The 'Salpeter Equation ' which has long been known as the 3D version of the 4D Bethe-Salpeter Equation under the Instantaneous Approximation, has a well-defined rationale that stems from the half-century old Markov-Yukawa Transversality Principle (M Y T P ) which not only effects an exact 3D reduction from the original (4D) BS form, but also provides an equally exact reconstruction of the 4D BS amplitude in terms of 3D ingredients. The second aspect which is new, opens up a vista of applications to transition amplitudes as 4D loop integrals.

Previous detailed studies of direct photon production from both fixed-target and collider experiments have witnessed a pattern of deviation between the measured inclusive cross sections and the corresponding theoretical expectations in the low transverse momentum (p T ) regime. Most data sets display steeper p T dependence than the next-to-leading-order ͑NLO͒ perturbative QCD ͑PQCD͒ calculations with standard choices of scales and parton distribution functions in this region. A simple implementation of higher-order soft-gluon corrections to the NLO PQCD predictions significantly improves the agreement between data and theory. This interesting feature motivated us to investigate the DO " and CDF measurements of inclusive photon cross section at ͱs ϭ1.8 TeV from the run 1b and also at ͱsϭ630 GeV. We use the latest updated parton distribution function CTEQ6M in the NLO QCD calculations for direct photon cross section to describe the data. The conventional theoretical uncertainties originating from scale dependence and gluon distributions have been illustrated. We estimate the impact of additional soft-gluon radiation on the direct photon production using PYTHIA ͑LO PQCD͒, which adds transverse momentum k T to initial-state partons through a Gaussian smearing. The impact of k T effects on the discrepancy in the low-p T region is explored using a phenomenological model, wherein we merge the NLO calculations with k T correction factors. We show that this approach provides a much more acceptable description of the Fermilab Tevatron data.

Study of direct photon production in high-energy hadronic collisions provides a clean tool for testing the essential validity of perturbative quantum chromodynamics ͑PQCD͒ predictions as well as for constraining the gluon distribution of nucleons. These attractive considerations prompted us to study the characteristics of direct photons at CERN LHC energy (ͱsϭ14 TeV). In order to validate our simulation results, we first describe the direct photon data at ͱsϭ1.8 TeV in the central pseudorapidity () region. We used next-to-leading-order ͑NLO͒ QCD calculations and leading-order ͑LO͒ PYTHIA estimates with the latest parton distribution function, CTEQ5M1. At ͱsϭ14 TeV, the LO and NLO QCD predictions for direct photon cross section are presented as a function of transverse momentum of photon (p T ) in the kinematical region 20 GeVϽp T Ͻ400 GeV and ͉͉Ͻ3. The sensitivity of the theoretical predictions to the choice of renormalization scales and gluon distributions is also demonstrated. The pseudorapidity () and cone size dependence of the direct photon cross section is also discussed.