ar X iv : h ep - p h / 01 02 19 8 v 1 1 5 Fe b 20 01 Drell - Yan Massive Lepton - Pair ’ s Angular Distributions at Large Q T

By measuring Drell-Yan massive lepton-pair’s angular distributions, we can identify the polarization of the virtual photon of invariant mass Q which decays immediately into the lepton-pair. In terms of a modified QCD factorization formula for Drell-Yan process, which is valid even if QT ≫ Q, we calculate the massive lepton-pair’s angular distributions at large QT . We find that the virtual photons produced at high QT are more likely to be transversely polarized. We discuss the implications of this finding to the J/ψ mesons’ polarization measured recently at Fermilab. PACS Numbers: 12.38.Bx, 12.38.cy, 13.85.Qk, 14.70.Bh Typeset using REVTEX 1 Recent data on J/ψ polarization measured by CDF collaboration at Fermilab Tevatron seem to be inconsistent with the predictions from various models of J/ψ production [1]. The CDF data shows that the J/ψ mesons produced at √ S = 1.8 TeV become more longitudinally polarized as the transverse momentum (QT ) increases [1]. On the other hand, the various theoretical calculations predict the J/ψ mesons to be more transversely polarized at large QT [2]. In order to help solving this puzzle, it was proposed to measure the Drell-Yan massive lepton-pair’s angular distributions at the kinematics similar to that of J/ψ production, and to extract the virtual photon’s polarization from the lepton-pair’s angular distributions [3,4]. Production of the virtual photons in the Drell-Yan process at large QT and small Q 2 has a lot in common with the production of J/ψ mesons at high QT . They both have two large physical scales: QT and Q , which is equal to M J/ψ in the case of J/ψ production; and Q 2 T is much larger than Q. If the collision energy √ S is large enough, and the logarithmic contributions from resumming all powers of lnn(QT/Q ) dominate the production cross sections, the virtual photon and J/ψ production will share the same partonic subprocesses, labeled by the R in Fig. 1. Then, the only difference between the virtual photon and J/ψ production at large √ S and high QT is the difference in the fragmentation functions. The virtual photon fragmentation functions are completely perturbative if Q ≫ ΛQCD [4,5], while the parton to J/ψ fragmentation functions involve final-state nonperturbative soft interactions [6]. The measurements of the virtual photon and J/ψ polarization at high QT can help us to isolate the final-state effect in J/ψ production, and to narrow the questions about J/ψ formation. In this letter, we calculate Drell-Yan massive lepton-pair’s angular distributions in Quantum Chromodynamics (QCD). We present the polarization parameter αDY as a function of QT , which can be in principle measured at Fermilab Tevatron. We find that the virtual photons at high QT are likely to be transversely polarized, which is different from the data on the polarization parameter αJ/ψ measured at Fermilab [1]. If our predictions for the αDY are confirmed by future experiments, we may conclude that the non-perturbative final-state interactions are very important for the formation of J/ψ mesons. When QT and Q 2 are both large, cross sections for Drell-Yan massive lepton-pair production in hadronic collisions, A(PA) + B(PB) → γ(→ ll̄(Q)) +X, can be systematically calculated according to QCD factorization theorem [7,8]. Since we are mainly interested in the cross sections at high QT and low Q , we neglect the Z channel contributions in the following discussions. After integrating over the azimuthal angle distribution, the Drell-Yan lepton-pair’s angular distributions, as sketched in Fig. 2, can be expressed as [9] dσAB→ll̄(Q)+X dQ2 dQT dy d cos θ = dσAB→ll̄(Q)+X dQ2 dQT dy 3 2(3 + αDY) [