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{\LARGE Vacuum Structure and QCD Sum Rules:}\\[5pt]
{\LARGE Introduction}\\

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{\large M. \ Shifman}\\
\vspace{0.5cm}
{\large\em Theoretical Physics Institute, University of Minnesota,}\\
{\large\em Minneapolis, MN 55455, USA}\\[2pt]



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 The story of this article is as follows. Shortly after my arrival to 
the United States I got a letter from Professor Hector Rubinstein
who at that time was the Coordinating Editor
of {\em Current Physics --- Sources and Comments}, a serial North-Holland publication
of reprint volumes on high-energy physics. Each volume was supposed to
present a selection of essential source
  material on
a given  important topic
compiled by  an independent specialist editor,
supplemented by extensive editorial commentaries and mini-reviews.
Professor  Rubinstein invited me to make a volume devoted to the
QCD sum rules.\footnote{This project was aborted in 1992.
In fact, the Volume {\em Vacuum Structure and QCD Sum Rules}
of which I was the editor, was the tenth and the last in the series.}
 After some hesitations I agreed.
The work turned out to be much more
time and labor-consuming than I had expected.
In several cases (Chapter 1, 8 and in some other cases)
I failed to find
among the published papers the one which I could consider satisfactory;
then I had to write the corresponding sections myself.

Hector's idea was to put a historical introduction/foreword, which I was supposed
to write, in  the beginning of the book.
By  deadline
I had only an unpolished and unfinished draft. Other urgent commitments prevented
me from 
 completing the article in time. Therefore, I had to settle for a short technical foreword which
appeared in print in 1992.  
The original rather long Foreword has never been published.
I used edited fragments of this article in various later publications.
Presented below is the original draft.

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The purpose of this Introduction is
to give a general perspective of the development of the method
which goes under an awkward name  {\em the QCD sum rules}
  -- one of the most productive tools for calculating hadronic 
parameters in  Quantum Chromodynamics. The second task is
 to convey the historic flavor of the exciting
time when the theory of hadrons  was making its first steps. 

It is, perhaps, worth starting from the 
second point. It seems fair to say that QCD was born 
after the talk of Gell-Mann and Fritzsch \cite{1} (see also Ref. \cite{2}) in 
which the color-octet gluons were introduced. The next step is 
certainly the discovery of asymptotic freedom in 1973 \cite{3}. In 
the 
first few years, roughly speaking till 1975, the theorists' attention 
was almost totally focussed on hard processes in which the 
short-distance physics plays the dominant role. This topic became 
hot and 
fashionable,  piles of new papers appearing daily. The main 
achievement of this period is  that people learned how to reliably 
isolate the short distance contributions governed by the small 
coupling constant and how to generalize  electrodynamical 
perturbative calculations to non-Abelian theories. 

A recent paper of Polyakov \cite{4} presenting his understanding of 
the 
development of  our field in the seventies is entitled ``A View from 
the Island" which gives a good idea of our place in the scientific 
process in Moscow in those days.  The isolation was almost complete, 
and we could not compete with  the western theorists in most 
fashionable directions where the results seemed to be on the surface, 
for obvious reasons. 

