%VM, you can compile by typing % LATEX E140X % DVIPS E140X %LPRPS E140X % This works fine on my SLACVM account, anyway. % I have made a bunch of minor editorial changes here and there, but % nothing substantial. Depending on how long the tables are, the % article should fit in the 4 page limit. You can save room by doing % the author list in the E143 title page style (see E143PRL1 TEX on % my VM account if you want to try it). % Dear Phys. Rev. Lett. Editor, ... % Steve, switch between these lines for preprint or prl format... %\documentstyle[preprint,prl,aps]{revtex} \documentstyle[prl,aps]{revtex} \begin{document} \title{ PRECISION MEASUREMENT OF $R= \sigma_L/\sigma_T$ ON HYDROGEN, DEUTERIUM AND BERYLLIUM TARGETS IN DEEP INELASTIC ELECTRON SCATTERING} % Steve - put in middle initials and check addresses !!! % Thia is now at CEBAF, I think. % Starting in Sept., Micheal will be at U. Penn. % What are present addresses for Pavel and Bob Walker? \author{The E140X Collaboration \break L.~H. Tao,$^{1}$ L.~Andivahis,$^{1a}$ P.~L.~Anthony,$^{3b}$ R.~G.~Arnold,$^{1}$ A.~Banerjee$^{4}$ A.~Bodek,$^{6}$ P.~E.~Bosted,$^{1}$ J.~Button-Shafer,$^{4}$ S.~Dasu,$^{7c}$ P.~de Barbaro,$^{6}$ F.~S.~Dietrich,$^{3}$ J.~Dunne,$^{1}$ M.~Frodyma,$^{9}$ R.~Gearhart,$^{7}$ J.~Gomez,$^{2}$ K.~A.~Griffioen,$^{5d}$ R.~A.~Hicks,$^{4}$ C.~Hyde-Wright,$^{9e}$ C.~Keppel,$^{1f}$ S.~E.~Kuhn,$^{8e}$ A. ~Lung,$^{1g}$ G.~A.~Peterson,$^{4}$ G.~G.~Petratos,$^{6h}$ M.~Riordan,$^{7}$ S.~E.~Rock,$^{1}$ S.~Rokni,$^{7}$ M.~Spengos,$^{1}$ L.~M.~Stuart,$^{3b}$ Z.~M.~Szalata,$^{1}$ K.~Van Bibber,$^{3}$ R.~Walker,$^{6i}$ K.~Wang,$^{4}$ J.~L.~White,$^{1b}$ U.~K.~Yang$^{6}$ } \address{ {$^{1}$The American University, Washington, D.C. 20016} \break {$^{2}$CEBAF, Newport News, Virginia 23606} \break {$^{3}$Lawrence Livermore National Laboratory, Livermore, California 94550} \break {$^{4}$University of Massachusetts, Amherst, Massachusetts 01003} \break {$^{5}$University of Pennsylvania, Philadelphia, Pennsylvania 19104}\break {$^{6}$University of Rochester, Rochester, NY 14627}\break {$^{7}$Stanford Linear Accelerator Center, Stanford, California 94309} \break {$^{8}$Stanford University, Stanford, California 94305} \break {$^{9}$University of Washington, Seattle, WA 98195} \break } \maketitle \abstract{ We report new results on a precision measurement of the ratio $R=\sigma_L/\sigma_T$ from hydrogen, deuterium and beryllium targets for deep inelastic electron scattering in the range $0.1 \leq x \leq 0.7$ and $0.5\leq Q^2 \leq 7$ (GeV/c)$^2.$ We find no measurable difference between $R^p$ and $R^d.$ Our results are consistent with and more precise than previous SLAC data. At high $x,$ $R$ is somewhat larger than order $\alpha_s^2$~ pQCD predictions, even when target mass effects are included.} } \pacs{PACS Numbers: 13.60.Hb, 12.38 Qk, 25.30Fj} \narrowtext % Steve, I suggest a physics introduction before launching into defs. The quantity $R,$ the ratio of longitudinal $(\sigma_L)$ to transverse $(\sigma_T)$ cross sections in deep inelastic scattering, is a sensitive measure of the spin of the nucleon constituents. Within the naive parton model with spin-1/2 partons, $R$ values are expected to be zero at large momentum transfer squared $(Q^2),$ whereas with spin-0 partons, $R$ values are expected to be large. Recent measurements \cite{dasu,whitlow} of the quantity $R,$ made at the Stanford Linear Accelerator Center (SLAC), found $R$ to be small (0.1-0.4) and to be decreasing with increasing $Q^2.