JET ALGORITHMS.
WRAPPING UP THE SUBJECT

F. V. Tkachov

Institute for Nuclear Research of Russian Academy of Sciences, Moscow 117312, Russia
ftkachov@ms2.inr.ac.ru, http://www.inr.ac.ru/~ftkachov


This postscriptum to the theory of jet definition 
summarizes the points which did not find their way into the main text.





Introduction 1 culminating in the design of a fast and robust Optimal
Jet Finder [5]; the code is available from [14]).
I've just been told that the subject of jet definition can
never be wrapped up.1 What the title actually means is There is a remarkable synergy between different
that this talk is supposed to close the series [1][5] in pieces, and none can be omitted without damaging the
which I was presenting the theory of jet definition [6][9] whole. From the above list, it should be clear why it took
as it evolved. The format and atmosphere of the QFTHEP 25 years to solve the problem of jet definition.
workshops made them an ideal venue for that. In
particular, all my useful interactions with experimen- Principles of the theory 3
talists occurred or started at QFTHEPs -- including the The theory is systematically developed in two long
contact with physicists from D0/ which resulted in the papers [7], [9]. It is based on the following metaphysical
dotting of an i in the observation of the top quark (see realizations, treated in detail in [7]:
Sec. 4). So, first of all:
(I) An absolute importance of the subject. Indeed:
Thanks to the or gani z er s!  data processing algorithms (=observables) are a
meeting point of experimental data and theoretical
Theoretical synthesis of the optimal jet definition 2 formulae;
I do believe that the subject of jet definition is closed  hadronic jets are a way to observe quarks and gluons;
in the sense that every thing relevant and important has  jets are everywhere in HEP.
found its proper place in the theory of optimal jet
definition (OJD): Realization of the absolute importance of the subject
 metaphysics (what is measurement? [7]); made me dismiss the sentiment2 that any reasonable
 piece of Fortran code can, in principle, be accepted as a
mathematical statistics (the theory of quasi-optimal jet definition. The sentiment is only an expression of
observables whose relevance extends beyond jets to any theoretical frustration at the 25 years' failure to find a
arXiv: 17 Dec 2000 parameter estimation problems where theoretical input is solid foundation on which to build a systematic theory of
represented by a Monte Carlo event generator [11]); jet definition.
 "high mathematics" (the surprising relevance of the (II) The theory of jet definition should be tightly linked
so-called *-weak topologies for description of calori- to quantum field theory, the theory of fundamental
metric detectors and hadronic energy flow [7]); interactions of which jets are a visible manifestation. In
 quantum field theory (the central role of energy corre- fact, my very first impression from the first explanations
lators and their fundamental expression in terms of the I received about jet algorithms (from W. Giele at
energy-momentum tensor [8]); Fermilab in 1992) was a surprise at how un-quantum-
 QCD (the issues of IR safety, etc. [12]); field-theoretical the popular jet algorithms were.3 It was
 numerical mathematics (algorithms for minimum obvious to me as the discoverer of the algorithms on
search in 2K dimensions) and software engineering (the which the flourishing industry of NNLO QCD
use of advanced software development tools [13])
2 Voiced by M. Mangano at [15].
3 There is a paradox here because G.Sterman and S. Weinberg each
1 The person who said that announced after the talk his willingness to published a textbook on QFT. I have an explanation for the paradox





eat his words but it has nothing to do with the subject of jets per se.




1


calculations is based ([16], [17]) that the conventional jet data processing algorithms, so that on the surface,
definitions do not conform to QFT at the basic kinema- dynamical issues play a subordinate role (see, however,
tical/structural level, resulting in complications for the discussion in Sec. 3.1).
systematic theoretical analyses. After the paper [7] was finished, a well-meaning
(III) Jet algorithms must be fully understood as an theorist advised me that I "should now do some data
instrument of physical measurement. An implication is processing". The advice was ignored; the complexity of
that the analysis of measurement errors, including the problem called for some division of labor; I just did
fluctuations due to the statistical nature of quantum what I could in my situation, and went to great lengths4
theory predictions -- most notably, how such errors sparing no effort5 to make my findings read by theorists
survive the jet-algorithms-based data processing -- must and experimentalists alike.
be a central issue to be addressed by the theory. This line As a reward for all the agony (not counting the
of thought led me to investigate the following damage my other projects suffered due to a few years'
fundamental analogy: neglect), the paper [7] earned me exactly three external
citations. To the experimental one I'll turn in Sec. 4.
ruler
length real number Of the other two, one was an incorrect attempt to literally
implement an ancillary interpretation quoted in a
calorimetric detector
energy flow
? footnote of [7] (see [9] for details). The other was a
prominent but non-specific citation in a review talk [20].

