Inclusive D* Production in Photon-Photon Collisions at Next-to-Leading Order QCD

TL;DR

This study analyzes inclusive $D^{*}$ production in $\gamma\gamma$ collisions, contrasting massive and massless charm treatments at NLO in QCD and across 3- and 4-flavour schemes. It derives and decomposes the LO and NLO cross sections, examines the $m\to 0$ limit to identify finite final-state interaction terms that act like a perturbative fragmentation function, and explores how fragmentation functions (perturbative and non-perturbative) modify predictions. Numerical results demonstrate rapid convergence of massive to massless predictions with increasing $p_T$, with finite-mass effects dominant at low $p_T$ and fragmentation effects dominating at higher $p_T$, especially when non-perturbative fragmentation functions are used. The analysis, complemented by comparisons to LEP II data, shows reasonable agreement once fragmentation and resolved contributions are properly modeled, underscoring the importance of fragmentation dynamics for reliable cross-section predictions in two-photon processes.

Abstract

The next-to-leading order cross section for the inclusive production of charm quarks in gamma-gamma collisions is calculated as a function of the transverse momentum pT and the rapidity y in approaches using massive or massless charm quarks. For the direct cross section we derive the massless limit from the massive theory with the result that this limit differs from the massless version with MSbar factorization by finite corrections. Subtracting or adding these corrections allows us to compare the two approaches on equal footing. We establish massless and massive versions with 3 and 4 initial flavours which are shown to approach the massless approximations very fast with increasing pT. With these results we calculate the inclusive D* cross section in gamma-gamma collisions using realistic evolved fragmentation functions with appropriate factorization scales and compare with recent data for dsigma/dpT from three LEP collaborations after single- and double-resolved contributions have been added.

Figures (8)

• Figure 1: (a) $p_T$ distribution $d\sigma/dydp_T$ for $e^+e^- \rightarrow \gamma \gamma \rightarrow c/\bar{c} + X \rightarrow D^{\ast\pm} + X$ (direct contribution, $BR(c \rightarrow D^{\ast\pm}) = 0.235$) at LO for $y=0$ in the massless (full line) and the massive calculation (dashed line) with $m=1.5$ GeV; (b) ratio of the massive and massless calculations.
• Figure 2: (a) $p_T$ distribution $d\sigma/dydp_T$ in the NLO 3-flavour scheme (FSI-coefficients $\Delta c_i$ added in the massless calculation, direct contribution including $BR(c \rightarrow D^{\ast\pm}) = 0.235$) for $y=0$ in the massless (full line) and the massive calculation (dashed line) for $M_I = M_F = m$; (b) ratio of the massive and massless calculations.
• Figure 3: (a) $p_T$ distribution $d\sigma/dydp_T$ in the NLO 4-flavour scheme (FSI-coefficients $\Delta c_i = 0$ in the massless calculation not resummed and subtracted in the massive calculation, direct contribution including $BR(c \rightarrow D^{\ast\pm}) = 0.235$) for $y=0$ in the massless (full line) and the massive calculation (dashed line) for $M_I = M_F = \sqrt{p_T^2 + m^2}$; (b) ratio of the massive and massless calculations.
• Figure 4: As in Fig. \ref{['fig3']}, but including $c \rightarrow D^*$ fragmentation according to (\ref{['dcc']}) (perturbative FF), i.e. FSI-terms resummed.
• Figure 5: As in Fig. \ref{['fig3']}, but including $c \rightarrow D^*$ fragmentation according to Ref. 5 (set OPAL NLO).