Old Dominion University ODU Digital Commons

Physics Faculty Publications Physics

2015 Measurement of the EMC Effect in the Deuteron K. A. Griffioen

J. Arrington

M. E. Christy

R. Ent

N. Kalantarians

See next page for additional authors

Follow this and additional works at: https://digitalcommons.odu.edu/physics_fac_pubs Part of the Elementary Particles and Fields and String Theory Commons, and the Nuclear Commons

Repository Citation Griffioen, K. A.; Arrington, J.; Christy, M. E.; Ent, R.; Kalantarians, N.; Keppel, C. E.; and Kuhn, S E., "Measurement of the EMC Effect in the Deuteron" (2015). Physics Faculty Publications. 225. https://digitalcommons.odu.edu/physics_fac_pubs/225 Original Publication Citation Griffioen, K. A., Arrington, J., Christy, M. E., Ent, R., Kalantarians, N., Keppel, C. E., . . . Zhang, J. (2015). Measurement of the EMC effect in the deuteron. Physical Review C, 92(1), 015211. doi:10.1103/PhysRevC.92.015211

This Article is brought to you for free and open access by the Physics at ODU Digital Commons. It has been accepted for inclusion in Physics Faculty Publications by an authorized administrator of ODU Digital Commons. For more information, please contact [email protected]. Authors K. A. Griffioen, J. Arrington, M. E. Christy, R. Ent, N. Kalantarians, C. E. Keppel, and S E. Kuhn

This article is available at ODU Digital Commons: https://digitalcommons.odu.edu/physics_fac_pubs/225 PHYSICAL REVIEW C 92, 015211 (2015)

Measurement of the EMC effect in the deuteron

K. A. Griffioen,1 J. Arrington,2 M. E. Christy,3 R. Ent,4 N. Kalantarians,3 C. E. Keppel,4 S. E. Kuhn,5 W. Melnitchouk,4 G. Niculescu,6 I. Niculescu,6 S. Tkachenko,7 and J. Zhang7 1College of William and Mary, Williamsburg, Virginia 23187, USA 2Argonne National Laboratory, Argonne, Illinois 60439, USA 3Hampton University, Hampton, Virginia 23668, USA 4Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA 5Old Dominion University, Norfolk, Virginia 23529, USA 6James Madison University, Harrisonburg, Virginia 22807, USA 7University of Virginia, Charlottesville, Virginia 22901, USA (Received 3 June 2015; revised manuscript received 29 June 2015; published 21 July 2015)

Rd = F d / F n + F p F n/F d We determined the structure function ratio EMC 2 ( 2 2 ) from recently published 2 2 data taken by the BONuS experiment using CLAS at Jefferson Lab. This ratio deviates from unity, with a slope dRd /dx =− . ± . x W> . EMC 0 10 0 05 in the range of Bjorken from 0.35 to 0.7, for invariant mass 1 4 GeV and Q2 > 1 GeV2. The observed EMC effect for these kinematics is consistent with conventional nuclear physics models that include off-shell corrections, as well as with empirical analyses that find the EMC effect proportional to the probability of short-range nucleon-nucleon correlations.

DOI: 10.1103/PhysRevC.92.015211 PACS number(s): 21.45.Bc, 25.30.Fj, 24.85.+p, 13.60.Hb