Filling the empty slot was the key issue I was Behind the scenes, there was (among other things) an
preoccupied with in [7]. earlier negative report on [6] which expressed a
conviction that "kinematics" is not what the theory of jet
In the practical aspect, ref. [7] introduced: algorithms is about -- and that the QCD dynamics was
(i) A large new class of generalized shape observables the real issue. My reply (systematically presented in [7])
(the so-called C-algebra), some interpreted as non- was that it may not be healthy to proceed to the dessert of
integer jet numbers, others -- so-called spectral dynamics without first doing away with the soup of
discriminators -- sensitive to the structure of multi-jet setting up the kinematics correctly.
substates. The motivation was to illustrate that: In fact, there are two potentially conflicting issues:
-- jet algorithms are, in principle, not needed to extract (a) Which jet definition is best for theoretical
the physical information usually obtained by their inter- calculations?
mediacy;
-- such information is best extracted using generalized (b) Which jet algorithm is best for extracting maximum
shape observables (this became a theorem in my second information from experimental data?
paper [9]); and finally that The theory of the popular kT algorithm [21] simply
-- jet algorithms are, from this viewpoint, only a means misses (b) and, settling on an ad hoc algorithmic scheme
for approximate construction of such observables. (successive binary recombinations), focuses on (a).
On top of that, convenience of theoretical calculations is
(ii) The notion of regularization of event cuts as an ef- judged from the standpoint of the Sudakov-Lipatov
fective means to suppress statistical fluctuations induced method of leading logarithmic approximation.
in answers and thus enhance the signal/background. No expert in diagrammatics can fail to appreciate the
(Ref. [9] offered a more systematic treatment and beauty of Sudakov's 1956 paper [22] -- or to be
provided new examples and prescriptions for frustrated (at least at first) by L.N. Lipatov's calculational
regularizations.) tornado -- yet to me, the LLA techniques is rather an
(iii) A binary recombination algorithm with an optimal antiquated piece; there are much more powerful ways to
recombination criterion which was derived uniquely handle diagrams [23].
from first principles (within the assumption of the binary In short, the argumentation behind the kT algorithm
recombination scheme) and which turned out to be a left me unimpressed.
geometric mean of the JADE [18] and Geneva [19]
criteria. (The optimal criterion was generalized in [9] into
a global recombination scheme to become the optimal jet
definition.)
4 like spending a 36-hours-long birthday passing customs, waiting for
In effect, the paper [7] introduced a novel, systematic a delayed plane and flying non-stop across the whole of Europe, the
point of view on jet algorithms as a means of construc- Atlantic, and a good part of USA -- all this heroism in order to drop
tion of observables for precision measurements; it is, in a the preprint [7] right where the action was.
sense, purely kinematical in that it starts from the 5 The outrageously un-academic -- but extremely effective --graphic
analysis of measurement errors and their evolution in on the first page was employed only after testing its effect on a few
unwary colleagues




