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recently the phenix collaboration has measured dilepton invariant mass spectrum from @xmath1 to @xmath2 gev in proton - proton collisions at @xmath3 gev@xcite .
it is believed that the main contribution to the dielectron continuum comes from so - called nonphotonic electrons which are produced in semileptonic decays of open charm and bottom mesons . to date , productions of charm and bottom was usually studied by standard measurements@xcite and pqcd calculations@xcite of single leptons inclusive distributions .
such predictions give rather good description of the experimental data , however the theoretical uncertainties are quite large what makes the situation somewhat clouded and prevents definite conclusions .
better statistics at present colliders gives a new possibility to study not only inclusive distributions but also correlations between outgoing particles .
kinematical correlations constitute an alternative method to study open charm and bottom production .
it gives also a great possibility to separate charm and bottom contributions what has a crucial meaning for understanding the character of heavy quarks interactions with the matter created in high energy nuclear collisions@xcite .
the process of nonphotonic electron production has three subsequent stages .
the whole procedure can be written in the following schematic way : @xmath4 where the symbol @xmath5 denotes a generic convolution .
the first term is responsible for production of heavy quarks / antiquarks .
next step is the process of formation of heavy mesons and the last ingredient describe semileptonic decays of heavy mesons to electrons / positrons . -6.5
the inclusive production of heavy quark / antiquark pairs can be calculated in the framework of the @xmath6-factorization@xcite . in this approach transverse momenta of initial partons
are included and the emission of gluons is encoded in so - called unintegrated gluon ( parton ) distributions . in the leading - order approximation within the @xmath6-factorization approach
the differential cross section for the @xmath7 or drell - yan process can be written as : @xmath8 where @xmath9 and @xmath10 are the unintegrated gluon ( parton ) distribution functions ( updfs ) .
there are two types of the lo @xmath11 subprocesses which contribute to heavy quarks production , @xmath12 and @xmath13 .
the first mechanism dominates at large energies and the second one near the threshold . at relatively low rhic energies rather intermediate @xmath14-values
become relevant so the kwiecinski updfs seem applicable in this case@xcite .
the hadronization of heavy quarks is usually done with the help of fragmentation functions .
the inclusive distributions of hadrons can be obtained through a convolution of inclusive distributions of heavy quarks / antiquarks and q @xmath15 h fragmentation functions .
the peterson fragmentation functions are often used in this context@xcite .
recently the cleo and babar collaborations have measured very precisely the spectrum of electrons / positrons coming from the weak decays of @xmath16 and @xmath17 mesons , respectively@xcite .
these functions can in principle be calculated .
this introduces , however , some model uncertainties and requires inclusion of all final state channels explicitly .
an alternative is to use proper experimental input which after renormalizing to experimental branching fractions can be use to generate electrons / positrons in a monte carlo approach .
the @xmath6-factorization method is very useful to study correlations between produced leptons because it can reproduce distributions in kinematical variables related to the transverse momentum of initial partons . in this part of our calculations
we take under consideration not only leptons from open charm / bottom decays but also leptons produced in drell - yan proccess , as well as leptons coming from elastic and inelastic processes initiated by photon - photon fusion . in the case of elastic reaction
we follow exact momentum space calculations with 4-body phase space and for inelastic scattering we have applied unique photon distributions in the nucleon mrst2004@xcite .
we have calculated the kinematical correlations between charged leptons from semileptonic decays of open charm / bottom as well as leptons produced in the drell - yan mechanism in proton - proton collisions at bnl rhic . presented production rates for open charm and bottom 
 were estimated by a detailed analysis of so - called nonphotonic electrons . 
 the distributions for charm and bottom quarks pairs are calculated in the @xmath0-factorization approach with the help of the kwieciski unintegrated parton distributions . 
 the hadronization of heavy quarks is done by means of peterson et al 
 . fragmentation function . 
 the semileptonic decay functions are found by fitting recent semileptonic data obtained by the cleo and babar . 
 we get good description of recent phenix data .