I. INTRODUCTION proton), but the deuteron too may exhibit an EMC effect. Several data-driven, model-dependent attempts [7,13,26]have In the early 1980s the European Muon Collaboration d d n p been made to determine R = F /(F + F ), in which (EMC) discovered that deep-inelastic scattering from atomic EMC 2 2 2 F n(p) nuclei is not simply the incoherent sum of scattering from 2 is the free neutron (proton) structure function. However, the constituent nucleons [1]. Their data suggested that quarks the lack of knowledge about the free neutron’s structure has with longitudinal momentum fraction x in the range 0.35 to clouded these efforts. Theoretical estimates of the deuteron EMC ratio have also been made [27–39], often with the goal 0.7 were suppressed in bound nucleons, and their observations p of isolating F n/F . were quickly confirmed at SLAC [2,3]. The deep-inelastic 2 2 d A R F x A A clean measurement of EMC is greatly needed. The structure function 2 ( ) for a nucleus with nucleons was compared to the equivalent quantity F d (x) for the deuteron, deuteron is weakly bound (by 2.2 MeV), and the nucleons d 2 pn such that RA = (F A/A)/(F /2). At intermediate x, RA are governed only by the interaction. Therefore, a precise EMC 2 2 EMC Rd is less than unity, and this deviation grows with A.Overthe measurement of EMC can shed light on the cause of the following three decades, subsequent dedicated measurements EMC effect. Because the deuteron has a weak mean field / / [4–8] confirmed the EMC effect with ever-increasing precision (1 MeV nucleon binding versus 8 MeV nucleon for heavier for a wide range of nuclei. Drell-Yan data from Fermilab [9], nuclei), but a substantial contribution from high-momentum pn however, which were largely sensitive to sea quarks, showed no pairs, it is a good test case. modifications of the antiquark sea for 0.1 electron beams up to 5.26 GeV. BONuS was increase with A; however, the 9Be slope is anomalously large, x F n/F p designed to measure the high- structure function ratio 2 2 suggesting perhaps that the EMC effect is dependent on local F n using a model-independent extraction of 2 that relies on density and that 9Be might be acting like two tightly bound the spectator tagging technique. The experiment used a α particles and a neutron. A recent analysis [13] suggests 7-atm gaseous deuterium target surrounded by a radial time dRA /dx that EMC is proportional to the probability of finding projection chamber capable of detecting recoil protons in short-range correlations in nuclei [14–19]. Recent work on this the range 70–200 MeV/c [40]. By selecting backward-going subject [20–25] concludes that although binding and Fermi and low-momentum spectators, final-state pn interactions and motion effects contribute, some modification of the bound off-shell effects were minimized, respectively [42]. Detection nucleon’s structure appears to be required to explain the EMC of the spectator proton ensured that the electron scattered effect. Whether this is caused by the nuclear mean field, short- from the neutron. The initial-state kinematics of the neutron range correlations, or both is still open to debate. were then calculated from the spectator momentum. This EMC ratios are usually taken with respect to the deuteron, F n/F d technique enabled the extraction of 2 2 over a wide range which is the best proxy for an isoscalar nucleon (neutron plus of x for 4-momentum transfer squared Q2 between 0.7 and

0556-2813/2015/92(1)/015211(5) 015211-1 ©2015 American Physical Society K. A. GRIFFIOEN et al. PHYSICAL REVIEW C 92, 015211 (2015)

