Model Independent Search for Deviations from the Standard Model ...

1.2. Hadron Collider Physics 9
1.2 Hadron Collider Physics
At a hadron collider, e.g. the Tevatron, protons collide with anti-protons. Both are not
pointlike particles, but they consist of several partons. The simple picture of three quarks
(uud) building the proton has to be replaced by the complex formalism of the proton's
structure function:
F 2 = ∑ i
q 2 i x[f i (x, Q 2 ) + ¯f i (x, Q 2 )] + ∑ j
q 2 j x[g j (x, Q 2 )] . (1.14)
Here the sum includes all quark avours i = u, d, ... ; q i is the specic charge of the quark
and Q is the momentum transfer of the interaction. In addition to the fermion part of 2 F 2 ,
bosonic partons with a color charge q j also contribute, accounting for the gluons inside
the nucleon. This structure function denes the composition of the proton:
The variable x is called Bjorken x and redistributes the four-momentum of the incoming
proton P . Each parton gets a fraction resulting in the four-momentum µ k , i.e. µ k µ = xP .
In deep inelastic scattering, only two partons interact. As each of the partons has a certain
µ
fraction x of the total momentum P , the entire center of mass energy of the accelerator
is not available for the reaction. This µ is the reason why the laboratory frame (detector) is
not the rest system, and most events are boosted along the z-axis.
f i (x, Q 2 ) is the parton density function (pdf), i.e. the density of quarks with avour i
which have a relative momentum between x and x+dx. Equivalently, g j (x, Q 2 ) represents
the gluon density. What Equation 1.14 means is that a proton consists of a combination
of all quarks, anti-quarks and gluons. In general, a distinction is drawn between valence
quarks (uud for proton) and sea quarks, which are both part of a hadron. The existence
of sea quarks, e.g. a virtual strange quark in a neutron, can be explained by the presence
ofgluonskeepingthehadrontogether. Besidestheexchangeofgluonsbetweentwovalence
quarks, the radiation of gluons converting into a quark anti-quark pair is also possible. As
a consequence, anti-quarks and heavy quarks can be created, even though their density
function for large x is naturally much smaller than, for example, the one of a u-quark, as
they are the consequence of radiation processes.
In addition to the momentum given to the sea quarks, experimental data show that the
gluons take about half of the initial momentum P . Figure 1.3 summarizes the dierent
sharesofthecomponentsoftheproton(valencequarkdensity, µ seaquarkdensityandgluon
density). One can see that for small x, the gluons and the sea quarks dominate.
In Equation 1.14, the structure function and all parton densities are not only a function
of x, but they also depend on the momentum transfer Q . This scaling violation results
in a structure function 2 F 2 which is shifted towards smaller x-values as |Q 2 | rises. If the
momentum transfer rises, gluon radiation is enhanced, and the proton is thus dominated
by gluons and sea quarks. At a TeV collider, valence quarks are no longer the main
contributor to the total cross section of inelastic scattering.
Thesepdf'sarealldeterminedbyexperiments(e.g. Hera)astheroreticalQCDcalculations
are very complicated. Monte Carlo simulations need these parton density functions as an