kt Effects in Direct-Photon Production

Abstract

We discuss the phenomenology of initial-state parton-kt broadening in direct-photon production and related processes in hadron collisions. After a brief summary of the theoretical basis for a Gaussian-smearing approach, we present a systematic study of recent results on fixed-target and collider direct-photon production, using complementary data on diphoton and pion production to provide empirical guidance on the required amount of kt broadening. This approach provides a consistent description of the observed pattern of deviation of next-to-leading order QCD calculations relative to the direct-photon data, and accounts for the shape and normalization difference between fixed-order perturbative calculations and the data. We also discuss the uncertainties in this phenomenological approach, the implications of these results on the extraction of the gluon distribution of the nucleon, and the comparison of our findings to recent related work.

Figures (15)

• Figure 1: $\langle p_T \rangle$ of pairs of muons, photons, and jets produced in hadronic collisions versus $\sqrt{s}$.
• Figure 2: Top: The CDF and DØ isolated direct-photon cross sections, compared to NLO theory without $k_T$ (dashed) and with $k_T$ enhancement for $\langle k_T \rangle$ = 3.5 GeV/$c$ (solid), as a function of $p_T$. Bottom: The quantity (Data--Theory)/Theory (for theory without $k_T$ adjustment), overlaid with the expected effect from ${k}_{T}$ enhancement for $\langle k_T \rangle$ = 3.5 GeV/$c$. The error bars have experimental statistical and systematic uncertainties added in quadrature.
• Figure 3: Top: The photon and $\pi^0$ cross sections from E706 at $\sqrt{s}$ = 31.6 GeV compared to ${k}_{T}$-enhanced NLO calculations. Bottom: The quantity (Data--Theory)/Theory for direct-photon production, using ${k}_{T}$-enhanced NLO calculations for several values of $\langle k_T \rangle$. The error bars have experimental statistical and systematic uncertainties added in quadrature. The points corresponding to calculations with different $\langle k_T \rangle$ are slightly staggered in $p_T$, to reduce the overlap of experimental error bars.
• Figure 4: Top: The photon and $\pi^0$ cross sections from E706 at $\sqrt{s}$ = 38.8 GeV compared to ${k}_{T}$-enhanced NLO calculations. Bottom: The quantity (Data--Theory)/Theory for direct-photon production, using ${k}_{T}$-enhanced NLO calculations for several values of $\langle k_T \rangle$. The error bars have experimental statistical and systematic uncertainties added in quadrature.
• Figure 5: Top: The photon and $\pi^0$ cross sections from E706 at $\sqrt{s}$ = 31.1 GeV for incident $\pi^-$ beam, compared to ${k}_{T}$-enhanced NLO calculations. Bottom: The quantity (Data--Theory)/Theory for direct-photon production, using ${k}_{T}$-enhanced NLO calculations for several values of $\langle k_T \rangle$. The error bars have experimental statistical and systematic uncertainties added in quadrature.