\documentclass[smus]{snow2e} \usepackage{epsfig} %\usepackage{graphics} \def\beq{\begin{equation}} \def\eeq{\end{equation}} \def\eq{\beq\eeq} \def\beqn{\begin{eqnarray}} \def\eeqn{\end{eqnarray}} \setlength{\titleblockheight}{6cm} %% or other graphics package of your choice. \begin{document} \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}} \maketitle %% Get rid of page numbering \thispagestyle{empty}\pagestyle{empty} \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 $2 GeV$^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. ... \begin{thebibliography}{2} \bibitem{top}{Report of the Top Quark Working Group, these proceedings.} \bibitem{alphas}{ Report of the $\alpha_s$ QCD Working Group, 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 proceedings. \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}, May, 1996, Williamsburg, VA.} \bibitem{spinwg}{Report of the Spin QCD Working Group, these proceedings.} \bibitem{cont}{A.~Contogourris, {\it et.al.} {\it Phys. Rev.}{\bf D48} (1995) 4902.} \bibitem{mt}{M.~Tannenbaum, {\it Proceedings~of~the~Adriatico~Research ~Conference~on Trends~in~Collider~Spin~Physics}, 4-8 Dec., 1995, Trieste, Italy.} \end{thebibliography} \end{document}