Abstract
The FONLL general-mass variable-flavour number scheme provides a framework for the matching of a calculation in which a heavy quark is treated as a massless parton to one in which the mass dependence is retained throughout. We describe how the usual formulation of FONLL can be extended in such a way that the heavy quark parton distribution functions are freely parameterized at some initial scale, rather than being generated entirely perturbatively. We specifically consider the case of deep-inelastic scattering, in view of applications to PDF determination, and the possible impact of a fitted charm quark distribution on F2c is assessed.
Highlights
Both problems are solved by introducing a fitted heavy quark PDF, which can describe a possible non-perturbative intrinsic component, and reabsorb in the initial condition the dependence on the choice of starting scale of the perturbative component. It is the purpose of the present paper to explain how the so-called FONLL approach of Ref. [8], for the treatment of heavy quarks with inclusion both of mass dependence, and resummation of collinear logs, can be generalized to include such a fitted heavy quark PDF
The FONLL approach, originally proposed in Ref. [9], applied there to heavy quark production in hadronic collisions, and generalized to deep-inelastic scattering in Ref. [8], is a general-mass, variable-flavour number (GM-VFN) scheme. Such schemes are designed to deal with the fact that hard processes involving heavy quarks can be computed in perturbative QCD using different renormalization and factorization schemes: a massive, or decoupling scheme, in which the heavy quark does not contribute to the running of αs or the DGLAP evolution equation, and it appears as a massive field in the computation of hard cross-sections; and a massless scheme, in which the heavy quark is treated as a massless parton
The FONLL scheme has the dual advantage that it can be generally applied to any hard electroor hadro-production process, and that it allows for the combination of a three- and four-flavour computation each performed at any desired perturbative order
Summary
Both problems are solved by introducing a fitted heavy quark PDF, which can describe a possible non-perturbative intrinsic component, and reabsorb in the initial condition the dependence on the choice of starting scale of the perturbative component. We define a correction term ∆F (x, Q2), which must be added to the standard FONLL structure functions F FLNR(x, Q2) of Ref. [8] in order to account for the inclusion of a fitted heavy quark PDF: the structure function Eq (1) is given by
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