Deep Inelastic Scattering Part 1 Dave Gaskell Jefferson Lab

Home , Nuclear density, Polarized target

CTEQ 2015 Summer School July 8-9, 2015

1 Outline

Day 1: 1. Introduction to DIS and the Quark Parton Model 2. Formalism àUnpolarized DIS àPolarized DIS 3. Results and examples

Day 2: 1. Nuclear Effects in DIS 2. Beyond inclusive scattering à Semi-inclusive reactions (SIDIS)

2 Disclaimer

• I am an experimentalist, very interested in nuclear effects à Much of what I will say comes from this perspective

• Most of my work has been at Jefferson Lab à You will be seeing a lot of examples from JLab

3 What is Deep Inelastic Scattering? Collective behaviorSome context: vs. two-body physics

DIS: Using lepton (electron, muon, neutrino) scattering to explore the partonic structure of hadronic matter ? Advantages of leptonic (vs. hadronic) probes

à It’s QED: at least one vertex is well understand à No complicated structure of the probe to deal with

à Small value of αQED = 1/137 means higher order corrections are small*High -momentum region: short-range

To access partonic structure (i.e.interactions, quarks and gluons) mainly we need 2-body “high” physics, energies and large inelasticities à want to avoid the complicationslargely from exciting A-independent resonances

*Well, usually. Not always true. 4 Could these Short-Range Correlations be dense enough to modify the quark structure of protons and neutrons?

Cioffi Degli Atti, et al, PRC53, 1689 (1996)

11 What is Deep Inelastic Scattering?

Lepton scattering cross Nuclear elastic sections have rich, complex structure

à Elastic scattering à Production of excited quark bound states – Resonance resonances!

We are primarily Quasielastic interested in the regime in which quarks act like quasi-free, weakly interacting particles

The boundary between these regimes not Figure from R.G. Roberts, The Structure of the Proton always so clear cut

5 DIS Experiments

• Plethora of data available from a variety of fixed target experiments – SLAC à Electrons at 10’s of GeV – CERN (EMC/BCDMS/NMC/COMPASS) à Muons at 100’s of GeV – HERMES à 27 GeV positrons and electrons – E665 à Muons at 490 GeV – JLab à 6 GeV electrons à 12 GeV • Only one source of collider DIS data (so far) – HERA (Zeus and H1) : 27 GeV positrons (electrons) on 920 GeV protons • Neutrinos à CCFR, CHORUS, NuTeV, MINERνA • Important information can also be gleaned from hadron colliders (RHIC, LHC, etc.)

6 Deep Inelastic Scattering

Kinematics:

Beam: k= (E, 0,0,p) à Typically ignore electron

mass so E=p Scattered electron: k’ = E’, θ

Target: P = (Ep, 0,0,P)

Useful quantities:

Electron 2 2 2 Q = q = (k k) momentum transfer Total energy in γ*p W 2 =(q + P )2 center of mass Q2 q P Bjorken scaling x = Inelasticity y = · k P variable 2p q · ·

7 Kinematics: Lab frame

Often DIS kinematics expressed in LAB frame (target at rest) à Experiments at HERA (or a future EIC) take place in collider

I tend to think in a fixed-target framework – some useful expressions for working in the lab: Q2 Q2 x = 2p q 2m = E E · p W 2 =(q + P )2 Q2 + m2 +2m p p q P y = · Fraction of electron energy transferred to nucleon k P E · 2 2 1 2 q e 1 y Ratio of long. to = 1+ tan = transverse photon | 2| 1 2 Q 2 1 y + y flux 2 8 DIS Cross Section

Unpolarized cross section:

dσ α 2 E = L W µν dΩdE / Q4 E / µν

Parity and time invariance à only two structure functions required

2 / 2 dσ 4α (E ) ⎡ 2 2 θ 2 2 θ ⎤ / = 4 W2 (ν,Q )cos + 2W1(ν,Q )sin dΩdE Q ⎣⎢ 2 2⎦⎥

W1 and W2 parameterize the (unknown) structure of the proton 9 DIS Cross Section

Unpolarized Cross section:

dσ α 2 E = L W µν dΩdE / Q4 E / µν

2 / 2 dσ 4α (E ) ⎡ 2 2 θ 2 2 θ ⎤ / = 4 W2 (ν,Q )cos + 2W1(ν,Q )sin dΩdE Q ⎣⎢ 2 2⎦⎥

In the limit of large Q2, 2 2 MW1(ν,Q ) → F1(x) Q structure functions scale 2 x = νW2 (ν,Q ) → F2 (x) 2Mν

10 DIS Cross Section

Virtual photon cross d section: = (T + L) ddE

2 2 1 Longitudinal 2 q e Transverse photons = 1+ | | tan photons Q2 2 2 2 E K 1 W m = K = p 22 E Q2 1 2m p

K K Q2 W = W = ( + ) 1 42 T 2 42 Q2 + 2 L T

Pure transverse Transverse and longitudinal 11 DIS Cross Section

2 / 2 dσ 4α (E ) ⎡ 2 2 θ 2 2 θ ⎤ / = 4 W2 (ν,Q )cos + 2W1(ν,Q )sin dΩdE Q ⎣⎢ 2 2⎦⎥

2 2 Replacing W1 and W2 MW1(ν,Q ) → F1(x,Q ) 2 2 νW2 (ν,Q ) → F2 (x,Q )

And defining: 4M 2x2 F (x, Q2)= 1+ F (x, Q2) 2xF (x, Q2) L Q2 2 1

d 42 = 2xF (x, Q2)+F (x, Q2) ddE x(W 2 M 2) 1 L 12 Deep Inelastic Scattering

At very high energies (HERA) – contributions from Z exchange can no longer be ignored de± 22(1 + (1 y)2) 1 (1 y)2 y2 = F˜ xF˜ F˜ dxdQ2 Q4x 2 1 + (1 y)2 3 1 + (1 y)2 L F˜ = F v F Z + 2 (v2 + a2)F Z 2 2 Z e 2 Z e e 2 F˜ = F v F Z + 2 (v2 + a2)F Z L L Z e L Z e e L xF˜ = a xF Z + 2 2v a xF Z 3 Z e 3 Z e e 3 Q2 1 Vector weak coupling Axial-vector weak Z = =-1/2 Q2 + M 2 2 2 2 coupling 13 Z 4 sin W cos W =-1/2+2sin θW Quark Parton Model

