Odderon Effects Research Articles

Some applications of the eikonal model with Coulomb and curvature corrections in pp and p¯p scattering

Using a simple eikonal approach to the treatment of Coulomb-nuclear interference and form-factors effects and taking into account the curvature effects in high-energy $pp$ and $\overline{p}p$ scattering, we determine the basic parameters $B$, $\ensuremath{\rho}$, and ${\ensuremath{\sigma}}_{\mathrm{tot}}$ from fits to experiment at $W=\sqrt{s}=53\text{ }\text{ }\mathrm{GeV}$, 62.3 GeV, 8 TeV, and 13 TeV. We then investigate the differential cross sections in the dip region for $pp$ and $\overline{p}p$ elastic scattering at $W=53\text{ }\text{ }\mathrm{GeV}$ and 1.96 TeV. We find that the results of the basic parameters calculated using the simple eikonal approach agree well with the values determined in other analyses. We also find that Coulomb effects are significant in the dip region at 53 GeV and 1.96 TeV, and must be taken into account in searches for odderon effects through cross section differences in that energy region.

The ReBB model and its H(x) scaling version at 8 TeV: Odderon exchange is a certainty

The Real Extended Bialas-Bzdak (ReBB) model is shown here to describe, in the 0.37 le -t le 1.2 GeV^2 region, the proton-proton elastic differential cross section data published by the TOTEM Collaboration at LHC at sqrt{s} = 8 TeV center of mass energy. In this kinematic range, corresponding to the diffractive minimum-maximum region, a model-dependent Odderon signal higher than 18 sigma is obtained by comparing the ReBB model prediction for the p{bar{p}} elastic differential cross section to this TOTEM measured pp elastic differential cross section data at 8 TeV. However, when combining this signal with the Odderon signals from the ReBB model in the 0.37 le -t le 1.2 GeV^2 four-momentum-transfer range at sqrt{s} = 1.96, 2.76 and 7 TeV, it turns out that the combined significance is dominated not by the new 8 TeV but by that of earlier 7 TeV TOTEM data, that carry an even larger Odderon effect. Thus, in any practical terms, within the framework of the ReBB model, the Odderon signal in the limited 0.37 le -t le 1.2 GeV^2 and 1.96 le sqrt{s} le 8 TeV kinematic region is not a probability, but a certainty. We show also that the H(x) scaling version of the ReBB model works reasonably well at 8 TeV in the 0.37 le -t le 0.97 GeV^2 region.

Isolating the Odderon in central production in high energy pA and AA collisions

We study the rapidity dependence of the central exclusive production cross sections of C-even mesons in pA and AA collisions, where A is a heavy ion. We observe qualitatively different behaviour of the contributions arising from gamma -Odderon and Pomeron–Pomeron fusion mechanisms. This can be used to extract the Odderon signal from the events of f_2 mesons exclusively produced in the forward region. Estimates, obtained using expected values of the Odderon cross section, indicate that the gamma -Odderon contribution may exceed by a few times the Pomeron-induced background in Pb–Pb collisions. Moreover, the Odderon effect can be clearly seen in terms of the asymmetry in pA and AA collisions with the beam and target reversed. It is particularly interesting to note that the asymmetry for gamma -Odderon fusion reaches its maximum value close to 1 in the forward direction, whereas the asymmetry for the Pomeron–Pomeron fusion contribution is small. The role of additional interactions of the f_2 meson with nucleons in the heavy ion, and also the contributions from secondary Reggeons, are estimated. The photon–Odderon contribution has a large normalisation uncertainty but the enhanced cross-section in the forward region combined with a large asymmetry increases the chance of experimentally detecting the Odderon.

Odderon effects in the differential cross-sections at Tevatron and LHC energies

In the present paper, we extend the Froissaron-Maximal Odderon (FMO) approach at t different from 0. Our extended FMO approach gives an excellent description of the 3266 experimental points considered in a wide range of energies and momentum transferred. We show that the very interesting TOTEM results for proton–proton differential cross-section in the range 2.76–13 TeV, together with the Tevatron data for antiproton–proton at 1.8 and 1.96 TeV give further experimental evidence for the existence of the Odderon. One spectacular theoretical result is the fact that the difference in the dip-bump region between {bar{p}}p and pp differential cross-sections is diminishing with increasing energies and for very high energies (say 100 TeV), the difference between {bar{p}}p and pp in the dip-bump region is changing its sign: pp becomes bigger than {bar{p}}p at |t| about 1 GeV^2. This is a typical Odderon effect. Another important – phenomenological – result of our approach is that the slope in pp scattering has a different behavior in t than the slope in {bar{p}}p scattering. This is also a clear Odderon effect.

