aa r X i v : . [ nu c l - e x ] A p r Unpolarized Structure Functions at Jefferson Lab
M. E. Christy and W. Melnitchouk Hampton University, Hampton, Virginia 23668, USA Jefferson Lab, Newport News, Virginia 23606, USA
Abstract.
Over the past decade measurements of unpolarized structure functions withunprecedented precision have significantly advanced our knowledge of nucleon structure. Thesehave for the first time allowed quantitative tests of the phenomenon of quark-hadron duality,and provided a deeper understanding of the transition from hadron to quark degrees offreedom in inclusive scattering. Dedicated Rosenbluth-separation experiments have yieldedhigh-precision transverse and longitudinal structure functions in regions previously unexplored,and new techniques have enabled the first glimpses of the structure of the free neutron, withoutcontamination from nuclear effects.
1. Introduction
Throughout the modern history of nuclear and particle physics, measurements of structurefunctions in high-energy lepton-nucleon scattering have played a pivotal role. The demonstrationof structure function scaling in early deep-inelastic scattering (DIS) experiments at SLAC inthe late 1960’s [1] established the reality of quarks as elementary constituents of protons andneutrons — a feat recognized by the award of the 1990 Nobel Prize in Physics to Friedman,Kendall and Taylor. This paved the way to the development of quantum chromodynamics(QCD) as the theory of strong nuclear interactions, and its subsequent confirmation severalyears later through the discovery of logarithmic scaling violations in structure functions [2].The interpretation of structure functions in terms of quark and gluon (or parton) momentumdistributions resulted in the emergence of a remarkably simple and intuitive picture of thenucleon [3], allowing a vast amount of scattering data to be described in terms of a few universalfunctions — the parton distribution functions (PDFs). At leading order (LO) in α s , the F structure function of the proton, for example, could be simply represented as a charge squared-weighted sum of PDFs, F = X q e q x ( q + ¯ q ) = 49 x ( u + ¯ u ) + 19 x ( d + ¯ d ) + 19 x ( s + ¯ s ) + · · · , (1)where q and ¯ q are the quark and antiquark momentum distribution functions, usually expressedas functions of the momentum fraction x of the nucleon carried by the parton, at a scale givenby the momentum transfer squared Q .Over the ensuing decades concerted experimental DIS programs at SLAC, CERN, DESYand Fermilab have provided a detailed mapping of the PDFs over a large range of kinematics,with Q and x spanning several orders of magnitude. To manage the ever increasing numberof data sets, from not only inclusive DIS but also other high energy processes such as Drell-Yan, W -boson and jet production in hadronic collisions at Fermilab, sophisticated global fittingfforts were developed [4, 5, 6, 7] that now include perturbative corrections calculated to next-to-leading order (or higher) in the strong coupling constant α s . With the increasing energiesavailable at facilities such as the DESY ep collider HERA (and in future the Large HadronCollider at CERN), PDF studies turned their attention primarily to exploring the region of verysmall x (down to x ∼ − ), where the structure of the nucleon is dominated by its sea quarkand gluon distributions. However, while opening the door to exploration of phenomena suchas saturation and Q evolution in new kinematic regimes, one can argue whether DIS at low x measures the intrinsic structure of the nucleon or the hadronic structure of the virtual photon, γ ∗ . Because the virtual photon in the DIS process can fluctuate into q ¯ q pairs whose coherencelength λ ∼ /M x becomes large at small x , DIS at x < ∼ . γ ∗ N interactionrather than the structure of the nucleon or the γ ∗ separately. At high x , in contrast, the virtualphoton is point-like and unambiguously probes the structure of the nucleon [8].Moreover, despite the impressive achievements over the past 4 decades, there are stillsome regions of kinematics where our knowledge of structure functions and PDFs remainsunacceptably poor, with little progress made since the 1970’s. A striking example is the regionof large x ( x > ∼ . Q are either nonexistent or have large uncertainties. With theavailability of continuous, high luminosity electron beams at the CEBAF accelerator, the firstdecade of experiments at Jefferson Lab has seen a wealth of high-quality data on unpolarizedstructure functions of the nucleon, penetrating into the relatively unexplored large- x domainand the transition region between resonances and scaling.The new data in the resonance region confirmed in spectacular fashion the phenomenonof quark-hadron duality in the proton F structure function, and revealed intriguing detailsabout the workings of duality in a number of other observables. The impact of this has beena re-evaluation of the applicability of perturbative QCD to structure functions at low Q , andhas allowed a much larger body of data to be used in global PDF analyses [9]. Jefferson Labhas also set a new standard in the determination of Rosenbluth-separated longitudinal andtransverse structure functions, which eliminates the need for model-dependent assumptions thathave plagued previous extractions of structure functions from cross section data.On the theoretical front, the region of large x and low Q brings to the fore a number of issueswhich complicate structure function analysis, such as 1 /Q suppressed target mass and highertwist corrections, and nuclear corrections when scattering from nuclear targets. Controlling thesecorrections requires more sophisticated theoretical tools to be developed, and has motivatedtheoretical studies, many of which are still ongoing. It has also paved the way towards the12 GeV experimental program, in which structure functions will be measured to very high x inthe DIS region, addressing some long-standing questions about the behavior of PDFs as x → F p structure functions and their moments are reviewed in Sec. 3,together with their role in the verification of quark-hadron duality. Data on the deuteron F d structure function are presented in Sec. 4, and the extraction from these of the neutron F n structure function F n is discussed in Sec. 5. Section 6 reviews new measurements ofthe longitudinal structure function F L , while Sec. 7 surveys results from semi-inclusive pionproduction. Finally, in Sec. 8 we describe the impact that the Jefferson Lab data have hadon our understanding of nucleon structure in a global context, and briefly outline prospects forfuture measurements in the 12 GeV era. . Formalism Because of the small value of the electromagnetic fine structure constant, α = e / π , theinclusive scattering of an electron from a nucleon, e ( k ) + N ( p ) → e ′ ( k ′ ) + X , can usually beapproximated by the exchange of a single virtual photon, γ ∗ ( q ), where q = k ′ − k . In termsof the laboratory frame incident electron energy E , the scattered electron energy E ′ , and thescattering angle θ , the photon virtuality is given by − q ≡ Q = 4 EE ′ sin θ/
