Development of the Baldin approach to analysis of hadronic and nuclear processes at high energies
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evelopment of the Baldin Approach to Analysis of Hadronic and Nuclear Processes at High Energies1 A. Malakhov*, D. Artemenkov, and G. Lykasov Joint Institute for Nuclear Research, Dubna, Moscow oblast, 141980 Russia *e-mail: [email protected] Abstract⎯This article presents the development of the A.M. Baldin approach using a description relativistic nuclear interactions in the four velocity space. This approach allows one to perform calculations of pion yields in hadron-hadron interactions in the central rapidity region depending on the transverse momentum. Results of our calculations have coincided with experimental data in a wide energy range with high precision. This approach gives a good description of the experimental results at high (LHC) and at lower energies (the Nuclotron). DOI: 10.1134/S1063779617060375
1. INTRODUCTION In the 70-ies of the previous century by the initiative of academician A.M. Baldin in Dubna at the Laboratory of High Energies (LHE) of the Joint Institute for Nuclear Research (JINR) a new research direction—relativistic nuclear physics, – was founded. This was, first of all, conditioned by accelerating the relativistic deuterons at the energy of 4.5 GeV/nucleon at the Synchrophasotron of the LHE, where academician A.M. Baldin was the director at that time. In addition, A.M. Baldin in [1] made a prediction of the so-called nuclear cumulative effect, subsequently discovered at the Synchrophasotron by the group of professor V.S. Stavinskiy [2]. All this allowed one to begin intensive studies of relativistic nucleus interactions at energies up to 4.5 GeV/nucleon. Later A.M. Baldin was invited to consider relativistic nuclear interactions in the four dimension velocity space [3]. The approach of studying relativistic nuclear interactions in the four dimension velocity space proved to be very fruitful [4]. This article presents further development of this approach. 2. THE PARAMETER OF SELF-SIMILARITY In their time together with A.M. Baldin and A.I. Malakhov published an article [5] with the predictions of the ratios of the particle outputs in the collisions of nuclei at high energies.
Let us put down the interaction of nucleus I with nucleus II resulting in the inclusive particle 1 production as follows:
I + II → 1 + …
(1)
According to Baldin’s assumption more than one nucleon in the nucleus I can participate in the interaction 1. The value of N I = λ ⋅ AI is the efficient number of nucleons inside the nucleus I , participating in the interaction which is called the cumulative number. Its values lie in the region of 0 ≤ N I ≤ AI . The cumulative area complies with N I > 1. Of course, the same situation will be for the nucleus II , and you can enter the cumulative number of N II . For reaction (1) with the production of the inclusive particle 1, we can write the law of conservation of four-momentum in the following form:
(N I PI + N II PII − p1) 2 = (N I m0 + N II m0 + M ) 2, (2) where N I and N II are cumulative numbers (the number of nucleons involved in the interaction); PI , PII , p1 a
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