DIS can be described as inelastic scattering from non- interacting, point-like constituents in the nucleon Consequences:

At fixed x, inelastic structure functions scale:

MW (ν,Q2 ) → F (x) 1 1 Large Q2 2 νW2 (ν,Q ) → F2 (x)

2 Spin ½: F2(x)= ei xqi(x) F2(x)=2xF1(x) Callan-Gross i relation R = L =0 T 14 Quark Parton Model

DIS can be described as inelastic scattering from non- interacting, point-like constituents in the nucleon 2 F2(x)= eqx(q(x)+¯q(x)) q q 1 2 gV = 2eq sin W Z q ±2 F2 (x)= 2eqgV x(q(x)+¯q(x)) q u=+, d=- Z q 2 q 2 F2 (x)= [(gV ) +(gA) ]x(q(x)+¯q(x)) 1 q gq = A ±2 F Z (x)= 2e gq (q(x) q¯(x)) 3 q A q F Z (x)= [(gq )2 +(gq )2](q(x) q¯(x)) 3 V A q 15 G. MILLER et al.

7.0— R=0.18 Scaling – SLAC-MIT6.0 —resultW 2.6 GeV from 1970

A series of experiments at SLAC (performed by SLAC-MIT collaboration) gave 2MpW1 first hints that the partonic hypothesis was valid5.0 à Cross sections at large angles (momentum transfers) larger than if proton was an amorphous blob-like object à Analogous to Rutherford’s alpha scattering experiments 0 VoLUME 2), NUMBER 16 PHYSICAL REVIEW0.6 LETTERS 20 GcTQBER 1969 FIG 6 2AfpSL and vW& R=0.18 are shown as functions of u for 8 =0.18, S'&2.6 GeV, 0/&2. 6 GeV range of q' and W. with a resolution of 0.3 mrad. The measured and q2& 1 (GeV/e)2. %e observe the excitation of several nucleon solid angle of the instrument was 6&&10 ' sr with resonances' ' whose cross sections fall rapidly an uncertainty of +2%. with increasing q'. The region beyond 8'= 2 GeV Extensive tests showed that there could be sig- exhibits a surprisingly weak q' dependence. This nificant reductions in target density due to beam Letter describes the experimental procedure and heating. In order to correct for changes in the reports cross sections for W» 2 GeV. Discus- density a second spectrometer" was simulta- sion of the results and a detailed description of neously used to measure protons from elastic the resonance region will follow. ' electron-proton scattering at low momentum The incident energies at 0 =10' were 17.7, 15.2, transfer. The angle and momentum settings of 0.1 Phys.Rev.Lett.13.5, 11, and 7 GeV, 23 (1969)and at 8=6930-934were 16, 13.5, this spectrometer remainedQfixed2=1-7for GeVeach 2spec- 10, and 7 GeV. For fixed E and 8, along a spectrum. Usually the density reductions were less trum of decreasing E', W increases and q' de- than 4%, with the maximum value being 13%. creases. The maximum range of these variables An uncertainty of +1% was assigned to the mea- overBeama single energymeasured up tospectrum ~ 20 GeVoccurred at an sured cross sections for this correction. incident energy of 17.7 GeV and an anglePhys.Revof 10',diffractive. D5 (1972)Themodelsmainfor 528A,triggerbut we findfor thatan eventA is was providedin parton models.by " For this integral we find small for values of 2M~v/q' to about 8 and not where W varied from one proton mass to 5.2 a logical "or" betweenup x=0.25the total-absorptionis x=0.120d(dcount- 16 with kinematics. —vS' = 0.172 + 0.009 t strongly varying 2 GeV, and q' from 7.4 to 1.6 (GeV/c)'. For each er and a coincidence of two scintillation triggerJ Q)2 E' The new data permit further investigation of sum spectrum was changed in overlapping steps ofrules involvingcountersvtV2 reportedplaced beforewith the 6'andandafter10' the hodoscopes.which is about one half the value predicted on the 2% from elastic scattering, through the observeddata. ' UsingThe 8event= 0.18,informationinterpolations wasof bothbufferedthe andbasiswrittenof a simple quark model of the proton, and resonance region, to W= 2 GeV. Then steps cor-small- andon large-anglemagnetic datatapewereby useda SDS-9300to deter- on-lineis comput-also too small for a proton described by a quark mine vW, at a constant value of q' = l.5 {GeV/c)'. model with three "valence" quarks, in a sea of responding to a change in 8' of 0.5 GeV were er, which also provided preliminary on-line da- The evaluation of the integral in the Gottfried sum quark-antiquark pairs. made. rule, "basedta analysis.on a nonrelativistic pointlike quark Recently, Bloom and Gilman" have proposed a The electron beam from the accelerator was model of theThepxoton,crossgivessections were determined constant-q',from an finite-energy sum rule based on scal- v' momentum analyzed with values of bp/p between event-by-event analysis of the hodoscopesing inand {Ref. 19) that equates an integral over = 0.78+0.04 vS', in the resonance region with the corresponding 1 25 and then 7-cm —thevW, +0. and +0. % passed through a electron-pion discrimination counters.integralCor-over the asymptotic expression for vS', . liquid-hydrogen target. Two toroid charge moni-when integratedrectionsoverwerethe rangemadeof forour data.fast-electronicsTheyandhavecorn-pointed out that the applicability of the tors measured the integrated beam current with %e haveputeralso evaluateddead times,the Callan-Gross"hodoscope-countersum inefficien-sum rule to spectra which have prominent reso- uncertainties of less than 0.5%. Electrons scat-rule, whichcies,is relatedmultipleto thetracks,equal-timeinefficieneiescommuta- ofnanceselectronis indicative of a substantial nondiffractive tor of the current and its time derivative and which component in pR', The sum rule requires that, at tered in the target were momentum analyzed by identification, and target-density fluctuations. . is also equal to the mean square charge per parton constant q', J, equal J, with a double-focusing magnetic spectrometer' cap- Yields from an empty replica of the experimental able of momentum analysis to 20 GeV/c. Parti- target, typically t%, were subtracted from the cles selected by the spectrometer passed through full-target measurements. Electrons originating a system of four hodoscopes to determine their from 7t' decay and pair production were measured trajectories and then into a pion-electron separa- by reversing the spectrometer polarity and mea- tion system based on the different cascade-show- suring positron yields. This correction is impor- er properties of electrons and pions. This sys- tant only for small E' and amounted to a maxi- tern considered of a 1-radiation-length slab of mum of 15%. The error associated with each lead followed by three scintillation counters (dE/ point arose from counting statistics and uncer- dx counters) to detect showers initiated in the tainties in electron-detection efficiencies, added lead. The showers were then further developed in quadrature. in a total-absorption counter consisting of six- The data were analyzed separately at the Stan- teen 1-radiation-length lead slabs alternated with ford Linear Accelerator Center (SLAC) and Mass- Lucite Cherenkov counters. The dE/dx counters achusetts Institute of Technology (MIT) and aver- increased the pion-electron separation efficiency aged before each group began radiative correc- by about a factor of 20 at lower E', but were not tions. The results of the analyses were in excel- required for values of E' near the elastic peak. lent agreement. For the results given in Table I, The electron-detection efficiency decreased with the two analyses differed from their mean by an E' and wa. s 88'%%uo at 5 GeV. The uncertainty in the average value of 0.35% with an rms deviation of

