J/psi Production at LEP: Revisited and Resummed

TL;DR

The paper addresses prompt J/ψ production at LEP within NRQCD, showing that large logarithms from both z~1 and small-z regions require resummation. It develops a fragmentation-function framework with DGLAP evolution for high-z logs and a Mueller-based angular-ordered resummation for small-z soft-gluon effects, then interpolates between regimes using data. By fitting LEP data, it extracts a more precise color-octet matrix element and demonstrates that the resummed predictions align better with measurements, including characteristic small-z enhancements. The work strengthens the NRQCD color-octet test at LEP and provides tighter constraints on nonperturbative matrix elements, with implications for moments of the rate as clean tests of the mechanism.

Abstract

We present the leading order differential and total rates for J/ψproduction at LEP. By leading order we mean all terms of the form alpha_s[alpha_s log(M_Z^2/M_{psi}^2)]^n and alpha_s^{n+1} log^l(z^2) log^m(M_Z^2/M_{psi}^2), (l+m=2n-1), in the regions z=2E_psi/M_Z ~ O(1) and z << 1, respectively. In the intermediate region we interpolate using the available data. This resummation eliminates the O[alpha_s(M_psi)/alpha_s(M_Z)]~ 2 theoretical uncertainties in previous calculations. The log(z) resummation results in a suppression of the small z region due to coherent gluon emission. Comparing the zeroth moment with the LEP data we find the value for the effective octet matrix element to be <\hat O_8^ψ(^3S_1)>=0.019 GeV^3. The theoretical uncertainties are substantially smaller than those from Tevatron extractions. Using this value of the octet matrix element we make a prediction for the first moment of the differential rate and find that the resummed differential decay rate is in much better agreement with preliminary data than the color singlet result or the unresummed color octet prediction.

Figures (3)

• Figure 1: Differential rate ${d\Gamma \over dz}$ for the octet channel with (solid line) and without (dashed line) evolution, and for the singlet channel with (dotted line) and without (dot-dashed line) evolution, as a function of $z = 2 E_\psi/ M_Z$. The octet matrix element has been extracted from the Tevatron (see text).
• Figure 2: Typical ladder diagrams which lead to the leading logs. To include coherence effects, angular ordering is imposed such that the angle between two branching partons is smaller than the angle of the previous pair.
• Figure 3: Differential rate ${d\Gamma \over dz}$ as a function of $z = 2 E_\psi/ M_Z$ vs data. The dashed line is the sum of the tree-level octet and singlet results and the solid line is the interpolation between the large and small $z$ region octet resummation plus the singlet resummation.