2


But what about dynamics?6 3.1 For convenience of discussion I divide the algorithms
considered in [25] into two groups: the "good" algo-
In the language of theory, "dynamics" is nothing more rithms (variations of the venerable Luclus8 and the kT)
than qualitative properties of QCD matrix elements. and the "bad" algorithms (JADE and Geneva).
The most basic such property is the collinear It was, of course, superfluous to include into com-
singularities with the probability density behaving as parison the optimal criterion of [7] because its behavior
-1
~ d , 3.2 can be easily deduced from the results for the two "bad"
algorithms. The latter fact being not mentioned in [25],
where is the collinear angle of the emitted parton. here are some comments.
The leading power behavior 3.2 is exactly what deter- The optimal, Geneva, and JADE criteria have, respec-
mines the specific form of the usual conditions of IR tively, the following forms:
safety as explicitly formulated in [24]. So making one's
observables IR safe already includes the most important ( -
E + E ) 1 E E  (1- cos < y , 3.4
a b a b ab ) cut
dynamical information into the picture. This is the case ( -
E + E ) 2 E E  (1- cos < y , 3.5
a b a b ab )
e.g. with OJD -- both the 2 1 recombination version cut
of [7] and the global N E E  (1- cos < y . 3.6
a b ab )
part N jets variant of [9]. cut
If the collinear singularities were more severe, e.g. The optimal criterion happens to be a geometric mean of
2
- , then restrictions would have to be imposed not only the other two. It is perfectly clear that its behavior should
on the values of observables but also on their first also be a median one.
derivatives, and the entire theory [9] together with the Now the several graphs presented in [25] (e.g. Figs.
resulting OJD would have changed accordingly. 18, 19, etc.) show that the behavior of JADE is always
Compared with the leading power behavior, logarith- the worst, Geneva behaves erratically, and the "good"
mic corrections -- resummed or not -- play a subor- algorithms populate the band between JADE and
dinate role (this is particularly clear in the context of the Geneva.
theory [7], [9] which offers a constructive model for the The band turns out to be pretty wide (proving that the
notion of "physical information of the event"). effect of what one expects to be insignificant algorithmic
So as no surprise comes the evidence (see Sec. 3.3) variations such as changes in the order of recombina-
that the behavior of various flavors of kT algorithm would tions, is large and not incomparable with the difference
differ from the binary version of OJD within the uncer- between the "good" and "bad" algorithms).
tainties of the kT-type algorithms. It is also perfectly obvious that the optimal criterion is
Moreover, ref. [9] contains an argument which demon- bound to be among the "good" algorithms. An implica-
strates that OJD is optimal not only in the kinematical tion is that its global analog -- the OJD -- must behave
sense but -- which was not a priori expected -- also in a similarly to the "good" algorithms.
properly formulated dynamical sense. This shows that
the IR safety (reflecting the singular structure 3.2) is all Now on to the experimental citation of [7].
that really must be taken into account in the definition of
jets; anything on top of that is best treated as something
only theorists should worry about in their calculations.
This conclusion is corroborated by the findings of [25] to
which I now turn.

Comparison of different binary recombination
algorithms 3.3

Another theoretical paper which came to my attention
after the completion of [9] is the comparison of various
versions of the iterative 2 1 recombination scheme per-
formed by acknowledged experts in such matters [25].
The comparison contains a number of results which are
visible confirmations of some a priori claims made in [7]
and [9]; for many, such explicit calculations may be more
convincing than the logical arguments.7 (where such experiences may be common knowledge) rather then the
specific one being dealt with (where such principles can be a novelty
and, as such, are greeted with suspicion).
6 A question by S. Catani at [15]. 8 Note that the definition of Luclus changed compared with the 1983
7 A difficulty with synthetic solutions is that they often involve logical original [26]: the 1998 Luclus [25] is equivalent to the 1995 optimal
patterns which abstract experiences from other problem domains criterion [7] with the angular factor square-rooted.




3


The top signal in the all-jets channel at D0/ 4 made the effort of finding me at Fermilab (where I was
able to visit thanks to a G. Soros grant and the hospitality
Recall that the two collaborations which reported the of FNAL theorists), showed me around the D0/ detector
discovery of the top at FNAL in 1995, CDF and D0/, and brought me into contact with other members of the
were in very different positions: CDF had the SVX b- all-jets group (S.Ahn and H.Prosper), and we had a nice
tagging hardware which proved to be a powerful means long discussion about regularization of cuts and spectral
for selecting the events with top. In particular, at the time discriminators. N. Sotnikova (a member of both D0/ and
of the top discovery in 1995, D0/ could not see the top the QFTHEP team) ensured that the draft of [7] was well
signal in the all-jets channel. So there was a strong advertised and plentifully available at D0/ . The next time
competitive pressure on D0/ to seek alternative methods. I heard about the D0/ all-jets group was at QFTHEP'96
The preprint release of [7] could not be more timely. from E.Boos who mentioned some striking results but
I'd like to emphasize that the initial contact with D0/ could not provide any details. I tried to get into contact
physicists occurred at QFTHEP'93 [1]. Another peculiar with D0/ but failed. I heard nothing from them since then
circumstance is that both physicists (A. Klatchko and -- and switched to asymptotic expansions of Feynman
D. Stewart) who are to be credited for bringing the new diagrams, the subject neglected since 1992 in favor of
theory to the attention of the D0/ all-jets team, had to jets -- until I ran across ref. [10] while at CERN in
leave physics. March, 2000. Their page 59 contains the following
At QFTHEP'93 A. Klatchko picked up a copy of my passage which I cannot resist quoting:
talk and brought it to Fermilab. The copy was inherited
by D. Stewart. Although about to leave physics too, he