electron-detection efficiency was +1.5%%uo above 1.2 /0. E'=5 GeV and increased to +4%%uo at E'=3 GeV. The radiative-correction procedures had two The momentum acceptance of the spectrometer steps. The first was the subtraction of the cal- was bp/p =3.5%% with momentum resolution of culated radiative tail of the elastic peak from 0.1/o. The angular acceptance was b.tt ='I mrad each spectrum. Using the measured form factors Scaling – SLAC-MIT result from 1970 A series of experiments at SLAC (performed by SLAC-MIT collaboration) gave first hints that the partonic hypothesis was valid

x=0.25

SLAC-PUB 796 (1970) 17 R=σL/σT SLAC-MIT also performed initial L-T separations, suggesting R was not large à536 L-T separations experimentallyG. challengingMILLER et– preciseal. extractions came later VOLUME 61, NUMBER 9 PHYSICAL REVIEW LETTERS 29 AUGUST 1988

BEST FIT I:I g= 18' ~ g= e-6. 26 This Expt A CDHS l:1 BCDMS ~ This Expt X E87 g= o g =,$g$'-:: IO I I I I I II i I 1 i I I i R=0.23+/-0.23l5 15 R=0.18+/-0.18 (i 25 (a) x = 0.5 0.3 0.3 ~- x E87 0 0.2 V E89- x = 2 , 20 0. IO 10 O 0.1 cU q2 4(GeV/c)2 q~= 4(GeV/c) (3 02 W=3 GeV W=2 GeV 15 &C R=O.I8+O.I8 R =0.23t 0.23-: (b) x = 0.35 0cU x =0.35 I I 0.3 Lt LLI 5 0 40 10 0.2 II x =0.5 CU CC 0.1 QCD+ TM -- QCD l 0 I iil 30 0 (c) x = 0.2 5 10 0.3 q = I.5(GeV/c) W=3 W=3 GeV GeV Q 2 [(Gey/c) R =0.20+-O. I4 R = 0.37-'0,20 0 0.2—5 10 15 20 25 30 ] I 20 W~ (Gev~) 0.5 I.O 0 I.O 0.1 FIG. 2. The values of F2 extracted from our data at x 0.2,

