A Variable Flavour Number Scheme for Charged Current Heavy Flavour Structure Functions

Abstract

The Thorne-Roberts variable flavour number scheme (VFNS) for heavy quarks is presented in detail for the specific case of charged current DIS. As in neutral current DIS this provides a smooth extrapolation from the fixed flavour number scheme (FFNS) appropriate at low $Q^2$ to the zero-mass variable flavour number scheme (ZM-VFNS) appropriate as $Q^2 \to \infty$, and differs from alternative versions of a VFNS by the definition of the coefficient functions at each order, and the strict ordering of the expansion in $α_S$. However, there are subtle differences from the neutral current case which are addressed here. We discuss both the LO and NLO expressions, the latter unfortunately requiring some (minimal) modelling due to the current lack of some necessary ${\cal O}(α^2_S)$ FFNS coefficient functions.

Figures (5)

• Figure 1: Charm quark contribution to the structure functions, $F_{2}(x,Q^2)$ for $x=0.1$, $x=0.01$ and $x=0.001$ calculated using our LO prescription, our input parton distributions evolved at LO and renormalization scale $\mu^2=Q^2$. Also shown are the continuation of the LO FFNS expression and the ZM--VFNS expression both calculated using the same parton distributions and same choice of scale.
• Figure 2: Same as Fig. 1, but for $F_3(x,Q^2)$.
• Figure 3: Charm quark contribution to the structure functions, $F_{2}(x,Q^2)$ for $x=0.1$, $x=0.01$ and $x=0.001$ calculated using our NLO prescription, our input parton distributions evolved at NLO and renormalization scale $\mu^2=Q^2$. Also shown are the continuation of the FFNS expression with LO coefficient functions (those at NLO being unavailable) and the NLO ZM--VFNS expression both calculated using the same parton distributions and same choice of scale. Also shown for comparison is the VFNS result when $C^{(1)VF}_{2,\bar{\tilde{s}}}$ is set equal to zero.
• Figure 4: Same as fig. 3, but for $F_3(x,Q^2)$.
• Figure 5: The NLO prediction for $\Delta xF_3(x,Q^2)$ using our VFNS prescription, along with the data measured by CCFR unki. The prediction has been corrected for heavy target effects using badkwie.