4.5 GeV2, which covers the resonance region and part of certainties. To explore the region x>0.45 we pushed our the deep-inelastic region. For the present analysis we have analysis into the resonance region (1.4 . Rd scattering region at the same x [47]. Therefore, we expect 1 4 GeV to determine EMC. The primary data from BONuS are the ratios F n/F d that an average over many different Q2 values washes out any 2 2 Rd x obtained from measuring tagged neutron event rates in CLAS resonance structure and that duality ensures EMC at fixed , and dividing them by the untagged deuteron rates recorded averaged over W, approaches the deep-inelastic limit. These simultaneously at the same kinematics [42]. Consequently, assumptions were tested and confirmed within statistical and detector acceptance and other systematic effects largely cancel, systematic uncertainties by looking for a Q2 dependence of F n Rd within each x bin and by considering variations in Rd and the accuracy of this ratio is far better than that of 2 alone. EMC EMC The overall normalization of the BONuS data, which takes among four kinematic cases: into account the spectator proton detection efficiency, was 2 p (1) W>1.4 GeV and Q2 > 1GeV , initially chosen [41]tomakeF n/F at x = 0.3 agree with the 2 2 (2) W>1.8 GeV and Q2 > 1GeV2, CTEQ–Jefferson Lab (CJ) [43] global fit for this point. There (3) W>2.0 GeV and Q2 > 1GeV2, and is a 3% normalization uncertainty associated with this choice. (4) W>2.0 GeV and Q2 > 2GeV2. For the final BONuS results [42], which include the resonance χ 2 F n/F d W region, the normalization minimized the of the full data The 2 2 data were sorted into 20-MeV-wide bins set with respect to the most recent update [44]oftheChristy and into logarithmic Q2 bins (13 per decade) with edges at and Bosted (CB) fits [45,46]. In this case, the convolution 0.92, 1.10, 1.31, 1.56, 1.87, 2.23, 2,66, 3.17, 3.79, 4.52, and model of Refs. [25,36] allowed for a self-consistent extraction 5.40 GeV2. F n F p F d of 2 from 2 and 2 and better control over the relative The analysis consisted of forming the quantity normalization of F n and F d . The new model produced no 2 2 F n F p change in the 5-GeV normalization, but a 10% increase in the r(W,Q2) = 2 + 2 , (1) F d F d magnitude of the 4-GeV data. 2 2 Figure 1 shows the BONuS F n/F d data set taken with a 2 2 in which the first term is the measured BONuS ratio and the 5.26-GeV beam. The red points correspond to values of the second term is the parametrization of world data [44–46]. All struck neutron’s invariant mass W above 1.4 GeV, whereas the data falling within one of the 20 x bins of width 0.05 were black points (W<1.4 GeV) are excluded from this analysis combined using to eliminate the  resonance.    With the new normalization, both the 5.26- and 4.22-GeV xi 1 x= , (2) data sets yield consistent results within the statistical un- σ 2 σ 2 i i i i   ri 1 r= , (3) σ 2 σ 2 10 2 2 i i i i Q =4.8 GeV    Q2=4.1 GeV2 1 r = 1 , (4) stat σ 2 8 Q2=3.4 GeV2 i i   Q2=2.9 GeV2 r ,i 1 r = sys , (5) sys σ 2 σ 2 2 2 i i d 6 Q =2.4 GeV i i 2

/F 2 2 σ r n Q =2.0 GeV in which i are the statistical uncertainties and sys,i are 2 n d F the corresponding systematic uncertainties for the ith F /F 4 2 2 2 2 Q =1.7 GeV datum. d 2 2 R Q =1.4 GeV The final values for EMC were then calculated as

2 2 d 2 Q =1.2 GeV R = /r, EMC 1 (6) Q2=1.0 GeV2 Rstat = r /r2, shift: +1.0 EMC stat (7) 0 Rsys = r /r2. EMC sys (8) 0.2 0.4 0.6 0.8 1 x III. UNCERTAINTIES

FIG. 1. (Color online) BONuS data for F n/F d vs Bjorken x Several checks on our results were made. First, the analysis 2 2 d 2 2 R = /r taken with a 5.26-GeV beam. Only data for Q  1 GeV are shown. was performed by directly calculating EMC 1 using The red points (W>1.4 GeV) are used in this analysis. Error bars thesame20x bins. The final answers were nearly identical are statistical only. Each spectrum is shifted upward by 1.0 from the to those in which inversion was the last step. The statistical set below it. spread in the ratio r in each x bin was used to calculate a

015211-2 MEASUREMENT OF THE EMC EFFECT IN THE DEUTERON PHYSICAL REVIEW C 92, 015211 (2015) standard error. This error agreed very well with rstat, which CJ12 supports the hypothesis that variations in r within a bin are 1.06 systematic errors Kulagin and Petti purely statistical. Systematic bias was also studied using a cut W>1.4 GeV; 4 GeV data 1.04 2 2 Q2 > 2 4+5 GeV; W>1.4 GeV; Q >1 GeV for 2GeV , which in the region of comparison showed -0.10(5)x+1.03(2) Q2 1.02 no significant deviation from the data that include lower ) n 2 values. 1 +F p

Overall systematic uncertainties were estimated by varying 2 p d 0.98 the models for F /F and the kinematic cuts. The model /(F