2, where theelectron mass has been neglected. The invariant mass squared of the final hadronic state X is W = ( p + q ) = M + 2 M ν − Q = M + Q (1 − x ) /x , where M is the nucleon mass, ν = E − E ′ is the energy transfer, and x = Q / M ν is the Bjorken scaling variable.In the one photon exchange approximation the spin-averaged cross section for inclusiveelectron-nucleon scattering in the laboratory frame can be written as d σd Ω dE ′ = α Q E ′ E L µν W µν , (2)where the leptonic tensor L µν = 2 (cid:16) k µ k ′ ν + k ′ µ k ν − g µν k · k ′ (cid:17) , and using constraints from Lorentz,gauge and parity invariance the hadronic tensor W µν can in general be written as M W µν = (cid:18) − g µν + q µ q ν q (cid:19) F ( x, Q ) + (cid:18) p µ − p · qq q µ (cid:19) (cid:18) p ν − p · qq q ν (cid:19) F ( x, Q ) p · q . (3)The structure functions F and F are generally functions of two variables, but becomeindependent of the scale Q in the Bjorken limit, in which both Q and ν → ∞ with x fixed.At finite values of Q a modified scaling variable is more appropriate [10, 11], ξ = 2 x ρ , with ρ = | q | ν = q Q /ν , (4)which tends to x in the Bjorken limit.In terms of cross sections for absorbing helicity ± σ T and σ L , the cross section can be written as d σd Ω dE ′ = Γ (cid:16) σ T ( x, Q ) + ǫ σ L ( x, Q ) (cid:17) , (5)where Γ = ( α/ π Q )( E ′ /E ) K/ (1 − ǫ ) is the flux of transverse virtual photons, with the factor K = ν (1 − x ) in the Hand convention [12], and ǫ = " ν Q ! tan θ − (6)is the relative flux of longitudinal virtual photons. Equating Eqs. (2) and (5), the structurefunctions can be written in terms of the photoabsorption cross sections as F ( x, Q ) = K π α M σ T ( x, Q ) , (7) F ( x, Q ) = K π α ν (1 + ν /Q ) h σ T ( x, Q ) + σ L ( x, Q ) i , (8)which reveals that F is related only to the transverse virtual photon coupling, while F isa combination of both transverse and longitudinal couplings. One can also define a purelylongitudinal structure function F L , F L = ρ F − xF = 2 xF R , (9)here R = σ L /σ T is the ratio of longitudinal to transverse cross sections.The separation of the unpolarized structure functions into longitudinal and transverse partsfrom cross section measurements can be accomplished via the Rosenbluth, or longitudinal-transverse (LT), separation technique [13], by making measurements at two or more values of ǫ for fixed x and Q . Fitting the reduced cross section σ/ Γ linearly in ǫ yields σ T (and therefore F ) as the intercept, while the ratio R is obtained from the slope. Note that F can only beextracted from cross sections either by measuring at ǫ = 1 or by performing LT separations. Attypical Jefferson Lab kinematics the contribution of F L to F can be significant.The above discussion assumed the dominance of the one-photon exchange amplitude indescribing the neutron current electron scattering cross section. In principle there are additionalcontributions arising from the exchange of a Z boson, and in particular the interferencebetween γ ∗ and Z exchange. The interference is in fact very relevant for parity-violatingelectron scattering, discussed elsewhere in this volume in connection with extractions of strangeelectromagnetic form factors from parity-violating asymmetries. The theoretical basis for describing the Q dependence of structure functions in QCD is Wilson’soperator product expansion (OPE) [14]. The quantities most directly amenable to a QCDanalysis are the moments of structure functions, the n -th moments of which are defined as M ( n )1 ( Q ) = Z dx x n − F ( x, Q ) , M ( n )2 ,L ( Q ) = Z dx x n − F ,L ( x, Q ) . (10)As will become relevant in the discussion of duality in Sec. 3 below, at large Q ≫ Λ the moments can be expanded in powers of 1 /Q , with the coefficients in the expansion givenby matrix elements of local operators corresponding to a certain twist , τ , defined as the massdimension minus the spin, n , of the operator. For the n -th moment of F , for instance, one hasthe expansion M ( n )2 ( Q ) = ∞ X τ =2 , ... A ( n ) τ ( α s ( Q )) Q τ − , n = 2 , , . . . (11)where A ( n ) τ are the matrix elements with twist ≤ τ . As the argument suggests, the Q dependenceof the matrix elements can be calculated perturbatively, with A ( n ) τ expressed as a power seriesin α s ( Q ). For twist two, the coefficients A ( n )2 are given in terms of matrix elements of spin- n operators, A ( n )2 p µ · · · p µ n + · · · = h p | ¯ ψγ { µ iD µ · · · iD µ n } ψ | p i , where ψ is the quark field, D µ isthe covariant derivative, and the braces {· · ·} denote symmetrization of indices and subtractionof traces.The leading-twist terms correspond to diagrams such as in Fig. 1 (a), in which the virtualphoton scatters incoherently from a single parton. The higher-twist terms in Eq. (11) areproportional to higher powers of 1 /Q whose coefficients are matrix elements of local operatorsinvolving multi-quark or quark-gluon fields, such as those depicted in Fig. 1 (b) and (c). Thehigher twists therefore parametrize long-distance multi-parton correlations, which can provideclues to the dynamics of quark confinement.The additional terms (referred to as the “trace terms”) in the twist-two matrix elementsinvolve structures such as p g µ i µ j and are thus suppressed by powers of p /Q ∼ Q /ν . Whilenegligible in the Bjorken limit, at finite Q these give rise to the so-called target mass corrections (TMCs), and are important in the analysis of Jefferson Lab data at large values of x . Becausetheir origin is in the same twist-two operators that give rise to structure function scaling, TMCs a) (b) (c) Figure 1. (a)
Leading-twist (“handbag”) contribution to the structure function, (b) higher-twist (“cat’s ears”) four-quark contributions, (c) higher-twist quark-gluon interactions.are formally twist-two effects and are kinematical in origin. Inverting the expressions for the fullmoments including the trace terms, the resulting target mass corrected F structure function inthe OPE is given by [15, 16] F TMC2 ( x, Q ) = x ξ ρ F (0)2 ( ξ, Q ) + 6 M x Q ρ Z ξ du M xQ ρ ( u − ξ ) ! F (0)2 ( u, Q ) u , (12)where F (0)2 is the structure function in the M /Q → F and F L structure functions [15, 16]. One should note, however, that the OPE result forTMCs to structure functions is not unique; in the collinear factorization approach, for example,in which parton distributions are formulated a priori in momentum space, different expressionsfor TMCs arise [17]. While both formalisms give the same results in the Bjorken limit, thedifferences between these at finite Q can be seen as representing an inherent prescriptiondependence and systematic uncertainty in the analysis of structure functions at low Q .
