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\title{QCD: Challenges for the Future
\thanks{The work of  S.D.   supported by 
DOE contract number DU-AC02-76CH00016.  
 }}
\author{P.~Burrows$^a$,S. Dawson$^b$, L.~Orr$^c$,  and
W.~Smith$^d$
\\
$^a$ {\it  MIT, Cambridge, MA~~02138}\\
$^b$  {\it Brookhaven National Laboratory, Upton, NY  11973}\\
$^c$ {\it University of Rochester, Rochester, NY~~ 14627}\\
$^d$ {\it University of Wisconsin, Madison, WI~~53705}}
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\begin{abstract}
Despite many experimental verifications of the correctness of
our basic understanding of  QCD, there
remain numerous
 open questions in strong interaction physics and we 
focus on the role of future colliders in  addressing these questions.
We discuss possible  advances in the measurement of
$\alpha_s$, in the study  of parton distribution functions,
and in the understanding of low $x$ physics at
present colliders and  potential
new facilities.  We also touch briefly
on the role of spin physics in advancing our understanding of QCD.  
\end{abstract}

\section{Introduction} 
  QCD is a successful theory of the strong interactions which
has been tested by confronting theory and experiment in both
the perturbative and non-perturbative regimes. 
It  is an unbroken symmetry with a single coupling constant, $\alpha_s$,
whose measurement over a wide range of energy scales is crucial
for verifying the consistency of the theory.  In fact, QCD is the
only theory where relativistic quantum field theory can be tested 
beyond a few orders in perturbation theory.    

Today, we have numerous measurements where the predictions of
QCD are rigorously tested.  New and increasingly more precise
jet data are being gathered in $e^+e^-$, hadron, and $ep$ collisions
to be compared with theoretical calculations beyond the lowest order.
For example, the latest results from the jet $E_T$ spectrum
obtained by CDF and D0 challenge our understanding of both
QCD jet calculations and our knowledge of
parton distribution functions.  
Before we can interpret results such as these as indications
of new physics, we must have a solid understanding of what we
expect from QCD. 
Hadron collider, photoproduction, and deep inelastic scattering data
are giving us new information on the parton structure functions, while   
recent data from HERA on the rise of the structure function, $F_2$, 
at low $x$ are stimulating new theoretical understanding.  
The study of QCD is thus a perfect example of the necessary 
synergism between theory and experiment.  
  
The discovery of the top quark provides a new arena for
testing the predictions of QCD.  Indeed, the jet energy
calibration remains the dominant source of experimental
 error, while perturbative QCD calculations stubbornly persist
in predicting a cross section slightly above the experimental
measurement.  The physics
involving the top quark has many interesting
QCD issues, but  is not covered here.
Instead it is discussed in a separate 
 contribution by the Top Quark Working Group.\cite{top}.


Despite many successes, 
however, the  regimes  of the strong interactions
where perturbative QCD is not applicable   are 
in general  
not well understood.  We have,
for example,  an incomplete understanding of quark confinement, of the
high temperature and high density phases of QCD, of the absence or unnatural
smallness of strong CP violation, and of
 how a partonic picutre of QCD is connected with non-
perturbative regimes, including bound states.  The list goes on.   
  
Some of these  questions will be addressed by lattice gauge  
theory computations in coming years as more computing power
becomes available and progress is made in the development of
algorithms.  Already lattice calculations of $\alpha_s$ are 
competitive in precision
 with experimental derivations.\cite{alphas}
Reliable and convincing calculations of the hadron mass spectrum
and weak matrix elements are realistic goals for the near future.   
 
The measurement of $\alpha_s$ is a precise test of the predictions
of perturbative QCD.  Current measurements  at
the $Z$ mass are at the $\pm 5\%$
level, while the goal is a measurement of $\delta\alpha_s/\alpha_s
\sim 1\%$ over a wide range of $Q^2$.  Such measurements have the potential
to limit new physics scenarios and to constrain physics at
the GUT scale.  Section II describes techniques for measuring
$\alpha_s$ through $\nu$ physics at low $Q^2$, in $e^+e^-$ 
and $ep$ colliders at $Q^2\leq (.5-1~TeV)^2$, and at high energy
hadron colliders such as the LHC which will probe $Q^2\leq (4~TeV)^2$. 