2 2 d 2 dependence was explored using the published CB fits and F 0.96 two later improvements applied to kinematic case 1 using the 5-GeV data. The kinematic dependence was explored using 0.94 kinematic cases 1–4 for the 5-GeV data and case 1 for the 0.92 4-GeV data. In order to separate the overall normalization 0.9 uncertainty from other systematic uncertainties, we fit the 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 . . Rd uncertainty. For case 2 with 0 4, EMC tends to be higher we looked at the contents of each x bin separately. Figure 1 than for case 1. This arises in a region of significantly lower shows that each x bin covers a wide enough Q2 range to study statistics on account of the higher-W cut and fewer kinematic Q2 variations within that bin. For this study each data point points available for resonance averaging. Although the slope Rd d was converted into EMC as described above, and instead of dR /dx 2 EMC in this case is consistent with zero, we find this averaging, all values were fit to a straight line versus Q . result unstable to small changes in kinematics. Case 2 at high dRd /dQ2 = . d Fitting to a constant slope yields EMC 0 0037(45), x R 2 figures into the systematic errors on our quoted EMC values, which is consistent with no observable Q variation. however. Although the BONuS F2 data were extracted assuming that 2 Since the data span a large and relatively low Q range the longitudinal-to-transverse cross section ratio R cancels in 2 Rd starting at 1 GeV , one needs to worry about whether EMC is the neutron-to-deuteron ratios, the associated uncertainty is included in the published results. Some nuclear dependence to R could, however, slightly modify our EMC results [48]. TABLE I. EMC results for the deuteron. The columns correspond to the number of kinematic points, average x and Q2, the EMC ratio, IV. RESULTS the statistical and systematic errors from the BONuS data, and the p total systematic error including modeling of F /F d . Our final result uses the new self-consistent convolution 2 2 F p/F d model [44]for 2 2 , which was used to determine the F n/F d Q2 absolute normalization of the final published BONuS 2 2 N x 2 Rd Rstat Rsys Rsys data [42]. It provides an excellent representation of F for our (GeV ) EMC EMC EMC tot 2 kinematics. Our result uses the combined 5.26- and 4.22-GeV 28 0.177 1.09 0.995 0.003 0.002 0.015 data with cuts Q2 > 1GeV2 and W>1.4 GeV. A linear fit for 55 0.224 1.24 0.991 0.003 0.003 0.010 . 0.5 71 0.472 1.85 0.983 0.004 0.009 0.009 continues the trend of the lower-x data, with a hint of the 56 0.523 2.01 0.967 0.004 0.011 0.012 x = . RA expected rise above 0 7 as seen in EMC for heavier nuclei, 47 0.572 2.30 0.994 0.006 0.013 0.014 x 41 0.619 2.54 0.974 0.007 0.017 0.017 but these high- values are more uncertain because there are 26 0.670 2.97 0.984 0.011 0.020 0.021 fewer data points for resonance averaging. The black circles 21 0.719 3.39 1.019 0.019 0.023 0.025 are the combined results for 4 and 5 GeV, which are clearly 11 0.767 4.03 1.075 0.041 0.024 0.029 dominated by the 5-GeV data. The 4-GeV data by themselves (red triangles) are consistent with the combined data set. The

015211-3 K. A. GRIFFIOEN et al. PHYSICAL REVIEW C 92, 015211 (2015) two points between x = 0.5 and 0.6 seem to be off the trend, 0.7 one being high and the other low. Because this is consistent χ2 0.6 0.105(4)R2N, /dof=1.22 197 for the two beam energies, we suspect that there is a slight 0.094(3)R , χ2/dof=1.15 Au mismatch between the model form factors and the data in this 2N 56 0.5 Fe region. 12

/dx C Table I gives our numerical results, in which N is the 0.4 9 n d Be number of F /F points contributing to a bin with average IMC 4