I I vs Q2. point-to- R=0.20+/-0.14 R=0.32+/-0.2 FIG. 4. The0 kinematic plane in q and W is shown 0.35, and 0.5 are plotted Only statistical and FIG. 3. Typical examples illustrating the separate de- along with lines 1of;.I(„'onstant5 ~,10the scaling50 variable point systematic errors are shown. There is an additional nor- The line bounds all data mea- termination of o& and oz. The straight solid lines are 2M& p/q . hdavy Q [(Gey/c) ] points malization error of ~ 3%. The QCD structure function best fits to Eq. (1). The dashed lines indicate the one- sured at 6', 10', 18', 26', and 34'. The region marked (dashed curve), and the prediction for F2 including the target- standard-deviation Phys.Revvalues of the. D5fits. (1972)The assumption 528 of FIG.. "Separation1. The valuesRegion"of Rincludesat (a) xall 0.points5, (b)wherex =0.data35, andat (c) mass effects (solid curve) are also plotted. Data from SLAC and im- three or morePhys.Rev.Lett.angles exist. 61Various (1988)values 1061of ~ are in- one-photon exchange made in calculating oz oz x 0.2 are plotted vs Q, with statistical and systematic errors experiment E87 are also plotted at x 0.5 for comparison. plies that linear fits should be satisfactory. For the two dicated with co =~ coinciding with the q2 =0 abscissa and added in quadrature. Predictions from perturbative QCD upper graphs measured data exist at each angle. For the ~ =1 corresponding to elastic scattering F2 =0.88 GeV2).18 (quark-gluon interaction effects, the dashed curve), QCD with two lower graphs the data were interpolated. Effects of Region I indicates the region where the data are consis- target-mass effects (solid curve), Ekelin and Fredriksson di- tent with scaling in cu = Region II indicates the over-all systematic errors are not included. 2M~&/q . scaling violations in F2 (see Fig. 2) are also not de- quark extensionmodel (dot-dashedof the scalingcurve),regionandifearlierthe datadataare fromplottedexperi- well these interaction effects ments againstE87 andcu' =1+E89W2/q2.at SLAC,The rangesand A,CDHSB, and (v-Fe),C in the and scribed very by QCD alone. which include measurements of 8, confirm the BCDMSvariable(p-C//H)~ indicatedat CERNin theare figurealso plotted.are discussed in the QCD calculations are not too sensitive to the value of A scaling behavior of vW, as a function of ~ for text. used (A 200 MeV). Target-mass effects introduce q' & 1 (GeV/c)' as indicated by the earlier 6' and terms proportional to M /Q and give large contribu- 10' data. Though these studies cover an extensive and 5 show a clear falloff tions and small and for Our andresults(b) inat thex =0.kinematic2, 0.35, region0. covered by our to R Fz at Q large x. Our data kinematic region, we would, however, give greater of Rmeasurements,with increasing q'g and. Thev mayagreementnot be largewith ainconstantthe R and Fz are in good agreement (X /NDF =10/10) with emphasis to conclusions based on data from the valuesenseof R of=0.the2 isBjorkenpoor (Zlimit/NnFand=34/10).parametrizationThe high-Qin theory when target-mass effects by Georgi and Politzer separation region in Fig. 4 where the analysis re- resultstermsfromof thesomeCERN-Dortmund-Heidelberg-Saclay'variable other than ~ might have (GP) are added to perturbative QCD. The variation of lies on interpolations between measured values of (CDHS)physicalandsignificance.Bologna-CERN-Dubna-Munich-Saclay' R with x in the range 0.2» x ~0.5 is weak, in agree- R. (BCDMS)The questioncollaborationsnaturally fora,risesv-Fewhetherand p-C/Hthe otherscat- ment with these predictions. However, the controversy As a byproduct of studying the behavior of the tering,structurerespectively,function,are W„alsoalso plotted.exhibitsThesescalingresultsbe-rein- about possible inconsistencies ' in the original GP large-angle data at small ~ we discovered that for forcehavior.the conclusionA study thatof ourR decreasesresults showswith that,increasingwithinQ . target-mass-effect calculations is yet to be resolved the whole range of ~ the scaling region is extended ' Our errors,results atW,allscalesshowas a onlyfunctiona weakof &ux(ordependencee') over in unambiguously. The QCD interactions and target- from W= 2.6 GeV down to W= 1.8 GeV (which is Q the rangethe same0.2~kinematicx ~ 0.5. range as vW, . mass and higher-twist effects can be thought of as giving approaching a resonance bump) if a new variable Figurevalues 6 showsobtained2M~W, andfromvW,theasfitsfunctionsto vsofeeare transverse momentum In naive co'—= &a+a/q' is used instead of ~. The constant a The of F2 a/I (kT) to the quarks. the for W~ 2.6 GeV, and Fig. 7 shows these quantities determined to be 0.95 +0.07 (GeV/c)' fitting plotted against Q at various x in Fig. 2. These results parton model R 4(kT)/Q, and the data indicate a (kr2) was by as functions of co' for W~ 1.8 GeV. The data pre- the data with W& 1.8 GeV and q' & 1 (GeV/c)'. ' The are preliminary because studies of the absolute normali- ~alue of 0.10 (GeV/c) (Z /NnF =18/10). sented in both figures are for q' & 1 (GeV/c)' and quoted error on a was derived from the covari- zation (presently known to ~ 3%) are not complete. A Several authors have speculated that two of the use 8 = 0.18 in the evaluation of the points. The ance matrix of the fit and does not include system- weak Q dependence is evident. Earlier SLAC data2 are valence quarks in a nucleon may form a tightly bound observed scaling behavior in e and e' is impres- or contribution from the uncertain- shown for comparison. Note that these early data were spin-0 diquark. The spin-0 diquarks are predicted to atic errors any sive for both structure functions over a large ki- in A. The statistical significance of a being dif- radiatively corrected with use of the peaking approxima- give large contributions to R at large x and low . Our ty nematic region. Q ferent from zero is greatly reduced in a fit to the tion calculations. Detailed studies of F2 from all SLAC highest x (=0.5) results for R do not favor this possibili- Since W, and W, of Eg. (3) are related by data for W&2.6 GeV, implying that functions of experiments with our improved radiative corrections and ty. QCD with target-mass effects appears to account for either ~ or e' give satisfactory statistical fits to parametrization2M' of R will be reported in a future com- all the Q dependence of R, and therefore speculations the data in this kinematic range. In what follows munication.vW2 that dynamical higher-twist contributions to R (for we use a =&~'=0.88 (GeV/c)', which gives ~' = ~ In perturbative QCD (to the 2M~order a, ) hard gluon x ~ 0.5) are large are not supported by our data. + M~'/q' = 1+W'/q'. Regarding u&' we note that (a) bremsstrahlung from quarks1 and photon-gluon interac-(4) An empirical parametrization of the perturbative u' 1+8 (d tg (d v in- the Bjorken limit becomes equal to e so the tion effects yield contributions to the lepton-nucleon QCD calculations of R, with an additional 1/g term two variables have the same asymptotic properties, it can be seen that scaling in W, accompanies scal- scattering cross section. The leading Q dependence of fitted to our data, is given by the structure functions is in a„and is therefore logarith- a(1 —x)~ y(I —x) mic in g . The new R data (see Fig. 1) are not in agree- ( z) + ment with these calculations' (X /NoF =98/10). The ln(g'/A') g'

