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To relate the hadronic final state to
the underlying hard partonic behaviour
it is generally necessary to apply a jet algorithm.
The JADE algorithm [11] has been used in the following analyses
as it was, at the time, the only algorithm
which allowed comparison to the NLO calculations (PROJET [12]
and DISJET [13]).
The JADE algorithm
is a cluster
algorithm based on
the scaled invariant mass-squared
for any two objects i and j
assuming that these objects are massless.
W2 is the squared invariant mass
of the hadronic final state and is the angle
between the two objects of energies Ei and Ej.
The minimum yij
of all possible combinations is found. If
the value of this minimum yij is less than
the variable cut-off parameter , the two objects i and
j are
merged into a new object by adding their four-momenta and the process is
repeated until all . The surviving
objects are called jets which represent the underlying partonic
structure that is dependent on .
Figure 3:
Jet production rates Rj as a function of the jet
resolution parameter ycut for Q2 in the range
(a) 120<Q2<240 GeV2, (b) 240<Q2<720 GeV2,
(c) 720<Q2<3600 GeV2, and (d) 120<Q2<3600 GeV2.
Only statistical errors are shown.
Two NLO QCD calculations, DISJET and PROJET,
each with the value of obtained from the fit at
ycut=0.02, are also shown.
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Figures 3a-d show the ZEUS jet rates using data taken
in 1994,
R1+1, R2+1
and R3+1 as a function of
ycut for data compared with the DISJET and PROJET NLO QCD calculations
for three Q2 intervals
120<Q2<240 GeV2, 240<Q2<720 GeV2,
720<Q2<3600 GeV2, and the combined region
120<Q2<3600 GeV2.
There is good agreement between the
corrected 1+1 and 2+1
jet rates and the NLO QCD calculation over most of the
range in ycut shown.
Both programs agree well in their prediction of the jet-rate dependence
as a function of ycut.
Figure 4:
Left: Values and total error of from
various processes.
The solid line indicates the world average and the band its total error.
Right: (Q) from HERA (open symbols) and other processes
with increasing Q (closed circles):
and
, event shapes and in e+e-.
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The values of (Q) extracted
by the H1 [14] and ZEUS [15]
collaboration as a function of Q
are shown in Fig. 4.
The value of was determined by varying the scale parameter
in the QCD
calculation until the best fit to the ratio R2+1 was obtained
at a particular value of ycut.
The measured decreases with increasing Q, consistent
with the running of the strong coupling constant, with Q2 taken as
the
scale.
In addition the figure shows the curves for
= 100, 200, and 300 MeV.
An extrapolation to (Mz) yields:
which are consistent with other values obtained from
a large variety of different processes as shown Fig. 4
(see [16] for references).
Even with the current statistics
the HERA measurements are already
competitive with those made elsewhere.
Recently two new, more flexible
NLO calculations (MEPJET [17] and
DISENT [18]) have become
available allowing the experiments
to analyze the data using any particular jet algorithm.
The kT algorithm [19] is particularly suited for DIS
as it allows factorization between the beam fragmentation and the hard
process [20].
The ZEUS collaboration has reanalyzed [21] their 1994 data using
this algorithm.
The preliminary values of (Q) obtained
in the three bins of Q are shown (with statistical
errors only) in Fig. 4 and
are consistent with the results obtained
with the JADE algorithm.
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Up: Hadronic Final States in
Previous: DIS Kinematics
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