Radiative Corrections to the Photon + 1 Jet Rate at LEP

Abstract

We present the results of a calculation of the rate for the annihilation of an $e^+e^-$ pair into a jet containing an energetic photon and a single further jet at order $αα_{s}$. By comparing these results with the existing data on the photon + 1 jet rate from the ALEPH Collaboration, we make a first determination of the process independent quark-to-photon fragmentation function $D_{q \to γ}(z,μ_{F})$ at order $αα_{s}$. We also compare our prediction for the inclusive photon energy spectrum with the recent OPAL measurement.

Figures (6)

• Figure 1: Parton level subprocesses contributing to the photon + 1 jet rate at ${\cal O}(\alpha\alpha_s)$.
• Figure 2: Sum of all ${\cal O}(\alpha\alpha_s)$ contributions to the total photon + 1 jet rate for a single quark of charge $e_q$ such that $\alpha e_q^2 = 2\pi$, $\alpha_s (N^2-1)/2N = 2\pi$ using the Durham jet algorithm with $y_{{\rm cut}}=0.1$, and integrated for $z>0.7$.
• Figure 3: Comparison of the 'photon' + 1 jet rate at ${\cal O}(\alpha)$ and ${\cal O}(\alpha\alpha_s)$ with the ALEPH data ($y_{{\rm cut}}=0.06$), including the fitted quark-to-photon fragmentation function.
• Figure 4: The measured quark-to-photon fragmentation function at leading aleph and next-to-leading (this study) order for a quark of unit charge. The factorization scale is taken to be $\mu_F=M_Z$.
• Figure 5: The integrated photon + 1 jet rate above $z=0.95$ as function of $y_{{\rm cut}}$, compared with the ${\cal O}(\alpha)$ and ${\cal O}(\alpha \alpha_s)$ order calculations including the appropriate quark-to-photon fragmentation functions.