1063 QPM and QCD The quark parton model is the asymptotic limit of the real theory of strong interactions à QCD • In reality – structure functions (and parton distributions) are not Q2 independent – even for large values of Q2 • Struck quark radiates hard gluons – leads to logarithmic Q2 dependence Q2 evolution can be described by DGLAP equations: Non singlet quark distributions: qNS = q q¯ Splitting function – probability for quark to radiate gluon dqNS(x, Q2) 1 dy x = s qNS(y, Q2)P ( ) d ln Q2 2 y qq y x S Gluon quark singlet distributions: q = qi +¯qi S 2 1 i S x 2 d q (x, Q ) s dz Pqq(z) Nf PqG(z) q ( z ,Q ) = x d ln Q2 G(x, Q2) 2 z PGq(z) PGG(z) G( ,Q2) x z DGLAP =Dokshitzer–Gribov–Lipatov–Altarelli–Parisi 19 2 Q Dependence of F2

2 • Overall, Q dependence of F2 well-described by NLO DGLAP evolution

• Note that near x=0.1-0.2, the Q2 dependence is rather small à early SLAC measurements

• At small x, Q2 dependence becomes quite large

20 Q2 Dependence 19.of Structure PDFs functions 13

1 1 2 NNPDF2.3 (NNLO) g/10 2 10 GeV 0.9 0.9 10,000 GeV xf(x,µ2=10 GeV2) xf(x,µ2=104 GeV2) s 0.8 0.8 g/10 0.7 0.7 d 0.6 0.6 u v c 0.5 0.5 uv 0.4 0.4 u dv 0.3 0.3 b d s v 0.2 0.2 d u 0.1 0.1 c 0 0 -3 -3 10 10-2 10-1 1 10 10-2 10-1 1 x x Figure 19.4: The bands are x times the unpolarized parton distributions f(x) (where K.A.f Olive= uv,d etv al., u, (d,Particle s s,¯ Data c =¯c, Group), b = ¯b, gChin.) obtained Phys. inC, NNLO38, 090001 NNPDF2.3 (2014). global 2≃ 2 2 4 2 2 analysis [45] at scales µ =10GeV and µ =10 GeV ,withαs(MZ)=0.118. DGLAP evolutionThe analogous allows results us obtained to use inmeasurements the NNLO MSTW at analysis an arbitrary [43]canbefoundin scale and evolve them to anotherRef. [62]. à PDFs not scale independent γ γ γ γ where we have used F2 =2xFT + FL,nottobeconfusedwithF2 of Sec. 19.2. Complete formulae are given, for example, in the comprehensive reviewofRef.80. γ 2 21 The hadronic photon structure function, F2 ,evolveswithincreasingQ from the ‘hadron-like’ behavior, calculable via the vector-meson-dominance model, to the dominating ‘point-like’ behaviour, calculable in perturbative QCD. Due to the point-like γ 2 coupling, the logarithmic evolution of F2 with Q has a positive slope for all values of x, see Fig. 19.15. The ‘loss’ of quarks at large x due to gluon radiation is over-compensated by the ‘creation’ of quarks via the point-like γ qq¯ coupling. The logarithmic evolution was ﬁrst predicted in the quark–parton model→ (γ∗γ qq¯)[81,82],andtheninQCDin the limit of large Q2 [83]. The evolution is now known→ to NLO [84–86]. The NLO data analyses to determine the parton densities of the photon can be found in [87–89].

19.5. Diffractive DIS (DDIS) Some 10% of DIS events are diffractive, γ∗p X + p, in which the slightly deflected proton and the cluster X of outgoing hadrons→ are well-separated in rapidity. Besides 2 x and Q , two extra variables are needed to describe a DDIS event: the fraction xIP of the proton’s momentum transferred across the rapidity gapandt,thesquareofthe 4-momentum transfer of the proton. The DDIS data [90,91] are usually analyzed using D two levels of factorization. First, the diffractive structurefunctionF2 satisfies collinear

August 21, 2014 13:18 Experimental Challenges - Kinematics

Large x typically pursued at fixed JLab 6 GeV phase space target machines à Can reach large Q2, but need large luminosities 19. Structure functions 11 à Large energies required to avoid resonance region at largest x

Colliders excellent for accessing smallest values of x à As x shrinks, ever increasing energies needed to achieve even modest Q2 range

Figure 19.3: Kinematic domains in x and Q2 probed by fixed-target and collider experiments. Some of the final states accessible at the LHC are indicated in the appropriate regions, where y is the rapidity. The incoming partons have ±y x1,2 =(M/14 TeV)e with Q = M where M is the mass of the state shown in blue in the figure. For example, exclusive J/ψ production at high y at the LHC may probe the gluon PDF down to x 10−5. | | ∼ sections) calculated with the full mQ dependence, with the all-order resummation of contributions via DGLAP evolution in which the heavy quarks are treated as massless. The ABM analysis uses a FFNS where only the three light (massless) quarks enter the evolution, while the heavy quarks enter the partonic cross sections with their full mQ dependence; transition matrix elements are computed, following [53], which provide the boundary conditions between nf and nf +1 PDFs. The GM-VFNS and FFNS approaches 2 2 yield different results: in particular αs(MZ)andalarge-x gluon PDF at large Q are both significantly smaller in the FFNS. It has been argued [36,37,60] that the difference

August 21, 2014 13:18 e e’ e e’ Experimentale Challengese’ - Radiative Corrections a) Born b) Vacuum c) Vertex Polarization Correction e e’ e e’ Radiative corrections pose e e’ additionale e’ experimentale e’ challenge for the analysis of DIS data e e’

a) Born b) Vacuum c) Vertex à Reliable RC requires Polarization Correction knowledged) Bremsstrahlung of the process ofe) Multi−Photon interest over a wide kinematicsEmission e e’ e e’ region since events can “radiate e e’ in” to the acceptance

d) Bremsstrahlung e) Multi−Photon Emission

Other processes (elastic scattering) p X can also contribute to experimental A A A A−1 A yield a) Elastic b) Quasi−Elastic c) Inelastic

