File E.1. HELP.DOCUMENT. <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><> APPENDIX E OF DEEP INELASTIC STRUCTURE FUNCTIONS FROM ELECTRON SCATTERING ON HYDROGEN, DEUTERIUM, AND IRON AT .56<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><> File contains 816 total lines of 72 characters each. File contains documentation for Files E.1 through E.19. Appendix E consists of a set of 19 files, of which, this file is the first. These files are: E. 1: HELP.DOCUMENT E.11: SPECTRA.FORTRN E. 2: SIGMA.HYDROGEN E.12: R1990.FORTRN E. 3: SIGMA.DEUTRIUM E.13: F1990.FORTRN E. 4: F2.HYDROGEN E.14: F1990.MATRICES E. 5: F2.DEUTRIUM E.15: R.HYDROGEN E. 6: F2.DPRATIO E.16: R.DEUTRIUM E. 7: SPECTRA.BCDMS E.17: R.WORLD E. 8: SPECTRA.BCDMSZ E.18: SPECTRA.F2NF2P E. 9: SPECTRA.EMC E.19: SPECTRA.F2NF2PZ E.10: SPECTRA.EMCZ These files are archived on Apple Macintosh, IBM PC/AT, and IBM PS/2 formatted diskettes and also exist online at SLACVM. A copy of the thesis, SLAC-REPORT-357 and/or these diskettes can be obtained from: SLAC Publications, Mail Bin 68, P.O. Box 4349, Stanford, CA 94309-4349, (415)926-2677. This set of files can also be obtained via bitnet (during the foreseeable future) from LWW@SLACVM, SER@SLACVM, or EMR@SLACVM. ======================================================================== Important Preliminary Remarks: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ This set of 19 files may be copied and distributed freely. It is suggested that for clarity these files be distributed as a complete set. Any use of the data contained herein should contain a reference to: L.W. Whitlow, Ph.D. Thesis, Stanford University, 1990, SLAC-REPORT-357 (1990), as our forthcoming publications will not contain data tables of any form. Throughout this appendix, all uses of the word "Reference" (with a capital "R") are in reference to SLAC-REPORT-357. In general, these files span the full linewidth from character 1 through character 80. BEWARE, if you have one of those archaic printers which interprets character 1 as being somehow meaningful. As the SLAC laser- printers do not print character 80, we try to avoid using that charac- ter position. We adopt the notation "A¢N" to denote "A superscript N," which in some contexts is to be interpreted as "A raised to the power of N." Similarly, we use the notation "A_N" to denote "A subscript N." Errors are given either as "fractional" or "absolute." In general, errors in R are absolute and errors in cross sections and F_2 are fractional. The only exception to this rule are errors in the F_2 data from EMC and BCDMS which are given (as received from them) absolutely. ======================================================================== Files E.2 and E.3: SIGMA.HYDROGEN and SIGMA.DEUTRIUM ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Files contain final cross sections from our global reanalysis of the SLAC deep inelastic data. Cross sections have been re-radiatively corrected using our new Bardin/Tsai radiative corrections prescription (see Reference). Cross sections have been mutually cross-normalized with statistical and systematic errors well below the 1% level (see Reference). The anchor for overall normalization is the recent high precision experiment E140. In total, roughly 3000 deep inelastic cross section measurements have been included in our study. Since most of these measurements are at very nearly identical kinematics (see Reference), we present here a ``condensed'' table of measurements. This is exactly the condensing procedure discussed in detail in Section 5.2.1 of Reference. Intui- tively, this fairly obvious technique can be briefly summarized as follows: cross sections at the same scattering angle and beam energy (from the same experiment) are combined together over maximum kinematic spans of delta_x=.03 , delta_{Q¢2}/Q¢2=6% , delta_{epsilon}=.05 , and the new condensed cross section is assigned the weighted mean scattering kinematic of the condensed group. In general, the tables presented here are vastly more useful than the original set. Systematic effects introduced by this condensing process are estimated to be below the .1\% level, and so, are ignored. I = running counting index provided for convenience and correspondence. J = experiment number, as ordered in Table 1.1 of Reference: (1=E49a,2=E49b,3=E61,4=E87,5=E89a,6=E89b,7=E139,8=E140). Note that there are no hydrogen data from E139 and E140. Eo = incident beam energy (GeV). E' = scattered electron energy (GeV). theta = scattering angle (degrees). x = Bjorken scaling variable. Q¢2 = 4-momentum transfer squared (GeV¢2). epsilon = polarization of virtual photon, epsilon-element-of-[0,1]. W¢2 = mass squared of final (unmeasured) hadronic state (GeV¢2). C¢{RC} = radiative correction factor applied to raw cross section, calculated according to our new Bardin/Tsai prescription. sigma = final measured cross section, corrected for all known systematic effects. Units are [pb/srGeV] and [per nucleon] for deuterium. stat = total fractional random error, uncorrelated point to point. stat=sqrt(dST¢2+dSR¢2), where dST and dSR are defined in Chapter 4 of Reference and to a lesser degree in the documen- tation to Files E.4 and E.5. Values for dST and dSR are presented in Files E.4 and E.5. syst = total fractional experimental systematic error, correlated between neighboring points. syst=sqrt(dSY¢2+dSE¢2+dN1¢2 +dN2¢2), where dSY, dSE, dN1, and dN2 are defined in Chapters 4 and 5 of Reference and to a lesser degree in the documenta- tion to Files E.4 and E.5. Values for dSY, dSE, dN1, and dN2 are presented in Files E.4 and E.5. General remarks: ^^^^^^^^^^^^^^^^ stat and syst should be used primarily for making plots of the data. For very sensitive analyses, the user should use the specific (dST,dSR,dSY,dSE,dRC,dN1,dN2,dNM) error vector presented in Files E.4 and E.5 for the corresponding dataline (as labeled by the counting index I). An example of the correct propogation of these components of the error vector is given by program SPECTRA in File E.11. The uncertainty dRC in the measured cross sections due to radiative corrections is given by Equation 3.12 of Reference: dRC = abs[-.014+.017*epsilon] , also defined fractionally. Additionally, there are overall normaliza- tion uncertainties, denoted by dNM, of size dNM¢{hydrogen} = .021 , dNM¢{deuterium} = .017 , also defined fractionally. Note that the datalines from Files E.2 and E.3 do not match kinematic- ally. This is because both hydrogen and deuterium were not measured at all kinematics in all experiments. Deuterium/hydrogen cross section ratios are presented in File E.6 wherever cross sections have been measured on both targets at identical or nearly identical kinematics. ======================================================================== Files E.4 and E.5: F2.HYDROGEN and F2.DEUTRIUM ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Files contain F_2 values extracted from each cross section of Files E.2 and E.3. Note that the counting index I is used to tie each cross section measurement to its corresponding F_2 extraction. The F_2 extractions are performed assuming R=R¢{1990}, where R¢{1990} is a best fit model to the world R data (supplied in File E.17), including our new extractions of Chapter 5 of Reference. A Fortran implementation of R¢{1990} is presented in File E.12. I = running counting index provided for convenience and correspondence. J = experiment number, as ordered in Table 1.1 of Reference: (1=E49a,2=E49b,3=E61,4=E87,5=E89a,6=E89b,7=E139,8=E140). Note that there are no hydrogen data from E139 and E140. x = Bjorken scaling variable. Q¢2 = 4-momentum transfer squared (GeV¢2). F_2 = final extracted structure function. Units are [per nucleon] for deuterium. dFST = fractional statistical COUNTING uncertainty in F_2. This is the same as the dST uncertainty in the measured cross sections of Files E.2 and E.3, and so, the columns are labeled with both. dFSR = fractional random systematic uncertainty in F_2. This is the same as the dSR uncertainty in the measured cross sections of Files E.2 and E.3, and so, the columns are labeled with both. [This uncertainty is due to FLUCTUATIONS in beam charge, in scattering kinematics, in target density, and in detector efficiencies -- and so, is random in nature.] dFSY = fractional systematic uncertainty in F_2 due to background contamination. This is the same as the dSY uncertainty in the measured cross sections of Files E.2 and E.3, and so, the columns are labeled with both. When propagated within an experiment, assume perfectly correlated. When propagated between experiments, assume uncorrelated. [This uncertainty is due to uncertainties in calibrations of scattering kine- matics and uncertainties due to background contamination.] dFSE = fractional systematic uncertainty in F_2 due to the E' depen- dence of the spectrometer acceptance. This is the same as the dSE uncertainty in the measured cross sections of Files E.2 and E.3, and so, the columns are labeled with both. Because these errors are perfectly correlated with E', they carry a (+/-) sign to keep track of (+/anti) correlations. When propagated within an experiment, assume correlated and respect the sign. When propagated between experiments, assume uncor- related and ignore the sign. [This uncertainty is due to the possibility that the spectrometer acceptance is dependent upon the E' setting of the central momentum.] dFRC = fractional systematic uncertainty in F_2 due to the radiative corrections. This is NOT the same as dRC because the epsilon- correlation of dRC effects the extraction of F_2. The general formula for dFRC is given by Equation 5.39 of Reference: dFRC = .023(epsilon-.85+(1+.5R)(Rfac-1)/(Rfac(1+R)), where Rfac = 1+(1-epsilon)/(epsilon(1+R)). For x<.1 or Q¢2<1GeV, we increase this uncertainty by a factor of 1.5. When propagated within or between experiments, assume perfectly correlated. dFN1 = fractional statistical uncertainty in F_2 due to the relative normalization uncertainties of the experiments. This is the same as the dN1 uncertainty in the measured cross sections of Files E.2 and E.3, and so, the columns are labeled with both. When propagated within an experiment, assume perfectly correlated. When propagated between experiments, assume uncorrelated (as in the sample Fortran program of File E.11) although they are distinctly, positively correlated as indi- cated in Table 5.4 of Reference. [This uncertainty reflects possible statistical errors in our global normalization procedure.] dFN2 = fractional systematic uncertainty in F_2 due to the relative normalizations of the experiments. This is the same as the dN2 uncertainty in the measured cross sections of Files E.2 and E.3, and so, the columns are labeled with both. When propagated within an experiment, assume perfectly correlated. When propagated between experiments, assume uncorrelated. [This uncertainty reflects possible systematic errors in our global normalization procedure.] dFSZ = fractional systematic uncertainty in F_2 due to the experi- mental uncertainty in R=R¢{1990}, and so, does not correlate to an uncertainty in the measured cross sections. This error does not include the uncertainty in F_2 due to [the uncer- tainty in R¢{1990} due to (the uncertainty in radiative corrections)], which is explicitly included in dFRC above. When propagated within or between experiments assume perfectly correlated. stat = total fractional random error, uncorrelated point to point. stat=sqrt(dFST¢2+dFSR¢2). Note that this is the same quantity defined as "stat" in the documentation to Files E.2 and E.3. syst = total fractional experimental systematic error, correlated between neighboring points. syst=sqrt(dFSY¢2+dFSE¢2+dFRC¢2 +dFN1¢2+dFN2¢2+dFSZ¢2). Note that this is NOT the same quantity defined as "syst" in the documentation to Files E.2 and E.3. General remarks: ^^^^^^^^^^^^^^^^ stat and syst should be used primarily for making plots of the data. For sensitive analyses, the user should use the specific (dFST,dFSR, dFSY,dFSE,dFRC,dFN1,dFN2,dFSZ) error vector. An example of the correct propogation of these components of the error vector is given by program SPECTRA in File E.11. Additionally, there are overall normalization uncertainties, denoted by dFNM, of size dFNM¢{hydrogen} = .021 , dFNM¢{deuterium} = .017 , also defined fractionally, which are the same, of course, as the dNM of the measured cross sections of Files E.2 and E.3. Note that the datalines from File E.4 and E.5 do not match kinematic- ally. This is because both hydrogen and deuterium were not measured at all kinematics in all experiments. Deuterium/hydrogen structure function ratios are presented in File E.6 wherever cross sections have been measured on both targets at identical or nearly identical kinematics. ======================================================================== File E.6: F2.DPRATIO ^^^^^^^^^^^^^^^^^^^^^^ File contains deuterium/hydrogen F_2 ratios extracted from the cross sections of Files E.2 and E.3, assuming that R¢d=R¢p (see Reference). Note, given this assumption, this file also presents deuterium/hydrogen cross section ratios. Deuterium/hydrogen structure function ratios are presented wherever cross sections have been measured on both targets at identical or nearly identical kinematics. Thus, the counting index, I, used here is NOT related the counting index used previously. See documentation to Files E.4 and E.5 for a full description of the propagational properties of the errors dFSR, dFNM1, and dFNM2. I = running counting index provided for convenience and correspondence. J = experiment number, as ordered in Table 1.1 of Reference: (1=E49a,2=E49b,3=E61,4=E87,5=E89a,6=E89b) Note that there are no hydrogen data from E139 and E140. x = Bjorken scaling variable. Q¢2 = 4-momentum transfer squared (GeV¢2). F2d/F2p = final extracted structure function ratio. Units are [per nucleon] for deuterium, and so, ratios are typically < 1. dST = fractional statistical counting uncertainty in F_2 ratios. dSR = fractional random systematic uncertainty in F_2 ratios. dN1 = fractional statistical uncertainty in F_2 ratios due to the relative normalizations of the experiments. dN2 = fractional systematic uncertainty in F_2 due to the relative normalizations of the experiments. stat = total fractional random error, uncorrelated point to point. stat=sqrt(dST¢2+dSR¢2). syst = total fractional experimental systematic error, correlated between neighboring points. syst=sqrt(dN1¢2+dN2¢2). General remarks: ^^^^^^^^^^^^^^^^ stat and syst should be used primarily for making plots of the data. For sensitive analyses, the user should use the specific (dST,dSR,dN1,dN2,dNM) error vector. Note that errors of type dSY, dRC, dSZ become negligible in the structure function (or cross section) ratio, and are thus ignored. Similarly, errors of type dSE are identically zero in the ratio. Additionally, there is an overall normalization uncertainty, denoted by dNM, of size dNM = .010 , also defined fractionally. ======================================================================== Files E.7 and E.9: SPECTRA.BCDMS and SPECTRA.EMC ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Files contain the hydrogen and deuterium F_2 values plotted in Figures 5.14 through 5.17 of Reference. These F_2 values have been binned into "x-spectra" so that scaling violation studies can be made. The most famous earlier versions of these plots are included in: A.C.Benvenuti, et al., Phys. Lett. B223, 485 (1989). A.C.Benvenuti, et al., CERN-EP/89-170 (1989), submitted to Phys. Lett. B. T.Sloan, CERN-EP/87-188 (1987), presented at Int'l Europhysics Conf. on High Energy Physics, Uppsala, 1987, Figure 4. File E.7 contains our new SLAC data binned in bins of x=[.07,.1,.14,.18, .225,.275,.35,.45,.55,.65,.75,.85] which matches the published binning of the BCDMS collaboration. File E.8 contains the corresponding BCDMS data suitably corrected for our new knowledge of R given by R¢{1990} (see below). File E.9 contains our new SLAC data binned in bins of x=[.08,.125,.175, .25,.35,.45,.55,.65,.75,.85] which matches the published binning of the EMC collaboration. File E.10 contains the corresponding EMC data suitably corrected for our new knowledge of R given by R¢{1990} (see below). The program that creates these x-spectra from the data of Files E.4 and E.5 is program SPECTRA, and it is given in File E.11 as an example of a (very nearly) exact propagation of the full F_2 error vector. x = Bjorken scaling variable. counts = number of elements in each x-spectra. Q¢2 = 4-momentum transfer squared (GeV¢2). F_2 = combined extracted structure function. Units are [per nucleon] for deuterium. stat = total fractional random error, uncorrelated point to point. syst = total fractional experimental systematic error, correlated between neighboring points. Exp'ts = delineates the experiment numbers (J's from files E.4 and E.5) of those experiments which contribute to the F_2 value given. This is presented primarily as a convenience so that you can work backward from the F_2 values given in this table. For example, the first dataline in File E.7 originates from a single cross section measurement from experiment 1 (=E49a). For example, the fourth dataline in File E.7 originates from two cross section measurements from experiment 1 (=E49a) and one cross section measurement from experiment 6 (=E89b). This data is stored in an 8-digit Fortran integer. However, because as many as 12 different cross sections are combined together, it is (in general) required to use two such Fortran integers. Thus, both integers are printed out (in a 2i9 format). The second integer is most frequently zero and if zero, should be ignored. ======================================================================== Files E.8 and E.10: SPECTRA.BCDMSZ and SPECTRA.EMCZ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Files contain, respectively, BCDMS and EMC F_2 values ready for plots of "x-spectra." These files supply the BCDMS and EMC data corresponding to the SLAC x-spectra of Files E.7 and E.9, respectively. Sorry about the abrupt change in format between E.7 and E.9 and these files. Comparisons of SLAC-vs-BCDMS and SLAC-vs-EMC can be made by plotting [File E.7 with File E.8] and [File E.9 with File E.10], respectively. These plots will recreate Figures 5.14 through 5.17 of Reference, updating the rather famous comparisons found in the three references given above in the documentation to files E.7 and E.9. BCDMS references: A.C.Benvenuti, et al., Phys. Lett. B223, 485 (1989). A.C.Benvenuti, et al., CERN-EP/89-170 (1989), submitted to Phys. Lett. B. EMC references: J.J.Aubert, et al., Nucl. Phys. B259, 189 (1985); J.J.Aubert, et al., Nucl. Phys. B293, 740 (1987); M.Arneodo, et al., CERN-EP/89-121, submitted to Nucl. Phys. B. Note that the EMC and BCDMS F_2 values have been corrected for the new model of R, namely R¢{1990} (supplied in File E.12). I = convenient counting index for x-bins. J = convenient counting index for Q¢2-bins. Note that the negative (and some small nonnegative) values of J encountered in File E.10 are from Arneodo, et al. x = Bjorken scaling variable. Q¢2 = 4-momentum transfer squared (GeV¢2). F_2 = final structure function corrected for R=R¢{1990}. Units are [per nucleon] for deuterium. stat = total ABSOLUTE random error, uncorrelated point to point. syst = total ABSOLUTE experimental systematic error, correlated between neighboring points. syst includes the contribution from dRfac, discussed below. R1989c = The value of R assumed in correcting the F_2 data from R=0. Note that an early version of model R¢{1990} was used for this correction. This version, R¢{1989c}, differs negligibly from R¢{1990}. Rfac = The correction factor applied to the F_2 data to correct for the difference in R between R¢{1990} and the value assumed in the extraction of F_2 (namely, R=0). The correction is largest at low x and high Q¢2 because epsilon is small for these kinematics at CERN beam energies. dRfac = The uncertainty in Rfac due to the total uncertainty in R¢{1990}, including all sources of uncertainty in R including radiative corrections. This error is included in the total systematic uncertainty quoted in column syst (see above). ======================================================================== Files E.11: SPECTRA.FORTRN ^^^^^^^^^^^^^^^^^^^^^^^^^^^ File contains a sample program which illustrates the correct propagation of the systematic error vector (dFST,dFSR,dFSY,dFSE,dFRC,dFN1,dFN2,dFSZ) through a binning and averaging process. Specifically, SPECTRA takes as input the F_2 data in Files E.4 and E.5, shuffles the data together, bins the data in x, and then condenses the data with respect to [logQ¢2] to achieve the x-spectra of Files E.7 and E.9. For the users convenience, the I/O of program SPECTRA has been designed to accept as input exactly Files E.4 and E.5; and yield as output exactly Files E.7 and E.9 (without the text at the head of these files). Program SPECTRA is easily modified to match any x-binning. Likewise, it can be used to bin in Q¢2 or in x and Q¢2 simultaneously, with some slight modifications. Additional documentation for this program can be found as comment lines within the Fortran text of the file. We do not, a priori, recommend such a detailed error propogation for all applications of these data. Because, in general, the non-random systematic components of the error vector are smaller than the random components (dFST and dFSR), it is often (though not always) possible to make simplifying assumptions about the propogation of the non-random components. In sensitive analyses it may be necessary to propagate the error vector exactly. In those cases, program SPECTRA should serve as an invaluable example. ======================================================================== Files E.12: R1990.FORTRN ^^^^^^^^^^^^^^^^^^^^^^^^^ File contains a Fortran implementation of the best fit model to the world's R data (tabulated for convenience in File E.17) as a function of (x,Q¢2). This Fortran subroutine also returns an estimate of the total error in R. This total error is the quadrature sum of three uncertainties, namely: 1) the statistical uncertainty, evaluated in SUBROUTINE DR1990, which is also supplied; 2) an estimate of the bias introduced by our choice of models; 3) possible errors in the radiative corrections, given by +/-.023(1+.5R) (see Equation 4.5 of Reference). NOTE: In some applications, most notably the extraction of F_2 from the measured cross sections, it is more correct not to use 3) in the supplied program (as noted above in the discussion of dFRC in the documentation to Files E.4 and E.5, this avoids the double propagation of radiative correction errors). See Section 5.4 of Reference for more details. NOTE: R¢{1990} is designed to return realistic values of R for all (x,Q¢2), with uncertainty estimates that reflect the actual measurement errors. Outside the SLAC and EMC/BCDMS kinematic range, these uncertainty estimates are "realistic," but ad hoc. NOTE: This program should NOT be used at Q¢2<.3 GeV¢2. Additional documentation for this program can be found as comment lines within the Fortran text of the file. ======================================================================== Files E.13: F1990.FORTRN ^^^^^^^^^^^^^^^^^^^^^^^^^ File contains a Fortran implementation of the two best fit models to the SLAC structure function data for F_2. See Section 5.4.1 of Reference for details. Model choice is an input parameter, MODEL=[9,12]: Model= 9 gets the best fit 9-parameter OMEGA9 model [Reference: Section 5.C of Bodek, et al., Phys. Rev. D20 1471 (1979)]; Model=12 gets the best fit 12-parameter LAMBDA12 model [Reference: ad hoc, but inspired by Section 6.6 of J.J.Aubert, et al., Nucl. Phys. B259 189 (1985)]. Program output is [per nucleon] for deuterium. This Fortran subroutine also returns the total statistical error in F_2 and the systematic error in F_2 due to bias in the choice of models. There is a significant difference between these models at x<.1 and at x>.5 and very large Q¢2. See Figures 5.9 and 5.10 of Reference for a comparison of these models. In general, the LAMBDA12 model fits the data better at large \x, while the OMEGA9 model fits the data better at \x\sl.1. The LAMBDA12 model is the one preferred by the author for most applications within the SLAC Q¢2 range. The systematic error returned by the Fortran subroutine does not include the overall normalization uncertainty of the SLAC data, which is +/-2.1% for hydrogen and +/-1.7% for deuterium. Nor does it include errors due to radiative corrections, which (as shown in the discussion of dFRC in the documentation to Files E.4 and E.5) are everywhere less than +/-.5%. NOTE: F¢{1990} is only guaranteed to be accurate in the SLAC deep inelastic neighborhood. Program returns a warning message for calls which are outside this neighborhood. See program for specific details. This program requires as input the four large matrices stored in File E.17. See Reference for more details. Additional documentation for this program can be found as comment lines within the Fortran text of the file. ======================================================================== Files E.14: F1990.MATRICES ^^^^^^^^^^^^^^^^^^^^^^^^^^^ File contains the covariance matrices for the two best fit models to structure function data for F_2, for hydrogen and deuterium, and is accessed by F1990 FORTRN. This file was originally stored in 180 character lines, formatted as (9F15.10) and (12F15.10), and when stored in this way is much more accessible to the unaided mind. We have folded the file up so as to keep the record length below 80 and have altered the READ statement within F1990 FORTRN to accept this folded version. ======================================================================== Files E.15 and E.16: R.HYDROGEN and R.DEUTRIUM ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Files contain the values of R extracted from the global reanalysis of SLAC deep inelastic data. For most purposes, the user is suggested to utilize the average of the hydrogen and deuterium values as presented in File E.17. This exploits our conclusion that R¢p=R¢d (=R¢n) and reduces the statistical scatter of the data. Also, some parts of the systematic error in R¢p are expected to be correlated to some parts of the syste- matic error in R¢d. The average results, given in File E.17, display the correct propagation of all such errors. Note that there is one misalignment between these files. While each file contains 88 datalines, there was no hydrogen extraction at (x,Q¢2) =(.7,5) and no deuterium extraction at (x,Q¢2)=(.625,4). x = Bjorken scaling variable. Q¢2 = 4-momentum transfer squared (GeV¢2). R = the extracted value of R¢p or R¢d. stat = total ABSOLUTE random error in R, uncorrelated point to point. syst = total ABSOLUTE experimental systematic error, complexly correlated between neighboring points. syst=sqrt(dRSY¢2+dRSE¢2 +dRN1¢2+dRN2¢2), where dRSY, dRSE, dRN1, and dRN2 are defined below, and in more detail in Chapters 4 and 5 of Reference. dRSY = absolute systematic uncertainty in R due to background contamination and kinematic calibration uncertainties. dRSE = absolute systematic uncertainty in R due to the E' dependence of the spectrometer acceptances. dRN1 = absolute statistical uncertainty in R due to the statistical uncertainties in the relative normalizations of the experiments. dRN2 = absolute systematic uncertainty in R due to the systematic uncertainties in the relative normalizations of the experiments. General remarks: ^^^^^^^^^^^^^^^^ The errors dRSY, dRSE, dRN1, and dRN2 are VERY complexly correlated between data points. The correct propagation of these errors is discussed in Section 5.3.1 of Reference, and is not reconstructible from the information provided here. When making fits to the data, simply assume that syst is uncorrelated between points, and let the weights for the fitting procedure be determined by 1/(stat¢2+syst¢2). When averag- ing these values together, on the other hand, make the conservative assumption that each of these errors is perfectly correlated across all measurements. NOTE: When manipulating these data, beware that the uncertainty distri- butions are NOT gaussian. See Appendix B.2 of Reference for the best way to deal with this fact. The uncertainty dRRC due to radiative corrections uncertainties is not included in this table and is given by Equation 4.5 of Reference: dRRC = .023(1+.5R) , also defined absolutely and perfectly correlated across all measurements on both targets. ======================================================================== File E.17: R.WORLD ^^^^^^^^^^^^^^^^^^^ File contains the world measurements of R averaged over all targets whenever those measurements are at the same (x,Q¢2). In particular: the E140 measurements are averaged over deuterium (D), iron (F), and gold (A); the SLAC measurements from the combined global analysis are averaged over hydrogen (H) and deuterium; and the EMC measurements are averaged over hydrogen and iron. Note that the E140 data is independent of the SLAC data. Even though we used E140 as a normalization anchor, and we eventually combined E140 F_2 data with the other 7 SLAC experiments, we did not include the E140 data in the global extraction of R, and so these data represent independent measurements. This file reproduces Tables 4.6 and 5.8 from Reference and also includes R measurements from EMC, CDHSW, and BCDMS. References for these R measurements are as follows: SLAC: the Reference; which supersedes all other reports prior to March 1990. E140: the Reference, superceding S.Dasu et al., Phys. Rev. Lett. 61 1061 (1988) and all other reports prior to March 1990. CDHSW: P.Berge et al., CERN-EP/89-103 (1989), submitted to Z. Phys. C. BCDMS: A.C.Benvenuti, et al., Phys. Lett. B223, 485 (1989); A.C.Benvenuti, et al., CERN-EP/89-170 (1989), submitted to Phys. Lett. B. EMC: J.J.Aubert et al., Nucl. Phys. B259 189 (1985); J.J.Aubert et al., Nucl. Phys. B272 158 (1986). x = Bjorken scaling variable. Q¢2 = 4-momentum transfer squared (GeV¢2). = the extracted value of R averaged over all targets. stat = total ABSOLUTE random error in R, uncorrelated point to point. syst = total ABSOLUTE experimental systematic error, complexly correlated between neighboring points for SLAC and E140 data (though independent between SLAC and E140). syst=sqrt(dRSY¢2 +dRSE¢2+dRN1¢2+dRN2¢2), where dRSY, dRSE, dRN1, and dRN2 are defined as below, and in more detail in Chapters 4 and 5 of Reference. dRSY = absolute systematic uncertainty in R due to background contamination. dRSE = absolute systematic uncertainty in R due to the E' dependence of the spectrometer acceptances. dRN1 = absolute statistical uncertainty in R due to the relative normalization uncertainties of the experiments. dRN2 = absolute systematic uncertainty in R due to the relative normalization uncertainties of the experiments. Expt = experimental effort responsible for measurement. Targets = targets averaged over, using notation defined above. General remarks: ^^^^^^^^^^^^^^^^ The errors dRSY, dRSE, dRN1, and dRN2 in the SLAC and E140 data are VERY complexely correlated between data points (though independent between SLAC and E140). The correct propagation of these errors is discussed in Section 5.3.1 of Reference, and is not reconstructible from the informa- tion provided here. When making fits to the data, simply assume that syst is uncorrelated between points, and let the weights for the fitting procedure be determined by 1/(stat¢2+syst¢2). When averaging these values together, on the other hand, make the conservative assumption that each of these errors is perfectly correlated across all measure- ments. NOTE: When manipulating these data, beware that the uncertainty distri- butions are NOT gaussian. See Appendix B.2 of Reference for the best way to deal with this fact. The uncertainty dRRC in the SLAC and E140 data due to radiative corrections uncertainties is not included in this table and is given by Equation 4.5 of Reference: dRRC = .023(1+.5R) , also defined absolutely and perfectly correlated across all measurements on both experiments and all targets. ======================================================================== Files E.18: SPECTRA.F2NF2P ^^^^^^^^^^^^^^^^^^^^^^^^^^^ File contains smeared neutron/proton F_2 ratios for the SLAC data. The smeared F_2 ratios are defined as [F_2¢n/F_2¢p]_{smeared} = (2*F_2¢d/F_2¢p)-1 . F_2 ratios from File E.6 have been shuffled together, and binned in x-bins so that studies of this ratio as a function of Q¢2 can be made. This file is the neutron/proton equivalent of Files E.7 and E.9. Plots of these data are presented in Figures 5.20 and 5.21 of Reference. This file contains the SLAC ratios binned into 12 x-spectra matching the x-binning of BCDMS and into 10 x-spectra matching the x-binning of EMC (note that above x=.35 the binning is identical). The corresponding plot files for the BCDMS and EMC data are obtained directly from Files E.8 and E.10, respectively, and are presented below in File E.19. In making plots 5.20 and 5.21 of Reference, we make the simplifying assumption that all systematic errors for BCDMS and EMC cancel in the deuterium/hydrogen structure function ratio. x = Bjorken scaling variable. counts = number of elements in each x-spectra. Q¢2 = 4-momentum transfer squared (GeV¢2). F2n/F2p = smeared neutron/proton F_2 structure function ratio. stat = total fractional random error, uncorrelated point to point. syst = total fractional experimental systematic error, correlated between neighboring points. Exp'ts = delineates the experiment numbers (J's from files E.4 and E.5) of those experiments which contribute to the F_2 value given (see discussion in documentation to Files E.7 and E.9). ======================================================================== Files E.19: SPECTRA.F2NF2PZ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^ File contains smeared neutron/proton F_2 ratios for the BCDMS and EMC data. The smeared F_2 ratios are defined as above, namely, [F_2¢n/F_2¢p]_{smeared} = (2*F_2¢d/F_2¢p)-1 . These F_2 ratios are calculated directly from Files E.8 and E.10, thereby duplicating the method used to calculate the SLAC ratios of File E.18. Comparisons with the SLAC data are presented in Figures 5.20 and 5.21 and discussed in Section 5.4.4 of Reference. File contains the plot files for the BCDMS and EMC smeared ratios. For references, see the documentation to Files E.8 and E.10. x = Bjorken scaling variable. Q¢2 = 4-momentum transfer squared (GeV¢2). F2n/F2p = smeared neutron/proton F_2 structure function ratio. stat = total ABSOLUTE random error, uncorrelated point to point. syst = total ABSOLUTE experimental systematic error, correlated between neighboring points, presented ONLY for EMC. General Remarks: ^^^^^^^^^^^^^^^^ In Reference, we make the simplifying assumption that all BCDMS and EMC systematic errors cancel in the deuterium/hydrogen structure function ratio. For completeness only, we present the EMC values of syst, which are quoted in [J.J.Aubert et al., Nucl. Phys. B293 740 (1987)] as the systematic errors on the neutron/hydrogen structure function ratios including the calculated smearing corrections. ======================================================================== End of file HELP.DOCUMENT. 816 lines in total.