Because of the total censorship preprints and journals from the West 
used to come with enormous delays, and our own papers could be 
submitted to the Western journals only after a complicated 
procedure of getting clearance from half a dozen of different 
instances,  typically a waste of  a few months.  Publication of 
preprints was  an adventure due to bureaucratic limitations.  For 
instance, one and the same paper could not be issued as a preprint 
and, then, in a journal, and the preprint version could not be longer 
than 25 typewritten pages (or 35, I do not remember exactly).  So we 
had a lot of ``fun" trying to muddle and deceive our censors  by 
making different titles in  the preprint and journal versions of one 
and the same work, changing the order of the authors or  serializing 
preprint publications  like a detective story in a popular newspaper 
(unlike the latter case, though, we had to make  an impression  that 
each successive part is not connected to the previous).  Quite often 
these tricks created a terrible mess, to say nothing about wasted
efforts.  Occasionally, in the most 
important cases, one would risk to bypass the standard procedure by 
using different ``illegal" channels, mostly our Western friends. By the 
way,  any contacts with the latter were also severely constrained.  
There is a famous story about one of the scientific bosses in Dubna 
who was instructing the Soviet participants of a conference before its 
opening. He said: ``Well..., we had to organize this conference, and 
even invite some foreigners. Unfortunately, to my deep
regret, this time it will be impossible to completely avoid
contacts..."  
Conferences in the West were open for a handful of  specially 
selected,
through a humiliating procedure; and  even those few which took 
place  in  the 
Soviet Union were not always accessible. I remember,  for instance, 
that a colleague  of mine  from ITEP and I were not granted 
permission to participate in ``Neutrino --77" in Baksan.  The decision to 
throw us out from the list of
participants was made in the very last moment, and the only reason 
behind this decision I
could think of was the fact that we both were Jewish.

Some words of the Soviet newspeak made me sick.
One of such words was {\em Glavlit}.
As I just said, to publish a
scientific paper was much more than just typing the manuscript and
mailing it to the publisher.  There was a long latent period, associated
with getting all sorts of clearances. First, the so-called Expert
Commission (a group of authorized fellow physicists in the given
institution) was supposed to study the paper and recommend its
publication. According to the official rules they had to certify that
 no new discoveries  were reported, because
if they were, the Expert Commission had to recommend to classify the
paper right away. Of course, people tended to stretch the official rules,
otherwise not a single breakthrough  paper would have ever appeared 
in the Soviet Union.

At the next stage the paper would go to the so called Regime
Department whose task was to check that no references to classified
work or undesirable persons were made, no subversive ideas put 
forward,
and so on. With all this paperwork done, the decision to allow
(disallow) publication was to be made by the Director
of the Institute. This is not the
end of the story, however. All materials  intended for publication
had to be cleared through the
so-called GLAVLIT, the almighty agency whose sole obligation was to
ensure  total Censorship in the country. 
If, at the previous stages the author would
have at least some minimal control over what was going on with his
(her) paper, GLAVLIT was a total black box. 

The process of getting all
clearances could extend anywhere from weeks to 
many months, and the paper
was officially nonexistent until the very end. The author could not
even refer to it in his/her further work.
 
This is a long saga, and I could easily write many pages on this topic, 
but now it is  clearly time to stop. To make the long story short I will 
only say that making our results known was a difficult, nervous and 
time-consuming part of our job. This largely predetermined the 
choice of topics we could work on and formed in the ITEP theory 
group and elsewhere a very special atmosphere, now gone forever.  

ITEP of 1970's had one of the best groups in the world, an 
excellent collection of enthusiasts whose attitude to physics was 
totally ``non-commercial".  People were always eager  to discuss with 
each other every interesting scientific question  emerging  during the 
seminar talks or  elsewhere, and these discussions quite often would 
last till midnight.  You could easily find  experts in any conceivable 
field or  direction who would  gladly share  their knowledge with 
you. Our  common enemies  and common isolation created, as a 
counter-reaction, very strong  friendly and scientific ties, as the only 
way of survival,  and helped develop protective values; the tacit 
understanding that good physics was above all was among these 
values. 

The only drawback I can think of now, in retrospect, is the 
general 
negative attitude to field theories in the very end of 1960's and 
the beginning of 1970's when I just appeared in ITEP. The reason 
is obvious, 
of course: the  influence of Landau and his discovery of the 
zero-charge property in QED~\cite{Land} -- the influence which was 
alive and 
very strong in the ITEP theory group in those days. The attitude to 
the 
field theory as to something absolutely not serious was so deeply 
rooted
that the fact of the {\em anti}screening of the gauge coupling 
constant in 
non-Abelian 
theories which was reported in ITEP at least twice 
\cite{Tere},
\cite{Khri} in the {\em sixties} has not been appreciated and 
recognized 
\cite{Vany}. 
A restructuring in minds started only after the very same fact, the 
surprising fall-off of the gauge charge at large distances, became 
known 
from Ref.~\cite{3}.

