Abstract
We show how to extend systematically the FONLL scheme for inclusion of heavy quark mass effects in DIS to account for the possible effects of an intrinsic charm component in the nucleon. We show that when there is no intrinsic charm, FONLL is equivalent to S-ACOT to any order in perturbation theory, while when an intrinsic charm component is included FONLL is identical to ACOT, again to all orders in perturbation theory. We discuss in detail the inclusion of top and bottom quarks to construct a variable flavour number scheme, and give explicit expressions for the construction of the structure functions $F^c_2$, $F^c_L$ and $F^c_3$ to NNLO.
Highlights
Heavy quarks and factorizationThe definition of light and heavy quarks is somewhat arbitrary: being ‘light’ or ‘heavy’ is a relative concept
The use of a so-called variable flavour number scheme (VFNS): calculations involving heavy quarks in DIS in different schemes with different numbers of active flavours participating to DGLAP evolution are combined to derive an expression for the coefficient functions which is valid both close to threshold, and far above it
We show how to extend systematically the FONLL scheme for inclusion of heavy quark mass effects in DIS to account for the possible effects of an intrinsic charm component in the nucleon
Summary
The definition of light and heavy quarks is somewhat arbitrary: being ‘light’ or ‘heavy’ is a relative concept. We cannot safely assume that at Q0 the charm distributions c(x, Q0) and c(x, Q0) are strictly zero, even if Q0 is below the threshold for perturbative charm production, since nonzero distributions (commonly called ‘intrinsic charm’) may be generated by nonperturbative effects To take this into account we need to treat charm in the same way that we treat the light partons q = u, d, s, q = u, d, sand g, with an initial (fitted) PDF at Q0, evolved up to scales Q > Q0 using perturbation theory. The extension of this discussion to the bottom and top quark is straightforward, so the details are postponed to section 4
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