, which arises from the so-called Odderon, and which depends weakly on energy, is expected in perturbative QCD 1 , see in particular [4,5,6] and for reviews e.g. [7,8]. However the naive estimates show that its contribution is rather small; say, ∆ρ Odd ∼ 1mb/σ tot < ∼ 0.01 [9] at the LHC energies.On the other hand, it is possible to introduce the Odderon phenomenologically as an object which does not violate first principles and the axiomatic theorems. In fact it was stated in [10] that the new TOTEM result is a definitive confirmation of the experimental discovery of the Odderon in its maximal form.

Several Effects Unexplained by QCD

“…This decrease is sometimes interpreted as an indication on observation of Odderon -the C-odd analogue of Pomeron [26]. However there are some arguments [27] that the unitarity might be violated in this interpretation. Anyway, these values definitely show that the contribution of the real part of the amplitude to the differential cross section (quadratic in ρ) is at the level of about 1% inside the diffraction cone.…”

Pomeron/glueball and odderon/oddball trajectories

“…The nature of the odderon, and the behaviour of its trajectory, are still shrouded in mystery [4,5,6]. The experimental signatures of odderon exchanges continue to be hotly debated within the community [7,8,9].…”

Proton-proton forward scattering at the LHC

“…More specifically, in perturbative QCD the Odderon can be associated to a colorless C-odd t-channel state with an intercept at or near one. The TOTEM results have since then triggered an intense debate on the question of whether or not the combined behavior of σ tot and ρ at high energies is actually a manifestation of the Odderon [14,16].…”