3. Proton F structure function Measurements of the proton F p structure function have been taken at Jefferson Lab over arange of kinematics, from Q as low as 0.1 GeV and below (to study the transition to thephotoproduction point, Q = 0) and up to Q = 8 GeV (to study the large- x behaviorand quark-hadron duality). At the larger Q values the high luminosity provided by theCEBAF accelerator has allowed significant improvement in the statistical precision of high- x measurements over all previous experiments. In addition, with the HMS spectrometer inHall C well understood, LT separated cross sections have been measured with better than 1.6%systematic point-to-point uncertainties and typically less than 1.8% normalization uncertainties.Precision F p spectra extracted from cross sections measured in Hall C [18, 19, 20] are shownin Fig. 2 (left) as a function of x for several Q values ( Q = 0 . , . , ), togetherwith previous SLAC [21] and NMC [22] data at lower x . The data have been bin-centered tothe common Q values shown for all measurements within the range of 20% of the central value,utilizing a fit [23] to the DIS data and a global fit [24] to Jefferson Lab resonance region data.In addition to the Hall C measurements, there now also exists a large body of F p data fromHall B covering a significant range of kinematics, which is afforded by the large acceptance ofthe CLAS spectrometer. An example of the F p spectrum extracted from CLAS is shown inFig. 2 (right) at Q = 0 .
775 GeV . In Table 1 we present a complete list of all unpolarizedinclusive and semi-inclusive measurements on the proton and deuteron performed at JeffersonLab through 2010, including their current status. The proton F p data in Fig. 2 illustrate the intriguing phenomenon of quark-hadron duality,which relates structure functions in the nucleon resonance and DIS regions. First observed by x F (x) Figure 2. ( Left ) Proton F p structure function data from Hall C [18, 19, 20], SLAC [21],and NMC [22] at Q = 0 . , . , , compared with a fit [24] to the transverse andlongitudinal resonance cross sections from photoproduction to Q = 9 GeV (solid), and a globalfit [23] to DIS data (dashed). ( Right ) Proton F p from CLAS in Hall B at Q = 0 .
775 GeV (stars) [25], compared to earlier Hall C data (open circles) [26].Bloom and Gilman [37] in the early inclusive SLAC data (hence also referred to as “Bloom-Gilman duality”), the structure functions in the resonance region are found on average to equalthe structure functions measured in the “scaling” region at higher W . The resonance dataoscillate around the scaling curve and slide along it with increasing Q , as seen in Fig. 2 (left).The early F p data from SLAC were extracted from cross sections assuming a fixed valuefor R (= 0.18), and with a scaling curve parametrizing the limited data available in the early1970’s [38]. Since the original measurements, the F p structure function has become one ofthe best studied quantities in lepton scattering, with data from laboratories around the worldcontributing to a global data base spanning over five orders of magnitude in both x and Q . Withthe advent of the Jefferson Lab data, precise F p measurements now also exist in the resonanceregion up to Q ≈ , allowing many new aspects of duality to be quantified for the firsttime [39].While the early duality studies considered only the F structure function [37], Jefferson Labexperiments have in addition revealed the presence of duality in other observables. For example,Fig. 3 shows new LT-separated data from Jefferson Lab experiment E94-110 for the protontransverse ( F p ) and longitudinal ( F pL ) structure functions in the nucleon resonance region [18].LT-separated data from SLAC, predominantly in the DIS region, are also shown for comparison[42]. Where they refer to the same kinematic values, the Jefferson Lab and SLAC data arein excellent agreement, providing confidence in the achievement of the demanding precisionrequired of this type of experiment. In all cases, the resonance and DIS data merge smoothlywith one another in both x and Q .The availability of leading twist PDF-based global fits [4, 5, 6, 7, 9] allows comparison ofthe resonance region data with leading twist structure functions at the same x and Q . Theresonance data on the F and F L structure functions are also found to oscillate around theperturbative QCD (pQCD) curves, down to Q as low as 0.7 GeV . Because most of thedata lie at large values of x and small Q , it is vital for tests of duality to account for theeffects of kinematical target mass corrections [15], which give large contributions as x → able 1. Listing of Jefferson Lab unpolarized inclusive and semi-inclusive electron-nucleonscattering experiments.Experiment Hall Target Observable Reference StatusE94-110 C p R in resonance region [18, 27, 28, 29] data taken in 1999,analysis completedE99-118 C p, d nuclear dependence of [30] data taken in 2000, R at low Q analysis completedCLAS B p, d inclusive cross sections [25, 31] e1/e2 run periodsE00-002 C p, d F at low Q [20] data taken in 2003,analysis completed,pub. in progressE00-108 C p, d semi-inclusive π ± [32, 33] data taken in 2003,electroproduction analysis completedE00-116 C p, d inclusive resonance [19] data taken in 2003,region cross sections analysis completedat intermediate Q E02-109 C d R in resonance region [34] data taken in 2005,analysis in progressE03-012 B d ( n ) neutron F n via [35] data taken in 2005,(BoNuS) spectator tagging analysis completed,pub. in progressE06-009 C d R in resonance region [36] data taken in 2007,& beyond: extension of analysis in progressE02-109 to Q = 4 GeV This is clear from Fig. 3, where the data are compared with leading twist structure functionscomputed from PDFs to next-to-next-to-leading order (NNLO) accuracy from Alekhin [40] andMRST [41, 43]. The latter are shown with (solid) and without (dotted) target mass corrections,and clearly demonstrate the importance of subleading 1 /Q effects at large x . In particular,TMCs give additional strength at large x observed in the data, which would be significantlyunderestimated by the leading twist functions without TMCs.The phenomenological results raise the question of how can a scaling structure functionbe built up entirely from resonances, each of whose contribution falls rapidly with Q [44]? Anumber of studies using various models have demonstrated how sums over resonances can indeedyield a Q independent function (see Ref. [39] for a review). The key observation is that while D S F Q = 0.7 GeV Q = 1.5 GeV F Q = 2.5 GeV Q = 3.5 GeV X D S F Q = 0.7 GeV Q = 1.5 GeV F L Q = 2.5 GeV Q = 3.5 GeV X Figure 3.