$ To compare with theoretical calculations, $R$ can be expressed in terms of the longitudinal structure function $F_L$ and the structure function $F_2.$ In perturbative Quantum Chromodynamics (pQCD), $F_L\propto \alpha_s$ \cite{six} and thus $R$ is expected to decrease logarithmically with increasing $Q^2.$ Very recent calculations of order $\alpha_s^2$ terms \cite{neerven} as well as greatly improved parton density models \cite{mrsa,grv,cteq} have increased the precision of pQCD calculations, particularly at low $Q^2.$ However, in the low $Q^2$ regime, target mass and non-perturbative effects give contributions to $F_L$ and $F_2$ which are proportional to $1/Q^2.$ Accurate data over a large range of $Q^2$ and Bjorken $x$ can determine the size of the non-perturbative effects in the high $x$ region and check the validity of the pQCD calculations in the low $x$ region. Accurate values of $R$ are also vital for the extraction of $F_2$ from unpolarized cross sections and the polarized structure functions $g_1$ and $g_2$ from asymmetry measurements. The new data on $R$ reported here expand the previous range of measured kinematics\cite{dasu}. Included are measurements of $R^d-R^p$, the difference in $R$ for deuterium and proton targets, and checks (with a single experiment) on the results for $R$ from the SLAC global analysis \cite{whitlow}, which was dependent on normalizing data from several different experiments. The differential cross section for scattering of an unpolarized charged lepton with an incident energy $E$, scattering angle $\theta$ and final energy $E^{\prime}$ can be written in terms of $F_L$ and $F_2$ or $\sigma_L$ and $\sigma_T$ as: \begin{equation} {d^2\sigma \over{d\Omega dE^\prime}} = \sigma_M\Bigl[{F_2(x,Q^2)\over \nu\epsilon} - {2 F_L(x,Q^2)\over Mx}\tan^2(\theta/2)\Bigr] \end{equation} \begin{equation} =\Gamma \Bigl[\sigma_T(x,Q^2) + \epsilon\>\sigma_L(x,Q^2)\Bigr] \end{equation} where $\sigma_M=4\alpha^2E^{\prime 2}\cos^2(\theta/2)/Q^4$ is the Mott cross section, $M$ is the proton mass, $\nu=E-E^{\prime},$ $Q^2=4EE^{\prime}\sin^2(\theta/2)$, $x=Q^2/2M\nu$ is a measure the longitudinal momentum carried by the quarks, $ \Gamma = \alpha (1-x) E^{\prime}/[4\pi^2 x M E(1-\epsilon)],$ and $\epsilon = [1+2(1+{\nu^2/Q^2}) \tan^2 (\theta/2)]^{-1}$ representing the virtual photon flux and relative longitudinal polarization respectively. $R$ is defined as: \begin{equation} R(x,Q^2)=\sigma_L/\sigma_T=F_L/[(1+4M^2x^2/Q^2)F_2 -F_L] \end{equation} The SLAC electron beams and the 8 GeV spectrometer facility were used to measure cross sections to better than $1\%$ accuracy in the kinematic range $0.1\leq x\leq 0.7$ and $0.5\leq Q^2 \leq 7$ (GeV/c)$^2.