International Journal of Modern Physics A Vol. 19, No. 26 (2004) 4455–4473 c  World Scientific Publishing Company SEARCH FOR ODDERON IN THEORY AND EXPERIMENT FAZAL-E-ALEEM, HARIS RASHID, SOHAIL AFZAL TAHIR, M. ALAM SAEED and M. QADEER AFZAL Centre for High Energy Physics, University of the Punjab, Lahore-54590, Pakistan Received 12 September 2003 The presence of Odderon at high energy has been in question for quite some time. We have confronted the Odderon description to the available data especially for pp and ¯ pp scattering including the most recent measurements by UA4/2, E710, CDF and E811 Collaborations. The Odderon in perturbative and nonperturbative QCD has also been discussed along with some phenomenological approaches. A comparison of the Odderon description with other models has also been made for p(¯ p)p data including the measurements from cosmic ray, which corresponds to the LHC energy of 14 TeV. Our study especially focuses on the measurements at RHIC and LHC and the presence or otherwise of Odderon. Keywords : Odderon; Pomeron; differential cross-section. 1. Introduction There has been a hot pursuit for the knowledge of Odderon for the last three decades. Theorists as well as experimentalists are exploring it in both elastic and deep inelastic scattering. A lot of work has been carried out in theory and the object has firm footings in perturbative QCD. Work has also been published elaborating nonperturbative treatment of the same. Search for Odderon at HERA has not succeeded. With the possibility of observing Odderon in deep inelastic scattering, extensive theoretical work was carried out in the recent past in this direction. These attempts are briefly described in the short reviews. 1,2 With no success at HERA, focus is now shifting on observing Odderon at RHIC and LHC where measurements for pp elastic scattering will be undertaken in the GeV and TeV range, providing us an opportunity to compare some of the results with ¯ pp scattering. In this paper we will take up different aspects of the Odderon study with a focus on pp and ¯ pp scattering. The paper is subdivided into six parts: Experimental data, Odderon description, Odderon and QCD, Phenomenological studies, Search for Odderon in experiment and Conclusions. 4455