Purely transverse (left) and longitudinal (right) proton structure functions 2 xF and F L in the resonance region [18] (triangles), compared with earlier data from SLAC (squares).The curves are leading twist structure functions computed at NNLO from Alekhin (dashed)[40] and MRST [41] with (solid) and without (dotted) target mass corrections. The prominentresonance regions (∆, S , F ) are indicated by the arrows along the abscissa.the contribution from each individual resonance diminishes with Q , with increasing energynew states become accessible whose contributions compensate in such a way as to maintainan approximately constant strength overall. At a more microscopic level, the critical aspectof realizing the suppression of the higher twists is that at least one complete set of evenand odd parity resonances must be summed over for duality to hold [45]. For an explicitdemonstration of how this cancellation takes place in the SU(6) quark model and its extensions,see Refs. [45, 46, 47]. The degree to which quark-hadron duality holds can be more precisely quantified by computingintegrals of the structure functions over x in the resonance region at fixed Q values, R x res x th dx F ( x, Q ), where x th corresponds to the pion production threshold at fixed Q , and x res = Q / ( W − M + Q ) indicates the x value at the same Q where the traditional delineationbetween the resonance and DIS regions at W = W res ≡ W ,deep-inelastic data, at the same Q and over the same interval of x . The early phenomenologicalfindings [26] suggested that the integrated strength of the resonance structure functions above Q ≈ was indeed very similar to that in the deep-inelastic region, including in each ofthe individual prominent resonance regions. In this section we explore the duality between theresonance and deep-inelastic structure functions in the context of QCD moments.According to De Rujula, Georgi and Politzer [48], one can formally relate the appearance ofquark-hadron duality to the vanishing suppression of higher twist matrix elements in the QCDmoments of the structure functions [14]. Namely, if certain moments of structure functionsare observed to be independent of Q , as implied by duality, then from Eq. (11) the momentsmust be dominated by the leading, Q independent term, with the 1 /Q τ − higher twist termssuppressed. Duality is then synonymous with the suppression of higher twists, which in partoniclanguage corresponds to the suppression, or cancellation, of interactions between the scattereduark and the spectator system such as those illustrated in Fig. 1 (b) and (c). Conversely, ifthe moments display power-law Q dependence, then this implies violation of duality; moreover,if the violation is not overwhelming, the Q dependence of the data can be used to extractinformation on the higher twist matrix elements [49]. M ( ) M ( ) Q (GeV ) M L ( ) Figure 4.
Total n = 2 moments of the proton F p (top) , F p (center) and F pL (bottom) structurefunctions determined from global fits to existing DIS data and Jefferson Lab resonance regiondata [50], compared with moments computed from the leading twist PDFs from MRST at NNLO[41].The first determination [51] of the F p moments from Jefferson Lab data was made utilizingstructure functions measured in Hall C [26], while a later evaluation [25] included the large bodyof additional data from CLAS. More recently, the extraction of F p has been further enhancedby LT-separated data from Hall C, shown in Fig. 2 along with the fit [24] to the LT separatedcross sections. The n = 2 moments for the proton F p , F p , and F pL structure functions are shownin Fig. 4 versus Q , as determined from integrating this fit. For F p they are found to be in verygood agreement with the earlier measurements. Also shown is the leading-twist contributioncalculated from the MRST parameterization [41], corrected for target mass effects [15].One of the most striking features of the results in Fig. 4 is that the elastic-subtracted momentsexhibit the same Q dependence as the PDF fits down to Q ≈ . Even with the elasticcontribution included, which vanishes in the Bjorken limit and is hence pure higher twist, thereis excellent agreement between the resonance and DIS data for Q > ∼ . Until very recently[6, 9], this fact has not been widely appreciated or utilized in global PDF fitting efforts [4, 5],which typically impose cuts on data of Q > ∼ and W > ∼
12 GeV .While the OPE provides a systematic approach to identifying and classifying higher twists,it does not reveal why these are small or how duality is realized globally and locally. To furtherexplore the local aspects of duality within a perturbative QCD context, a ground-breaking newpproach using “truncated” moments of structure functions, developed recently by Forte et al. [52] and extended by Kotlorz & Kotlorz [53], was applied by Psaker et al. [54] to Jefferson Labdata. The virtue of truncated moments is that they obey a similar set of Q evolution equationsas those for PDFs themselves, which therefore enables a rigorous connection to be made betweenlocal duality and QCD. It allows one to quantify the higher twist content of various resonanceregions, and determine the degree to which individual resonances are dominated by the leadingtwist components.Defining the n -th truncated moment M n of a PDF q ( x, Q ) between x min and x max as M n ( x min , x max , Q ) = Z x max x min dx x n − q ( x, Q ) , (13)the evolution equations for the truncated moments can be written as d M n dt = α s ( Q )2 π (cid:0) P ′ n ⊗ M n (cid:1) , t = ln (cid:16) Q / Λ (cid:17) . (14)The symbol ⊗ denotes the Mellin convolution of the truncated moment and the “splittingfunction” P ′ n , which is related to the usual DGLAP evolution splitting function P [55] by P ′ n ( z, α s ( Q )) = z n P ( z, α s ( Q )). The extent to which nucleon structure function data inspecific regions in x (or W ) are dominated by leading twist can be determined by constructingempirical truncated moments and evolving them to different Q . Deviations of the evolvedmoments from the experimental data at the new Q then reveal any higher twist contributionsin the original data.A next-to-leading order (NLO) analysis [54] of data on the proton F p structure function fromJefferson Lab covering a range in Q from 1 GeV to ≈ revealed intriguing behaviorof the higher twists for different nucleon resonance regions. Assuming that F p data beyond alarge enough Q (taken to be Q = Q = 25 GeV in Ref. [54]) are dominated by leading twist,the truncated moments were computed at Q and evolved to lower Q . Note that the truncatedmoments are computed over the range W th ≤ W ≤ W max , where the W th = M + m π is theinelastic threshold. At Q = 1 GeV this corresponds to the integration range x min ≤ x ≤ x th ,where x th = (cid:2) m π ( m π + 2 M ) /Q (cid:3) − ≃ . W max at Q = 1 GeV , with and without target mass corrections. Including theeffects of TMCs, the leading twist moment differs from the data by ∼