$ The electron beam was provided by the NPI injector in the normal accelerator mode (2 $\mu$sec spill) for energies less than 6.5 GeV and in the SLED mode (100 nsec spill) for energies up to 10 GeV. Individual settings of the 8 GeV spectrometer detected electrons scattered between angles of $11^{\circ}$ and $50^{\circ},$ with momenta from 0.6 to 8 GeV/c. Electrons were identified from a background of pions and other particles using a gas \v Cerenkov counter and a lead glass electromagnetic calorimeter. Ten planes of wire chambers were used for tracking. Several additional planes of scintillation counter hodoscopes were installed for this experiment \cite{taothesis} to handle the high instantaneous rates. Measurements were made on 4 cm and 15 cm targets of liquid $D_2$ and $H_2$ and a 2.1 cm Be target at up to four different values of $\epsilon$ for each value of $(x,Q^2)$, with a typical $\epsilon$-range of 0.4. To compensate for the small cross sections at $x \geq 0.5$ we used a new large acceptance optical tune of the 8 GeV spectrometer and the Be target to give a luminosity an order of magnitude greater than using the normal tune and liquid targets. Since $R$ is a ratio measurement, the absolute spectrometer acceptance cancels. Other normalization errors such as absolute beam intensity, absolute target density, and absolute detector efficiency also cancel. The results for the difference $R^d-R^p$ have smaller systematic errors than those for the absolute value of $R$ because many systematic uncertainties which depend on the spectrometer angle and momentum, and the beam energy and intensity cancel. In addition, the targets were changed frequently to avoid systematic errors due to changing efficiencies or beam conditions. The systematic errors, summarized in Table I, are similar to those in a previous experiment\cite{dasu} except for the large acceptance mode of the spectrometer. For that configuration, the momentum-dependence of the acceptance was compared with that of the normal mode at $x=0.5$ and found to be constant within the statistical errors of 1.0\%. The value of $R$ measured with normal and large acceptances agreed to within the statistical error of 0.026. Radiative corrections were calculated using the complete prescription of Mo and Tsai \cite{tsai} for the ``external" part and that of Bardin et al. \cite{bardin} for the ``internal'' part in a manner which has been implemented and tested in previous experiments \cite{dasu}. Internal corrections were checked using an improved version \cite{dasu} of the ``exact" formalism of Tsai \cite{tsai} and these agreed with Bardin et al. calculations to better than $1.0\%$ at each $(x,Q^2,\epsilon)$ point. In addition, the corrections calculated with different parameterizations of structure functions in both the resonance region \cite{stuart,bodek} and the deep inelastic region \cite{bodek,whitlow2} agreed to better than $ 0.8\%$ in cross section and show a consistent behavior as a function of $\epsilon.$ The radiative elastic tail from hydrogen and the quasi-elastic tail from deuterium are independent of input model \cite{ijl} to within $\pm0.2\%.$ The radiative elastic tail from deuterium is also independent of input model \cite{bardin,tjon} to within $\pm0.2\%$. A test of the external corrections was performed during this experiment by inserting an additional 4\% radiator upstream of the 1.5\% r.l. hydrogen target at the kinematics $Q^2=3.6,$ $x=0.5.$ The measurements with and without additional radiator agreed to $1.5\% \pm 1.0\%$ stat. $\pm 0.3\%$ syst. We assign an $\epsilon$-correlated error due to radiative corrections equivalent to $0.5\%$ in cross section or 0.012 in $R.