One-particle inclusive distribution in the unitarized pomeron models

1. Motivation - topicality of presented question is rided by forthcoming extensive studies of diffractive processes in experiments on LHC. Measuring of elastic and inelastic processes, which are determined by exchange of pomeron at LHC energies, are going to be carried out. In spite of numerous investigations in this field, the model is still unclear and there is a number of unsolved problems. The aim – to study different ways of restoring unita-rityof pomeron contribution to scattering amplitude and to show a possibility to reproduce main features of the high energy data in the context of considered models . Pomeron physics Inclusive particle production Due to generalized optical theorem differential cross section of one-particle inclusive production in the central kinematical region is related to shown diagram. More exactly for simple pomeronpole: where , - coupling vertices, , - transferedmomentum and maximal value of rapidity of inclusive hadron. The multiplicity of hadrons is given by Due to Regge theory asymptotic ( ) behavior of the scattering amplitude is Such behavior violates unitarity condition, which states, that the total cross-section Thus the model can only be considered as phenomenological tool and must be improved to restore unitarity. Summing multipomeron diagrams allows to avoid violation of unitarity bound. As a re- sult we can obtain the following expression for total cross section: It turned out, that, this expression coincides with an amplitude of one triple pole exchange. This result leads to a possibility to consider more complicated singularities of partial amplitude just from the beginning. Theory One-particle inclusive distribution in the unitarizedpomeron models Pomeron hardness Considering arbitrary hardness of pomeron we can obtain If pomeron contribution to partial amplitude at t=0 proportional to a then and Experimental data Triple pole • We would like to demonstrate a possibility of considered model to to reproduce main features of the high energy data: • slope effect – changing with energy slope, which can be • explained due to the subasymptotic contributions; • changing an exponential increasing at small • transverse momentum for a power like one at • higher . • However another set of data, namely is more interes- • ting for our aim. It can be obtained from : • Explicit form of - dependence is not crucial, we are interested in dependence on rapidity. We parameterize in a some form to reproduce existing data: Generally there are four terms to be accounted in this model: triple (t), double (d) and simple (p) pomeron poles with intercept sdffdf together with f-reggeon. where , and . . Double pole Experimental data In this case we take into account only dipole, simple pomeron pole and f-reggeon. Simplepole In simple pole model we consider two pomeron poles: one (“supercritical”) has intercept , and another has . The data fit We consider the data on at = 200, 540, 630, 900, 1800 GeV (240 points) and on normalized to . Parameters of the model as well as obtained and description of the data is demonstrated. Theoretical curves in three models are very close each to other, at least for energies, where data exist. In fact parameters of the tripole and simple models mimic the dipole pomeron model. However, a difference between the models’ predictions is Increasing with energy. It can be seen on the energy dependence of and . C o n c l u s I o n s Thus we have shown that the high energy experimental data on one-particle inclusive distribution can be described well in the models of unitarizedpomeron, which do not violate unitarity restrictions. The dipole (tripole) pomeron model, correspondingly lead to aaaaaaaassssssssssaaaaa and . . These models predict a small difference in and at low LHC energies which, however, is increasing with energy. • 1 • 1 • 1 • 2 • 2 • A.Alkin , E. Martynov , O. Romanetc , V. Pauk • BogolyubovInstitute for Theoretical Physics, • Metrologichna 14b, Kiev, UA-03680, Ukraine • National Taras Shevchenko University of Kiev, • AcademicaGlushkova 02/1, Kiev, UA-03022, Ukraine • e-mail: paukvp@gmail.com • 2