15% for W max > . Q , several intervals in W are considered: W ≤ W ≤ (∆(1232) or first resonanceregion); 1 . ≤ W ≤ . ( S (1535) or second resonance region); and 2 . ≤ W ≤ . ( F (1680) or third resonance region). The higher twist contributions to M in these regionsare shown in Fig. 5(b) as ratios to moments of the data.The results indicate deviations from leading twist behavior of the entire resonance region data(filled circles in Fig. 5(b)) at the level of < ∼
15% for all values of Q considered, with significant Q dependence for Q < ∼ . The strong Q dependence of the higher twists is evidenthere in the change of sign around Q = 2 GeV , with the higher twists going from ≈ −
10% at Q = 1 GeV to ≈ Q ∼ − . At larger Q the higher twists are naturallyexpected to decrease, once the leading twist component of the moments begins to dominate.Interestingly, the magnitude of the higher twist contributions in the ∆ region (diamonds) issmallest, decreasing from ≈ −
15% of the data at Q = 1 GeV to values consistent with zeroat larger Q . The higher twists are largest, on the other hand, for the S region (squares),where they vary between ≈ −
15% of the data at Q = 1 GeV and 20–25% at Q ∼ .Combined, the higher twist contribution from the first two resonance regions (dotted curve) is W max (GeV) m o m e n t r a ti o data / (LT+TMC)data / LT (a) Q = 1 GeV Q (GeV ) -0.2-0.100.10.20.3 H T / d a t a D S W max = 2.5 GeV F W max = 3.1 GeV W max = 4 GeV (b) n = 2 Figure 5. (a)
Ratio of the M truncated moments of the data to the leading twist + TMC(solid), and data to leading twist without TMC (dashed) at Q = 1 GeV , as a function of W max . (b) Q dependence of the fractional higher twist (HT) contribution to the n = 2 truncatedmoment data, for various intervals in W . < ∼
15% in magnitude for all Q . The rather dramatic difference between the ∆ and the S , may,at least in part, be due to the choice of the differentiation point of W = 1 . . A lower W choice, for instance, would lower the higher twist content of the S at large Q , while raisingthat of the ∆. However, this W choice corresponds to the local minimum between these tworesonances in the inclusive spectra, and is the one most widely utilized.The higher twist content of the F region (open circles) is similar to the S at low Q , butdecreases more rapidly for Q > . The higher twist content of the first three resonanceregions combined (dashed curve) is < ∼ Q ≤ . Integrating upto W = 4 GeV (filled circles), the data on the n = 2 truncated moment are found to beleading twist dominated at the level of 85–90% over the entire Q range.The results in Fig. 5 can be compared with quark model expectations [45, 46], which predictsystematic deviations of resonance data from local duality. Assuming dominance of magneticcoupling, the proton data are expected to overestimate the DIS function in the second andthird resonance regions due to the relative strengths of couplings to odd-parity resonances; thepositive higher twists observed in Fig. 5(b) for Q > ∼ indeed support these predictions.
4. Deuteron F measurements Together with hydrogen, inclusive lepton scattering from deuterium targets has provided anextensive data base of F structure function measurements over a large range of kinematics.While a significant quantity of F d data was collected from experiments at CERN and SLAC,the quasi-elastic and nucleon resonance regions, especially at low and moderate Q ( ≈ fewGeV ), were only mapped precisely with the advent of Jefferson Lab data [26, 31]. Similarly,Jefferson Lab contributed with precision F d data in the region of x > F d data in select regions of x and Q , whileinclusive cross section measurements in CLAS have covered a continuous two-dimensional regionover the entire resonance region up to Q = 6 GeV . This combination is rather useful fordetermining moments of F . In such extractions one usually assumes that the ratio R for thedeuteron is similar to that for the proton at scales Q of a few GeV [57]. New measurementshich will test this assumption will be reviewed in Sec. 6. Table 2.
Lowest two moments (for n = 2 and 4) of the isovector F structure function.Experimental results for Q ≈ are compared with lattice calculations extrapolated tothe chiral limit. n Niculescu et al. [58] Osipenko et al. [59] Detmold et al. [60](Hall C) (Hall B) (lattice)2 0.049(17) 0.050(9) 0.059(8)4 0.015(3) 0.0094(16) 0.008(3)The results of the moment analyses are shown in Table 2, expressed as the isovector (protonminus neutron) combination, and compared with isovector moments from lattice QCD [60, 61].For simplicity the neutron moments here are defined as the difference between the deuteron andproton moments — see, however, Sec. 5.1 below. The n = 2 moments from the Hall B [59] andHall C [58] analyses agree well with each other, and with the lattice extraction, which includesthe effects of pion loops and the intermediate ∆(1232) resonance in the chiral extrapolation.For the n = 4 moment the comparison between the Hall B and Halls C results shows a slightdiscrepancy, which may be reduced once precision high- x data at Q ∼ are included inthe extractions.Analysis of the Q -dependence of the deuteron F moments in Ref. [31] suggests a partialcancellation of different higher twist contributions entering in the OPE with different signs,which is one of the manifestations of quark-hadron duality. The slow variation with Q of thestructure function moments, down to Q ≈ , was also found in the analysis of protondata [51], where such cancellations were found to be mainly driven by the elastic contribution.Furthermore, by comparing the proton and (nuclear corrected) neutron structure functionmoments, the higher twist contributions were found to be essentially isospin independent [62].This suggests the possible dominance of ud correlations over uu and dd in the nucleon, andimplies higher twist corrections that are consistent with zero in the isovector F structurefunction.More recently, high precision deuteron cross sections in the resonance region have beenmeasured in Hall C [34, 36] with the aim of providing LT separated deuteron structure functionsof comparable precision and kinematic coverage to those performed for the proton. These higherprecision LT separated data will allow for a significant further reduction in the uncertainties inthe current nonsinglet F extractions.