$ The difference $R^d-R^p$ was determined by making linear fits, weighted by the statistical and point-to-point ($\epsilon$-uncorrelated) systematic errors, to the ratio of cross sections, \begin{equation} \sigma^d/\sigma^p = \sigma^d_T/\sigma^p_T (1+\epsilon^{\prime} (R^p-R^d)), \end{equation} versus $\epsilon^{\prime}=\epsilon/(1+\epsilon R^d).$ The average $\chi^2$ per degree of freedom for the goodness of fit was 0.4, indicating that the estimate of systematic point-to-point uncertainty is conservative. The results are plotted versus $x$ for various $Q^2$ values in Fig.~1 along with the results from the SLAC global analysis \cite{whitlow} and previous data from the NMC experiment \cite{NMC}. Both the old and new values are consistent with zero within the errors. The average $R^d-R^p$ from this experiment is $-0.013\pm 0.023\text{ (stat) }\pm 0.006 \text { (syst).}$ Combining all the SLAC data shown gives an average of $-0.005\pm 0.011,$ while combining all the data shown gives an average of $0.005\pm0.010.$ We conclude that $R^d-R^p$ is consistent with zero, and also with the pQCD calculations including target mass corrections, shown as the solid curve. There is no evidence for higher twist effects contributing to $R$ differently for the proton and deuterium. The results are inconsistent with the diquark model prediction\cite{diquark}. Also shown in Fig.~1 is the single measurement of $R_{Be}-R_p$ at $x=0.5$ which, in agreement with experiments with other nuclear targets \cite{dasu}, is also consistent with 0. %Steve, doesnt the solid curve need a reference? The values of $R$ were extracted from cross sections measured at various values of $\epsilon$ at fixed $(x,Q^2)$ by making linear fits, weighted by the statistical and point-to-point systematic uncertainty, to $\sigma/\Gamma$ versus $\epsilon$ (see Eq. 2). The average $\chi^2$/d.f. for these fits is 0.5. The results are shown in Table 2. % Steve, does this mean they are TOO conservativie ?? Since the differences $R^d-R^p$ are consistent with zero, the results shown in Figs.~2 and 3 and Table 3 are an average over all targets. For the $x\geq0.6$ measurements, we make the reasonable assumption that $R^d = R^{Be}$. This is supported by the data at lower $x$ on heavier nuclei, the small size of the EMC effect for Be, \cite{EMC} and pQCD calculations. The new results, shown as solid circles, are consistent with the previous results and also with the previous SLAC empirical parameterization $R_{world}$\cite{whitlow} shown as the solid curve. The present data join smoothly to the higher energy muon data of BCDMS \cite{BCDMS} and EMC \cite{EMCR} and neutrino data of CDHSW \cite{CDHSW}, CDHS \cite{CDHS} and CHARM \cite{CHARM}. The pQCD calculations \cite{neerven}, based on the work of Van Neerven et al., to order $\alpha_s,$ called $R^{(1)},$ and $\alpha_s^2,$ called $R^{(2)},$ are shown as dotted and dot-dash curves respectively. We used the MRS(A) \cite{mrsa} NLL parton distributions evolved down to $Q^2=0.625$ (GeV/c)$^2.$ For lower $Q^2$, the MRS(A) distributions were matched to the GRV\cite{grv} distributions which are valid down to $Q^2=0.3$ (GeV/c)$^2.