J/ψ Production from Electromagnetic Fragmentation in Z decay

The rate for Z0 → J/ψ+ l+l− is suprisingly large with about one event for every million Z0 decays. The reason for this is that there is a fragmentation contribution that is not suppressed by a factor of M2 ψ/M 2 Z . In the fragmentation limit MZ → ∞ with Eψ/MZ fixed, the differential decay rate for Z 0 → J/ψ + l+l− factors into electromagnetic decay rates and universal fragmentation functions. The fragmentation functions for lepton fragmentation and photon fragmentation into J/ψ are calculated to lowest order in α. The fragmentation approximation to the rate is shown to match the full calculation for Eψ greater than about 3Mψ. Introduction Fragmentation is the decay of a high transverse momentum parton into a collinear hadron. The differential cross section for the inclusive production of such a hadron in e+e− annihilation factors into differential cross sections dσ̂ for the production of large transverse momentum partons and fragmentation functions D(z) [1]. The fragmentation function gives the probability for the splitting of a parton into the hadron with momentum fraction z. These functions are independent of the subprocess that creates the fragmenting particle, and can be evolved to any scale via the Altarelli-Parisi evolution equations. It has recently been shown that it is possible to calculate the fragmentation functions for heavy quarkonium states using perturbative quantum chromodynamics (QCD) [2]. Fragmentation functions for several of these states have been calculated explicitly [2, 3, 4, 5, 6]. In particular the paper of Braaten, Chueng and Yuan on charm quark fragmentation [3] is most relevant to the work presented here. Their analysis focuses on decays of the Z into hadrons showing that charmonium production is dominated by charm quark fragmentation. In an analagous manner it is shown here that decays of the Z into charmonium plus electromagnetic particles (leptons and photons) are dominated by electromagnetic fragmentation. The process Z → ψ + l+l−, which is of order α, where α is the electromagnetic coupling constant, has a branching ratio of 7.5× 10−7. This is an order of magnitude larger than the order-α process Z → ψγ [7], which has a branching ratio of 5.2 × 10−8. That makes Z → ψ+ l+l− the dominant ψ production mechanism in electromagnetic Z decays. The unexpectedly large rate can be explained by a fragmentation contribution which is not suppressed by a factor of M ψ/M 2 Z [2]. In this paper, it is shown that in the fragmentation limit MZ → ∞ with Eψ/MZ fixed, the rate for Z → ψ + l+l− factors into subprocess rates for electromagnetic decays and individual fragmentation functions . At leading order in α there is a contribution from the fragmentation function Dl→ψ for a lepton to split into a ψ, and a contribution from the fragmentation function Dγ→ψ for a photon to split into a ψ. The fragmentation functions are calculated in a manner that is independent of the hard process that produces the fragmenting parton, and the fragmentation calculation is shown to match the full calculation for Eψ greater than about 3Mψ.