Figures from V. Tvaskis (PhD Thesis) 23 p X A A A A−1 A a) Elastic b) Quasi−Elastic c) Inelastic Radiative Corrections

Radiative effects can be broken 1.2 into 2 contributions: Deuterium E = 5.648 GeV 1 Beam o 1. Radiation in field of nucleus θ = 10.566

b/sr/GeV) 0.8 σMeasured

from which electron scatters µ σ

( Born à Internal / σ 0.6 el 2. Radiation if field of other σinel /dE σqel nuclei à External Ω

/d 0.4 σ

External typically only an issue d 0.2 for fixed target experiments 2 (Model) δα σBorn 0 0 1 2 3 4 5 Cross sections must be extracted iteratively – updating the “Born E/ (GeV) model” at every iteration

à In the end, the need to avoid large radiative corrections can Typical requirement: limit kinematic reach y<0.85

Figures from V. Tvaskis (PhD Thesis) 24 Polarized DIS

In addition to unpolarized structure functions, polarized targets and beams are sensitive to polarized structure functions: g1(x) and g2(x)

Longitudinally polarized target, longitudinally polarized beam: 2 2 d 4 E 2 Q 2 ( )= (E + E cos )g (x, Q ) g (x, Q ) ddE MQ2 E 1 2

Transversely polarized target, longitudinally polarized beam: 2 2 d 4 sin E 2 2 ( )= 2 2 g1(x, Q )+2Eg2(x, Q ) ddE MQ E

25 g1 in Quark Parton Model

In QPM, g1 is weighted sum of polarized quark distributions

1 2 1 2 F (x)= e q (x) g1(x)= ei qi(x) 1 2 i i 2 i i Polarized Unpolarized

q(x)=q(x) q(x)

parallel to antiparallel target spin

26 19. Structure functions 21 NOTE: THE FIGURES IN THIS SECTION ARE INTENDED TO SHOW THE REPRESENTATIVE DATA. THEY ARE NOT MEANT TO BE COMPLETE COMPILATIONS OF ALL THE WORLD’S RELIABLE DATA. World data* on F2 and g1 x i ) * 2 2 7 10 H1+ZEUS

(x,Q BCDMS 2

F E665 6 NMC 10 SLAC

10 5

10 4

10 3

10 2

-1 10

-2 10

-3 10 -1 2 3 4 5 6 10 1 10 10 10 10 10 10 Q2 (GeV2) p Figure 19.8: The proton structure function F2 measured in electromagnetic scattering of electrons and positrons on protons (collider experiments H1 and ZEUS for Q2 ≥ 2GeV2), in the kinematic domain of the HERA data (see Fig. 19.10 for data at smaller x and Q2), and for electrons (SLAC) and muons (BCDMS,Great increase in amount of data on g1 in E665, NMC) on a fixed target. Statistical and systematic errorsaddedinquadratureareshown.Thedata are plotted as a function of Q2 in bins of fixed x.Somepointshavebeenslightlyoffset in Q2 for clarity.recent years – sill not even close to F2 The*COMPASS H1+ZEUS combined binning data in x is usedon in thisg plot; missing all other data are rebinned to the x values of p 1 ix 27 these data. For the purpose of plotting, F2 has been multiplied by 2 ,whereix is the number of the x bin, ranging from ix =1(x =0.85) to ix =24(x =0.00005). References: H1 and ZEUS—F.D. Aaron et al., JHEP 1001,109(2010);BCDMS—A.C. Benvenuti et al.,Phys.Lett.B223,485(1989)(asgivenin[78]); E665—M.R. Adams et al.,Phys.Rev.D54,3006(1996);NMC—M. Arneodo et al.,Nucl.Phys.B483,3 (1997); SLAC—L.W. Whitlow et al.,Phys.Lett.B282,475(1992). Quark contribution to spin of the nucleon19. Structure functions 27

Particle Data Group - 2014 p

Using quark parton model, g 1 0.08 1 EMC

x g E142 of proton and neutron, can 0.06 E143 SMC HERMES extract quark contribution to 0.04 E154 E155 JLab E99-117 nucleon spin 0.02 COMPASS CLAS 1 0 d q = dxq(x) -0.021

x g 0.04 0 0.02 EMC (Phys. Lett. B 206 (2): 364) estimated quark 0 n

contribution to spin of proton -0.021 to be (assuming Δs =0 ) x g 0.02

ΔΣ=0.14 ± 0.09 (stat) +/- 0.21 (sys) 0 Spin Crisis! -0.02 -4 -3 -2 -1 10 10 10 10 1 x More recent HERMES result (Phys. Rev. D 75 (2007) 012007) Figure 19.14: The spin-dependent structure function xg1(x)oftheproton,deuteron,andneutron(from 3He target) measured in deep inelastic scattering of polarized electrons/positrons: E142 (Q2 ∼ 0.3 − 10 GeV2), E143 (Q2 ∼ 0.3 − 10 GeV2), E154 (Q2 ∼ 1 − 17 GeV2), E155 (Q2 ∼ 1 − 40 GeV2), JLab E99-117 ΔΣ=0.330 ± 0.011((Q2 ∼theo.2.71 − 4.83) GeV± 20.025(exp.)), HERMES (Q2 ∼ 0.18 −±20 0.028( GeV2), CLASevol (Q2 ∼ .)1 − 5GeV2)andmuons:EMC (Q2 ∼ 1.5 − 100 GeV2), SMC (Q2 ∼ 0.01 − 100 GeV2), COMPASS (Q2 ∼ 0.001 − 100 GeV2), shown28 at the measured Q2 (except for EMC data given at Q2 =10.7GeV2 and E155 data given at Q2 =5 GeV2). Note n d p that g1 (x)mayalsobeextractedbytakingthediﬀerence between g1(x)andg1(x), but these values have been omitted in the bottom plot for clarity. Statistical and systematic errors added in quadrature are shown. References: EMC—J. Ashman et al.,Nucl.Phys.B328,1(1989);E142—P.L. Anthony et al.,Phys.Rev. D54,6620(1996);E143—K. Abe et al.,Phys.Rev.D58,112003(1998);SMC—B. Adeva et al.,Phys.Rev. D58,112001(1998),B.Adevaet al.,Phys.Rev.D60,072004(1999)andErratum-Phys.Rev.D62,079902 (2000); HERMES—A. Airapetian et al.,Phys.Rev.D75,012007(2007)andK.Ackerstaﬀ et al.,Phys.Lett. B404,383(1997);E154—K. Abe et al.,Phys.Rev.Lett.79,26(1997);E155—P.L. Anthony et al.,Phys. Lett. B463,339(1999)andP.L.Anthonyet al.,Phys.Lett.B493,19(2000);Jlab-E99-117—X. Zheng et al.,Phys.Rev.C70,065207(2004);COMPASS—V.Yu. Alexakhin et al.,Phys.Lett.B647,8(2007), E.S. Ageev et al.,Phys.Lett.B647,330(2007),andM.G.Alekseevet al.,Phys.Lett.B690,466(2010); CLAS—K.V. Dharmawardane et al.,Phys.Lett.B641,11(2006)(whichalsoincludesresonanceregiondata not shown on this plot). g2 Polarized Structure Function g2 does not have a simple interpretation in the Quark Parton Model

