Inclusive D* production in gamma-gamma collisions: including the single-resolved contribution with massive quarks

TL;DR

The study develops a massive-charm scheme with MS-bar subtraction to extend NLO single-resolved gamma-gamma cross sections for D*-meson production, ensuring compatibility with standard photon PDFs and fragmentation functions defined in MS-bar. By deriving and subtracting finite terms in the m -> 0 limit, the authors produce predictions that smoothly converge to massless MS-bar results as p_T increases. The approach is validated against LEP2 data (ALEPH, L3, OPAL), showing good agreement for p_T above ~2 GeV and highlighting sizeable mass effects only at very low p_T; the double-resolved component is largely driven by charm in the photon and is treated with massless inputs. The work also discusses the potential switch to a three-flavor scheme at small p_T to improve behavior in the near-threshold region.

Abstract

We have calculated the next-to-leading order cross section for the inclusive production of charm quarks as a function of the transverse momentum p_T and the rapidity in two approaches using massive or massless charm quarks. For the single-resolved cross section we have derived the massless limit from the massive theory. We find that this limit differs from the genuine massless version with MS-bar factorization by finite corrections. By adjusting subtraction terms we establish a massive theory with MS-bar subtraction which approaches the massless theory very fast with increasing transverse momentum. With these results and including the equivalent results for the direct cross section obtained previously as well as double-resolved contributions, we calculate the inclusive D*+- cross section in gamma-gamma collisions using realistic evolved non-perturbative fragmentation functions and compare with recent data from the LEP collaborations ALEPH, L3 and OPAL. We find good agreement.

Figures (13)

• Figure 1: Feynman diagrams for the virtual NLO corrections to $\gamma + g \rightarrow c + \bar{c}$.
• Figure 2: Feynman diagrams for the bremsstrahlung contributions $\gamma + g \rightarrow c + \bar{c} + g$ (a) and for the process $\gamma + q \rightarrow c + \bar{c} + q$ (b).
• Figure 3: Comparison of the massive and massless calculations for the bremsstrahlung contributions $T_1-T_6$ (a$-$f), see text.
• Figure 4: Comparison of the massive and massless calculations for the virtual contributions $T_{\rm a-e}-T_{\rm h}$ (a$-$d), see text.
• Figure 5: Comparison of the massive calculation (dashed lines) with its massless limit (full lines) for the terms proportional to $N_C$ for the process $\gamma + g \rightarrow c + \bar{c} + X$. In (a), the sum of all ratios defined in eq. (\ref{['tratio']}) is shown, in (b) the difference of the sums for the massless limit and the calculation with $m\neq 0$. The dotted lines represent the results of the massless limit with subtracted $\Delta c_i$, i.e. the calculation with $\overline{\rm MS}$ factorization LG.