5. Neutron F structure function A complete understanding of the valence quark structure of the nucleon requires knowledge ofboth its u and d quark distributions. While the u distribution is relatively well constrainedby measurements of the proton F p structure function, in contrast the d quark distribution ispoorly determined due to the lack of comparable data on the neutron structure function F n .The absence of free neutron targets makes it necessary to use light nuclei such as deuterium aseffective neutron targets, and one must therefore deal with the problem of extracting neutroninformation from nuclear data. F data In standard global PDF analyses, sensitivity to the d -quark from charged lepton scattering isprimarily provided by the neutron in the deuteron. Usually the neutron F n structure functions extracted by subtracting the deuteron and proton structure function data assuming thatnuclear corrections are negligible. At large x , however, the ratio of the deuteron to free nucleonstructure functions is predicted to deviate significantly from unity [63, 64, 65, 66], which canhave significant impact on the behavior of the extracted neutron structure function at large x [9, 67].Even when nuclear effects are considered, there exist practical difficulties with extractinginformation on the free neutron from nuclear data, especially in the nucleon resonance region,where resonance structure is largely smeared out by nucleon Fermi motion. A recent analysis[68] used a new method [66] to extract F n from F d and F p data, in which nuclear effects areparameterized via an additive correction to the free nucleon structure functions, in contrast tothe more common multiplicative method [69] which fails for functions with zeros or with non-smooth data. In the standard impulse approximation approach to nuclear structure functions,the deuteron structure function can be written as a convolution [65, 66] F d ( x, Q ) = X N = p,n Z dy f N/d ( y, ρ ) F N ( x/y, Q ) , (15)where f N/d is the light-cone momentum distribution of nucleons in the deuteron (or “smearingfunction”), and is a function of the momentum fraction y of the deuteron carried by the strucknucleon, and of the virtual photon “velocity” ρ (see Eq. (4)). The smearing function encodes theeffects of the deuteron wave function, accounting for nuclear Fermi motion and binding effects,as well as kinematical finite- Q corrections. Although not well constrained, nucleon off-shelleffects have also been studied [63, 64, 65]; their influence appears to be small compared withthe errors on the existing data, except at very large x . x F ( x , Q ) dpnd (recon) Q = 1.7 GeV x F neutron (BoNuS)neutron (Bosted/Christy Model)proton (Christy/Bosted Model) = 1.7 GeV Q Figure 6. (Left)
Neutron F n structure function extracted from inclusive deuteron and protondata at Q = 1 . [68], together with the reconstructed F d . (Right) Neutron structurefunction extracted from the BoNuS experiment [35], compared with the Bosted/Christy modelof the neutron F n [70] and the corresponding Christy/Bosted parametrization for F p [24].In Fig. 6 we illustrate the results of a typical extraction of F n from Jefferson Lab F d and F p data at Q = 1 . . The proton data show clear resonant structure at large x , which ismostly washed out in the deuteron data. The resulting neutron F n is shown after two iterationsof the procedure with an initial guess of F n = F p . Clear neutron resonance structure is visiblein the first (∆) and second resonance regions, at x ∼ .
75 and 0.55, respectively, with sometructure visible also in the third resonance region at x ∼ .
45, albeit with larger errors. Thedeuteron F d reconstructed from the proton and extracted neutron data via Eq. (15) indicatesthe relative accuracy and self-consistency of the extracted F n .Of course it is not possible to avoid nuclear model dependence in the inversion procedure,and some differences in the extracted F n will arise using different models for the smearingfunctions f N/d . To remove, or at least minimize, the model dependence in the extracted freeneutron structure, several methods have been proposed, such as utilizing inclusive DIS from A = 3 mirror nuclei [71, 72, 73], and semi-inclusive DIS from a deuteron with spectator tagging[35, 74]. In addition, experiments involving weak interaction probes [75, 76, 77] can provide theinformation on the flavor separated valence quark distributions directly. In the next section wediscuss in detail one of these methods for determining the free neutron structure, namely theBoNuS experiment at Jefferson Lab [35]. To overcome the absence of free neutron targets, the Hall B BoNuS (Barely Off-shell NeUtronStructure) experiment has measured inclusive electron scattering on an almost free neutron usingthe CLAS spectrometer and a recoil detector to tag low momentum protons. The protons aretracked in a novel radial time projection chamber [78] utilizing gas electron multiplier foils toamplify the proton ionization in a cylindrical drift region filled with a mixture of Helium andDi-Methyl Ether, and with the proton momentum determined from the track curvature in asolenoidal magnetic field. Slow backward-moving spectator protons are tagged with momentaas low as 70 MeV in coincidence with the scattered electron in the reaction D ( e, e ′ p s ) X . Thistechnique ensures that the electron scattering took place on an almost free neutron, with itsinitial four-momentum inferred from the observed spectator proton. Cutting on spectatorprotons with momenta between 70 and 120 MeV and laboratory angles greater than 120 degreesminimizes the contributions from final state interactions and off-shell effects to less than severalpercent on the extracted neutron cross section.While inclusive scattering from deuterium results in resonances which are significantlybroadened (often to the point of being unobservable), determination of the initial neutronmomentum allows for a dramatic reduction in the fermi smearing effects and results inreconstructed resonance widths comparable to the inclusive proton measurements. In addition,the large CLAS acceptance for the scattered electron allowed for the tagged neutron cross sectionto be measured over a significant kinematic range in both W and Q at beam energies of 4.2 GeVand 5.3 GeV. BoNuS F n data extracted at a beam energy of 5.3 GeV and Q = 1 . areshown in Fig. 6 (right panel) for x values from pion production threshold through the resonanceregion and into the DIS regime. This will allow for the first time a unambiguous study of theinclusive neutron resonance structure functions.An extension of BoNuS has been approved [79] to run at a beam energy of 11 GeV after theenergy upgrade of the CEBAF accelerator. The kinematic coverage will allow the extractionof the ratio of neutron to proton structure functions F n /F p to x as large as 0.8, and thecorresponding d to u large x parton distribution ratio. Other quantities which BoNuS willmake possible to measure include the elastic neutron form factor, quark-hadron duality on theneutron, semi-inclusive DIS and resonance production channels, hard exclusive reactions suchas deeply-virtual Compton scattering or deeply-virtual meson-production from the neutron, aswell as potentially the inclusive structure function of a virtual pion.
6. Longitudinal structure function F L The unpolarized inclusive proton cross section contains two independent structure functions.While F p has been measured to high precision over many orders of magnitude in both x and Q , measurements of the longitudinal structure function F pL (and the ratio R ) have beenignificantly more limited in both precision and kinematic coverage. This is due in part tothe challenges inherent in performing LT separations, which typically require point-to-pointsystematic uncertainties in ǫ to be smaller than 2% to obtain uncertainties on F L of less than20%.While the inclusive cross section is proportional to 2 xF + ǫF L , the F structure function ∼ xF + F L , so that F is only proportional to the cross section for ǫ = 1. At high Q thescattering of longitudinal photons from spin-1/2 quarks is suppressed, and in the parton modelone expects F L (and R ) to vanish as Q → ∞ . At low Q , however, F L is no longer suppressed,and could be sizable, especially in the resonance region and at large x . On the other hand, F L is dominated by the gluon contribution at small x , where new measurements from HERA [80]have shown that it continues to rise. In the kinematic range of Jefferson Lab F L has been foundto be typically 20% of the magnitude of F , which is consistent with earlier SLAC measurementswhere the kinematic regions overlap.An extensive program of LT separations has been carried out in Hall C, includingmeasurements of the longitudinal strength in the resonance region for 0 . < Q < . for both proton [18] and deuteron [34, 36] targets. The Jefferson Lab experiments listed inTable 1 for which LT separations have been performed for the proton or deuteron are E94-110,E99-118, E00-002, E02-109, and E06-009. The Jefferson Lab data complement well the previousresults at smaller x from SLAC and NMC in this Q region, and improve dramatically on thefew measurements that existed below Q = 8 GeV in this x region, which had typical errors on R and F L of 100% or more — see Fig. 7 (left).The recent precision LT separated measurements of proton cross sections [18] have allowedfor the first time detailed duality studies in all of the unpolarized structure functions and theirmoments. The results of the proton separated structure functions in the resonance region werepresented in Fig. 3 in Sec.3. Although significant resonant strength is observed in F L (or R ),evidence of duality is nonetheless observed in this structure function, along with F and F .In addition to the proton data, Jefferson Lab experiment E02-109 measured the LT separated F and F L structure functions of the deuteron, in the same W and Q ranges, and with thesame high precision as E94-110 did for the proton. This will allow quantitative studies of dualityin both the longitudinal and transverse channels for the deuteron. If duality holds well for boththe proton and neutron separately, it will hold to even better accuracy for the deuteron since theFermi motion effects intrinsically perform some of the averaging over the resonances. However, ifduality does not hold for the LT separated neutron structure functions, this should be observablein the deuteron data, and will thus provide a critical test for models of duality.In addition to the resonance region, measurements of the inclusive longitudinal proton anddeuteron structure have also been performed at lower x (higher W ) and lower Q . While thelongitudinal strength is significant at Q of several GeV , the proton F L structure function isconstrained by current conservation to behave, for fixed W , as F L ∼ Q for Q →
