Parton Density Functions

NC data from ZEUS and H1 have been used to extract the parton densities ($q$, $\bar{q}$ and $G$) of the proton. An example of data from ZEUS and NMC are shown in figures 2.2 and 2.3 together with the PDF fit which uses the DGLAP evolution [2] done by the ZEUS experiment. The figures have been taken from [3].

Figure 2.2: Structure function $F_2$ for various values of $Q^2$ ( $60\,{{\mbox{\rm GeV}}}^2\,<\,{Q^2}\,<\,800\,{{\mbox{\rm GeV}}}^2$) as a function of ${x}$ as measured by the ZEUS collaboration. The curves indicate a QCD NLO fit to the data. The ${Q^2}$ values are indicated in ${{\mbox{\rm GeV}}}^2$.

Figure 2.3: Structure function $F_2$ for various values of $Q^2$ ( $1200\,{{\mbox{\rm GeV}}}^2\,<\,{Q^2}\,<\,5000\,{{\mbox{\rm GeV}}}^2$) as a function of ${x}$ as measured by the ZEUS collaboration. The curves indicate a QCD NLO fit to the data. The ${Q^2}$ values are indicated in ${{\mbox{\rm GeV}}}^2$.

Many other groups have performed fits such as GRV [4], CTEQ [5] and MRS [6] which are available as PDFLIB [7]. These groups have used more data than just DIS but give an equally good description of ZEUS data.

The subject of this thesis is charged current positron proton scattering. As seen from equation (2.14) the charged current process selects a subset of quarks inside the proton. This allows investigation of the flavor decomposition of the parton densities.

Previous data on CC scattering stem from $\nu$ scattering ([8,9,10]). The energy of the $\nu$ beam is restricted to about $300\,{\mbox{\rm GeV}}$ which yields an $s$-value of about $600\,{{\mbox{\rm GeV}}}^2$ compared to the $90200\,{{\mbox{\rm GeV}}}^2$ available at HERA. An example of the structure functions for $\nu p$ scattering is shown in figure 2.4. The data have been taken from [8]. The curve shows the CTEQ4D parameterization of the measured structure function. The agreement is not more than reasonable. This is most likely due to the transformation of the measured data to one fixed $Q^2$ for which the authors use a power law behavior with a fixed slope below $x = 0.2$ and a different slope above $x = 0.2$. However the overall features and magnitude are still reasonably described by the parameterization.

Fixed target experiments reach up to a ${Q^2}$ of about $25\,{{\mbox{\rm GeV}}}^2$ for measurements on protons and of ${Q^2}$ of approximately $100\,{{\mbox{\rm GeV}}}^2$ and $x\,>\,0.1$ for measurements on $Fe$ targets.

Figure 2.4: The figure shows the data on the structure function $q^\nu (x) = (x*(d(x)+s(x)))$ as measured by [8] at ${Q^2}\,=\,14.2\,{{\mbox{\rm GeV}}}^2$ Also shown is the CTEQ4D structure function parameterization at this $Q^2$ value.

The current parton density functions which fit the NC data predict total cross sections for NC and CC scattering at HERA of

$${\sigma}_{\mbox{\em nc}}^{\mbox{\em tot}}(Q^2 > 1 {{\mbox{\rm GeV}}}^2) = \mbox{$1.15\,{\mu {\mbox{\rm b}}}$}$$

$${\sigma}_{\mbox{\em cc}}^{\mbox{\em tot}}(Q^2 > 1 {{\mbox{\rm GeV}}}^2) = \mbox{$38.7\,\mbox{\rm pb}$}$$