$ Other parton distributions \cite{grv,cteq} yield similar results over the range of $Q^2$ for which these distributions are valid. We use $\alpha_s(M_Z)=0.117\pm0.005$ \cite{alpha} (the average result from LEP and deep inelastic data). We have used three light flavors in the calculation, and the effect of massive charm production by gluons was included\cite{yang} according to Laenen et al.\cite{neerven}. The effects of including the mass of the charm quark was significant only at the lowest value of $x,$ while at higher $x$ the results were the same as the calculation assuming three light flavors. The values of $R^{(2)}$ are significantly larger than $R^{(1)}$ in the kinematic range where the pQCD calculations are significant. Comparing the experimental data to the $R^{(2)}$ calculation we find that: 1) At $x=0.1,$ $Q^2>1$(GeV/c)$^2$ the $\alpha_s^2$ calculation is close to the data (and global fit to data). 2)At $x=0.1,$ $Q^2<1$ (GeV/c)$^2$ (Fig. 2) the measured value of $R$ is far below the steeply rising $R^{(2)}$ indicating that we may be outside the range of pQCD validity. A value of $\alpha_s(M_Z)=0.123$ (LEP average) gives values of $R^{(2)}$ which are much higher. 3) For larger values of $x,$ eg. $x\geq0.25,$ $Q^2\sim 3{\rm (GeV/c)^2}$ (Fig. 3) $R^{(2)}$ is less than half the measured value. The addition of target mass effects \cite{georgi}, which go as $x^3M^2/Q^2,$ are shown by the dashed curve in the figures $(R^{(2TM)})$. This effect becomes visible at higher values of $x,$ but even for $x\geq0.3,$ $Q^2 \leq 3$(GeV/c)$^2,$ $R^{(2TM)}$ is still significantly lower then the data and the global fit. The addition of an empirical higher twist term of the form $0.37 (Q^2 -1.34)/(Q^4+0.12)$ (not shown) gives an excellent fit over the entire data set with $\chi^2$/d.f.=1.1. In conclusion, the new data are consistent with previous determinations of $R$ and confirms the global analysis extraction over a wide range of $x$ and $Q^2.$ Calculations using second order pQCD combined with target mass corrections can match the data at low $x$ for $Q^2\geq 1$, but higher twist contributions are necessary for the higher $x$ region. We acknowledge the support of Dr. B. Richter and the SLAC staff, which was crucial for the success of this experiment. This research was supported by Department of Energy Contracts Nos. DE-AC02-76ER13065, DE-AC02-76ER02853, and DE-AC03-96SF00515; and National Science Foundation Contracts No. PHY91-14958. % Steve, need to put in correct A.U. and other grant numbers....... % In 1991, our grant number was 9114958. \begin{references} \bibitem[a]{AMRON} Present address: Amron Corp. Arlington VA 22202. \bibitem[b]{SLC} Present address: SLAC, Stanford, CA 94309. \bibitem[c]{UOW} Present address: U. of Wisconsin, Madison WI 53706. \bibitem[d]{WAM} Present address: College of William and Mary, Williamsburg VA 23187. \bibitem[e]{ODU} Present address: Old Dominion U., Norfolk, VA 23529. \bibitem[f]{VUU} Present address: Virginia Union U., Richmond, VA 23220. \bibitem[g]{CAL} Present address: Cal Tech, Pasadena CA 91125. \bibitem[h]{KNT} Present address: Kent State University, Kent OH 44242. \bibitem[i]{EMCORE} Present address: Emcore Corp., Sommerset NJ 08875. \bibitem{dasu} S. Dasu et al., Phys. Rev. Lett. 61, 1061 (1988); Phys. Rev. {\bf D 49}, 5641 (1994). \bibitem{whitlow} L. Whitlow et al., Phys. Lett. {\bf B250}, 193 (1990). Note that in Eq. 6 $b1$ should be 0.06347, not 0.635. \bibitem{six} G. Altarelli \& G. Martinelli, Phys. Lett. {\bf 76B,} 89 (1978). \bibitem{neerven} E. Laenen, S. Riemersma, J. Smith and W. L. van Neerven Nucl. Phys. {\bf B392}, 162 (1993); E.