0. However,even with the new Jefferson Lab data, which extend down to Q = 0 .
15 GeV [81], the Q atwhich this behavior sets in has not yet been observed.Another interesting test provided by the E99-118 data is whether the relative longitudinalcontribution to the cross section embodied in R is different in the deuteron and proton at theselow Q values. While the higher Q data from SLAC and NMC exhibit no significant differencein the deuteron and proton R , the Jefferson Lab results shown in Fig. 7 (right) suggest apossible suppression of R in the deuteron relative to the proton for Q < . Althoughthis suppression is consistent with the two lowest Q data points from SLAC, the uncertaintiesare dominated by systematic errors and the combined significance of the effect is still less than2 σ . Conclusive experimental evidence for the possible suppression of R in deuterium at low Q will likely be provided when the results from additional data from E00-002 are finalized in verynear future. Q = 1.24 GeV W = 2.78 GeV R = 0.208 ± = 2.84 GeV W = 2.28 GeV R = 0.257 ± s r ( m b / s r ) Q = 0.71 GeV W = 2.28 GeV R = 0.115 ± e -0.5-0.4-0.3-0.2-0.100.10.20.30.40.510 -1 Q [ GeV ] R D - R H E99-118NMCSLAC
Figure 7. (Left)
Sample LT separations from Jefferson Lab experiment E94-110 [18]. (Right)
Difference between the ratios R in deuterium and hydrogen versus Q , from E99-118 [81],compared with previous NMC and SLAC measurements.
7. Semi-inclusive deep inelastic scattering
In addition to the traditional F and F L structure function observables, a number of otherprocesses have been studied at Jefferson Lab over the past decade, with potentially importantconsequences for our understanding of the workings of QCD at low energy. In this section wefocus on semi-inclusive pion electroproduction.An analysis of the semi-inclusive process e N → e h X , where a hadron h is detected inthe final state in coincidence with the scattered electron, has recently been made using datafrom Hall C in the resonance–scaling transition region [32, 33]. One of the main motivationsfor studying semi-inclusive meson production is the promise of flavor separation via tagging ofspecific mesons in the final state. In the valence quark region a produced π + ( π − ) meson, forexample, primarily results from scattering off a u ( d ) quark in the proton.The semi-inclusive cross section at LO in α s is given by a simple product of quark distributionand quark → hadron fragmentation functions, dσdxdz ∼ X q e q q ( x ) D hq ( z ) ≡ N hN ( x, z ) . (16)Here the fragmentation function D hq ( z ) gives the probability for a quark q to fragment to a hadron h with a fraction z = p h · p/q · p = E h /ν of the quark’s (or virtual photon’s) laboratory frameenergy. Although at LO the scattering and particle production mechanisms are independent,higher order pQCD corrections give rise to non-factorizable terms, which involve convolutionsof the PDFs and fragmentation functions with hard coefficient functions [82].For hadrons produced collinearly with the virtual photon, the invariant mass W ′ of theundetected hadronic system X at large Q can be written [83] W ′ ≈ M + Q (1 − z )(1 − x ) /x ,where the hadron mass is neglected with respect to Q . In the elastic limit, z →
1, the hadroncarries all of the photon’s energy (with W ′ → M ), so z is also referred to as the “elasticity”.hile formally the LO factorized expression for the cross section (16) may be valid atlarge Q , at finite Q there are important corrections arising from the finite masses of thetarget and produced hadron. One can show, however, that the LO factorization holds evenat finite Q , provided the parton distribution and fragmentation functions are expressed interms of generalized scaling variables [84], q ( x ) D hq ( z ) → q ( ξ h ) D hq ( ζ h ), where ζ h = ( z h ξ/ x )(1 + q − x M m h ⊥ /z Q ) and ξ h = ξ (1 + m h /ζ h Q ), with m h ⊥ = m h + p h ⊥ . Not surprisingly,these effects become large at large x and z when Q is small; however, for heavier producedhadrons such as kaons or protons, significant effects can also arise at small values of z [84].The validity of the factorized hypothesis in Eq. (16) relies on the existence of a sufficientlylarge gap in rapidity η = ln [( E h − p zh ) / ( E h + p zh )] / η ≈ z ; atlow energies, however, this can only be reached at larger values of z . On the other hand, at fixed x and Q the large- z region corresponds to resonance dominance of the undetected hadronicsystem X (corresponding to small W ′ ), so that the factorized description in terms of partonicdistributions must eventually break down. It is vital therefore to establish empirically the limitsbeyond which the simple x and z factorization of Eq. (16) is no longer valid.It is intriguing in particular to observe whether W ′ can play a role analogous to W for dualityin inclusive scattering, when the undetected hadronic system X is dominated by resonances W ′ < ∼ N ∗ , and their subsequent decays into pions (or othermesons) and lower-lying resonances, N ′∗ . The hadronic description must be rather elaborate,however, as the production of fast outgoing pions in the current fragmentation region at highenergy requires nontrivial cancellations of the angular distributions from various decay channels[44, 45, 86], N hN ( x, z ) = X N ′∗ (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)X N ∗ F γ ∗ N → N ∗ ( Q , W ) D N ∗ → N ′∗ h ( W , W ′ ) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (17)where F γ ∗ N → N ∗ is the N → N ∗ transition form factor, which depends on the masses of thevirtual photon and excited nucleon ( W = M N ∗ ), and D N ∗ → N ′∗ h is a function representing thedecay N ∗ → N ′∗ h .A dedicated experiment (E00-018) to study duality in π ± electroproduction was performedin Hall C [32, 33], in which a 5.5 GeV electron beam was scattered from proton and deuterontargets at Q between 1.8 and 6.0 GeV , for 0 . ≤ x ≤ .