2 2 A x Q2 Rstat Rsys 0.3 He kinematic values and .Here EMC and EMC are the statistical and systematic uncertainties that come -dR 3He Rsys 0.2 from the BONuS data themselves, and tot is the total d Rsys systematic uncertainty that includes EMC plus the modeling 0.1 F p/F d and normalization uncertainties in 2 2 . The current results can be compared to the SLAC model- 0 Rd 0 1 2 3 4 5 dependent extraction from Ref. [7]. Here EMC was esti- R2N(A/d) mated assuming the hypothesis of Ref. [50] that 1 + REMC is proportional to the nucleon density. The SLAC slope dRd /dx =− . ± . FIG. 3. (Color online) EMC slopes per isoscalar nucleon, EMC 0 098 0 005 is similar to our own, but its −dRA /dx, vs the relative probability with respect to the quoted uncertainty takes no account of the model dependence. IMC deuteron of short-range correlations, R2N (A/d). Fits assume that The assumption of density dependence gives consistent results dRA /dx / R A/d ( IMC ) ( 2N ( )) is constant. The red points are from with our measurements for the deuteron. Semi-empirical Ref. [13]. The blue points are from Ref. [20] and are corrected models like that of Ref. [36] (blue dashed curve in Fig. 2), for isospin and for x normalized to a maximum of x = A.Their which include Fermi motion, binding, and off-shell effects, uncertainties are the same as for the red points. Rd are able to describe the shape of EMC quite well. Our data are also consistent with the CJ12 [49] band in yellow. We have explored whether the Nachtmann variable RA in Ref. [13]. The nuclear EMC ratio EMC can be multiplied ξ = 2x/(1 + 1 + 4M2x2/Q2) (with M the nucleon mass) by the deuteron EMC ratio Rd to obtain RA . Hence, to x Rd A EMC A IMC d would be better suited than to represent EMC, since our data good approximation, dR /dx = dR /dx + dR /dx. 2 IMC EMC EMC are at relatively low Q . The authors of Refs. [8,47] too have Figure 3 shows the results. The data are consistent with the addressed this question. They and we prefer x, which has been dRA /dx R A/d ansatz that IMC is directly proportional to 2N ( ), the common variable of discourse and calculation. Our EMC the short-range correlation probability, with a proportionality ratios are determined using data and model at precisely the constant 0.105 ± 0.004 (χ 2/DOF = 1.22). This effect persists 2 same values of W and Q . Therefore, plotting versus ξ merely for the isospin and nuclear-x-corrected data from Ref. [20] redistributes the EMC points along the x axis. Generally, ξ is (blue points), which have the same uncertainties as the red smaller than x. Consequently, more of the high-x resonances points. The linear relationship between short-range correla- in the data set now contribute to the EMC slope. Thus, using tions and EMC slopes, with the shift for the deuteron EMC ξ to reduce the effect of resonances actually increases their effect, is now consistent with an intercept of zero, and the influence. A fit over the rescaled interval [0.35,0.65] yields relationship becomes a straight proportion described by a dRd /dξ =− . ± . EMC 0 08 0 06. The slope is slightly smaller and single free parameter. the uncertainty slightly larger than when we plot versus x. Resonance states above x = 0.7 drive the slope to slightly smaller values than the fit versus x. VI. SYNOPSIS The analysis of Ref. [13] finds a linear relationship In summary, we find an EMC-like slope in the ratio of of the EMC slopes dRA /dx versus the relative short- EMC deuteron to free nucleon structure functions, using the BONuS range correlation probability R N (A/d) in a nucleus A with 2 data (which are partially in the nucleon resonance region above respect to the deuteron. From that analysis the authors the  resonance). This slope is consistent with conventional conclude that the deuteron EMC slope should be dRd /dx = EMC nuclear physics models that include off-shell corrections, −0.079 ± 0.006. This value is somewhat smaller than our as well as with short-range-correlation models of the EMC result of −0.10 ± 0.05 but is consistent within 1σ.Amore effect. This first, direct measurement of the magnitude of the recent analysis along these same lines brackets the slope EMC effect in deuterium demonstrates that the new BONuS between −0.079 and −0.106 [19], and suggests that the experiment at 11 GeV using CLAS12, with its better precision, uncertainties of Ref. [13] are underestimated. larger average Q2, and deep-inelastic kinematics, will be able to determine Rd with good accuracy. d EMC V. REMC AND SHORT-RANGE CORRELATIONS We are able to use our results to estimate the in-medium RA = F A/A F n + F p dRA /dx ACKNOWLEDGMENTS correction IMC 2 2 ( 2 2 ) with slope IMC , for which the normalizing factor is the isoscalar free nucleon. We thank the staff of the Jefferson Lab accelerator and RA = + dRA /dx x − x We write EMC 1 ( EMC )( 0 ) assuming that all Hall B for their support on the BONuS experiment. This nuclei have ratios of unity at x0 = 0.31 ± 0.04, as found work was supported by the United States Department of