"... Additional cuts are applied to remove events with noise from the Main Ring. After these cuts, about 280,000
events remain. At this stage, the signal to background ratio is about 1:1000. Requiring an SLT b-tag increases the
signal/background by about an order of magnitude, leaving 6000 events.

To make further progress, D0 performs a multivariate analysis using thirteen variables, described briefly in
Table 10. The principal ones are jet1 jet2
H , H H - E - E A
N
3 , the average jet count , the aplanarity A , the
T T T T T jets


centrality jet
C H E p
jets , and the transverse momentum of the muon . A particularly powerful (and
T T

unusual) variable is the average jet count, defined by


 55 GeV  55 GeV

A
N  E N  E dE E dE (17)
jets ,
T T T T T
15 GeV 15 GeV


where N (> E is the number of jets with transverse energy greater than E . This variable, inspired by the work
T ) T

of Tkachov90 is interesting in that it assigns a nonintegral "number of jets" to the event.

These thirteen variables are combined using feed-forward neural networks ..." (90 = [7])

The final result of the procedure is observation of the top events differ. They might have replaced 's with the
excess of events containing top over background in the equivalent integral quantities N (> E (similarly to how
T )
total cross section at the level of 3.2. this is done in the probability theory to avoid directly
To appreciate the work behind the observable (17), dealing with singular probability densities) and then
note that it has no direct analog in [7]. I can think of the used event generators to study the corresponding patterns
following way to arrive at it. In [7], the so-called spectral for background events and events with top to arrive at
discriminators were introduced which, for narrow jets, their observable (see Sec. 4.2).
allowed representations At this point, I cannot help reminiscing how a promi-

d w( )
( - S ), 4.1 nent QCD expert told me he'd found ref. [7] incompre-
j
j hensible -- apparently, because there were in it no
where summation runs over all (multi-)jets of the event leading logarithms, no parton distributions -- in short,
and S none of what QCD theorists swear by. Another expert
j is a variable like invariant mass (or transverse
energy) of the (multi-)jet. This kind of observables are advised me that the things I discussed were not what
not usually considered, and D0/ must have simply ignored experimentalists really needed. Also, shortly after the
what I wrote about how such observables can be defined release of [7] an American theorist P. ventured to run
bypassing jets, and focused on the simplest case, i.e. tests of spectral discriminators. Despite obtaining pic-
distribution of event's jets along the axis E tures which fully agreed with the qualitative expectations
T , and tried to
see how the resulting patterns for background events and of [7], P. strangely made an exactly opposite conclusion.
My guess is, he simply coded the formulae of [7] as is