55, with z in the range 0 . − D − /D + was constructed, where D + corresponds to a pion containing the struck quark ( e.g. , π + froma struck u or ¯ d quark), while D − describes the fragmentation of a quark not contained inthe valence structure of the pion ( e.g. , a d quark for the π + ). Since at moderate x thedependence on PDFs cancels, the fragmentation function ratio is approximately given by D − /D + = (4 − N π + d / N π − d ) / (4 N π + d / N ⌈ π − − N πd is the yield of produced pions inEq. (17).The Jefferson Lab data for D − /D + from E00-108 are shown in Fig. 8 as a function of z atfixed x = 0 .
32 and Q = 2 . [32], and compared with earlier HERMES data at higherenergies [87]. Despite the different energies, there is good overall agreement between the twomeasurements, even though the Jefferson Lab data sit slightly higher. Furthermore, the D − /D + ratio extracted from the Jefferson Lab data shows a smooth dependence on z , which is quiteremarkable given that the data cover the full resonance region, 0 . < W ′ < . . This igure 8. The ratio of unfavored to favored fragmentation functions D − /D + as a function of z extracted from deuterium data, for x = 0 .
32 [32].strongly suggests a suppression or cancellation of the resonance excitations in the π + /π − crosssection ratio, and hence in the fragmentation function ratio.Similar cancellations between resonances naturally arises in quark models, such as thosediscussed by Close et al. [45, 47] for the γN → π ± N ′∗ reaction. The pattern of constructive anddestructive interference, which was a crucial feature of the appearance of duality in inclusivestructure functions, is also repeated in the semi-inclusive case when one sums over the states N ′∗ . Moreover, the smooth behavior of the fragmentation function ratio D − /D + in Fig. 8 canbe qualitatively understood from the relative weights of the matrix elements, which are always 4times larger than for π − production. In this case the resonance contributions to this ratio cancelexactly, leaving behind only the smooth background as would be expected at high energies. Thismay account for the striking lack of resonance structure in the resonance region fragmentationfunctions in Fig. 8.
8. Outlook
The first decade of unpolarized structure function measurements at Jefferson Lab has hadsignificant impact on our understanding of nucleon structure, both for leading twist partondistributions and for the resonance–scaling transition and related studies of quark-hadronduality. With most of the data concentrated in the low- W region in the Q ∼ few GeV range, the greatest influence on the global data base has naturally been at large x .Recently a new global PDF analysis was performed [9], exploring the possibility of reducingthe uncertainties at large x by relaxing the constraints on the kinematics over which data areincluded in the fit. The data sets combined proton and deuteron DIS structure functions fromJefferson Lab, SLAC and CERN (NMC) with new ep collider data from HERA, as well as newDrell-Yan, W asymmetry and jet cross sections from pp and pd collisions at Fermilab. The new fit(referred to as “CTEQ6X”) allowed for a significant increase in the large- x data set ( e.g. , a factorof two more DIS data points) by incorporating data for W > and Q > .
69 GeV ,lower than in the standard global fits [5, 88] which typically use W > .
25 GeV and Q > . The new analysis also systematically studied the effects of target mass andhigher twist contributions, and realistic nuclear corrections for deuterium data.Results from the CTEQ6X fit are shown in Fig. 9 (left) for the u and d quark PDFs,normalized to the earlier CTEQ6.1 fit, which had no nuclear or subleading 1 /Q correctionsapplied. The biggest change is the ∼ d quark at x ∼ .
8, which isfound to be stable with respect to variations in the W and Q cuts, provided both TMC andhigher twist corrections are included. The effect of the expanded data base is more dramatically igure 9. (Left) CTEQ6X fit for u and d quark PDFs, normalized to the earlier CTEQ6.1 fit[88]. The vertical lines show the approximate values of x above which PDFs are not directlyconstrained by data. The error bands correspond to ∆ χ = 1. (Right) Relative errors on u and d quark PDFs, normalized to the relative errors in the reference fit.illustrated in Fig. 9 (right), which shows the relative u and d PDF errors for a range of W and Q cuts (“cut0” being the standard cut, “cut3” the more stringent CTEQ6X cut, and intermediatecuts “cut1” and “cut2”), normalized to those of a reference fit with “cut0” and no nuclear orsubleading corrections. The result is a reduction of the errors by up to 40–60% at x > ∼ .
7, whichwill have a profound impact on applications of PDFs in high energy processes, such as those asthe LHC, as well as in constraining low-energy models of quark distributions.
Uncertainties in PDFs will be further reduced with the availability of data at even larger x and Q from Jefferson Lab after its 12 GeV energy upgrade, which will determine the d quark distributionup to x ∼ . x the earliermeasurements of low-momentum, backward protons in semi-inclusive scattering from deuterium(Sec. 5.2); the MARATHON experiment [73], which plans to extract F n /F p from the ratio of He to H structure functions, in which the nuclear corrections cancel to within ∼
1% [71, 72];and the program of parity-violating DIS measurements on hydrogen [76], which will be sensitiveto a new combination of d/u in the proton, free of nuclear corrections.In the resonance region, experiment E12-10-002 [89] will extend proton and deuteron structurefunction measurements up to Q ∼
17 GeV and enable tests of quark-hadron duality over amuch larger kinematic range, ultimately providing stronger constraints on large- x PDFs. Andfinally, a new avenue for exploring nucleon structure at 12 GeV will be opened up with semi-inclusive meson production experiments [90], which will test the factorization of scattering andfragmentation subprocesses needed for a partonic interpretation of semi-inclusive cross sections.A successful program of semi-inclusive measurements tagging specific mesons in the final statewould allow unprecedented access to the flavor dependence of PDFs in previously unexploredregions of kinematics. cknowledgments
We thank R. Ent and C. E. Keppel for their contributions to this review in the early stages ofits development. This work was supported by the U.S. Department of Energy under ContractNo. DE-FG02-03ER41231, and DOE contract No. DE-AC05-06OR23177, under which JeffersonScience Associates, LLC operates Jefferson Lab.
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