What does the W transverse momentum distribution say about the W + 1 jet / W + 0 jet ratio ?

We compute the W transverse momentum distribution at large transverse momentum at fixed next-to-leading order (i.e. O(αs)) and find good agreement with the preliminary measurements reported by DØ . We find that the W transverse momentum distribution is typically significantly larger than the exclusive one-jet rate for a given value of pWT or E jet T , mainly because two or more jet events are excluded. As a consequence, we find that theoretically the W + 1 jet to W + 0 jet ratio R is smaller than the analogous quantity defined in terms of pWT , R W . This hierarchy is preserved under changes of renormalisation/factorisation scales, strong coupling constant and jet algorithm. However, this appears to be in contradiction with the preliminary experimental results which suggest R > R . CERN–TH/97–173 July 1997 During the past year the DØ collaboration has reported preliminary measurements of the ratio R [1] defined by [2, 3], R(E T ) = σ(W + 1 jet) σ(W + 0 jet) , (1) where the jets are defined with transverse energy above some E T . At present the data appears to indicate larger values of R than those obtained in next-to-leading order QCD predictions for the same quantity [4, 5, 1, 6, 7]. There have already been several suggested explanations for this excess. For example, Balázs and Yuan [8] have considered the effect of soft gluon resummation on the related quantity R , R (p T ) = σ(W, pWT > p W,min T ) σ(W, pWT < p W,min T ) . (2) New physics effects are also possible and Choudhury et al. [9] have considered the effect that a massive vector boson with the quantum numbers of both a W boson and a gluon would have on the observed value of R. A more mundane explanation is that an increase in the gluon parton distribution at medium Bjorken x values would boost the W + 1 jet rate, which receives contributions from qg scattering, while having little effect on the zero jet rate [1]. Here we discuss the relationship between the large transverse momentum distribution of the W boson, for which the DØ collaboration recently reported a preliminary measurement [10], and the R ratio. We also consider the extent to which we can accurately theoretically predict each of these quantities. At leading order in perturbative QCD the large pT distribution of the W boson is given by the W recoiling against a single parton. Typically, the parton will hadronize into an observed jet, with the jet ET balancing the W transverse momentum, so that, R (p T ) ≃ R (E T = p W,min T ) . (3) Beyond lowest order this relationship is no longer strictly true at the parton level, however it makes the quantity R worth studying in the context of the measured DØ excess in R. At the moment DØ make no direct measurement of the R ratio. However, for a different analysis [10] they have made a preliminary measurement of the normalised transverse momentum distribution of the W ,1/σ dσ/dpWT , and from this measurement we can construct R ,