4


without trying to understand their meaning, and naively The entire theory of jet algorithms now reduces to
expected to see exactly the bumps I draw there. Instead, studying ways of construction of such approximations.
he saw a shoulder, and a steeply rising background to the
left of it. The presence of the shoulder was a clear indi- It is this embedding of the problem of jet definition into a
cation that the signal was there, and one only had to broader context which provides an unambiguous
study its evolution and to figure out a simple way to criterion for deciding which algorithm is best:
extract the numerical information (e.g. a wavelet filter
would do nicely). But, apparently, there are easier ways The best jet algorithm is that which allows one to
construct the best observable for measurements of a
for a theorist equipped with a computer and a MC given parameter; the best observable is that which
generator to produce a publication than deep experimen- yields the best precision for the parameter.
tation with novel ways to process data. (For fairness'
sake, the dominant software engineering platform in Second, I now derived the most general N
part N jets
HEP -- Fortran, C, etc. -- does not encourage such recombination criterion for finding jets. The criterion
experimentation.) required minimization of a multi-axes generalization of
Power of regularizations 4.2 the well-known thrust. (An e-mail from W. Giele about a
forthcoming session of the jet definition working group
An important trick in the construction of good at FNAL in March, 2000 stimulated exploration of
observables is regularization. This is a concept widely algorithmic implementations of OJD, resulting in an
used in applied mathematics (see [7] for references). efficient code [5].)
In [7] and [9], I only gave simple examples to illustrate Third, there were systematically motivated ways to
potential benefits of regularizations (which, by the way, treat the problem of non-uniqueness of jet configurations
come in many flavors, although with the same via association of multiple (appropriately weighted) jet
underlying principles). The above D0/ observable (17) configurations with the same event. For details, the
offers a great real-world discovery-class example of how reader is referred to [9].
useful a regularization can be.
Quasi-optimal observables 5.1
Indeed, suppose one has noticed that top events tend
to produce more energetic jets. Then one would consider Pondering the D0/ observable (17), one is faced with a
the observable N (> c) ("the event has N jets with ener- natural question: Is there a way to obtain such
gies above c") with some c . An integer-valued obser- "particularly powerful" observables in this and similar
vable is discontinuous, and its discontinuities are, on problems with less guesswork than had been involved in
general grounds, sources of non-optimality (loss of the finding of (17)? The answer is yes, and the corres-
physical information due to unnecessary enhancement of ponding prescriptions are called the theory of quasi-
statistical fluctuations in the transition from raw data to optimal observables. In view of its general importance,
the values of the observable; see [9]). Such non-optima- it was posted separately [11] rephrased in the jargon of
lities are eliminated by introducing a continuous regulari- parameter estimation of mathematical statistics. The
zation, e.g. in the form of a smearing over the cut c . theory is simple and closely related to the Rao-Cramer
General principles do not fix details like the weight used inequality; see [9] or [11].
for the smearing. At this point some experimentation is Quasi-optimal observables are a means to approach
needed. Finding an optimal shape of regularization, how- the quality of the maximal likelihood method in situa-
ever, is a much more specific task than the original one. tions where its application is problematic such as
Note that the smearing as a way to regulate a hard cut encountered in HEP (infinite dimensionality of the under-
was not explicitly mentioned in [7] (although smearings lying event space and a probability density in the form of
were mentioned in other contexts). event generator rather than an explicit formula).
A conclusion from the D0/ experience is as follows: Although maximal likelihood is widely used (see e.g.
[10]), the method of quasi-optimal observables is
Learn to use regularizations. simpler, more flexible, and offers new options both for
design of general-purpose software tools and for data
processing in specific applications.
Optimal jet definition: the final form 5 For instance, instead of the observable (17), I would
The second part of the theory, ref. [9], improved upon simply MC-generate a quasi-optimal observable in the 6-
the first in almost every point. I now had a proof that dimensional space of the variables jet
E (e.g. using a
T
observables which yield the theoretically best precision rectangular grid; the formal parameter to be estimated
for a particular parameter are always the generalized would be the coupling to produce top-antitop pairs).
shape observables; jets-based observables can only yield If constructed with enough care, such an observable
approximations to such optimal observables. As a result: might well obviate the need for neural networks.



5


(This would certainly be the case for a quasi-optimal quasi-optimal observables. As a result, OJD (unlike
observable constructed for the variables including the six binary recombination algorithms, whether optimal or kT)
jet
E plus all the variables from Table 10 which cannot offers natural regularizations to solve such problems as
T the potential non-uniqueness of jet configurations (which
be expressed in terms of these.) reflects the fact that different parton configurations may
 generate the same hadronic final state).
It would be interesting to develop universal adaptive
software to automatically generate quasi-optimal obser- On the difficulty of computer implementation 5.3
vables given a sample of events and a number of (more
or less ad hoc) variables. From [25] I learned that generalizations of thrust were
proposed for jet definition in the early 80's [28].
(It looks like this could be done without recurring to The exact form of OJD (in particular, the treatment of
fancy techniques such as neural networks etc.) soft energy via an additive term) could, of course, not
A practical conclusion is this: have been guessed a priori. On the other hand, ref. [25]
concluded that jet search based on optimization of thrust-
Learn to construct quasi-optimal observables. like shape observables was computationally prohibitive.
To this I note the following:

