How can the odderon be detected at RHIC and LHC?

Abstract

The Odderon remains an elusive object, 33 years after its invention. The Odderon is now a fundamental object in QCD and CGC and it has to be found experimentally if QCD and CGC are right. In the present paper, we show how to find it at RHIC and LHC. The most spectacular signature of the Odderon is the predicted difference between the differential cross-sections for proton-proton and antiproton-proton at high s and moderate t. This experiment can be done by using the STAR detector at RHIC and by combining these future data with the already present UA4/2 data. The Odderon could also be found by ATLAS experiment at LHC by performing a high-precision measurement of the real part of the hadron elastic scattering amplitude at small t. Paris 6 et Paris 7, Associée au CNRS The Odderon is defined as a singularity in the complex J-plane, located at J = 1 when t = 0 and which contributes to the odd-under-crossing amplitude F − . The concept of Odderon first emerged in 1973 in the context of asymptotic theorems [1]. 7 years later, it was possibly connected with 3-gluon exchanges in perturbative QCD [2-4], but it took 27 years to firmly rediscover it in the context of pQCD [5]. The Odderon was also rediscovered recently in the Color Glass Condensate (CGC) approach [6,7] and in the dipole picture [8].One can therefore assert that the Odderon is a crucial test of QCD.On experimental level, there is a strong evidence for the non-perturbative Odderon: the discovery, in 1985, of a difference between (dσ/dt)p p and (dσ/dt) pp in the dip-shoulder region 1.1 < |t| < 1.5 GeV 2 at √ s = 52.8 GeV [9,10]. Unfortunately, these data were obtained in one week, just before ISR was closed and therefore the evidence, even if it is strong (99,9 % confidence level), is not totally convincing. Moderate evidence for the existence of the non-perturbative Odderon also comes from the dramatic change of shape in the polarization in π − p → π 0 n, in going form p L = 5 GeV/c [11,12] to p L = 40 GeV/c [13], but this Odderon corresponds to a different type of Odderon as compared with the one identified in pQCD. Finally, weak evidence for the non-perturbative Odderon comes from a strange structure seen in the UA4/2 dN/dt data forpp scattering at √ s = 541 GeV, namely a bump centered at |t| = 2 · 10 −3 GeV 2 [14]. This structure could correspond to oscillations of a very small period due to the presence of the Odderon [15]. All the above mentioned experimental results point towards the maximal Odderon [1, 16], a special case corresponding to the maximal asymptotic (s → ∞) behavior allowed by the general principles of strong interactions: σ T (s) ∝ ln 2 s, as s → ∞ (1) and ∆σ(s) ≡ σp p T (s) − σ pp T (s) ∝ ln s, as s → ∞ .Interestingly enough, an important stream of theoretical papers concern precisely the maximal behavior [1], which was first discovered by Heisenberg in 1952 [17] and later proved, in a more rigorous way by Froissart and Martin [18,19]. Half a century after the discovery of Heisenberg, this maximal behavior (1) was also proved in the contex...

Introduction to the physics of the total cross section at LHC

“…At LHC running at √ s = 14 TeV (LHC14) the position of the dip is expected at |t| ∼ 0.35 GeV 2 , to be compared with the position at the ISR at |t| 1.3 GeV 2 and the position at LHC7 reported by TOTEM at |t| ∼ 0.53 GeV 2 . We will discuss now in detail the parametrisation in [209]. The starting point is the maximal asymptotic behaviour of the total cross sections, consistent with data, i.e.…”

“…To discuss the proposal to detect the Odderon at RHIC and LHC by Avila, Gauron and Nicolescu (AGN2006) [209], we start with the model by Avila, Campos, Menon and Montanha (ACMM2006) which incorporates both the Froissart limiting behavior as well as Pomeron and Regge exchanges [210].…”

“…Avila, Gauron and Nicolescu (AGN2006) [209] examine the data in light of the possible existence of the Odderon, a QCD effect corresponding to a singularity in the complex Fig. 72 Data for the elastic differential cross section forp p scattering from the three experiments at the Tevatron, compared with UA4 data, from [323].…”

“…With such parametrisation, at LHC energies a dip is expected both for pp andp p scattering, something which cannot be proved experimentally at LHC. In [209] the suggestion is advanced to try to check the presence of the dip at RHIC, namely at √ s = 500 GeV. The AGN2006 analysis describes the ISR data at √ s = 52.8 GeV where both pp andp p elastic differential cross sections were measured.…”

“…According to [209], the choice of a maximal behaviour of the total cross section is not necessarily implying that the imaginary part of F − (s, 0) is also maximal, i.e. that F − (s, 0) ∼ log s, but, the authors argue, it is the natural choice that strong interactions be as strong as possible.…”