10 - H1 - Desy

1.5 Analysis motivation and goals 27
variables are estimators of the longitudinal momentum fractions carried by the parton
which enter the hard interaction from the proton side x and from the photon side x γ ,
already introduced in section 1.2. These leading order definitions of the estimators do
not use the energy of the jet. The latter is expected to be reconstructed with relatively
low resolution and thus the leading order estimators yield a higher correlation between
the generated and reconstructed levels. The usage of the variable x LO
γ is recommended
in [49,50] to reduce infrared sensitivity. The variable x LO
p is discussed e.g. in [51]. The
accompanying hadronic jet is required to be within the pseudorapidity range of −1.3 <
η jet < 2.3 and has the transverse energy above 4.5 GeV. The asymmetric energy cut on
the photon and the jet is required to ensure the validity of the NLO calculation [49,52,53]
The prompt photon phase space with additional jet requirement is later on referred to as
exclusive or photon+jet phase space.
Another interesting measurement is the study of the transverse correlations between the
prompt photon and the accompanying jet. For direct events in leading order and at
sufficiently low Q 2 , the measured acoplanarity is directly sensitive to the transverse momentum
k T of the parton entering the hard interaction. The mentioned effect can be
studied using two variables ∆Φ and p ⊥ defined as
p ⊥ ≡ |⃗p γ
T
× ⃗p
jet
T
|
|⃗p jet
T
|
= E γ T
· sin∆Φ. (1.42)
and sketched in the transverse plane 5 in figure 1.22.
p
γ
T
p
∆Φ
Transverse plane
p
jet
T
Figure 1.22: Definition of the variables ∆Φ and p ⊥
between prompt photon and the leading jet.
used to study the correlations
The azimuthal acoplanarity between the photon and the jet ∆Φ and the photon momentum
perpendicular to the jet direction p ⊥ were chosen such as to avoid usage of the jet
energy measurement and thus minimising the potential degradation of the resolution. If
the jet perfectly balances the photon candidate, p ⊥ is equal to zero and ∆Φ is equal to
5 For a definition of the transverse plane the reference system is needed. It is introduced in section 3.2
where transverse plane is also defined.