Large Mass Time - like Muon Pairs in Radronic Interactions ?

Utilizing a simple field-theoretic model we consider the production of time-like muon pairs via a massive virtual photon in high energy hadronic collisions. We predict the differential cross section m'tbe mass-squared of the muon pair as well as the total cross section. We find that our form factors do not possess the analogue of the Bjorken scaling associated with deep inelastic electron scattering, but are scale functions multiplied by the usual Bremsstrahlung factor < t average >/S.We consider the interaction initiated by a hadron (proton or pion) p(n) + nucleon-(,u'/A-) + (hadronic states) (1) I where the muons are produced via a very virtual photon. We investigate the asymptotic region analogous to that of deep inelastic electron scattering. In this kinematic region the invariant mass-squared of the muon pair q2 and the center of mass energy squared, s, of the initial hadrons are both very large,) We take fl and 1J;' to be the four momenta of the two initial hadrons and q' to be four momentum of the muon pair (see Figure 1). We work in the kinematic region where the variables q2, g,P, qP1, P-P1-~0 but the various ratios of these variables are held finite; i. e. , the ratios (q'/P.P$, (qP,/q'), etc. are all finite. It is our, hope that these limits are relevant in the experimentally accessible kinematical regions. Jf process (1) is summed over all hadronic states and averaged over initial spins then the differential cross section da l.J+l-J-is proportional to the following tensor: Wpy = (2) (2) {d4neSiqx< PePl I Jcl(x)JV(0)I PapI T (2) + " zc ((P-~q~(Pl-~q~+P~Pl)..(gU~jwl 2M where M is the nucleon mass and Jp(x) is the full electromagnetic current. The matrix element involved in Eq. (2) is similar to the case considered by Bjorken for inelastic electron scattering-3-except that the initial state contains two hadrons rather than one photon, and the mass of the virtual photon is time-like rather than space-like'. It will turn out that the form factors analogous to " W3 and Wl of deep inelastic electron scattering, namely (q*P)W2A, (q*Pl)WzB, ,/mW2C, and Wl do not scale in the Bjorken sense but are functions of the form average S where < t > average w (300 MeV)' is the average momentum transfer in purely hadronic interactions. In an attempt to predict the total muon pair cross section as well as the differential cross section in the photon …