The understanding of parton distribution functions is
critical to many measurements at present and future
colliders.  Section III contains a survey of the $x$ and
$Q^2$ regions  where progress in our knowledge of structure
functions might be obtained at future facilities.
  Particular attention is paid 
to obtaining a consistent definition of the errors in the
structure functions.
This section also discusses some problems in jet physics.  

The prospects for low $x$  and diffractive
physics are presented in Section IV.  The
scattering 
region with $x<10^{-5}$ is a new strong interaction frontier
 which has begun to be probed by HERA.  Extention of these studies
may yield insight into the role of the BFKL pomeron.  Forward
physics ($.1<x_F<.9$) and diffractive scattering can also provide
information about  the non-perturbative regime.  Possible collider 
experiments which are sensitive to forward
and diffractive physics 
 at both the Tevatron and the LHC are discussed.  
 
Spin physics has the potential to open a new window on QCD
and is discussed in Section V.  Experiments with
polarized protons and electrons can lead to new measurements
of polarized structure functions and asymmetries.  

\section{Measurements of $\alpha_s$}
\section{Parton Distribution Functions and Jets}

\section{Low-{\Large$\lowercase{x}$} \& Diffractive Physics}

\subsection{ep collisions}

A renewed interest in diffractive phenomena has been sparked by ep events
that occur at high $Q^2$ and small $x$. The observation at HERA of deep
inelastic scattering events with a large rapidity gap in the final state
between the proton direction and the first energy deposit in the detector is
an indication of diffractive scattering \cite{HERADF}. The flatness of the
rapidity gap distribution, as well as other properties of the events such as
independence of the cross section on $W$, are consistent with photon
diffractive dissociation off a Pomeron. Studies of these events are
providing insights into the transition from perturbative to non-perturbative
scattering and promise to provide more information as the low-$Q^2$
transition region is further mapped out.

The strong rise in the proton structure function, $F_2(x,Q^2)$ at small x
and large $Q^2$, which indicates a strong rise in the $\gamma^*p$ total
cross section, underscores the importance of understanding the role of
diffraction at low $x$\cite{diffwg}.

While previous studies of diffraction at HERA are based on the rapidity gap 
method, more recent data have been collected with Leading Proton
Spectrometers (LPS) involving ``Roman Pot Detectors". These data provide a
sample of events  with smaller statistics and different systematics but also
with a cleaner  interpretation as diffraction and with less background from
Reggeon exchanges\cite{diffwg}.

Exclusive reactions, such as elastic vector meson production, provide
stringent tests of calculations in  perturbative QCD, as well as new methods
for extracting gluon distributions.

Inclusive reactions both in deep inelastic scattering and photoproduction
have produced insights into diffractive phenomena. Rapidity gap events form
about 10\% of the total deep inelasti scatterng cross section and have been
used to measure a diffractive proton structure function. Studies of hard
diffractive photoproduction at HERA have focussed on   high $p_T$ jet
production and jets separated by a large rapidity gap. These studies suggest
a dominant gluon content to the pomeron and also that production may be
taking place by a direct photoproduction in addition to resolved
photoproduction.

Additional diffraction studies at HERA with increased luminosity and
extended coverage (i.e. LPS) in the very forward proton region will
undoubtedly lead to a  better understanding of the nature of the diffractive
process and how it  relates to QCD.

Increased statistics will enable the study of the diffractive charm
structure  function which is very sensitive to the gluonic component of the
exchange  mechanism~\cite{mehta}. 

However, it is also important to consider the advantages of going to higher
CM  energies for a lepton-hadron (ie lepton-quark) collider. Studies 
suggest that in order to reach values of $x < 10^{-6}$ for $Q^2 > $2
GeV$^2$,  one should consider a high energy lepton-hadron collider option at
one of the  future hadron-hadron colliders under consideration\cite{sfwg}.  

