Inclusive Photoproduction of D* Mesons with Massive Charm Quarks

TL;DR

This work compares two NLO frameworks for inclusive $D^{*}$ photoproduction in $\gamma p$ collisions at HERA: a massive charm (FFN) scheme with renormalization–scale–invariant $\overline{\rm MS}$ subtraction and a conventional massless scheme. By incorporating finite charm-mass effects into the direct part and absorbing logarithmic terms into charm PDFs and the $c\to D^{*}$ fragmentation function, the authors study the transition to the massless limit as transverse momentum increases and quantify the direct versus resolved contributions under ZEUS kinematics. Their numeric analysis shows mass effects are most significant at low $p_T$ (up to ~20% in some regions) but largely cancel when the resolved channel is included, with photon-charm in the resolved part dominating the cross section at low $p_T$. Comparison with preliminary ZEUS data yields generally good agreement, particularly for $p_T$-dependent distributions, while highlighting residual tensions at low $p_T$ and in certain rapidity observables that may be alleviated by switching to a three-flavor scheme at very small $p_T$ or by using alternative photon PDFs.

Abstract

We have calculated the next-to-leading order cross sections for the inclusive production of D* mesons in gamma-p collisions at HERA in two approaches using massive or massless charm quarks. The usual massive theory for the direct cross section with charm quarks only in the final state was transformed into a massive theory with MS-bar subtraction by subtracting the mass divergent and additional finite terms calculated earlier in connection with the process gamma+gamma -> D*+X. This theory approaches the massless theory with increasing transverse momentum. The difference between the massive and the massless approach with MS-bar subtraction is studied in detail in those kinematic regions relevant for comparison with experimental data. With these results and including the resolved cross section which is dominated by the part originating from the charm in the photon, we compute the fully inclusive D* cross section and compare it with preliminary data from the ZEUS collaboration at HERA. We find on average good agreement.

Figures (9)

• Figure 1: Direct contribution to $\gamma + p \rightarrow D^{\ast} + X$ with massive (dashed lines) and massless charm quarks (full lines) for $|y| < 1.6$ (a) and $-1.6 < y < -0.8$ (b).
• Figure 2: $p_T$ distribution for $|y| < 1.6$. (a) shows the direct (dashed lines) and resolved (dotted line) parts and the sum (full lines) compared with preliminary ZEUS data Zeus (inner errorbars show statistical, outer errorbars include systematic errors). (b) displays separate parts of the resolved contribution (full line): $\alpha$ is the contribution due to light quarks and gluons in the initial state, $\beta$ includes in addition charm from the proton.
• Figure 3: Ratios of massive over massless cross sections $d\sigma/dp_T$ (see text for details).
• Figure 4: $K$ factors for the cross sections $d\sigma/dp_T$. Dashed lines are obtained from the direct massless (lower curves at low $p_T$) and direct massive calculations (upper curves at low $p_T$). Dotted lines are for the resolved contribution and full lines correspond to the full cross section (again the massless and massive approaches corresponding to lower and upper curves at low $p_T$).
• Figure 5: The complete cross section (full lines) and the direct contribution (dashed lines) with varied factorization and renormalization scales $2\mu_R = \mu_I = \mu_F = 2\xi \sqrt{p_T^2+m^2}$, $\xi = 0.5$ (upper), 1.0 (middle) and 2.0 (lower curves).