L\'evy Imaging of Elastic Hadron--Hadron Scattering: Odderon and Inner Structure of the Proton

A novel model-independent L\'evy imaging method is employed for reconstruction of the elastic $pp$ and $p\bar p$ scattering amplitudes at low and high energies. The four-momentum transfer $t$ dependent elastic slope $B(t)$, the nuclear phase $\phi(t)$ as well as the excitation function of the shadow profile $P(b)$ have been extracted from data at ISR, Tevatron and LHC energies. We found qualitative differences in properties of $B(t)$ and $\phi(t)$ between $pp$ and for $p\bar p$ collisions, that indicate an Odderon effect. A proton substructure has also been identified and found to have two different sizes, comparable to that of a dressed quark at the ISR and of a dressed diquark at the LHC energies, respectively.

Odderon and proton substructure from a model-independent L\xe9vy imaging of elastic pp and pbar{p} collisions

We describe a new and model-independent Lévy imaging method of quality fits to the published datasets and reconstruct the amplitude of high-energy pp and pbar{p} elastic scattering processes. This method allows us to determine the excitation function of the shadow profile P(b), the elastic slope B(t) and the nuclear phase phi (t) functions of pp and pbar{p} collisions directly from the data. Surprisingly, notable qualitative differences in B(t) for pp and for pbar{p} collisions point towards an Odderon effect. As a by-product, we clearly identify the proton substructure with two different sizes at the ISR and LHC energies, that has striking similarity to a dressed quark (at the ISR) and a dressed diquark (at the LHC). We present model-independent results for the corresponding sizes and cross-sections for such a substructure for the existing data at different energies.

Convergence properties of Lévy expansions: implications for Odderon and proton structure

We detail here the convergence properties of a new model-independent imaging method, the Lévy expansion, that seems to play an important role in the analysis of the differential cross section of elastic hadron-hadron scattering.We demonstrate, how our earlier results concerning the Odderon effects in the differential cross-section of elastic proton-proton and proton-antiproton scattering as well as those related to apparent sub-structures inside the protons were obtained in a convergent and stable manner.

Photoproduction of π + π − pairs in a model with tensor-pomeron and vector-odderon exchange

We consider the reaction (gamma p) to (pi+ pi- p) at high energies. Our description includes dipion production via the resonances rho, omega, rho-prime and f2, and via non-resonant mechanisms. The calculation is based on a model of high energy scattering with the exchanges of photon, pomeron, odderon and reggeons. The pomeron and the C=+1 reggeons are described as effective tensor exchanges, the odderon and the C=-1 reggeons as effective vector exchanges. We obtain a gauge-invariant version of the Drell-Soeding mechanism which produces the skewing of the rho-meson shape. Starting from the explicit formulae for the matrix element for dipion production we construct an event generator which comprises all contributions mentioned above and includes all interference terms. We give examples of total and differential cross sections and discuss asymmetries which are due to interference of C=+1 and C=-1 exchange contributions. These asymmetries can be used to search for odderon effects. Our model is intended to provide all necessary theoretical tools for a detailed experimental analysis of elastic dipion production for which data exist from fixed target experiments, from HERA, and are now being collected by LHC experiments.

Possible odderon effects in inclusive hadron production

We consider the possible contribution of odderon (reggeon with αOdd(0)∼1 and negative signature) exchange to the differences in the inclusive spectra of particle and antiparticle in the central region. The energies and/or accuracy of the currently available experimental data do not allow for a clear conclusion on the presence of an odderon component, but the upcoming LHC data should finally elucidate the question of the existence of the odderon.

The importance of the measurement of ϱ for the understanding of high energy hadron-hadron scattering

We first show, both on general and phenomenological grounds, why the most suitable parameter for exploring odderon effects in the present energy range is the ϱ-parameter (the ratio of the real over the imaginary part of the forward hadron amplitude). We perform an almost model-independent analysis of the experimental data by taking into account the analyticity constraints and the assumption og maximality. Using the maximal odderon approach as a guide, we establish the following very constrained bound at √s=546 GeV: ϱ pp ≲0.23 . Our bound leads to the conclusion that an experimental UA4/2 value centred around 0.20, say 0.20±0.02, will constitute a strong and unambiguous signal of odderon effects and will indicate that at high energy σ T pp > σ T p p .