more or less everybody knows about the
concept of electric charge. Charge comes as positive or negative, and
like-sign charges repel each other whilst opposite-sign charges feel
an attractive force towards each other. Electric charge can be considered
as a property of an object, for example an elementary particle.
Perhaps the simplest and best-known electrically charged fundamental
particle is the electron - where `fundamental' means
point-like according to our current knowledge.
Some decades ago, however, the idea evolved that there might be other
properties of particles which merit the name `charge' because these
properties also give rise to attractive or repulsive forces. One of
these properties was labelled `color charge' or simply `color' and
comes in three kinds which are named `red', `blue' and `green'. Just
as the theory of electromagnetism describes the behaviour of
electrically charged particles, a theory called Quantum
Chromodynamics (QCD) was developed, which describes the
dynamics of colored objects.
As far as we know today, there are basically two kinds of
color-charged elementary objects, which we call
quarks and gluons. The quarks were
once suggested as a purely theoretical concept, but later turned out
to be the basic building blocks of all complex particles and,
therefore, of the macroscopic world around us. The gluons, according
to QCD, bind the quarks together and thereby make possible the
existence of complex particles such as the proton.
The proton is now known to be built from three `valence' quarks with colors
red, blue and green, resulting in an overall `white' or
color-neutral object. QCD governs the way in which the valence quarks
interact with one another.
QCD is much richer and more complex than the theory of
the electromagnetic force. One important difference is that colored
objects are `confined' - only color-neutral objects can exist on their
own. This is why we were never able to observe isolated quarks or
gluons - in contrast to electrons. So if one wants to
investigate QCD, one somehow has to look inside composite particles like the
proton and study the behaviour of the quark and gluon building blocks.
This is one of the reasons for the construction of the HERA
accelerator which collides, at very high energies, protons with
electrons. The electron acts as a probe that explores the structure
and the dynamics within the proton.
In the high energy electron-proton interactions at HERA, the electron
can scatter violently from
an electrically charged component of the proton, i.e. a quark, but
not a gluon. The
quark can be kicked
out of the proton and can be observed as a collimated spray of
particles (a jet) hitting the H1 detector (remember that
quarks cannot be seen in isolation, so the struck quark drags accompagnying
particles litterally from nowhere - from the vacuum - in order to
neutralise its colour). Alternatively, a gluon inside the
proton can split into a quark-antiquark pair, allowing the electron to
couple to one of those two. In this case, two jets
might be observed, one from each of the two quarks into which
the gluon splits. There are even more possibilities, since
both quarks and gluons are also able to radiate gluons,
which may also split into even more quarks and gluons, ultimately producing
a `cascade' of particles between the struck quark and the remnants of the
proton. All of the particles of the cascade might emerge as jets.
A typical electron proton collision thus
results in very complex distributions of jets and particles in the detector.
One of the central aims of the HERA experiments is to obtain a deeper
understanding of the QCD dynamics involved in producing these complex patterns
of particle activity emerging from the interactions. In this publication,
we aim to improve this understanding
by studying the distributions of the produced jets
in terms of their energy transverse to the beam direction (ET)
and the angles at which they are produced, parameterised by the
Since QCD is a very complicated theory, predictions can only be made
using approximations. It is interesting and important to ask how
valid these approximations are in as many different experimental
situations as possible. The most successful approximation that we
have at present for the descripion of colour dynamics is
known as next-to-leading order (NLO) DGLAP. In this analysis, the
predictive power of this approximation is tested in detail
with the measured jets from data collected
with the H1 detector in the years 1996 and 1997.
One of the results of the analysis is shown in the plot below. In the upper
part of the figure we plotted as black points the probability (in some
complex notation) of finding a jet with a a certain ET. These data points
are compared to a solid line with
a yellow band around it. The line shows the NLO DGLAP
and the yellow band is the uncertainty in this prediction. The dashed
line shows the predictions of a less sophisticated approximation,
leading order (LO) DGLAP. In order to look more closely for discrepancies,
the bottom part of the figures shows the relative difference beteen
the NLO DGLAP theory and the measured data.
The analysis is done in three different regions of the detector - from
left to right, close to the direction of the outgoing electron beam,
in the middle of the detector, and close to the
direction of the outgoing proton beam.
A close look at the figure shows that
for jets produced in the central and outgoing electron directions,
the agreement between the data and the
theoretical predictions is impressive, thus increasing our confidence
in the predictive power of the theory in these experimental regions.
there is a clear discrepancy between the data points and the yellow
band in the right column of the figure, corresponding to jets produced
near to the remnants of the proton.
This last region is expected to be
the most difficult to describe and interesting, because it is furthest
from the interaction between the electron and the final struck quark.
It is thus the most sensitive to the details of the cascade of
quarks and gluons mentioned above. A variety of novel QCD effects have
been predicted for this region. However, the discrepancies between
data and theory near to the proton remnant are only present for low values
of the variable ET, where NLO DGLAP is known to be less complete than at
higher values. Just look at the difference between the LO and NLO predictions
in the upper right part of the plot. The most likely explanation seems to
be that a still more precise version of the theory is needed, for example
an extension of one more order to next-to-next-to-leading order (NNLO DGLAP).
What did we learn from this analysis? Firstly we confirmed the applicability
of the best approximation to QCD that we have to date (NLO DGLAP) for the
description of jets in a wide variety of circumstances. Secondly, it is
clear that our result should trigger additional effort in developing more
complete theoretical predictions. Only time will tell whether a refinement
of DGLAP to NNLO will be able to resolve the differences near to the proton
remnants or whether a whole
new approach, not based on the DGLAP approximation, will be required.
This analysis is one of the many small building blocks which together
give us a detailed picture of the
microscopic world and help us to understand better and ever better
the world we are living in.