à Can be written as a sum of 2 terms 2 WW 2 2 g2(x, Q )=g2 (x, Q )+¯g2(x, Q )

Twist-2 term (Wandzura and Wilczek) 1 dy gWW(x, Q2)= g (x, Q2)+ g (x, Q2) 2 1 1 y x Twist-3 + Twist-2 1 2 mq 2 2 dy g¯2(x, Q )= hT (y, Q )+(y, Q ) x y M y Quark gluon correlations 29 g2 Spin Structure Function New measurements from JLAB Proton – Hall C 3He (neutron) – Hall A

Whit Armstrong Solid curves = WW Phys.Rev.Lett. 113 (2014) 2, 022002 g2 30 Second moment of g2 d2 moment directly sensitive to “interesting” part of g2 1 1 2 2 d2 = dxx [3g2(x)+2g1(x)] = 3 dxx g¯2(x) 0 0

Neutron Proton – projected uncertainties

31 DIS at Large x

• At large x, cross sections are small à low rates – High luminosity required – historically the purview of fixed-target facilities • Moderate energies available at high luminosity, fixed target accelerators implies moderate Q2 measurements at sometimes rather low W – In this kinematic regime, so-called target mass corrections can be important • Additional complication comes about in extraction of neutron cross sections and structure functions – Nuclear effects

32 Target Mass Corrections

Q2 For massless quarks and targets (or Q2à∞) Bjorken scaling x = 2p q variable is the light-cone momentum fraction of target carried · by parton 2x Finite Q2, light-cone momentum fraction = given by Nachtmann variable 1+ 1+4x2M 2/Q2 A prescription for target mass corrections can be derived in terms of the Operator Product Expansion and moments of the structure functions à Result is “master equation” x2 6M 2x3 12M 4x4 F TMC(x, Q2)= F (0)(,Q2)+ h (,Q2)+ g (,Q2) 2 2r3 2 Q2r4 2 Q4r5 2

(0) Weighted integrals over F2 33 Target Mass Corrections J. Phys. G: Nucl. Part. Phys. 35 (2008) 053101 Topical Review J. Phys. G: Nucl. Part. Phys. 35 (2008) 053101 Topical Review

2 Q 2 (GeV ) 15 25 125 2.0 F2

1.8 TMC (0) F22 / F 1.6

1.4

1.2

1.0 0 0.2 0.4 0.6 0.8 1.0 X

2 Q 2 (GeV ) 15 25 125 2.0 TMC (0) F / F 1.8 33

1.6

1.4 F3 1.2

1.0

0 0.2 0.4 0.6 0.8 1.0 X

Figure 7. Ratio of the F2 and F3 structure functions with and without target mass corrections (F TMC/F (0),i 2, 3) versus x for Q2 1, 5, 25, 125 GeV2. Target Mass Effectsi ofi target= mass={ } 2 2 2 2 2 TMC 2 x (0) 6µx ξ h2(ξ) 12µ x ξ g2(ξ) correctionsF2 (x, Q ) canF be2 (ξ) quite1+ large+ – , Corrected = ξ 2r3 r F (0)(ξ) r2 F (0)(ξ) 2 ! 2 2 " highly2 2 Q dependent(0) with µ M /Q .ThestructurefunctionF2 appearing in the integrals in equations (18) and (20=)isadecreasingfunctionofx or ξ (see e.g. ﬁgure 10 below). Consequently, (0) (0) F2 can be evaluated at the lower integral limit, giving h2(ξ)< F2 (ξ) ξ (1 ξ) and (0) − g2(ξ)

21 Neutron Structure Functions

• Structure function information from the neutron is crucial for understanding the quark structure of nucleons n F2 1+4dv(x)/uv(x) p = F2 4+dv(x)/uv(x) • No free neutron targets – typically deuterium targets are used and the very simple approximation is used:

p D n F2 = F2 + F2

• At low x (x<0.3), nuclear effects are small – this approximation introduces minimal error • At larger x, this assumption becomes increasingly incorrect

35 CJ12 PDFs

Nuclear effects in deuteron lead to significant uncertainties in quark PDFs at large x

à This has been studied in some depth by the CTEQ-JLAB collaboration

up down

J. F. Owens, A. Accardi and W. Melnitchouk, Phys. Rev. D 87, 094012 (2013)

36 Extraction of Neutron Structure Functions

Early extraction of the n/p ratio tried to incorporate a model including corrections for Fermi smearing

