Correlation between transverse momenta in the string fusion model

We obtain an explicit analytic expression for the asymptotic behavior of the coefficient of correlation between the average transverse momenta of particles formed in a given event in rapidity-separated intervals. The asymptotic behavior is found for a large density of strings with their fusion taken into account by introducing a lattice in the transverse plane and using the translation invariance in rapidity of the string decay process at high energies. It is established that unlike the correlation between the momenta of individual particles, the correlation between the average transverse momenta of all particles created in a given event in two separated rapidity intervals does not decrease as the total number of formed strings increases, which makes this type of correlation promising for observation in nuclear collision processes at high energies. We also show that in this limit, the asymptotic behavior of the coefficient of correlation between the average transverse momenta is independent of the variance of the number of particles formed during the string fragmentation unlike previously studied correlations between multiplicities or between the average transverse momenta and the multiplicity.