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\section{\usemenu{slacpub7176::context::slacpub7176001}{Introduction}}\label{section::slacpub7176001}
The potential to study ``new physics'' at the next generation of accelerators
will to a large extent depend on the ability to control the strong
interaction background. Hence the present interest in making
QCD predictions for hard processes as quantitative as possible,
with an increasing understanding of the importance to study highertwist
effects which are suppressed by powers of the large momentum.
In general, highertwist effects reflect the ``leakage''
of contributions from large distances into the process of interest.
The theoretical status of these corrections is wellestablished in
the total $e^+ e^$ annihilation cross section and in deep inelastic
scattering (DIS) (and in related quantities),
where dispersion relations relate the physical observable
to the operator product expansion (OPE) of a Tproduct of currents at
small distances. The OPE does not allow us to calculate power corrections,
but one learns from the OPE the particular suppression
of higher twist effects  $1/Q^4$ for the total
$e^+e^$ annihilation cross section
versus $1/Q^2$ for the DIS structure
functions  and the processindependence (universality) of the uncalculable
higher twist matrix elements. The structure of powersuppressed effects
in ``geniune''
Minkowskian quantities is much less understood. There are phenomenological
and theoretical indications that in certain situations such corrections
are large  of order $1/Q$  and numerically important at all energies
available today. In this talk we
summarize the results of Ref.~1 on the structure of power
corrections and renormalons in DrellYan (lepton pair) production,
and speculate whether this example teaches us a lesson of general
validity.
DrellYan production, apart from its phenomenological significance, is
theoretically interesting because it
is the simplest hard process with two large, but disparate scales,
if we consider the production of the DrellYan pair (or heavy
vector boson) close to the kinematical threshold $z\sim 1$ where $z=Q^2/s$,
$Q^2$ being the mass of the pair and $s$ the total cms energy of
the colliding partons.
In this situation gluon emission into the final state
is suppressed by small phase space $(1z)Q \ll Q$,
and causes large perturbative corrections enhanced by
Sudakovtype logarithms $\ln(1z)$. Taking moments
$\sigma(N,Q^2) = \int dz z^{N1} d\sigma/dz$ and subtracting
collinear divergences by forming the ratio of the
DrellYan cross section and the quark distribution squared,
one is left with the perturbative expansion for the
logarithm of the ``hard'' cross section
\be
\ln \omega_{DY}(N,Q^2) = \omega_1\alpha_s\ln^2 N+
\omega_2\alpha_s^2\ln^3 N+\ldots
\omega_k\alpha_s^k\ln^{k+1} N+\ldots,
\label{seriesLLA}
\ee
where $\alpha_s=\alpha_s(Q)$ and we have shown terms with the leading power
of the large logarithm at each order of $\alpha_s$.
In leading logarithmic approximation (LLA), these terms are resummed to
all orders by the elegant formula
\be
\ln \omega_{DY}(N,Q^2) = \frac{2C_F}{\pi}
\int_0^1 dz\frac{z^N1}{1z}\int_{Q^2(1z)}^{Q^2(1z)^2}\!\!
\frac{dk^2_\perp}{k^2_\perp}\,\alpha_s(k^2_\perp).
\label{LLA}
\ee
Expansion of the running coupling under the integral in powers of
$\alpha_s(Q^2)$ generates a perturbative series which correctly reproduces
all coefficients in Eq.~\docLink{slacpub7176001.tcx}[seriesLLA]{1}. Eq.~\docLink{slacpub7176001.tcx}[LLA]{2}
takes into account soft and
collinear gluon emission, and can be improved systematically by
including nexttoleading logarithms etc. The leading
softcollinear contribution
has a geometrical interpretation in terms of the cusp (eikonal)
anomalous dimension; it is universal and appears in
resummation of threshold corrections to any hard QCD process.
However, the resummed cross section in the LLA now
appears to be sensitive to the infrared (IR) region at the level
of $1/Q$ corrections \cite{2,3}. Indeed, remove gluons with
energy $Q(1z)/2$ less than $\mu \sim \Lambda_{QCD}$ by
inserting the appropriate
$\theta$function in the $z$integral. A simple calculation shows that
the cross section changes then by $\sim \mu N/Q$. Given
this sensitivity to the IR region, one would
suspect that geniune power corrections of this magnitude exist.
The same conclusion can be obtained
from considering divergences of the perturbative expansion of Eq.~\docLink{slacpub7176001.tcx}[LLA]{2}
in large orders (renormalons). One easily checks, however, that the dangerous
IR contributions correspond to terms with less logarithms of $N$
than are resummed by the LLA and thus are beyond the accuracy
to which Eq.~\docLink{slacpub7176001.tcx}[LLA]{2} has been derived.
Thus this evidence is by itself not conclusive.
A more accurate analysis will clarify
two questions:
\begin{itemize}
\item{} Does the IR sensitivity (of order $1/Q$)
of the LLA resummed cross section
represent the `true' magnitude of power corrections to the DrellYan
process or is it artificially introduced by resummation, that is
by the procedure that separates those regions of higher order
Feynman diagrams which give rise to large logarithms?
\item{} If the exact DrellYan cross section has no $1/Q$ IR contributions,
can the resummation of large perturbative corrections to all orders
be made consistent with the IR behaviour of finiteorder Feynman diagrams?
Or is the (spurious) $1/Q$ sensitivity found in LLA intrinsic
and unavoidable for resummation of threshold corrections?
\end{itemize}
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