So, our start was relatively slow. 
By 1974, however, we were fully submerged in this subject,
and shortly after  it became clear that the 
cavalry attacks do not help to solve the 
problem of confinement and that the wide-spread expectations of a 
Messiah who would come soon and teach us the mystery of the 
solution had to be tempered. The fact that instantons \cite{5}, a 
beautiful 
theoretical construction which was a breakthrough in the qualitative 
understanding of the QCD vacuum \cite{6}, turned out to be useless 
in the 
quantitative sense because of the infrared divergences was a serious 
blow. So we adopted a less ambitious approach (by ``we" I mean 
Valya Zakharov, Arkady Vainshtein and myself). The idea was to 
start from short distances where the quark-gluon dynamics was 
essentially perturbative and we felt ourselves on a firm ground, and 
then to extrapolate to larger distances (where the hadronic states are 
presumably formed) including  non-perturbative effects ``step by 
step" and  using some kind of an approximate procedure  to extract 
information on  hadronic properties. Of course, this idea was rather 
vague at first, the program as we know it now has been crystallizing 
gradually. 

It is rather difficult to identify the work which, for us, 
was  the first crucial  step. With some reservations
I might say that the first step has been done in Ref. \cite{7}.
Perhaps now the sum rule for the charmed 
particle photoproduction obtained in \cite{7}  does not seem very 
impressive but this analysis carried important elements which where 
later laid  in the foundation of the sum rule method. A spectacular  
success came after we united our efforts with V. Novikov, L. Okun 
and M. Voloshin. It turned out that a whole variety of the 
charmonium parameters are predictable essentially from pure 
duality, and for about a year  we played the game of  constructing 
the  charmonium widths and mass ratios from simple numbers. In 
1977 a review report \cite{8} was submitted. At about that time it 
became clear that the progress was limited; the method presented in 
\cite{8} could not be reliably generalized to such typical 
representatives 
of the hadronic family as, say, $\rho$ mesons or nucleons. And the 
desire 
to get access to these hadrons was strong. 

The remainder of this story, including its culmination -- introduction 
of the gluon condensate \cite{9} in fall 1977 -- is described 
elsewhere 
\cite{10}.  It was a hot summer of 1977, just before the vacations.
Our big six-head strong collaboration ceased to exist.
We --- Valya, Arkady and myself ---
were leisurely discussing something when the first hints appeared.
The conjecture was that the vacuum was actually something like
a gluon ``medium," and the basic  particle properties are due to
the quark interaction with this medium which can be conveniently 
parametrized by certain
quark and gluon condensates. We worked out the first implications
of the gluon condensate in fall 1977. At first, we were discouraged
by a wrong sign of the gluon condensate term in our ``show-case" sum rule, 
the one for
the  $\rho$ meson. Then we suddenly understood
that this sign could be compensated by the four-quark
condensate --- a real breakthrough.
The accuracy of our results turned out to be much higher
that anyone could expect {\em a priori}.

The basic elements of the approach were already visible in the
first JETP Letters publication~\cite{9}, with  new important findings (e.g. 
borelization) coming later, one by one. We worked at a feverish pace for 
the whole academic year, accumulating a large number of results for 
the hadronic parameters. 

I can't help mentioning an eposide that occurred in the spring of
1978 when we were done with this work.
The episode could have been funny were it not so nerve-wrecking for me.
When we decided that this stage of the work was over, I collected
all my drafts (hundreds sheets of paper with calculations and formulas),
organized them in a proper order, selected all formulas and expressions
we might need for the paper and the future work, carefully rewrote them in a
thick notebook (remember, we had no access to photocopying
machines!), destroyed the drafts, put the the notebook in my briefcase
and went home. It was about midnight, and I was so exhausted
that I fall asleep while on the metro train. A loud voice announcing my stop
awoke me, and I jumped out of the train, leaving the 
briefcase were it was, on the seat. By the time I realized what happened
the train  was gone, and gone with it  forever my calculations ...
I have never recovered my briefcase with the precious
notebook... After a few agonizing days it became clear
that the necessary   formulas and expressions had to be recovered anew.
Fortunately, Arkady had kept lots of 
his own calculations. He never throws out anything.
Therefore, the problem with his drafts was to dig out
``informative" sheets of paper from the ``noise".  
(This was hindered by the
fact that he was in Novosibirsk while we were in Moscow.)
Some of my drafts survived 
in the drawers of a huge desk which I had inherited from Sudakov.
Moreover, many crucial calculations
were discussed so many times by us, over and over again,
 that I remembered them by heart. Nevertheless, I think it took a couple of 
uneasy weeks
to recover the contents of the lost notebook.

In late spring 1978 the question of how all this wealth 
could  be published became of prime concern to us. As usual, we had 
a 
lot of funny adventures  in preparing the manuscript, typing it and  
issuing preprints.  Needless to say, it was a serial publication, see 
above.  As for the  journal article, Nuclear Physics was a natural 
candidate, but previously we had bad luck with this journal: our 
paper on penguins \cite{11} was buried in the editorial office for 
more 
than two years. We were too tired, however, to invent anything new 
and decided to try our luck again. The report occupying the whole 
issue of Nuclear Physics \cite{12} appeared a year later.


Beginning in 1980, the approach we suggested   was tested, 
with a  remarkable success, in analyzing practically 
every static property of all established low-lying hadronic states. 
``Classic" mesons were supplemented by baryons \cite{Ioffe}. 
The approach  was then developed  in various directions ---  three-point 
functions,  inclusion of 
external  electromagnetic and other auxiliary fields, light-cone 
modifications  and so on. This  allowed one to expand the range of 
applicability, shifting the emphasis from the calculation of masses and 
coupling constants  of ``classic" resonances
to such  problems as magnetic moments \cite{MM}, form 
factors 
\cite{FF} at intermediate momentum transfers, weak 
decays \cite {WD}, structure functions \cite{SF} of deep inelastic  
scattering  at intermediate $x$, and many others.  A wealth of 
low-energy parameters -- dozens, if not hundreds -- were obtained with 
a typical theoretical uncertainty of 10 to 30\% essentially from the 
gluon and quark condensates and a couple of other  vacuum
mean values introduced later.  At the initial stage the method was 
essentially  unchallenged since the lattice calculations were lagging far 
behind.

At present, after the spectacular advances of lattice QCD,
the numerical aspect of the sum rule approach 
is somewhat overshadowed, in many instances, although even now
the QCD sum rules are quite competitive in  problems
with more complicated kinematics. At the same time,
theoretical insights and tools developed
 in connection with this method did not loose its significance, rather they 
gained more in the recent years. First and foremost, one should name
the operator product expansion (OPE). 

The idea of factorization of short and large distances, the central point of 
OPE,  dates back to
 classical  Wilson's work  where it was 
put forward in
connection with theories of strong interaction with conformal invariance
at short distances.  Shortly after Wilson formulated a very general 
procedure
of the renormalization-group flow (see e.g. \cite{WKog}) which became 
known as Wilsonean renormalization group. Wilson's formulation makes 
no reference to perturbation theory, it applies both to strongly and 
weakly coupled theories. The focus of Wilson's work was on statistical 
physics, where the program is also known as the block-spin approach.
 Starting from the microscopic degrees of freedom at the shortest 
distances $a$, one ``roughens" them, step by step, by constructing a 
sequence of effective (composite) degrees of freedom at distances $2a$, 
$4a$, $8a$, and so on. At each given step $i$ one constructs an effective 
Hamiltonian,
which fully accounts for dynamics at distances shorter than $a_i$
in the coefficient functions.  

Surprisingly, 
in high-energy physics of 1970's the framework of OPE was narrowed 
down to a very limited setting. On the theoretical side,
it was discussed almost exclusively  in perturbation theory, as is seen, 
for instance, from Refs.
\cite{pope}. On the practical side, in applications, people did not go 
beyond  the 
leading power effects. 
The OPE-based analysis of Christ {\em et al.} \cite{chm} of  
deep inelastic scattering (DIS) was implemented in QCD 
at the level of leading twists. Asymptotic freedom implies that 
the
power asymptotic behavior is determined by canonic dimensions of the 
operators involved. The  asymptotic behavior is modified by 
perturbative logarithms. This 
explains both the
Bjorken scaling in DIS as well as logarithmic
deviations from it. Similar logarithmic corrections were
found in weak decays (penguins!).
In essence, that was all one could find on the theoretical market of the 
day.

We were the first to adapt \cite{NSVZo}
the general Wilson construction to QCD,
extending  OPE to systematically include power suppressed
effects.  A consistent Wilsonean  approach requires
introduction of a normalization point $\mu$ which plays the role of 
a running parameter separating ``hard" contributions included in the 
coefficient functions and ``soft" contributions residing in local  operators
occurring in the expansion. The degree of locality is regulated by 
$\mu$ itself.

 Prevalent at those days was a misconception that
the OPE coefficients are determined exclusively by perturbation theory
while the matrix elements of the operators involved are purely 
nonperurbative. Attempts to separate
perturbation theory from ``purely nonperturbative" condensates
gave rise to multiple paradoxes and inconsistencies (see e.g.
\cite{David}) which questioned the very possibility of using the 
OPE-based methods in QCD.  We had to spend much effort
untangling these spurious paradoxes 
each time the claim of the failure of OPE has been made \cite{NSVZo}.
Surprisingly, such claims are being made till present.
This became a perennial problem reminding of
{\em perpetuum mobile} seekers. 

Certainly, Wilsonean OPE, being just a book-keeping procedure, cannot 
fail. The question of its practical implementation is a different story.
The coefficient functions summarize the hard contributions, which, to a 
good approximation, are given by perturbation theory.
However, strictly speaking, perturbation theory does not exhaust QCD
dynamics even at short distances. If there are small-size 
nonperturbative fluctuations, the coefficient functions acquire 
nonperturbative parts. An instructive example is provided by 
instantons. We found \cite{NSVZo} that in most cases their contribution
is suppressed and can be neglected. That is why our sum rules were
so successful in the family of the ``classic" mesons. But not in all cases!
We  managed to identify some exceptional channels
(which will  {\em not} be discussed 
in this book).  It is clear that if instantons can produce nonperturbative
parts of the coefficient functions, this can be possibly done
by other small-size field fluctuations. The work on identifying such
novel field fluctuations is on today's agenda. 

So much was said about the construction of consistent OPE in QCD 
because, after this  was done in connection with the QCD sum rules,
it gained a life of its own! The very same OPE constitutes the basis
of the heavy quark mass expansions (Voloshin + me, Yadernaya Fizika). 
The heavy quark theory 
accounts for most
significant  developments in QCD in the recent years. This is a branch of QCD where 
there still exists a direct live feedback from experiment, 
which gives a special weight to any advancement  in theoretical 
understanding. One of the most elegant results
established 
\cite{Vai} in the heavy quark physics, on the basis of   OPE, is the 
absence of the $1/m_Q$ correction to the total inclusive decay widths of 
the  heavy-flavor hadrons.
This theorem will undoubtedly make its way into text books,
let alone its practical importance for the precision determination of 
$V_{cb}$ from data.  

On the technical side, the progress of the OPE-based methods
we are witnessing now would hardly be possible without
the computational technique based on the
background field method. Back in 1978, when we entered this field, 
people used a very awkward approach, a direct evaluation of the
Feynman graphs. It worked okay as far as the leading power terms in 
OPE were concerned. We needed to go beyond the leading terms.
It became clear almost immediately, that one cannot go  further without 
perfecting the computational technique. The background field
formalism was known for a long time in QED, were it had been
developed mainly by J. Schwinger. 
It is extremely efficient and ideally suited for OPE-based calculations.
Somehow the QCD practitioners paid no attention to it. So, we adapted it 
to make it usable in the QCD environment. In fact, two versions were 
engineered:
one is based on the Fock-Schwinger gauge for the background field,
another is more general. They nicely supplement each other in various
problems. The
review paper \cite{NSVZr} (see Chapter 
3) summarizes our work on  the  background 
field formalism;  exploiting  it  became a routine practice from then on. 




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\bibitem{2}
H. Fritzsch,  M. Gell-Mann and H. Leutwyler,
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\bibitem{3}
D. Gross and F. Wilczek,
\newblock{\it Phys.\ Rev. \ Lett.\ }{\bf {30}} (1973) 1343; \\
H. D. Politzer,
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\bibitem{Tere}
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I.B. Khriplovich,
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\bibitem{Vany}
The paper of Vanyashin and TerentyevVanyashin and Terentyev is entitled 
{\em ``The vacuum polarization of 
a charged vector field}". Let me quote a passage from the concluding 
part 
of the paper: "Unlike the ordinary electrodynamics where the 
renormalized 
charge is smaller than the bare one our case gives $e^2>e_0^2$... As is 
well-known, in electrodynamics the restriction $0\leq Z\leq 1$ on 
the $Z$ 
factor (charge renormalization) follows from the 
most general principles... In our case it is impossible, generally 
speaking,
to get the restriction $0\leq Z\leq 1$ starting from these 
principles...
Nevertheless, the inequality $Z>1$ seems extremely undesirable." The 
first 
coefficient  of the Gell-Mann-Low function obtained in \cite{Tere} 
(for $SU(2))$ is $20/3$, instead of $22/3$ which we would get now
in the massless Yang-Mills. 
The difference is 
due to the contribution of the 
longitudinal polarizations, which in the modern
language would correspond to the Higgs fields.
Vanyashin and Terentyev worked before the Higgs mechanism;
they introduced the $W$-boson mass by hand.
This is okay at one loop.

 In Khriplovich's work a non-covariant 
(Coulomb) 
gauge was used which is ghost-free. In this gauge the charge 
renormalization is given by that of the $D_{00}$ component of the 
vector Green 
function. The logarithmically divergent part of $D_{00}$ is presented 
in 
eq. (61) of ref. \cite{Khri}. After taking into account an 
unconventional 
normalization of the coupling constant there we read off the famous 
$22/3$! Moreover, you additionally learn  from this expression that $22/3$ 
is actually $8-\frac{2}{3}$. The logarithms are of two different types. One 
is non-dispersive, corresponds to the instantaneous Coulomb interaction and 
is responsible for  antiscreening ({\em eight}). 
The second logarithm is normal 
dispersive; in full accordance with the general principles it gives the 
negative contribution ({\em minus two thirds}) characteristic of 
screening.  

\bibitem{5}
A. Belavin, A. Polyakov, A. Schwarz and Yu. Typkin,
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\bibitem{6}
V. Gribov, 1975, unpublished;\\
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\bibitem{7}
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\bibitem{10}
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\bibitem{12}
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\bibitem{Ioffe}
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\bibitem{MM}
B.L Ioffe and A.V. Smilga, {\it JETP Lett.} {\bf 37} (1983) 298;
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\bibitem{FF}
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410;\\
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B. Blok and M. Shifman,
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\bibitem{SF}
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\bibitem{WKog}
K. Wilson and J. Kogut, {\it Phys. Reports} {\bf 12}, 75 (1974).

\bibitem{pope}
K. Symanzik, {\it Commun. Math. Phys.} {\bf 23}, 49 (1971);\\
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