Unless I missed something in [10], the top mass has not The code and data structures of the OJD implemen-
yet been measured in the all-jets channel at D0/. This tation described in [5] take under 300K of RAM for
could be an excellent starting point. LEP2 events, and the algorithm finds jets for such an
event in a fraction of a second on a modest Pentium.11
The global N
part N jets recombination algorithm 5.2 Such an algorithm could be implemented even on a 1984
PC with 640K of RAM.
The derivation, description and discussion can be
found in [9]. A convenient brief summary of the defini- What was lacking was not hardware or even software
tion is given in [5]. Suffice it to say the following: (the old Fortran IV not to say Turbo Pascal 1.0 would
 have been sufficient) but expertise in numerical mathe-
OJD prescribes to determine the jet configuration via matics and software engineering as well as determina-
minimization of shape observables which generalize the tion. Determination could have only come from realiza-
venerable thrust to n axes. tion of the theoretical depths behind OJD. The software
 OJD is similar to a cone algorithm9 in that there is a engineering aspect is discussed in the notes collected in
parameter, R, which limits the cone radius, and the [29]. Here I would only like to point out that the displa-
resulting cones are less irregular than with binary cement of Fortran in favor of C++ (rather than strictly
recombinations. type-safe languages such as any version of Oberon-2; see
 Being a global version of the binary recombination e.g. [13]) in the physicists' software engineering is a
algorithm of [7], its behavior and properties (e.g. disaster of historic proportions (and a good part of the
stability) can only be better than for the binary explanation of inability of theorists to accomplish com-
recombination version (which as we saw in Sec. 3.3 plete 1-loop calculations for LEP2). It is also absolutely
should be on a par with other "good" jet algorithms10). irrational in view of the existence of simple and powerful
 alternative in the form of the Oberon-2 family of
The speed of jet search is expected to be languages representing the brilliant tradition of design of
O( N  N ) ; compared with the 2
O( N ) behavior
part jets part N. Wirth and his school starting from the old Pascal (see
of binary recombination schemes (including k [29] for more on this).
T), this
property alone might make OJD the jet algorithm of The harnessing of the digital revolution being a major
choice for future colliders such as LHC where multi- infrastructure problem in physics as elsewhere, a com-
plicities are much higher. petent and responsible policy of steering the HEP com-
 OJD is intrinsically connected with the theory of munity towards the use of safe programming languages
-- and redirecting human energy released thereby into
more productive activities than debugging C++ codes --
9 I incorrectly stated in a talk that OJD is equivalent to a cone would have a major positive impact on physics.
algorithm for events with well defined jets. However, the cone radius
in OJD depends on the distribution of energy around the jet axis, so
that the techniques of energy corrections developed for fixed cone
algorithms would have to be modified.
10 This has been confirmed in a number of un-premeditated tests run
on realistic MC event samples by Pablo Achard [27]. In at least one
graph I saw with my own eyes, OJD resolved partons significantly 11 For the events tested by Pablo Achard [27], the OJD implemen-
better (with an efficiency close to 100%) than kT (~70%) in the entire tation of [5] was somewhat slower -- but not significantly -- than kT.
interval of rapidities where both algorithms yielded meaningful Note that ref. [5] focused on feasibility studies and did not attempt to
results. implement all possible algorithmic optimizations.




