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

Chapter 1: Introduction and Theoretical Overview 8
1.3 Proton-proton collisions and Z boson production
at the LHC
In this thesis, we are concerned with the production of Z bosons in hard pp colli-
sions. Hard processes can include interactions that involve small and large transfers
of momentum, and we need to understand the effects of both in order to be able to
extract theoretical predictions for the Z cross-section. We need to know the momen-
tum distributions of partons, i.e. , quarks and gluons, inside the colliding protons.
Furthermore, since perturbative calculations are made as an expansion in the strong
coupling αs, we need knowledge of the renormalization procedure used to extract αs
at a given momentum scale. In this section, we review these topics in some detail.
1.3.1 Internal structure of a proton and parton distributions
functions
Protons are composed of quarks and gluons. In low energy interactions, the pro-
ton’s internal structure can be described as a collection of three valence quarks: two
of the up type and one of the down type, which interact via gluon exchange (see
Figure 1.1). The valence quarks determine the quantum numbers of the proton. In
addition, gluons can self-interact to produce quark-antiquark pairs as well as further
gluons. The additional qq pairs thus produced are known as sea quarks.
As mentioned in Section 1.2, the strength of the strong interaction decreases with
increasing energy scale of the interaction. Consequently, for hard interactions, i.e. ,
interactions involving large momentum transfers, the partons inside a proton can be
considered as being effectively free. Each parton carries a fraction of the proton’s
total momentum, and we can express the momentum of the ith parton as: