To be submitted to Physics Letters.  SLAC-PUB-7927, August 1998Measurements were made at SLAC of the cross section for scattering 29 GeV electrons from carbon at a laboratory angle of 4.5◦, corresponding to 0.03 < x < 0.1 and 1.3 < Q2 < 2.7 GeV2. Values of R = σL/σT were extracted in this kinematic range by comparing these data to cross sections measured at a higher beam energy by the NMC collaboration. The results are in reason- able agreement with pQCD calculations and with extrapolations of the R1990 parameterization of previous data. A new fit is made including these data and other recent results.Work supported by Department of Energy contract DE–AC03–76SF00515

Abe, K.

Akagi, T.

Anthony, P.L.

Antonov, R.

Arnold, R.G.

Averett, T.

Band, H.R.

Bauer, J.M.

Borel, H.

Bosted, P.E.

Breton, E.V.

Button-Shafer, J.

Chen, J.P.

Chupp, T.E.

Clendenin, J.

Comptour, C.

Coulter, K.P.

Court, G.

Crabb, D.

Daoudi, M.

Day, D.

Dietrich, F.S.

Dunne, J.

Dutz, H.

Erbacher, R.

Fellbaum, J.

Feltham, A.

Fonvieille, H.

Frlez, E.

Garvey, D.

Gearhart, R.

Gomez, J.

Grenier, P.

Griffioen, K.A.

Hoibraten, S.

Hughes, E.W.

Hyde-Wright, C.

Johnson, J.R.

Kawall, D.

Klein, A.

Kuhn, S.E.

Kuriki, M.

Lindgren, R.

Liu, T.J.

Lombard-Nelsen, R.M.

Marroncle, J.

Maruyama, T.

Maruyama, X.K.

McCarthy, J.

Meyer, W.

Meziani, Z.-E.

Minehart, R.

Mitchell, J.

Morgenstern, J.

Petratos, G.G.

Pitthan, R.

Pocanic, D.

Prepost, R.

Prescott, C.

Raines, P.

Raue, B.

Reyna, D.

Rijllart, A.

Roblin, Y.

Rochester, L.S.

Rock, S.E.

Rondon, O.A.

Sick, I.

Smith, L.C.

Smith, T.B.

Spengos, M.

St.Lorant, S.

Staley, F.

Steiner, P.

Stuart, L.M.

Suekane, F.

Szalata, Z.M.

Tang, H.

Terrien, Y.

Usher, T.

Walz, D.

Wesselmann, F.

White, J.L.

Witte, K.

Young, C.C.

Youngman, B.

Yuta, H.

Zapalac, G.

Zihlmann, B.

Zimmermann, D.

Calhoun, Institutional Archive of the Naval Postgraduate School

Calhoun: The NPS Institutional ArchiveFaculty and Researcher Publications Faculty and Researcher Publications1998-08þÿ M e a s u r e m e n t s   o f   R   =  Ã L /Ã T   f o r   0 . 0 3   <   x< 0.1 and Fit to World DataF. Staleyhttp://hdl.handle.net/10945/44958arXiv:hep-ex/9808028v1  26 Aug 1998SLAC-PUB-7927August 1998Measurements of R = σL/σT for 0.03 < x < 0.1 and Fit to World Data∗The E143 CollaborationK. Abe,15 T. Akagi,11,15 P. L. Anthony,11 R. Antonov,10 R. G. Arnold,1 T. Averett,16,‡‡ H. R. Band,18J. M. Bauer,6,§§ H. Borel,4 P. E. Bosted,1 V. Breton,3 J. Button-Shafer,6 J. P. Chen,16,♥ T. E. Chupp,7J. Clendenin,11 C. Comptour,3 K. P. Coulter,7 G. Court,11,∗ D. Crabb,16 M. Daoudi,11 D. Day,16 F. S. Dietrich,5J. Dunne,1,♥ H. Dutz,11,∗∗ R. Erbacher,11,12 J. Fellbaum,1 A. Feltham,2 H. Fonvieille,3 E. Frlez,16 D. Garvey,8R. Gearhart,11 J. Gomez,14 P. Grenier,4 K. A. Griffioen,10,17 S. Hoibraten,16,§ E. W. Hughes,11,‡‡ C. Hyde-Wright,9J. R. Johnson,18 D. Kawall,12,♦ A. Klein,9 S. E. Kuhn,9 M. Kuriki,15 R. Lindgren,16 T. J. Liu,16R. M. Lombard-Nelsen,4 J. Marroncle,4 T. Maruyama,11 X. K. Maruyama,8 J. McCarthy,16 W. Meyer,11,∗∗Z.-E. Meziani,12,13 R. Minehart,16 J. Mitchell,14 J. Morgenstern,4 G. G. Petratos,11,‡ R. Pitthan,11 D. Pocanic,16C. Prescott,11 R. Prepost,18 P. Raines,10,∞ B. Raue,9,† D. Reyna,1,∂ A. Rijllart,11,†† Y. Roblin,3 L. S. Rochester,11S. E. Rock,1 O. A. Rondon,16 I. Sick,2 L. C. Smith,16 T. B. Smith,7 M. Spengos,1,10 F. Staley,4 P. Steiner,2S. St.Lorant,11 L. M. Stuart,11 F. Suekane,15 Z. M. Szalata,1 H. Tang,11 Y. Terrien,4 T. Usher,11 D. Walz,11F. Wesselmann,9 J. L. White,1,∞ K. Witte,11 C. C. Young,11 B. Youngman,11 H. Yuta,15 G. Zapalac,18B. Zihlmann,2 D. Zimmermann161The American University, Washington, D.C. 200162Institut fu¨r Physik der Universita¨t Basel, CH–4056 Basel, Switzerland3LPC IN2P3/CNRS, University Blaise Pascal, F–63170 Aubiere Cedex, France4DAPNIA-Service de Physique Nucleaire, Centre d’Etudes de Saclay, F–91191 Gif/Yvette, France5Lawrence Livermore National Laboratory, Livermore, California 945506University of Massachusetts, Amherst, Massachusetts 010037University of Michigan, Ann Arbor, Michigan 481098Naval Postgraduate School, Monterey, California 939439Old Dominion University, Norfolk, Virginia 2352910University of Pennsylvania, Philadelphia, Pennsylvania 1910411Stanford Linear Accelerator Center, Stanford, California 9430912Stanford University, Stanford, California 9430513Temple University, Philadelphia, Pennsylvania 1912214Thomas Jefferson National Accelerator Facility, Newport News, Virginia 2360615Tohoku University, Sendai 980, Japan16University of Virginia, Charlottesville, Virginia 2290117The College of William and Mary, Williamsburg, Virginia 2318718University of Wisconsin, Madison, Wisconsin 53706To be submitted to Physics LettersMeasurements were made at SLAC of the cross section for scattering 29 GeV electrons fromcarbon at a laboratory angle of 4.5◦, corresponding to 0.03 < x < 0.1 and 1.3 < Q2 < 2.7 GeV2.Values of R = σL/σT were extracted in this kinematic range by comparing these data to crosssections measured at a higher beam energy by the NMC collaboration. The results are in reason-able agreement with pQCD calculations and with extrapolations of the R1990 parameterization ofprevious data. A new fit is made including these data and other recent results.∗Work supported by Department of Energy contract DE–AC03–76SF00515.1INTRODUCTIONThe spin-averaged cross section for lepton nucleon scattering can be written in terms of the two componentsfor virtual photon absorption: the longitudinal cross section σL(x,Q2), and the transverse cross section σT (x,Q2).Alternatively this can be expressed in terms of the structure functions F2 and R = σL/σTdσ(x,Q2, ǫ)dE′dΩ= Γ(x,Q2, ǫ)[σT (x,Q2) + ǫσL(x,Q2)]= σMott2MxF2(x,Q2)ǫQ2[1+ǫR(x,Q2)1+R(x,Q2)](1)where Q2 = 4EE′ sin2(θ/2) is the four-momentum squared of the virtual photon, x = Q2/[2M(E − E′)] is the light-cone momentum fraction of the struck parton, Γ is the virtual photon flux, ǫ−1 = 1 + 2(1 + Q2/4M2x2) tan2(θ/2),and θ and E′ are the scattered lepton scattering angle and momentum in the lab. R is determined by making crosssection measurements at fixed (x,Q2) as a function of ǫ by varying the beam energy and scattering angle. In thequark-parton model, R is sensitive to the spin of the struck partons: at large Q2, R is zero for spin 1/2 quarks whileat finite Q2 quark transverse momentum causes non-zero values. In pQCD calculations of R [1] the leading term isproportional to αs times integrals over the quark and gluon distributions, and is thus sensitive to the gluon content ofthe nucleon. At low Q2 and high x, target mass corrections [2] also contribute to R. Knowledge of R is important forextracting the unpolarized structure function F2 from cross section measurements and the spin structure functions g1and g2 from asymmetry measurements of polarized leptons on polarized nucleons.Previously a good parameterization was made of the world data on R (known as R1990) [3], but the fit is limitedin validity to x > 0.07, where input data existed. To extend our knowledge of R into the lower x region (where it isneeded for the extraction of g1) we made cross section measurements in the range 0.03 < x < 0.1. This was part ofSLAC experiment E143 [4], whose primarily goal was the measurement of g1 for the proton and deuteron.E143 CROSS SECTIONSWe measured the cross section for scattering of 29.1 GeV electrons from a 1.7 gm/cm2 carbon target at the EndStation A facilities of the Stanford Linear Accelerator Center. Scattered electrons in the momentum range of 6 to25 GeV/c (0.03 ≤ x ≤ 0.4) were detected in a magnetic spectrometer at θ = 4.5◦. We used two threshold Cˇerenkovcounters and a segmented lead glass shower counter to identify electrons. Electron momenta were determined fromtracking in a multi-plane hodoscope system and independently from the energy deposited in the shower counter.The system was designed to measure the spin structure functions of the nucleons and thus could operate at highrates. Details are given in [4]. The acceptance of the spectrometer was calculated with a model that used magneticmeasurements and survey information. Part of the acceptance of the spectrometer was also calibrated by re-measuringthe already known cross section in the kinematic region 0.1 < x < 0.3. These cross sections are accurately known atall values of ǫ from a fit to F d2 by the NMC collaboration [5], a fit to the A-dependence of lepton-nucleon scattering [6],and previously measured values of R [3]. The central momentum of the spectrometer was then lowered in several stepsto put scattered electrons corresponding to 0.03 < x < 0.1 into the calibrated acceptance region. Small adjustmentswere made to the spectrometer acceptance model until the overlaps between spectra with different central momentumsettings were in good agreement. The final corrections to the acceptance compared to the original model were in thefew percent range. Thus the overall normalization of our results are tied to those of the NMC fit.Absolute cross sections in the low x region for the carbon target were obtained taking into account the residualbackground contaminations, the experimental efficiency for detecting electrons, the trigger dead time, and the appli-cation of radiative corrections [7,8]. The results for carbon cross sections per nucleon are shown in Fig. 1a and TableI. The systematic errors include an overall normalization uncertainty of about 2.5% due the combined uncertaintiesin target thickness, beam charge and spectrometer acceptance. Other systematic errors increased with decreasing x,including detection efficiency, the spectrometer acceptance, and radiative corrections (about 3% at low x, decreasingto about 1% at the highest x). The Q2 for the points in Fig. 1a vary approximately linearly with x as in Table I.The curve on Fig. 1a is the predicted cross section using the NMC fit to F d2 [5], nuclear corrections [6], and R1990[3]. The good agreement between data and model for x < 0.1 is an indication that the extrapolation of R1990 tox = 0.03 works reasonably well.2RESULTS FOR RTo determine values for R, we used Eq. 1 with the E143 cross sections and those of NMC [5] at the same (x,Q2)values, but at much higher beam energies (higher values of ǫ). Since our cross sections are normalized to NMCcross sections at higher values of x, the normalization uncertainties between the two experiments are negligible thusreducing the systematic uncertainty on R.The results are shown in Fig. 1b and Table I together with various fits and calculations. The new data are inreasonable agreement with the R1990 parameterization (solid curve with dotted curves showing error band), plottedat the Q2 values of E143, although there is a tendency for the data to be slightly higher than R1990 at low x andlower than R1990 at high x. The lower x data are also higher than a calculation of NNLO pQCD plus target masscorrections [9] (dashed) using the MRS-R2 [10] parton distribution with four flavors.Since the R1990 was published, there has been a considerable body of new data on R from this experiment, fromSLAC E140X [11], NMC [12], and CCFR [13] as well as final results from CDHSW [14]. The data were recordedon a variety of targets, but since Rd = Rp = RA [11,15] to high accuracy we will combine them into a single dataset. The new data have extended the kinematic range to lower and higher values of x. Because R1990 has been usedextensively outside its range of validity at low x, it is important to compare it to the new data. The confidence levelfor R1990 to match the data is 61%. For the region x ≤ 0.07, outside the range of validity of R1990, the confidencelevel is 16%. We note that Rc, one of the three fits that were averaged to make R1990, has a confidence level of lessthan 1% to agree with the low x data, while the Ra and Rb are much more successful.We have performed a new fit using the present data [3,11–14], but excluding data with errors greater than 0.5 ormore than 3 standard deviations below zero. The final data set still included some values of R which, due to errors,were negative (unphysical). There were 237 points with a kinematic range of 0.005 ≤ x ≤ 0.86 and 0.5 ≤ Q2 ≤ 130.Figure 2 shows the distribution of points as a scatter plot. More parameters were added to the general form of theR1990 fits to try to accommodate the new data at low x. Three 6-parameter models were used based on the previousthree R1990 models:Ra =a1log(Q2/0.04)Θ(x,Q2) +a24√Q8 + a43[1 + a4x+ a5x2]xa6 ,Rb =b1log(Q2/0.04)Θ(x,Q2) + [b2Q2+b3Q4 + 0.32][1 + b4x+ b5x2]xb6 ,Rc =c1log(Q2/0.04)Θ(x,Q2) + c2[(Q2−Q2thr)2+ c23]−1/2(2)withQ2thr = c4x+ c5x2 + c6x3Θ(x,Q2) = 1 + 12( Q2Q2 + 1)( 0.12520.1252 + x2), (3)where the units of Q2 are GeV2. The coefficients of the fits are shown in Table II. As in the case of R1990, we defineR1998 to be the average of the three fits. The error associated with the fitting is approximately given by:δR(x,Q2) = 0.0078− 0.013x+0.070− 0.39x+ 0.70x21.7 +Q2.This error is largest at low Q2, reaching a maximum value for x ∼ 0.04. A systematic error associated with thefunctional form can be assigned from the spread of the three fits. Long range correlated errors such as those dueto radiative corrections will enhance the errors. The new fits result in a better agreement with the data, with aconfidence level of 73% for all the data and 38% when restricted to x ≤ 0.07.Fig. 3 shows the measured values of R as a function of Q2 in three ranges of x below x = 0.10, along with R1998and the pQCD plus target mass calculation used above. The value of R decreases with Q2 as had been observed[8] at higher values of x. At these low values of x, target mass effects make only a small contribution to the pQCDcalculation. The pQCD curve is below the data at low Q2 as previously noted. Fig. 4 shows the data as a functionof x for three ranges of Q2. R is not very strongly dependent on x in this Q2 range, continuing the trend observed for3x ≥ 0.07. The pQCD plus target mass calculation falls below the data at low Q2 and low x, but otherwise is in quitegood agreement. We note that Q2 ∼ 1GeV2 is a rather low value for pQCD calculations.In summary, our new measurements of R, as well as other recent results are consistent with extrapolations of theempirical parameterization R1990. The result are roughly consistent with pQCD plus target mass calculations. Ournew fit to the data (R1998), although similar to R1990, better reflects the wealth of new data obtained over the lastseveral years and is in better agreement with the low x data.We wish to acknowledge the tremendous effort made by the SLAC staff in making this experiment successful. Thiswork was supported by Department of Energy contracts: No. W-2705-Eng-48 (LLNL), No. DE-AC03-76SF00515(SLAC), No. DE-FG03-88ER40439 (Stanford), Nos. DE-FG05-88ER40390 and DEFG05-86ER40261 (Virginia), andNo. DE-AC02-76ER00881 (Wisconsin); by National Science Foundation Grants No. 9114958 (American), No. 9307710(Massachusetts), No. 9217979 (Michigan), and No. 9104975 (ODU); by the Schweizersche Nationalfonds (Basel); bythe Commonwealth of Virginia; and by the Ministry of Science, Culture and Education of Japan (Tohoku).‡‡ Present Address: California Institute of Technology, Pasadena, CA 91125.§§ Present address: University of Mississippi, University, MS 38677.∗ Permanent address: Oliver Lodge Lab, University of Liverpool, Liverpool, U. K.∗∗ Permanent address: University of Bonn, D-53113 Bonn, Germany.§ Permanent address: FFIYM, P.O. Box 25, N-2007 Kjeller, Norway.‡ Permanent address: Kent State University, Kent, Ohio 44242.†† Permanent address: CERN, 1211 Geneva 23, Switzerland.† Permanent address: Florida International University, Miami, FL 33199.♥ Present address: Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606.♦ Present address: Yale University, New Haven, CT 06520.∞ Present address: Stanford Linear Accelerator Center, Stanford, California 94309∂ Present address: DESY, D-22603 Hamburg[1] G. Altarelli & G. Martinelli, Phys. Lett. 76B, 89 (1978).[2] H. Georgi and D. Politzer, Phys. Rev. D14, 1829 (1976).[3] L. W. Whitlowet al., Phys. Lett. B250, 193 (1990).[4] SLAC E143, K. Abe et al., Phys. Rev. Lett. 74, 346 (1995); Phys. Rev. Lett. 75, 25, (1995); SLAC-PUB-7753 submittedto Phys. Rev. D.[5] NMC, M. Arneodo et al., Phys. Lett. B364, 107 (1995).[6] J. Gomez et al., Phys. Rev. D 49, 4348 (1994).[7] Y. S. Tsai, Report No. SLAC–PUB–848, 1971; Rev. Mod. Phys. 46 (1974), 815; D. Y. Bardin et al., Yad. Phys. 29, 499(1979); D. Y. Bardin et al., Nucl. Phys. B197, 1 (1982).[8] SLAC E140, S. Dasu et al., Phys. Rev. Lett. 61, 1061 (1988) and references within.[9] A. Bodek, S. Rock, and U. Yang, 1996 UR-1355 (Z. Phys. C to be published).[10] A.D. Martin, R.G. Roberts, W.J. Stirling, Phys. Lett B387, 419 (1996).[11] SLAC E140X, L.H. Tao et al., Z. Phys. C70, 387 (1996).[12] NMC, M. Arneodo et al., Nucl. Phys. B483, 3 (1997)[13] U.K. Yang et al., University of Rochester Prepring UR-1534 (1998), Preprint archives hep-ex/9806023. The data at thelowest x bin were excluded (private communication, U. K. Yang)[14] CDHSW, P. Berge et al., Z. Phys. C49, 187 (1991).[15] NMC, P. Amaudruz et al., Phys.Lett. B294, 120 (1992); M. Arneodo et al.,Nucl. Phys. B487, 3 (1997); Nucl. Phys. B481,23 (1996).4TABLE I. Cross sections for carbon from E143 in nb/GeV/sr (per nucleon) and R extracted from this experiment and NMCdeuterium data with statistical and systematic errors.x Q2 (GeV/c2) ǫ σ ± stat ±sys R ± stat ±sys0.0325 1.32 0.474 61.91 ± .46 ± 3.7 0.45 ± 0.01 ± 0.070.0375 1.47 0.519 60.81 ± .50 ± 3.6 0.51 ± 0.02 ± 0.090.0450 1.67 0.578 62.82 ± .53 ± 2.9 0.40 ± 0.01 ± 0.100.0550 1.90 0.641 65.64 ± .62 ± 2.3 0.28 ± 0.01 ± 0.090.0650 2.11 0.692 66.76 ± .66 ± 2.1 0.29 ± 0.02 ± 0.100.0750 2.29 0.734 69.61 ± .73 ± 2.4 0.18 ± 0.02 ± 0.110.0850 2.46 0.767 70.23 ± .73 ± 1.8 0.26 ± 0.03 ± 0.100.0950 2.60 0.795 72.03 ± .70 ± 2.2 0.25 ± 0.03 ± 0.140.1050 2.73 0.818 74.46 ± .71 ± 2.1 0.17 ± 0.03 ± 0.13TABLE II. Coefficients to 6-parameter fits a, b and c for R1998 with the corresponding χ2/df for 231 degrees of freedom .fit 1 2 3 4 5 6 χ2/dfa 0.0485 0.5470 2.0621 -0.3804 0.5090 -0.0285 0.9b 0.0481 0.6114 -0.3509 -0.4611 0.7172 -0.0317 0.9c 0.0577 0.4644 1.8288 12.3708 -43.1043 41.7415 1.05FIG. 1. (a) Cross sections from this experiment (E143) for 29.1 GeV electron scattering from carbon at 4.5◦. Inner (outer)error bars are statistical (systematic). The curve is calculated using the NMC fit to F2 [5], the R1990 fit to R [3], and theA-dependence of lepton-nucleon scattering [6]. (b) R extracted from this experiment (E143) combined with NMC. Inner (outer)error bars are statistical (systematic). The solid curve is the R1990 fit, with the dotted curves showing the error band evaluatedat the Q2 values of the data. The dashed curve is a pQCD calculation described in the text.FIG. 2. Kinematic distribution of data used for the R1998 fit.6FIG. 3. R as a function of Q2 for: a) 0.05 ≤ x ≤ 0.10; b) 0.03 ≤ x ≤ 0.05; c) 0.01 ≤ x ≤ 0.02. The solid curve is the averageof the new fits, R1998, and the dashed curve is the NNLO pQCD calculation described in the text.7FIG. 4. R as a function of x for: a) 3 ≤ Q2 ≤ 6(GeV/c)2; b) 1.5 ≤ Q2 ≤ 3 (GeV/c)2; c) 0.5 ≤ Q2 ≤ 1.5 (GeV/c)2. The solidcurve is the average of the new fits, R1998, and the dashed curve is the NNLO pQCD calculation described in the text.8

Measurements of R = σL/σT for 0.03 < x < 0.1 and Fit to World Data

Measurements were made at SLAC of the cross section for scattering 29 GeV electrons from carbon at a laboratory angle of 4.58, corresponding to 0.03-x-0.1 and 1.3-Q2-2.7 GeV2. Values of RssLrsT were extracted in this kinematic range by comparing these data to cross sections measured at a higher beam energy by the NMC collaboration. The results are in reasonable agreement with pQCD calculations and with extrapolations of the R1990 parameterization of previous data. A new fit is made including these data and other recent results. q1999 Published by Elsevier Science B.V. All rights reserved.This work was supported by Department of Energy contracts: No. W-2705-Eng-48 LLNL., No. DE-AC03-76SF00515 ŽSLAC., No. DE-FG03- 88ER40439 Stanford., Nos. DE-FG05-88ER40390 and DEFG05-86ER40261 Virginia., and No. DE- AC02-76ER00881 Wisconsin.; by National Science Foundation Grants No. 9114958 American., No. 9307710 Massachusetts., No. 9217979 Michigan., and No. 9104975 ŽODU.; by the Schweizerische Nationalfonds ŽBasel.; by the Commonwealth of Virginia; and by the Ministry of Science, Culture and Education of Japan Tohoku..This work was supported by Department of Energy contracts: No. W-2705-Eng-48 ŽLLNL., No. DE-AC03-76SF00515 ŽSLAC., No. DE-FG03- 88ER40439 ŽStanford., Nos. DE-FG05-88ER40390 and DEFG05-86ER40261 ŽVirginia., and No. DE- AC02-76ER00881 ŽWisconsin.; by National Science Foundation Grants No. 9114958 ŽAmerican., No. 9307710 ŽMassachusetts., No. 9217979 ŽMichigan., and No. 9104975 ŽODU.; by the Schweizerische Nationalfonds ŽBasel.; by the Commonwealth of Virginia; and by the Ministry of Science, Culture and Education of Japan ŽTohoku.

The E143 Collaboration

Breton, V.

Chump, T.E.

Maruyama, X.K

St. Lorant, S.

Calhoun: The NPS Institutional ArchiveDSpace RepositoryFaculty and Researchers Faculty and Researchers' Publications1999-04Measurements of R = L/T for 0.03 < x < 0.1and Fit to World DataThe E143 Collaboration; Abe, K.; Akagi, T.; Anthony, P.L.;Antonov, R.; Arnold, R.G.; Averett, T.; Band, H.R.; Bauer,J.M.; Borel, H....ElsevierAbe, K., et al. "Measurements of R= L/T for 0.03< x< 0.1 and Fit to WorldData." Physics Letters B 452.1-2 (1999): 194-200.http://hdl.handle.net/10945/62189This publication is a work of the U.S. Government as defined in Title 17, UnitedStates Code, Section 101. Copyright protection is not available for this work in theUnited States.Downloaded from NPS Archive: Calhoun15 April 1999Ž .Physics Letters B 452 1999 194–200Measurements of Rss rs for 0.03-x-0.1L Tand fit to world data 1E143 CollaborationK. Abe o, T. Akagi k,o, P.L. Anthony k, R. Antonov j, R.G. Arnold a, T. Averett p,2,H.R. Band r, J.M. Bauer f,3, H. Borel d, P.E. Bosted a, V. Breton c, J. Button-Shafer f,J.P. Chen p,4, T.E. Chupp g, J. Clendenin k, C. Comptour c, K.P. Coulter g,G. Court k,5, D. Crabb p, M. Daoudi k, D. Day p, F.S. Dietrich e, J. Dunne a,4,H. Dutz k,6, R. Erbacher k,l, J. Fellbaum a, A. Feltham b, H. Fonvieille c, E. Frlez p,D. Garvey h, R. Gearhart k, J. Gomez n, P. Grenier d, K.A. Griffioen j,q,S. Hoibraten p,7, E.W. Hughes k,2, C. Hyde-Wright i, J.R. Johnson r,D. Kawall l,8, A. Klein i, S.E. Kuhn i, M. Kuriki o, R. Lindgren p, T.J. Liu p,R.M. Lombard-Nelsen d, J. Marroncle d, T. Maruyama k, X.K. Maruyama h,J. McCarthy p, W. Meyer k,6, Z.-E. Meziani l,m, R. Minehart p, J. Mitchell n,J. Morgenstern d, G.G. Petratos k,9, R. Pitthan k, D. Pocanic p, R. Prepost r,C. Prescott k, P. Raines j,10, B. Raue i,11, D. Reyna a,12, A. Rijllart k,13,Y. Roblin c, L.S. Rochester k, S.E. Rock a, O.A. Rondon p, I. Sick b,L.C. Smith p, T.B. Smith g, M. Spengos a,j, F. Staley d, P. Steiner b, S.St. Lorant k,L.M. Stuart k, F. Suekane o, Z.M. Szalata a, H. Tang k, Y. Terrien d, T. Usher k,D. Walz k, F. Wesselmann i, J.L. White a,10, K. Witte k, C.C. Young k,B. Youngman k, H. Yuta o, G. Zapalac r, B. Zihlmann b, D. Zimmermann pa The American UniÕersity, Washington, D.C. 20016, USAb Institut fur Physik der UniÕersitat Basel, CH–4056 Basel, Switzerland¨ ¨c LPC IN2P3rCNRS, UniÕersity Blaise Pascal, F–63170 Aubiere Cedex, Franced DAPNIArSPhN, CEA-Saclay, 91191 GifrYÕette, Francee Lawrence LiÕermore National Laboratory, LiÕermore, CA 94550, USAf UniÕersity of Massachusetts, Amherst, MA 01003, USAg UniÕersity of Michigan, Ann Arbor, Michigan 48109, USAh NaÕal Postgraduate School, Monterey, CA 93943, USAi Old Dominion UniÕersity, Norfolk, VA 23529, USAj UniÕersity of PennsylÕania, Philadelphia, PA 19104, USAk Stanford Linear Accelerator Center, Stanford, CA 94309, USAl Stanford UniÕersity, Stanford, CA 94305, USAm Temple UniÕersity, Philadelphia, PA 19122, USAn Thomas Jefferson National Accelerator Facility, Newport News, VA 23606, USA0370-2693r99r$ - see front matter q 1999 Published by Elsevier Science B.V. All rights reserved.Ž .PII: S0370-2693 99 00244-0( )K. Abe et al.rPhysics Letters B 452 1999 194–200 195o Tohoku UniÕersity, Sendai 980, Japanp UniÕersity of Virginia, CharlottesÕille, VA 22901, USAq The College of William and Mary, Williamsburg, VA 23187, USAr UniÕersity of Wisconsin, Madison, WI 53706, USAReceived 2 November 1998Editor: K. WinterAbstractMeasurements were made at SLAC of the cross section for scattering 29 GeV electrons from carbon at a laboratory angleof 4.58, corresponding to 0.03-x-0.1 and 1.3-Q2 -2.7 GeV2. Values of Rss rs were extracted in this kinematicL Trange by comparing these data to cross sections measured at a higher beam energy by the NMC collaboration. The resultsare in reasonable agreement with pQCD calculations and with extrapolations of the R1990 parameterization of previousdata. A new fit is made including these data and other recent results. q 1999 Published by Elsevier Science B.V. All rightsreserved.PACS: 13.60.Hb; 29.25.Ks; 11.50.Li; 13.88.qe1. IntroductionThe spin-averaged cross section for lepton nu-cleon scattering can be written in terms of the twocomponents for virtual photon absorption: the longi-Ž 2 .tudinal cross section s x,Q , and the transverseLŽ 2 .cross section s x,Q . Alternatively this can beT1 Work supported by the National Science Foundation and theDepartment of Energy.2 Present Address: California Institute of Technology, Pasadena,CA 91125, USA.3 Present address: University of Mississippi, University, MS38677, USA.4 Present address: Thomas Jefferson National Accelerator Faci-lity, Newport News, Virginia 23606, USA.5 Permanent address: Oliver Lodge Lab, University of Liver-pool, Liverpool, UK.6 Permanent address: University of Bonn, D-53113 Bonn, Ger-many.7 Permanent address: FFIYM, P.O. Box 25, N-2007 Kjeller,Norway.8 Present address: Yale University, New Haven, CT 06520,USA.9 Permanent address: Kent State University, Kent, Ohio 44242,USA.10 Present address: Stanford Linear Accelerator Center, Stanford,California 94309, USA.11 Permanent address: Florida International University, Miami,FL 33199, USA.12 Present address: DESY, D-22603 Hamburg, Germany.13 Permanent address: CERN, 1211 Geneva 23, Switzerland.expressed in terms of the structure functions F and2Rss rsL Tds x ,Q2 ,eŽ .XdE dV2 2 2sG x ,Q ,e s x ,Q qes x ,QŽ . Ž . Ž .T L2 22 MxF x ,Q 1qeR x ,QŽ . Ž .2ss 1Ž .Mott 2 2e Q 1qR x ,QŽ .2 X 2Ž .where Q s4EE sin ur2 is the four-momentum2 w Ž X .xsquared of the virtual photon, xsQ r 2 M EyEis the light-cone momentum fraction of the strucky1 Žparton, G is the virtual photon flux, e s1q2 12 2 2 . 2Ž . XqQ r4M x tan ur2 , and u and E are thescattered lepton scattering angle and momentum inthe lab. R is determined by making cross sectionŽ 2 .measurements at fixed x,Q as a function of e byvarying the beam energy and scattering angle. In thequark-parton model, R is sensitive to the spin of thestruck partons: at large Q2, R is zero for spin 1r2quarks while at finite Q2 quark transverse momen-tum causes non-zero values. In pQCD calculations ofw xR 1 the leading term is proportional to a timessintegrals over the quark and gluon distributions, andis thus sensitive to the gluon content of the nucleon.2 w xAt low Q and high x, target mass corrections 2( )K. Abe et al.rPhysics Letters B 452 1999 194–200196also contribute to R. Knowledge of R is importantfor extracting the unpolarized structure function F2from cross section measurements and the spin struc-ture functions g and g from asymmetry measure-1 2ments of polarized leptons on polarized nucleons.Previously a good parameterization was made ofŽ . w xthe world data on R known as R1990 3 , but thefit is limited in validity to x)0.07, where input dataexisted. To extend our knowledge of R into theŽlower x region where it is needed for the extraction.of g we made cross section measurements in the1range 0.03-x-0.1. This was part of SLAC experi-w xment E143 4 , whose primary goal was the measure-ment of g for the proton and deuteron.12. E143 cross sectionsWe measured the cross section for scattering of29.1 GeV electrons from a 1.7 gmrcm2 carbontarget at the End Station A facilities of the StanfordLinear Accelerator Center. Scattered electrons in theŽ .momentum range of 6 to 25 GeVrc 0.03FxF0.4were detected in a magnetic spectrometer at us4.58.ˇWe used two threshold Cerenkov counters and asegmented lead glass shower counter to identifyelectrons. Electron momenta were determined fromtracking in a multi-plane hodoscope system and in-dependently from the energy deposited in the showercounter. The system was designed to measure thespin structure functions of the nucleons and thusw xcould operate at high rates. Details are given in 4 .The acceptance of the spectrometer was calculatedwith a model that used magnetic measurements andsurvey information. Part of the acceptance of thespectrometer was also calibrated by re-measuring thealready known cross section in the kinematic region0.1-x-0.3. These cross sections are accuratelyknown at all values of e from a fit to F d by the2w xNMC collaboration 5 , a fit to the A-dependence ofw xlepton-nucleon scattering 6 , and previously mea-w xsured values of R 3 . The central momentum of thespectrometer was then lowered in several steps to putscattered electrons corresponding to 0.03-x-0.1into the calibrated acceptance region. Small adjust-ments were made to the spectrometer acceptancemodel until the overlaps between spectra with differ-ent central momentum settings were in good agree-ment. The final corrections to the acceptance com-pared to the original model were in the few percentrange. Thus the overall normalization of our resultsare tied to those of the NMC fit.Ž . Ž . Ž .Fig. 1. a Cross sections from this experiment E143 for 29.1 GeV electron scattering from carbon at 4.58. Inner outer error bars areŽ . w x w xstatistical systematic . The curve is calculated using the NMC fit to F 5 , the R1990 fit to R 3 , and the A-dependence of lepton-nucleon2w x Ž . Ž . Ž . Ž .scattering 6 . b R extracted from this experiment E143 combined with NMC. Inner outer error bars are statistical systematic . Thesolid curve is the R1990 fit, with the dotted curves showing the error band evaluated at the Q2 values of the data. The dashed curve is apQCD calculation described in the text.( )K. Abe et al.rPhysics Letters B 452 1999 194–200 197Table 1Ž .Cross sections for carbon from E143 in nbrGeVrsr per nucleon and R extracted from this experiment and NMC deuterium data withstatistical and systematic errors2 2Ž .x Q GeVrc e s " stat "sys R " stat "sys0.0325 1.32 0.474 61.91 " .46 " 3.7 0.45 " 0.01 " 0.070.0375 1.47 0.519 60.81 " .50 " 3.6 0.51 " 0.02 " 0.090.0450 1.67 0.578 62.82 " .53 " 2.9 0.40 " 0.01 " 0.100.0550 1.90 0.641 65.64 " .62 " 2.3 0.28 " 0.01 " 0.090.0650 2.11 0.692 66.76 " .66 " 2.1 0.29 " 0.02 " 0.100.0750 2.29 0.734 69.61 " .73 " 2.4 0.18 " 0.02 " 0.110.0850 2.46 0.767 70.23 " .73 " 1.8 0.26 " 0.03 " 0.100.0950 2.60 0.795 72.03 " .70 " 2.2 0.25 " 0.03 " 0.140.1050 2.73 0.818 74.46 " .71 " 2.1 0.17 " 0.03 " 0.13Absolute cross sections in the low x region forthe carbon target were obtained taking into accountthe residual background contaminations, the experi-mental efficiency for detecting electrons, the triggerdead time, and the application of radiative correc-w xtions 7,8 . The results for carbon cross sections pernucleon are shown in Fig. 1a and Table 1. Thesystematic errors include an overall normalizationuncertainty of about 2.5% due the combined uncer-tainties in target thickness, beam charge and spec-trometer acceptance. Other systematic errors in-creased with decreasing x, including detection effi-ciency, the spectrometer acceptance, and radiativeŽcorrections about 3% at low x, decreasing to about. 21% at the highest x . The Q for the points in Fig.1a vary approximately linearly with x as in Table 1.The curve on Fig. 1a is the predicted cross sectiond w x w xusing the NMC fit to F 5 , nuclear corrections 6 ,2w xand R1990 3 . The good agreement between dataand model for x-0.1 is an indication that theextrapolation of R1990 to xs0.03 works reason-ably well.3. Results for RŽ .To determine values for R, we used Eq. 1 withw xthe E143 cross sections and those of NMC 5 at theŽ 2 .same x,Q values, but at much higher beam ener-Ž .gies higher values of e . Since our cross sectionsare normalized to NMC cross sections at highervalues of x, the normalization uncertainties betweenthe two experiments are negligible thus reducing thesystematic uncertainty on R.The results are shown in Fig. 1b and Table 1together with various fits and calculations. The newdata are in reasonable agreement with the R1990Žparameterization solid curve with dotted curves. 2showing error band , plotted at the Q values ofE143, although there is a tendency for the data to beslightly higher than R1990 at low x and lower thanR1990 at high x. The lower x data are also higherthan a calculation of NNLO pQCD plus target massw x Ž . w xcorrections 9 dashed using the MRS-R2 10 par-ton distribution with four flavors.Since the R1990 was published, there has been aconsiderable body of new data on R from thisw x w xexperiment, from SLAC E140X 11 , NMC 12 , andw xCCFR 13 as well as final results from CDHSWw x14 . The data were recorded on a variety of targets,d p A w xbut since R sR sR 11,15 to high accuracy wewill combine them into a single data set. The newFig. 2. Kinematic distribution of data used for the R1998 fit.( )K. Abe et al.rPhysics Letters B 452 1999 194–200198Table 2Coefficients to 6-parameter fits a, b and c for R1998 with the corresponding x 2rdf for 231 degrees of freedom2fit 1 2 3 4 5 6 x rdfa 0.0485 0.5470 2.0621 y0.3804 0.5090 y0.0285 0.9b 0.0481 0.6114 y0.3509 y0.4611 0.7172 y0.0317 0.9c 0.0577 0.4644 1.8288 12.3708 y43.1043 41.7415 1.0data have extended the kinematic range to lower andhigher values of x. Because R1990 has been usedextensively outside its range of validity at low x, itis important to compare it to the new data.The confidence level for R1990 to match the datais 61%. For the region xF0.07, outside the range ofvalidity of R1990, the confidence level is 16%. Wenote that R , one of the three fits that were averagedcto make R1990, has a confidence level of less than1% to agree with the low x data, while the R andaR are much more successful.bWe have performed a new fit using, in addition tow xthe data already used in 3 , the more recent dataw x3,11–14 , but excluding data with errors greaterthan 0.5 or more than 3 standard deviations belowzero. The final data set still included some values ofŽ .R which, due to errors, were negative unphysical .There were 237 points with a kinematic range of0.005FxF0.86 and 0.5FQ2 F130 GeV 2. Fig. 2shows the distribution of points as a scatter plot.More parameters were added to the general form ofthe R1990 fits to try to accommodate the new data atlow x. Three 6-parameter models were used basedon the previous three R1990 models:a1 2R s Q x ,QŽ .a 2log Q r0.04Ž .a2 2 a6q 1qa xqa x x ,4 548 4(Q qa3b1 2R s Q x ,QŽ .b 2log Q r0.04Ž .b b2 3 2 b6q q 1qb xqb x x ,4 52 4 2Q Q q0.3c1 2R s Q x ,QŽ .c 2log Q r0.04Ž .y1r222 2 2qc Q yQ qc , 2Ž .Ž .2 thr 3withQ2 sc xqc x 2 qc x 3 ,thr 4 5 6Q2 0.12522Q x ,Q s1q12 , 3Ž .Ž . 2 2 2ž /ž /Q q1 0.125 qxwhere the units of Q2 are GeV 2. The coefficients ofthe fits are shown in Table 2. As in the case ofR1990, we define R1998 to be the average of the2 . .Fig. 3. R as a function of Q for: a 0.05F xF0.10; b 0.03F x.F0.05; c 0.01F xF0.02. The solid curve is the average of thenew fits, R1998, and the dashed curve is the NNLO pQCDcalculation described in the text. For clarity, some data pointsfrom the same experiment have been combined while others havebeen shifted slightly in Q2.( )K. Abe et al.rPhysics Letters B 452 1999 194–200 199. 2 Ž .2 .Fig. 4. R as a function of x for: a 3FQ F6 GeVrc ; b2 Ž .2 . 2 Ž .21.5FQ F3 GeVrc ; c 0.5FQ F1.5 GeVrc . The solidcurve is the average of the new fits, R1998, and the dashed curveis the NNLO pQCD calculation described in the text. For clarity,some data points from the same experiment have been combinedwhile others have been shifted slightly in x.three fits. The error associated with the fitting isapproximately given by:dR x ,Q2 s0.0078y0.013 xŽ .0.070y0.39 xq0.70 x 2q .21.7qQThis error is largest at low Q2, reaching a maximumvalue for x;0.04. A systematic error associatedwith the functional form can be assigned from thespread of the three fits. Long range correlated errorssuch as those due to radiative corrections will en-hance the errors. The new fits result in a betteragreement with the data, with a confidence level of73% for all the data and 38% when restricted toxF0.07.Fig. 3 shows the measured values of R as afunction of Q2 in three ranges of x below xs0.10,along with R1998 and the pQCD plus target masscalculation used above. The value of R decreases2 w xwith Q as had been observed 8 at higher values ofx. At these low values of x, target mass effects makeonly a small contribution to the pQCD calculation.The pQCD curve is below the data at low Q2 aspreviously noted. Fig. 4 shows the data as a functionof x for three ranges of Q2. R is not very stronglydependent on x in this Q2 range, continuing thetrend observed for xG0.07. The pQCD plus targetmass calculation falls below the data at low Q2 andlow x, but otherwise is in quite good agreement. Wenote that Q2 ;1 GeV 2 is a rather low value forpQCD calculations.In summary, our new measurements of R, as wellas other recent results are consistent with extrapola-tions of the empirical parameterization R1990. Theresult are roughly consistent with pQCD plus targetŽ .mass calculations. Our new fit to the data R1998 ,although similar to R1990, better reflects the wealthof new data obtained over the last several years andis in better agreement with the low x data.We wish to acknowledge the tremendous effortmade by the SLAC staff in making this experimentsuccessful. This work was supported by DepartmentŽ .of Energy contracts: No. W-2705-Eng-48 LLNL ,Ž .No. DE-AC03-76SF00515 SLAC , No. DE-FG03-Ž .88ER40439 Stanford , Nos. DE-FG05-88ER40390Ž .and DEFG05-86ER40261 Virginia , and No. DE-Ž .AC02-76ER00881 Wisconsin ; by National ScienceŽ .Foundation Grants No. 9114958 American , No.Ž . Ž .9307710 Massachusetts , No. 9217979 Michigan ,Ž .and No. 9104975 ODU ; by the SchweizerischeŽ .Nationalfonds Basel ; by the Commonwealth ofVirginia; and by the Ministry of Science, Culture andŽ .Education of Japan Tohoku .Referencesw x Ž .1 G. Altarelli, G. Martinelli, Phys. Lett. B 76 1978 89.w x Ž .2 H. Georgi, D. Politzer, Phys. Rev. D 14 1976 1829.w x Ž .3 L.W. Whitlow, Phys. Lett. B 250 1990 193.w x Ž .4 SLAC E143, K. Abe et al., Phys. Rev. Lett. 74 1995 346;Ž .Phys. Rev. Lett. 75 1995 25; SLAC-PUB-7753 submittedto Phys. Rev. D.w x Ž .5 NMC, M. Arneodo et al., Phys. Lett. B 364 1995 107.w x Ž .6 J. Gomez, Phys. Rev. D 49 1994 4348.w x7 Y.S. Tsai, Report No. SLAC–PUB–848, 1971; Rev. Mod.Ž .Phys. 46 1974 815; D.Y. Bardin et al., Yad. Phys. 29Ž . Ž .1979 499; Nucl. Phys. B 197 1982 1.( )K. Abe et al.rPhysics Letters B 452 1999 194–200200w x Ž .8 SLAC E140, S. Dasu et al., Phys. Rev. Lett. 61 1988 1061,and references within.w x Ž9 A. Bodek, S. Rock, U. Yang, 1996, UR-1355 Z. Phys. C to.be published .w x10 A.D. Martin, R.G. Roberts, W.J. Stirling, Phys. Lett. B 387Ž .1996 419.w x Ž .11 SLAC E140X, L.H. Tao et al., Z. Phys. C 70 1996 387.w x Ž .12 NMC, M. Arneodo et al., Nucl. Phys. B 483 1997 3.w x13 U.K. Yang et al., University of Rochester Prepring UR-1534,1998, Preprint archives hep-exr9806023. The data at theŽlowest x bin were excluded private communication, U.K..Yangw x Ž .14 CDHSW, P. Berge et al., Z. Phys. C 49 1991 187.w x Ž .15 NMC, P. Amaudruz et al., Phys. Lett. B 294 1992 120; M.Ž .Arneodo et al., Nucl. Phys. B 487 1997 3; Nucl. Phys. BŽ .481 1996 23.

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Measurements of R = σL/σT for 0.03 < x < 0.1 and Fit to World Data

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