6


Conclusions 6 Appendix. The benefits of OJD compared with kT 6.1

To the best of my understanding, the subject of jet All the QCD argumentation behind kT boils down in
definition as a theoretical problem is closed. the end to the proposition that with it, better theoretical
The most important next task in regard of jet-related calculations are possible. However:
data processing appears to be for physicists to learn to  Experimental data are more valuable than theoretical
use OJD for construction of quasi-optimal observables numbers Preserving information from data is more
for specific applications. important than making it easier for theorists to do their
Psychologically, the main difficulty may be to stop calculations. OJD is optimal precisely because it
wasting human effort (and other valuable resources) on preserves the experimental information in the best
the obsolete jet definitions. manner possible.
 As regards calculations: nothing compares with shape
Acknowledgments observables such as thrust in regard of calculability (LLA
This work was supported in part by the Russian Foun- or NLLA) and amenability to theoretical analyses (power
dation for Basic Research (quantum field theory corrections), and OJD is based on such observables.
section12) under grant 99-02-18365.13 Furthermore, there are better ways to do complex
I am grateful to V. von Schlippe for a comment, and calculations than the archaic Lipatov-Sudakov
to S. Karshenboim for suggesting a term. techniques, namely, the systematic machinery of
asymptotic operation [23] whose euclidean version,
Finally, it is my greatest pleasure to thank the organi- remember, is behind most of the well-known NNLO
zers of the QFTHEP workshops (E.E. Boos, B.B, Lev- calculations in QCD.
tchenko, V.I. Savrin and N.A. Sveshnikov ) for their  Further, the binary recombination scheme per se is
invariable support over all these years. flawed (cf. the large variations between different variants
of "good" recombination criteria [25]).
 The kT algorithm behaves quadratically in the number
of particles, and OJD may run faster for LHC multipli-
12 There is far too much to my taste of this sort of things that goes cities.
unrecorded, so here is my contribution: in 1998 when the above
FNAL report was released, the HEP section of the Russian  OJD offers new options for a systematic construction
Foundation for Basic Research denied me support for my projects. of better observables -- options not available within any
If the support were not resumed by the quantum field theory section conventional jet definition schemes.
(and no, jets were not even mentioned in my grant application) you
would most certainly not learn about OJD.

This must have something to do (as I realize post factum) with the
old story of Landau vs. Bogolyubov reflected within the Russian
theoretical physics in the form of a certain gruppovschina, with the
two sections of RFBR influenced by the respective theoretical schools.
I do not see what I personally have to do with that old story except a
sufficient mathematical background to have drifted in my years of
innocence to Bogolyubov's cathedra (I do own a complete set of the
Landau and Lifshits textbooks too).

For fairness' sake, the fundamental reason for that bitter controversy
lied not so much in particular personalities (the mistake usually made)
but in the overcentralization of everything in Russia, so that the entire
hierarchy is affected by idiosyncrasies of the individuals at the top
multiplied by the centuries-old tradition of servility of subordinates.

There is an objective tendency for similar effects to occur wherever
individuals are endowed with considerable administrative powers
(Germany comes to mind, with perhaps servility replaced by
discipline) and wherever resource-allocation politics finds fertile soil
in complex hierarchies within which there often are no efficient checks
to deter individuals from irresponsibility in spreading their
"necessarily somewhat subjective" opinions.

13 I wish I could benefit from even a tiny fraction of the funds used up
by the two jet definition working groups (FNAL and Des Houches)
which operated during 1999 while the work on the final version of [9]
and on the software implementation of OJD [5], was in progress:
a mere 0.1% would have been enough for a mighty upgrade of my
computers. It is rather a paradox given the state of physics in Russia
that up to this point, the work on the theory of jets and OJD was
performed as a kind of charity for the international HEP community.




