We compare the results of the fixed-flavor scheme calculation of Laenen, Riemersma, Smith and van Neerven with the variable-flavor scheme calculation of Aivazis, Collins, Olness and Tung for the case of neutral-current (photon-mediated) heavy-flavor (charm and bottom) production. Specifically, we examine the features of both calculations throughout phase space and compare the structure function F2(x, Q 2 ). We also analyze the dependence of F2 on the mass factorization scale µ. We find that the former is most applicable near threshold, while the latter works well for asymptotic Q 2 . The validity of each calculation in the intermediate region is dependent upon the x and Q 2 values chosen. * SSC Fellow P P X P 1 1 2 Figure 1: The basic semi-inclusive deeply inelastic scattering process, ℓ 1 (ℓ 1 ) + N (P ) −→ ℓ 2 (ℓ 2 ) + Q(p 1 ) + X(P X ).
IntroductionSeveral experimental groups [1] have studied the semi-inclusive deeply inelastic scattering (DIS) process for heavyquark production ( Figure 1)(1)Most analyses of this process assume that the hadron is comprised only of the massless gluon (g), up (u), down (d) and strange (s) quarks, while the charm (c), bottom (b), and top (t) quarks are treated as massive objects which are strictly external to the hadron. This view of the heavy quarks as external to the hadron is appropriate when the energy scale of the process µ phy (for example the center-of-mass energy √ s) is not large compared to the mass of the heavy quark, i.e. M Q < ∼ µ phy . For most fixed-target facilities, this condition holds for the c, b and t quarks [3]. We are therefore justified in excluding c, b, and t as constituents of the hadron in the QCD-improved quark-parton model (QPM) for this case.With new data from HERA, the electron-proton collider at DESY, we can investigate the DIS process in a very different kinematic range from that available at fixed-target experiments [3]. In this new realm, the important question is: Should the c and b quarks be considered as partons, or as heavy objects extrinsic to the hadron? Given that HERA extends the kinematic reach of the DIS process by two orders of magnitude, we can not expect our assumptions that were valid for fixed-target processes to hold in a completely different kinematic regime. Aivazis, Collins, Olness and Tung (ACOT) have discussed this issue at length in reference [4] and approach the problem by invoking the variable flavor scheme (VFS), which varies the number of partons according to the relevant energy scale µ phy . The fundamental physical insight to the VFS is that in the region M Q ≫ µ phy , the heavy quark should be excluded as a constituent of the hadron as it is kinematically inaccessible. However, when M Q ≪ µ phy the heavy quark should be included as a parton since M Q is insignificant compared to µ phy . Although the physics is unambiguous in these kinematic extremes, most experimental data lies in between these clear-cut regions. In the intermediate region, the renormalization scheme of Collins, Wilczek and Zee (CWZ) [5] provides a ...
