A detailed study of fragmentation of vector mesons at the next-to-leading order (NLO) is given for e + e − scattering. A model with broken SU (3) symmetry uses three input fragmentation functions α(x, Q 2 ), β(x, Q 2 ) and γ(x, Q 2 ) and a strangeness suppression parameter λ to describe all the light quark fragmentation functions for the entire vector meson octet. At a starting low energy scale of Q 2 0 = 1.5 (GeV) 2 for three light quarks (u, d, s) along with initial parameterization, the fragmentation functions are evolved through DGLAP evolution equations at NLO and the crosssection is calculated. The heavy quarks contribution are added in appropriate thresholds during evolution. The results obtained are fitted at the momentum scale of √ s = 91.2GeV for LEP and SLD data. Good-quality fits are obtained for ρ, K * , ω and φ mesons, implying the consistency and efficiency of this model that explains the fragmentation functions of vector mesons both at the leading and the next to leading order in QCD.

Inclusive hadro production in e + e − annihilation processes is examined to study the fragmentation process. A broken SU(3) model is used to determine the quark and gluon fragmentation functions of octet vector mesons, ρ and K * , in a simple way with an SU(3) breaking parameter λ. These are expressed in terms of just two light quark fragmentation functions, V (x, Q 2 ) and γ(x, Q 2 ) and the gluon fragmentation function D g (x, Q 2 ). These functions are parameterized at the low input scale of Q 2 0 = 1.5 GeV 2 , evolved through LO DGLAP evolution including charm and bottom flavour at appropriate thresholds, and fitted by comparison with data at the Z-pole.The model is extended with the introduction of a few additional parameters to include a study of singlet-octet mixing and hence ω and φ fragmentation. The model gives good fits to the available data for x 0.01, where x is the scaled energy of the hadron. The model is then applied successfully to ω, φ production in p p collisions at the Relativistic Heavy Ion Collider, RHIC; these data form an important base-line for the study of Quark Gluon Plasma in heavy nucleus collisions at RHIC, and also in future at the LHC.

A combined analysis of both e + e − (LEP, SLD) and p p (RHIC-PHENIX) hadroproduction processes are done for the first time for the vector meson nonet at the next-to-leading order (NLO) using a model with broken SU(3) symmetry. The scale (p T ) and rapidity (y) dependence of the differential cross section for ω and φ mesons of the p p data are also discussed. The input universal quark (valence and singlet) fragmentation functions at a starting scale of Q 2 0 = 1.5 GeV 2 , after evolution, have values that are consistent with the earlier analysis for e + e − at NLO. However, the universal gluon fragmentation function is now well determined from this study with significantly smaller error bars, as the p p hadroproduction cross section is particularly sensitive to the gluon fragmentation since it occurs at the same order as quark fragmentation, in contrast to the e + e − hadroproduction process. Additional parameters involved in describing strangeness and sea suppression and octet-singlet mixing are found to be close to earlier analysis; in addition, a new relation between gluon and sea suppression in K * and φ hadroproduction has been observed.

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