015211-4 MEASUREMENT OF THE EMC EFFECT IN THE DEUTERON PHYSICAL REVIEW C 92, 015211 (2015)

Energy (DOE) Contract No. DE-AC05-06OR23177, under 06CH11357, No. DE-FG02-97ER41025, and No. DE-FG02- which Jefferson Science Associates, LLC operates Jefferson 96ER41003, respectively. I.N. and G.N. acknowledge support Lab. S.K., J.A., S.T., and K.G. acknowledge support from from the National Science Foundation (NSF) under Grant the DOE, Office of Science, Office of Nuclear Physics, No. PHY-1307196. M.E.C. acknowledges support from NSF under Grants No. DE-FG02-96ER40960, No. DE-AC02- Grants No. PHY-1002644 and No. PHY-1307415.

[1] J. Aubert et al. (European Muon Collaboration), Phys. Lett. B [24] S. A. Kulagin and R. Petti, Nucl. Phys. Proc. Suppl. 159, 180 123, 275 (1983). (2006). [2] A. Bodek, N. Giokaris, W. Atwood, D. Coward, D. Dubin, M. [25] Y. Kahn, W. Melnitchouk, and S. A. Kulagin, Phys. Rev. C 79, Breidenbach, J. E. Elias, J. I. Friedman, H. W. Kendall, J. S. 035205 (2009). Poucher, and E. M. Riordan, Phys. Rev. Lett. 51, 534 (1983). [26] R. Lednicky, D. Peshekhonov, and G. Smirnov, Sov. J. Nucl. [3] A. Bodek, N. Giokaris, W. Atwood, D. Coward, D. Sherden, D. Phys. 52, 552 (1990). Dubin, J. E. Elias, J. I. Friedman, H. W. Kendall, J. S. Poucher, [27] G. West, Phys. Lett. B 37, 509 (1971). andE.M.Riordan,Phys.Rev.Lett.50, 1431 (1983). [28] W. Atwood and G. B. West, Phys. Rev. D 7, 773 (1973). [4] S. Dasu et al., Phys. Rev. Lett. 60, 2591 (1988). [29] L. Frankfurt and M. Strikman, Phys. Lett. B 76, 333 (1978). [5] J. Ashman et al. (European Muon Collaboration), Phys. Lett. B [30] D. Kusno and M. J. Moravcsik, Nucl. Phys. B 184, 283 202, 603 (1988). (1981). [6] P. Amaudruz et al. (New Muon Collaboration), Z. Phys. C 51, [31] L. Kaptar and A. Y. Umnikov, Phys. Lett. B 259, 155 (1991). 387 (1991). [32] K. Nakano and S. Wong, Nucl. Phys. A 530, 555 (1991). [7] J. Gomez, R. Arnold, P. E. Bosted, C. Chang, A. Katramatou, [33] W. Melnitchouk, A. W. Schreiber, and A. W. Thomas, G. G. Petratos, A. A. Rahbar, S. E. Rock, A. F. Sill, Z. M. Phys. Lett. B 335, 11 (1994). Szalata, A. Bodek, N. Giokaris, D. J. Sherden, B. A. Mecking, [34] M. Braun and M. Tokarev, Phys. Lett. B 320, 381 (1994). and R. M. Lombard-Nelsen, Phys.Rev.D49, 4348 (1994). [35] V. Burov and A. Molochkov, Nucl. Phys. A 637, 31 (1998). [8] J. Seely et al., Phys. Rev. Lett. 103, 202301 (2009). [36] S. A. Kulagin and R. Petti, Nucl. Phys. A 765, 126 (2006). [9] D. Alde et al., Phys.Rev.Lett.64, 2479 (1990). [37] J. Arrington, J. G. Rubin, and W. Melnitchouk, Phys. Rev. Lett. [10] M. Arneodo, Phys. Rep. 240, 301 (1994). 