~B.~Zijlstra and W.~L.~van~Neerven, Nucl. Phys. {\bf B383}, 525 (1992); D.~I.~Kazakov et al., Phys. Rev. Lett. {\bf 65}, 1535 (1990). %Steve, is this a valid ref??? \bibitem{mrsa} A. D. Martin, R. G. Roberts, W. J. Stirling, RAL-94-055, DTP/94/34 June 1994; Phys. Lett. B 306 (1993) 146. and W.~J.~Stirling, private communication. \bibitem{grv} M. Gluck et. al., Z. Phys. {\bf C53}, 127 (1992). \bibitem{cteq} J. Botts et al., CTEQ collaboration, Phys. Lett. {\bf 304}, 159 (1993); and, W.~K.~Tung, private communication. \bibitem{taothesis} L. H. Tao, `Measurement of $x,Q^2$ and Hydrogen-Deuterium dependence of $R=\sigma_L/\sigma_T.$', Ph.D. Thesis, The American University, 1994. \bibitem{tsai} L. W. Mo and Y. S. Tsai, Rev. Mod. Phys. {\bf 41}, 205 (1969); Y. S. Tsai, Report No. SLAC-PUB-848 (1971); Y. S. Tsai, Lectures at the NATO Advanced Study Institute on Electron Scattering and Nuclear Structure, Cagliani, Italy, 1970. \bibitem{bardin} D. Y. Bardin et al., Yad. Phys. {\bf 29}, 499 (1979); D. Y. Bardin et al., Nucl. Phys. {\bf B197}, 1 (1982). \bibitem{stuart} L. Stuart et. al, SLAC-PUB-6305. \bibitem{bodek} A. Bodek et al., Phys. Rev. D {\bf 20}, 1471 (1979). \bibitem{whitlow2} L. Whitlow et al., Phys. Lett {\bf B282}, 475 (1992). \bibitem{ijl} F. Iachello, et. al., Phys. Lett {\bf 43B}, 191 (1973); G. Hohler et al., Nucl. Phys. {\bf B114}, 505 (1976);. P. Bosted, SLAC-PUB-6651, to be published in Phys. Rev. C. \bibitem{tjon} E. Hummel and J. A. Tjon, THU-993-100, Bulletin Board nucl-th@xxx. lanl.gov -93090. \bibitem{NMC} P. Amaudruz et al., Phys. Lett. {\bf B 294}, 120 (1992). \bibitem{diquark} S. Ekelin and S. Fredriksson, Phys. Lett. {\bf 162B}, 373 (1985). \bibitem{EMC} J. Gomez et al., Phys. Rev. D {\bf 49}, 4348 (1994). \bibitem{BCDMS} A. C. Benvenuti et al., Phys. Lett. {\bf B237}, 592 (1990). \bibitem{EMCR} J. J Aubert et al., Nucl. Phys. {\bf B259}, 189 (1985); Nucl. Phys. {\bf B293}, 740 (1987). \bibitem{CDHSW} P. Berge et al., Z. Phys. {\bf C49}, 187 (1991) . \bibitem{CDHS} A. Abramowicz al., Z. Phys. {\bf C17}, 283 (1983) . \bibitem{CHARM} F. Bergsma al., Phys. Lett. {\bf 141B}, 129 (1984) . \bibitem{alpha} Particle Data Group, Phys. Rev. {\bf D50}, 1297 (1994). \bibitem{yang} A. Bodek and U. K. Yang, UR-1375, Aug. 1994 (to be published in proceedings of DPF94, and Blois94; also A. Bodek, S. Rock and U. K. Yang, UR-1335, Sept. 1994 (submitted to Z. Phys. C). \bibitem{georgi} H.Georgi and D. Politzer, Phys. Rev. D {\bf 14}, 1829 (1976). \end{references} \begin{figure} \caption{ The results for $R^d-R^p$ as a function of $x$ for this experiment (solid circles) and from the SLAC global analysis \protect\cite{whitlow}. Statistical and systematic errors are added in quadrature. The results from NMC \protect\cite{NMC} are also shown. The solid curve is the prediction from pQCD including target mass corrections. The dashed line is the prediction from a diquark model \protect\cite{diquark}. } \end{figure} \begin{figure} \caption { The values of $R$ as a function of $Q^2$ at two values of $x$. The solid symbols are results from this experiment with statistical