Further exploration of color singlet exchange and searches for an
enhancement in its cross section would be enabled by an increase in the
rapidity coverage either from increased luminosity and an extended detector
coverage at HERA or  from an increase in the CM energy that would be
available at a higher energy  lepton-hadron collider.

\subsection{pp collisions}   Rapidity gaps have been found at the
Tevatron\cite{D0gap,CDFgap} and are now a subject of considerable interest.
In principle, such events are an excellent place to study high energy
semi-hard physics including the BFKL Pomeron. However, the analysis is
complicated by the presence of hadrons coming from soft interactions
involving the spectator quarks in the colliding hadrons. BFKL phenomena are
observed in pp collisions in events with either a rapidity gap between two
jets or between a jet and a beam fragment.

SIngle diffractive exchange occurs when one of the protons scatters almost
elastically and the other becomes a massive multipparticle
system\cite{diffwg}. Such events are used to study the structure of the
pomeron in the context of a model where the pomeron is composed of quarks
and gluons. If the quasi-elastically scattered proton is measured, the $t$
of the pomeron and its momentum fraction are known. If the quasi-elastically
scattered particle is not measured, then diffractive events are tagged by
the presence of a rapidity gap of typically more than 3 units. While there
is a higher rate of such events, their analysis requires integration over
$t$ of the pomeron and its momentum fraction.

When there are two high-$E_T$ jets in pomeron-proton collisions, it is
possible to reconstruct the momentum fractions of the scattered partons.
Both CDF and D0 have very good evidence for diffractive dijets from
observation of an excess of rapidity gaps in one beam direction. These are
single diffractive events where the high $X_F$ particle is not seen. They
correspond to about 1\% of the dijet cross section. CDF also has evidence
for diffractive  W production. With additional statistics, both experiments
should be able to constrain the pomeron structure function. Other venues for
exploration include diffractive heavy flavor production, and looking for
double pomeron exchange in events with two rapidity gaps. Both of these
processes will require substantially more statistics than presently
available. 

The increased luminosity of Tevatron Run II and  the upgrade of CDF and D0
will provide an important opportunity to enhance understanding of
diffractive physics. The principal difficulty will be the increased rate ot
multiple interactions, which will tend to obscure rapidity gaps. CDF and D0
plan to substantially increase their statistics for diffractive and forward
physics during Run II. An increase in statistics of more than 2 orders of
magnitude over that acquired in Run 1c is needed to provide an adequate
study of single diffractive exchange with tagged quasi-elastically scattered
(anti)protons. This will require longer running time with a constantly
active diffractive trigger (not dedicated runs), improved acceptance, the
installation of pots on both downstream arms if possible, and improved
triggers that veto on multiple interactions. If the detectors are equipped
with pots on both arms, they will be able to study fully constrained double
pomeron events. If CDF and D0 are able to increase their rapidity covereage,
they will enhance their gap detection and also extend their very-forward gap
physics.

There is also the possibility that a new experiment might be carried out in
the C0 intersection region at the Tevatron Collider for Run II. One option
for C0 is a detector devoted to forward and full acceptance physics proposed
by the T864 group. This experiment proposes to study rapidity gaps in soft
and hard diffraction, double diffractive dissociation, the onset of BFKL
enhancement, forward strangeness, charm and beauty production, multiparticle
correlations, and forward neutrons.

Diffractive physics at the LHC promises to be a rich source of information
since certain topologies will be cleaner. due to cleaner events. It will be
possible to look for diffractive Higgs events with reduced hadronic activity
in the rapidity region near the Higgs particle\cite{LHC}. Both single and
double pomeron exchange can be observed, particularly in $H \rightarrow
\gamma\gamma$ events. In addition, single diffraction at the LHC can be
studied in $b\bar{b}$ production.

The overall rapidity span at the LHC increases from that of the Tevatron by
15 to 19 units. The mass reach of diffractively produced states also
increases dramatically. An example is that for double pomeron exchange,
(with $x_F >$ 0.95) central masses extend to 90 GeV at the Tevatron and to
700 GeV at the LHC. This extended range enables the LHC to go beyond
high-$E_T$ jet physics to electroweak probes, W, Z.

