Doped Parton Distributions

TL;DR

The paper addresses the challenge of heavy-quark mass effects in high-energy processes by introducing the doped scheme, where $\alpha_s(Q)$ runs with $n_f=5$ above $m_b$ while DGLAP evolution uses $n_f=4$, providing a practical alternative to full 4FS-5FS matching. It presents NNPDF3.0 doped PDF sets, built from the $n_f=5$ fit at $Q^2=m_b^2$ and evolved with APFEL to NNLO and NLO, illustrating intermediate behavior between 4FS and 5FS in both $\alpha_s(Q)$ running and parton distributions. The results show that the doped PDFs yield gluon and light-quark evolutions that interpolate between schemes and can affect cross sections, especially for processes with multiple colored partons. The approach offers a consistent, computationally tractable way to improve heavy-quark predictions at the LHC without full FONLL-style matching, impacting differential distributions and overall cross sections.

Abstract

Calculations of high-energy processes involving the production of b-quarks are typically performed in two different ways, the massive four-flavour scheme (4FS) and the massless five-flavour scheme (5FS). For processes where the combination of the 4FS and 5FS results into a matched calculation is technically difficult, it is possible to define a hybrid scheme known as the doped scheme, where above the b-quark threshold the strong coupling runs with $n_f=5$, as in the massless calculation, while the DGLAP splitting functions are those of the $n_f=4$ scheme. In this contribution we present NNPDF3.0 PDF sets in this doped scheme, compare them with the corresponding 4FS and 5FS sets, and discuss their relevance for LHC phenomenology.

Figures (5)

• Figure 1: Running of the strong coupling $\alpha_s(Q)$ in the 5FS and 4FS, normalized to the 5FS result.
• Figure 2: Comparison of the NNPDF3.0 global fits in the 5F, 4F and doped heavy quark schemes, as a function of the factorization scale $Q$ for two different values of $x$, $x=10^{-4}$ (upper plots) and $x=0.1$ (lower plots). We show results normalized to the central value of the 5FS PDF set, for both NLO (left plots) and NNLO (right plots).
• Figure 3: Same as Fig. \ref{['fig:xg']} for the NLO down quark PDF.
• Figure 4: Differential distributions for vector boson production with a pair of $b$-quarks at the LHC 7 TeV: the $p_T^W$ of the $W$ boson in $Wb\bar{b}$ production (left) and the invariant mass of the $b\bar{b}$ pair in $Zb\bar{b}$ production (right). The results of the 4F and 5F schemes are compared with the doped scheme.
• Figure 5: Preliminary results for the comparison between the 4FS NLO, doped NLO and 5FS LO calculations with Sherpa using the corresponding NNPDF3.0 PDFs, and differential distributions from the recent ATLAS and CMS 7 TeV measurements of $Z$ production in association with $b$-jets.