Measurement of the Z boson cross-section in - Harvard University ...

Chapter 1: Introduction and Theoretical Overview 9
u
u
d
Figure 1.1: The three valence quarks in a proton interacting via gluon exchange.
Gluon self-interaction and the formation of ‘sea quarks’ are also shown.
pi = xpproton
(1.1)
where x is the fraction of the proton’s total momentum carried by the parton. The
probability that a parton will carry a given fraction of the proton’s momentum can
be expressed in terms of a probability distribution, referred to as a parton distribution
function (PDF) [40]. It is as yet not possible to calculate PDFs from the theory; they
are extracted from fits to experimental data (for example, see [80]). Figure 1.2 shows
a fit to deep inelastic scattering (DIS) data from the ZEUS experiment [29].
Note in Figure 1.2 that the PDFs are scale-dependent, i.e. , the fitting is done at
a particular momentum scale Q 2 . The scale-dependence of PDFs is logarithmic and
arises, as we shall see below (Section 1.3.3), because logarithmically divergent gluon
emission terms are absorbed into the definition of PDFs. For a given momentum
fraction x, the PDF fi(x, Q 2 ) expresses the density of the ith type of parton in the
proton integrated over a momentum range of 0 to Q.
Knowing the PDF of parton i, we can formulate a set of structure functions for
the proton as a function of x and Q 2 . For example,