A concern with rapidity gap physics at the LHC is the multiple interactions
caused by the high luminosity. The general purpose detectors, ATLAS and CMS,
also cover only about half of the rapidity range with their present designs.
A proposal that addresses these concerns is being developed for a full
acceptance detector called FELIX. It is composed of recycled components from
ALEPH and UA1 along with very forward calorimeters and trackers extending
for 450 m to enable elastic and diffractive measurements. The goal is to
measure charged particles, photons, muons and jets over the entire rapidity
range. Being a detector devoted to this physics program, it could run with
reduced luminosity to improve identification of rapidity gaps. ATLAS and CMS
could also improve their measurement of diffractive physics by installing
Roman pots to tag high-$x_F$ protons and to provide diffractive jet
triggers. These collaborations have such options under active investigation.

Beyond the LHC, the best venue for diffractive physics appears to be a very
large hadron collider with energy of 50 - 100 TeV per beam. This would yield
a rapidity range of 25 units. Pomeron-pomeron collisions of up to 5 - 10 TeV
may be reached, which puts them well into possible SUSY and Higgs sectors.
However, a machine with such beam energy will also require very high
luminosity and therefore experience as many as 100 interactions per
crossing. This suggests consideration of a second lower-luminosity
interaction region, dedicated to diffractive and forward physics, where
single interactions could be observed. One option would be to use 2 km long
partially instrumented straight sections on either side of a modest (i.e.
upgraded CDF or D0) central detector. This suggests incorporating a 4 km
straight section into future very large hadron collider designs. 


\section{Spin Physics}

 
Polarized processes involving hadrons
 satisfy a simple generalization of the factorization theorems 
used in hadronic physics,
\beqn 
\sigma&\sim& ({\rm{Structure~ Function}})
 \times \sigma({\rm{ Hard~ Scattering}})
\nonumber \\  &&
\times ({\rm{Fragmentation~ Function}}).
\eeqn   

  The hard scattering cross sections can be calculated in
perturbative QCD, but the parton structure and fragmentation
functions must be determined experimentally.  A primary focus
of spin experiments will clearly be the measurement of 
polarized structure functions and the verification of the sum
rules relating the various structure functions.
One would also like to measure the $x$ and $Q^2$ dependences
of the various structure functions and sum rules and compare
with the predictions of NLO QCD.  

  In 1988, the
EMC $\mu N$ scattering experiment obtained a measurement of
the nucleon spin structure function that violated the Ellis
-Jaffe sum rule.
The interpretation of this violation was that either the
 strange sea in the proton is highly polarized or that the valence
quarks carry little spin, while the remainder of the spin is
carried either by the gluons or by orbital
angular momentum.  This result and the apparent violation
of the sum rule has  stimulated a variety of spin experiments.  
\subsection{Polarized Structure Functions}
\begin{figure}[h]
\epsfig{file=g1p.eps,height=3.5in}
\caption{Measurements of $g_1^p$ at current (open circles)
and potential future experiments.
The solid dots show the statistical accuracy which might
be obtained at these hypothetical machines. This
figure from Ref. \protect\cite{spinwg}. }
\label{g1p}
\end{figure}
\subsubsection{Deep Inelastic Scattering}  
Current experiments at SLAC E143 and CERN SMC have provided
measurements of the $g_1$ structure function on protons 
with $x > 4\times 10^{-3}$.
Higher energies at HERA with a polarized proton beam or
at a fixed target experiment at an NLC, could 
 allow  
for measurements down to $x\sim 6\times 10^{-3}$.
  The study of structure functions 
at low $x$ is particularly interesting since current
data show a rise in $g_1^p$ at low $x$, (the open circles in
Fig. \ref{g1p}).  The QCD evolution equations, however, predict that
$g_1^p$ will change sign at low $x$ and higher $Q^2$
and actually become negative.\cite{sforte}
This prediction
challenges our theoretical understanding of QCD at low $x$ and
of higher twist effects which become relevant in this regime,
as well as requiring new 
 experimental data to verify the theoretical predictions.  
Fig. \ref{g1p} shows the statistical accuracy which could be obtained 
at HERA or an NLC with $?pb^{-1}$.