108, 252001 (2012). [11] D. F. Geesaman, K. Saito, and A. W. Thomas, Ann. Rev. Nucl. [38] J. Arrington, F. Coester, R. Holt, and T.-S. Lee, J. Phys. G 36, Part. Sci. 45, 337 (1995). 025005 (2009). [12] P. Norton, Rep. Prog. Phys. 66, 1253 (2003). [39] W. Melnitchouk and A. W. Thomas, Phys. Lett. B 377, 11 [13] L. B. Weinstein, E. Piasetzky, D. W. Higinbotham, J. Gomez, (1996). O. Hen, and R. Shneor, Phys. Rev. Lett. 106, 052301 (2011). [40] H. C. Fenker et al., Nucl. Instrum. Meth. A 592, 273 (2008). [14] L. L. Frankfurt, M. I. Strikman, D. B. Day, and M. Sargsyan, [41] N. Baillie et al. (CLAS Collaboration), Phys. Rev. Lett. 108, Phys. Rev. C 48, 2451 (1993). 199902 (2012). [15] K. Egiyan et al. (CLAS Collaboration), Phys. Rev. C 68, 014313 [42] S. Tkachenko et al. (CLAS Collaboration), Phys. Rev. C 89, (2003). 045206 (2014). [16] N. Fomin et al., Phys.Rev.Lett.108, 092502 (2012). [43] A. Accardi, W. Melnitchouk, J. F. Owens, M. E. Christy, [17] J. Arrington, D. Higinbotham, G. Rosner, and M. Sargsian, C. E. Keppel, L. Zhu, and J. G. Morfin, Phys.Rev.D84, 014008 Prog. Part. Nucl. Phys. 67, 898 (2012). (2011). [18] O. Hen et al., Science 346, 614 (2014). [44] N. Kalantarians, M. E. Christy, J. Ethier, and W. Melnitchouk [19] O. Hen, E. Piasetzky, and L. B. Weinstein, Phys.Rev.C85, (unpublished). 047301 (2012). [45] M. E. Christy and P. E. Bosted, Phys. Rev. C 81, 055213 (2010). [20] O. Hen, D. W. Higinbotham, G. A. Miller, E. Piasetzky, and [46] P. E. Bosted and M. E. Christy, Phys. Rev. C 77, 065206 (2008). L. B. Weinstein, Int. J. Mod. Phys. E 22, 1330017 (2013). [47] J. Arrington, R. Ent, C. E. Keppel, J. Mammei, and I. Niculescu, [21] C. Ciofi degli Atti, L. L. Frankfurt, L. P. Kaptari, and M. I. Phys.Rev.C73, 035205 (2006). Strikman, Phys.Rev.C76, 055206 (2007). [48] V. Guzey, L. Zhu, C. E. Keppel, M. E. Christy, D. Gaskell, P. [22] W. Melnitchouk, M. Sargsian, and M. Strikman, Z. Phys. A 359, Solvignon, and A. Accardi, Phys.Rev.C86, 045201 (2012). 99 (1997). [49] J. F. Owens, A. Accardi, and W. Melnitchouk, Phys. Rev. D 87, [23] J. Arrington, A. Daniel, D. B. Day, N. Fomin, D. Gaskell, and 094012 (2013). P. Solvignon, Phys. Rev. C 86, 065204 (2012). [50] L. Frankfurt and M. Strikman, Phys. Rep. 160, 235 (1988).

015211-5