7


References

[1] F.V. Tkachov: Calorimetric measurements and jet ~: Algebraic algorithms for multiloop calculations. The
counting [QFTHEP'93, Zvenigorod, Russia, 15-21 Sept. first 15 years. What's next?,  [NUIMA
1993, ed. B.Levtchenko, INP MSU, Moscow, 1994]. A389 (1996) 309].
[2] F.V. Tkachov: Optimizing computations of jet [17] F.V. Tkachov: On the operator product expansion in the
discriminators [QFTHEP'94, Zvenigorod, Russia, 16-22 MS scheme [Phys. Lett. 124B (1983) 212];
Sept. 1994, ed. B.Levtchenko, INP MSU, Moscow, 1995]. ~: Advanced methods for studying radiative corrections.
[3] F.V. Tkachov: From jet algorithms to C-algebra. Theory of asymptotic operation, 
Measurement errors and regularization of cuts, hep- [QFTHEP'92; Phys. Part. Nucl. 25 (1994) 649].
 [QFTHEP'95, Zvenigorod, Russia, 20-26 [18] JADE Collaboration (W. Bartel et al.), [Z. Phys. C33
Sept., ed. B.Levtchenko, INP MSU, Moscow, 1996]. (1986) 23].
[4] F.V. Tkachov: Status of the theory of jet observables [talk [19] S. Bethke, Z. Kunszt, D.E. Soper and W.J. Stirling: New jet
at QFTHEP'97, Samara, Russia, 4-10 Sept. 1997]. cluster algorithms: next-to-leading order QCD and ha-
[5] D.Y. Grigoriev and F.V. Tkachov: An efficient dronization corrections [Nucl. Phys. B370 (1992) 310].
implementation of the optimal jet definition, [20] G. Sterman: Recent progress in QCD, 
 [QFTHEP'99, Moscow, May 27 - June 2, [talk at APS Meeting of Division of Particles and Fields
1999. Eds. B.Levtchenko and V.Savrin, INP MSU, (DPF 99), Los Angeles, CA, 5-9 Jan. 1999].
Moscow, 2000]. [21] S. Catani, Y.L. Dokshitzer, M. Olsson, G. Turnock and
[6] F.V. Tkachov: Measuring the number of hadronic jets, B.R. Webber: New clustering algorithm for multijet cross
 [Phys. Rev. Lett. 73 (1994) 2405; Errata sections in e+e- annihilation [Phys. Lett. 269B (1991)
ibid. 74 (1995) 2618]. 432].
[7] F.V. Tkachov: Measuring multijet structure of hadronic [22] V.V. Sudakov: Vertex parts at very high energies in
energy flow, or, What is a jet?,  [FERMI- quantum electrodynamics [Sov. Phys. JETP 30 (1956)
LAB-PUB-95/191-T; Int. J. Mod. Phys. A12 (1997) 5411]. 87].
[8] N.A. Sveshnikov and F.V. Tkachov: Jets and quantum [23] F.V. Tkachov: Towards systematic near-threshold
field theory,  expansions in perturbative QFT ,  [Phys.
[Phys. Lett. B382 (1996) 403]. Lett. B412 (1997) 350];
[9] F.V. Tkachov: A theory of jet definition, ~: Distribution-theoretic methods in quantum field
 (revised Jan. 2000). theory,  [talk at the Bogolyubov Conf.,
[10] P.C. Bhat, H. Prosper and S.S. Snyder: Top quark physics Moscow-Dubna-Kyiv, 27 Sept.  6 Oct. 1999].
at the Tevatron,  [Int. J. Mod. Phys. A13 [24] G. Sterman: Mass divergences in annihilation processes.
(1998) 5113]. I. Origin and nature of divergences in cut vacuum
[11] F.V. Tkachov: Approaching the parameter estimation polarization diagrams [Phys. Rev. D17 (1978) 2773].
quality of maximum likelihood via generalized moments, [25] S. Moretti, L. Lonnblad and T. Sjostrand: New and old jet
. clustering algorithms for electron-positron events, hep-
[12] G. Sterman and S. Weinberg: Jets from quantum  [JHEP 9808 (1998) 1].
chromodynamics [Phys. Rev. Lett. 39 (1977) 1436]. [26] T. Sjstrand: Comp. Phys. Comm. 28 (1983) 229.
[13] Oberon Microsystems, Inc., http://www.oberon.ch. [27] Pablo.Achard@cern.ch (L3).
[14] http://www.inr.ac.ru/~ftkachov/projects/jets/index.htm. [28] J.B. Babcock and R.E. Cutkosky: Identification of jets
[15] F.V. Tkachov [talk the CERN Theory Div. Seminar, [Nucl.Phys. B176 (1980) 113].
March 2000]. [29] F.V. Tkachov: Theoretical physicist's personal software
[16] F.V. Tkachov: A theorem on analytical calculability of 4- engineering in the post-Java world [to be posted].
loop renormalization group functions [Phys. Lett. 100B
(1981) 65];





8