and systematic errors added in quadrature. The open diamonds are from the global analysis \protect\cite{whitlow} and the crosses are from CDHSW\protect\cite{CDHSW} and BCDMS. \protect\cite{BCDMS}. The perturbative QCD calculations \protect\cite{yang} $R^{(1)}$ (dotted) and $R^{(2)}$ (dot-dash) have been calculated to order $\alpha_s$ and $\alpha_s^2,$ respectively, including the effects of the mass of the charm quark \protect\cite{neerven}. The $R^{(2TM)}$ curve (dashed) also includes target mass effects in the order $\alpha_s^2$ pQCD calculation. The solid curve is an empirical parameterization of previous data \protect\cite{whitlow}. } \end{figure} \begin{figure} \caption { The values of $R$ as a function of $x$ at $Q^2\sim 3$(Gev/c$^2.$ Also shown is the measured elastic value of $R$ at $x$=1 ($\approx 0.328/Q^2$ for an isoscalar target assuming elastic form factor scaling).The notation is the same as in Fig. 2. } \end{figure} % Steve, where does elastic value come from? (ref) %Steve, here is how to do simple table in Latex. %Steve, here is how to do simple table in Latex. \begin{table}[t] \caption{Summary of typical point-to-point systematic errors. There is an overall normalization error of 2\% on the cross section which does not effect the $R$ measurement.} \begin{tabular}{cccc} Source & error(\%) & $\Delta\sigma (\%)$ & $\Delta R$ \\ \hline Beam energy & 0.1 & 0.3 & 0.015 \\ Beam charge & 0.2 & 0.2 & 0.010 \\ Spectrometer angle & 0.1 mr & 0.2 & 0.008 \\ Scattered momentum & 0.1 & 0.2 & 0.010 \\ Dead time & 0.2 & 0.2 & 0.010 \\ Efficiency & 0.1 & 0.1 & 0.005 \\ End Cap subtraction & 0.2 & 0.2 & 0.002 \\ $e^+/e^-$ background& 0.2 & 0.2 & 0.010 \\ Target density (liquid) & 0.3 & 0.3 & 0.015 \\ Target density (Be)& 0.1 & 0.1 & 0.005 \\ Acceptance (normal)& 0.1 & 0.1 & 0.005 \\ Acceptance (large) & 0.5 & 0.5 & 0.022 \\ \hline Total (Be) & & 0.8 & 0.035 \\ Total (H2,D2) & & 0.7 & 0.031 \\ \end{tabular} \end{table} \begin{table}[t] \caption{$R$ for different targets. There is an additional systematic error of 0.012 due to radiative corrections.} \begin{tabular}{ccccccc} $x$ & $Q^2$ & Target&Acceptance&$R$& $\Delta R^{stat}$ &$\Delta R^{sys}$ \\ \hline 0.10 & 0.5 & 4cm-H2 & N & 0.329 & 0.038 & 0.035 \\ 0.10 & 0.5 & 4cm-D2 & N & 0.259 & 0.031 & 0.033 \\ 0.10 & 1.0 & 4cm-H2 & N & 0.451 & 0.067 & 0.060 \\ 0.10 & 1.0 & 4cm-D2 & N & 0.349 & 0.059 & 0.054 \\ 0.35 & 3.0 &15cm-H2 & N & 0.189 & 0.030 & 0.022 \\ 0.35 & 3.0 &15cm-D2 & N & 0.233 & 0.032 & 0.026 \\ 0.50 & 3.6 &15cm-H2 & N & 0.199 & 0.027 & 0.028 \\ 0.50 & 3.6 &15cm-D2 & N & 0.194 & 0.028 & 0.028 \\ 0.50 & 3.6 & 4cm-D2 & L & 0.255 & 0.028 & 0.036 \\ 0.50 & 3.6 & Be & L & 0.182 & 0.026 & 0.032 \\ 0.60 & 5.0 & Be & L & 0.074 & 0.024 & 0.033 \\ 0.70 & 7.0 & Be & L & 0.099 & 0.035 & 0.038 \\ \end{tabular} \end{table} \begin{table}[t] \caption{$R$ averaged over Targets. There is an additional systematic error of 0.012 due to radiative corrections.} \begin{tabular}{ccccc} $x$ & $Q^2$ & $R$ & $\Delta R^{stat}$ &$\Delta R^{sys}$ \\ \hline 0.10 & 0.5 & .287 & 0.024 & 0.029 \\ 0.10 & 1.0 & .394 & 0.044 & 0.049 \\ 0.35 & 3.0 & .210 & 0.022 & 0.021 \\ 0.50 & 3.6 & .207 & 0.013 & 0.024 \\ 0.60 & 5.0 & .074 & 0.024 & 0.033 \\ 0.70 & 7.0 & .099 & 0.035 & 0.038 \\ \end{tabular} \end{table} \end{document}