\begin{figure}[h]
\epsfig{file=spin1.ps ,height=3.5in}
\caption{Expected sensitivities for $\Delta u/u$
and $\Delta d/d$ from the measurement of parity violating
effects in $W^\pm$ production at RHIC with $800/pb^{-1}$
at $\protect\sqrt{s}=500~GeV$. The solid curves are the
theoretical predictions. This figure from Ref.\protect \cite{mt}.}
\label{rhic}
\end{figure} 
\subsubsection{Polarized Protons}

The polarized beam capability proposed for RHIC offers
a unique array of spin measurements.  Both protons will be
highly polarized ($>70\%$, either transversely or longitudinally),
with high luminosity, ${\cal L}=2\times 10^{32}/cm^2/sec$, and
 energies between $\sqrt{s}=200$ and $500$ GeV.  This allows the
measurements of the gluon
structure function  $G(x)$ for nuclei, $\Delta G(x)$ for $pN$,
and  $h_1(x)$,
(which counts the valence quark polarization). 
The distribution  $h_1$ will be
measured with transverse spin asymmetries
using both $\gamma^*$  and
$Z^*$ production.  Gluon polarizations, $G(x)$ and $\Delta G(x)$, 
can be measured by using direct photons from the dominant
quark- gluon Compton scattering process, $q g \rightarrow \gamma  q$,   
and through medium $p_T$ jets, ($p_T\sim 20-50~GeV$), which are predominantly
quark- gluon produced.  $\Delta G(x)$ can then be extracted from the
longitudinal spin asymmetry, $A_{LL}$, which is predicted in NLO QCD to be
$10-20~\%$. \cite{cont}

Polarized protons at RHIC can also measure parity violating
asymmetries involving $W^\pm$ production (where the $W$ decays
leptonically).  Assuming $\Delta q$ is known from deep inelastic
scattering experiments, a precise measurement of the quark
structure  functions $\Delta u$ and $\Delta d$ can be extracted
from
the parity violating $W$ decays as shown in Fig. \ref{rhic}.\cite{mt}

\subsection{Spin Asymmetries}

Both single (one polarized beam) and double (both
beams polarized) spin asymmetries can yield useful
information about QCD.  Single spin effects in hard
scattering processes are negligible and so the measurement
of single spin asymmetries tests our understanding of higher twist
and non-perturbative physics.  The double spin asymmetries
can be used to extract moments such as
$g_1(x,Q^2)$ and $g_2(x,q^2)$, giving information
on the scale dependence and small $x$ behaviour of
the polarized structure functions.  



\section{Conclusions}
There remains much to be learned from the study of QCD
and strong interactions. ...  
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these proceedings.}

\bibitem{HERADF}
M. Derrick {\it et al.,} Phys.\ Lett.\ {\bf B338} 483, 1994; T. Ahmed {\it 
et al.,}  Nucl.\ Phys.\ {\bf B435} 3, 1995. 
 
\bibitem{mehta} A. Mehta, J. Phillips, and B. Waugh, ``Future Diffractive 
Structure Function Measurements at HERA", Proceedings of the 1996 HERA Workshop.

\bibitem{diffwg} Report of the Diffractive QCD Working Group, these proceedings.

\bibitem{sfwg} Report of the Structure Function QCD Working Group, these
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\bibitem{LHC}
G. Ingleman, LHCC Workshop, CERN, Nov., 1994.

\bibitem{D0gap}
S. Abachi {\it et al.}, Phys.\  Rev.\  Lett. {\bf 72}, 2332, 1994.

\bibitem{CDFgap}
F. Abe {\it et al.}, Phys.\  Rev.\  Lett. {\bf 74} 855, 1995. 
 

\bibitem{sforte}{S. Forte, {\it Proceedings~of~ PANIC96},
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\bibitem{spinwg}{Report of the Spin QCD Working Group,
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\bibitem{cont}{A.~Contogourris, {\it et.al.} {\it Phys. Rev.}{\bf D48} (1995)
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\bibitem{mt}{M.~Tannenbaum, {\it Proceedings~of~the~Adriatico~Research
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Italy.}



\end{thebibliography}

\end{document}




