Inclusive D^{*+-} Production in p p-bar Collisions with Massive Charm Quarks

TL;DR

This work develops a MS̄-consistent GM-VFN framework for inclusive D^{*±} production in p p̄ collisions, bridging massive FFN and massless ZM-VFN approaches. By deriving the m→0 limit of massive NLO cross sections and introducing finite subtraction terms, the authors show how to merge massive charm effects with MS̄ factorization, enabling a reliable interpolation to high transverse momentum via DGLAP-evolved fragmentation functions and charm PDFs. The methodology is validated through numerical tests and applied to Tevatron data, where the GM-VFN predictions, including charm-init and gluon/light-quark fragmentation contributions, reasonably describe the observed D^{*±} cross sections, albeit with some underprediction that depends on scale choices. The study highlights the non-negligible impact of mass-dependent corrections in the gg channel and the sizeable role of gluon fragmentation, suggesting further improvements with updated PDFs/FFs and potentially adjusted fragmentation functions to achieve closer agreement with experimental measurements.

Abstract

We calculate the next-to-leading order cross section for the inclusive production of D^{*+-} mesons in p p-bar collisions as a function of the transverse momentum and the rapidity in two approaches using massive or massless charm quarks. For the inclusive cross section, we derive 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 with increasing transverse momentum. With these results and including the contributions due to the charm and anti-charm content of the proton and anti-proton, we calculate the inclusive D^{*+-} cross section in p p-bar collisions using realistic evolved non-perturbative fragmentation functions and compare with recent data from the CDF Collaboration at the Fermilab Tevatron at center-of-mass energy root(S) = 1.96 TeV. We find reasonable, though not perfect, agreement with the measured cross sections.

Figures (8)

• Figure 1: $gg$ contribution to $p\bar{p} \to D^{*\pm} + X$ including Abelian and non-Abelian parts, normalized to the LO cross section with $m=0$. (a): Renormalization and factorization scales are $\mu_R = \mu_F = \mu_F^\prime = m$ (but fixed at $2.1m$ in $\alpha_s$, PDFs and FF). (b): Same as in part (a), but for $\mu_R = \mu_F = \mu_F^\prime = 2m_T$ including rescaling due to renormalization and initial-state factorization of singularities originating from internal gluons. (c): Same as in part (a), but including full rescaling to $\mu_R = \mu_F = \mu_F^\prime = 2m_T$.
• Figure 2: $p(q)+\bar{p}(\bar{q})$ contribution to $p\bar{p} \to D^{*\pm} + X$ including Abelian and non-Abelian parts, normalized to the LO cross section with $m=0$. (a): Renormalization and factorization scales are $\mu_R = \mu_F = \mu_F^\prime = m$ (but fixed at $2.1m$ in $\alpha_s$, PDFs and FF). (b): Same as in part (a), but for $\mu_R = \mu_F = \mu_F^\prime = 2m_T$ including rescaling due to renormalization and initial-state factorization. (c): Same as in part (a), but including full rescaling to $\mu_R = \mu_F = \mu_F^\prime = 2m_T$.
• Figure 3: (a): $p(q)+\bar{p}(g)$ contribution to $p\bar{p} \to D^{*\pm} + X$ including Abelian and non-Abelian parts, normalized to the LO cross section of the $gg$ channel with $m=0$. Renormalization and factorization scales are $\mu_R = \mu_F = \mu_F^\prime = m$ (but fixed at $2.1m$ in $\alpha_s$, PDFs and FF). Lower curves: observed charm, upper curves: observed anti-charm. (b): Same as in part (a) for observed charm, but with renormalization and factorization scales chosen as $\mu_R = \mu_F = \mu_F^\prime = 2m_T$. (c): Same as in part (b), but for observed anti-charm.
• Figure 4: Partial cross sections for $p\bar{p} \to D^{*\pm}+X$ in the ZM-VFN scheme. Renormalization and factorization scales are $\mu_R = \mu_F = \mu_F^\prime = 2m_T$. The sum of the $gg$, $q\bar{q}$, $gq$ and $g\bar{q}$ channels is labeled tot, the total cross section including incoming (anti-)charm quarks tot${}+c\bar{c}$.
• Figure 5: Partial cross sections normalized to the result for all contributions including the $c\bar{c}$ initial state. Lower and upper curves correspond to the massless and massive calculations, respectively.