For example, see: Phys.Rev. D20 (1979) 1471-1552

Bodek et al., Phys. Rev. Lett. 30, 1087 (1973) E. M. Riordan et al., Phys. Rev. Lett. 33, 561 (1974) J. S. Poucher et al., Phys. Rev. Lett. 32, 118 (1974). n p Figure 1: SLAC dataFigure on the nucleonfrom FJLab2 /F2 ratioproposal extracted E12-10-103 from proton and deuteron DIS measurements [11] with a Fermi-smearing model [12]. 37 change in the nuclear medium, at least for small and medium values of x. Measurements by the European Muon Collaboration (EMC) [14] over a large-x range at CERN invalidated Fe this view by observing a large x dependence for the ratio of the iron F2 per nucleon over d the deuteron F2 . This effect, the EMC effect, was confirmed in a subsequent analysis of old SLAC data [15], and an extensive study, using different nuclear targets, provided the exact x behavior of the effect versus the mass number A of nuclei [16]. The SLAC experimental data are shown in Figure 2 and indeed indicate a significant x and A dependence for the A d 4 A inelastic cross section ratio (σ /σ )is for several nuclei from He to Au. The σ and deuteron σd cross sections are per nucleon and the ratio has been adjusted for an isoscalar nucleus of mass number A. This cross section ratio is equal to the equivalent isoscalar structure A d function ratio (F2 /F2 )is.

6 n p Extraction of Neutron Structure larger F2 /F2 values as compared with the Fermi-motion only extracted values. As can be seen in Figure 3, the diﬀerence at x =0.85 can be up to 50%. ∼ Functions

Nuclear density model (scales like density dependent EMC effect)

Binding, offshell effects Later extractions attempted to include Fermi smearing nuclear effects

à Large variation in n/p ratio as xà 1!

n p Bodek et al., Phys. Rev. Lett. 30, 1087 (1973) Figure 3: The F2Figure/F2 ratio from extracted JLab fromproposal proton E12-10-103 and deuteron DIS measurements [11] with a) E. M. Riordan et al., Phys. Rev. Lett. 33, 561 (1974) a Fermi-smearing model (Bodek et al. [12]), b) a covariant model that includes bindingJ. S. and Poucher off- et al., Phys. Rev. Lett. 32, 118 (1974). shell effects (Melnitchouk and Thomas [34]), and c) the “nuclear density model” [39] that also 38 incorporates binding and off-shell effects (Whitlow et al. [36]).

Whitlow et al. [36] incorporated binding eﬀects using the “nuclear density model” of Frankfurt and Strikman [39]. In this model, the EMC eﬀect for the deuteron scales with nuclear density as for heavy nuclei:

d A F2 ρd F2 p =1+ 1 , (13) F + F n ρ ρ ! F d − " 2 2 A − d 2 A where ρd is the charge density of the deuterium nucleus, and ρA and F2 refer to a heavy n p nucleus with atomic mass number A. This model predicts for the ratio F2 /F2 values that

11 BONUS – d/u via Spectator Tagging BONUS = Barely Offshell Neutron Scattering Minimize nuclear effects by measuring DIS cross e section from neutrons with low Fermi momentum à Tag low momentum “spectator” protons at n backward angles; struck neutron almost on-shell p

Phys.Rev. C89 (2014) 045206, 39 straight multiples of 2.2 GeV single-pass machine conﬁgurations). The required beam time for the R measurements is 270 hours for the canonical beam current of 25 µA. Assuming an additional 10% of running with the polarity of the magnets of the spectrometers reversed (“positron running”, to measure contribution to the electron scattering rate from charge sym- metric processes in the target), the total beam time for the experiment will be 954 hours. Future MeasurementsAn additional i)of 12 hours willd/u be required for three angle-setting changes and surveys of the d / u 3 3 1 E12-10-103: H/ He 0.9 E12-06-113 – BONUS12 0.8

0.7 CHAPTER 2. MOTIVATION 22 0.6 SU(6) ➘ 0.5 for the hydrogen data. We estimate that we can obtain a 2% error on d/u over a range of x bins, with the highest having an average x =0.7, in 90 days of running. The achievable 0.4 precision is illustrated in Figure 2.9. 0.3 d/u = 1/5 0.2 ➘

0.1 d/u = 0 Figure 15: Projected inelastic data (W 2.0 GeV, except for the highest-x point for which W = ➘ ≥ 0 n p 3 3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.75 GeV) for the F2 /F2 structure function ratio from the proposed H/ He JLab experiment x* with a 11 GeV electron beam. The error bars include point-to-point statistical, experimental and This proposal, 90 days theoretical(follows uncertainties, MRST-2004) and an overall normalization uncertainty added in quadrature. The shaded Figure 38: Ratio of d/u quarks versus x⋆ converted from the data points shown in Fig. 37. band indicates the present uncertainty due mainly to possible binding eﬀects in the deuteron. The upper and lower curves represent the systematic uncertainties due to the two systematic error curvesJLAB-12 as in Fig. 37. GeV The shaded will band allow indicates theextraction present uncertainty of in extracting the d/u d/uratio from using the existing a variety data. of techniques 33

d p uncertainity1. forSpectator the ratio F2 /F2 due tagging to the RTPC acceptance(BONUS) will be reduced. The data we plan to collect will also allow for quark–hadron duality studies in the neutron resonance2. region PVDIS with very good precision. Measurements in the resonance region where carried out by experiment E03-012 and are3 being3 analyzed (seesection6). E12-10-007: PVDIS Although3. theMirror neutron resonance nuclei structure H/ functionHe and deep inelastic structure function data and parameterizations will obviously diﬀer from the proton, we believe this is a good example of the potential quality of the neutron data attainable with BoNuS. This experiment will extend the Q2 range and add statistics to the existing BoNuS measurement for W<2 40 n GeV as well as provide a more precise DIS structure function F2 to compare to. Finally, we will also be able to contribute to the world’s datasetonelasticneutronform Figure 2.9: Uncertainties2 in d/u together with error bars corresponding to results from factors. The expected statistical and systematic errors foreachmeasuredQ at W = Mn are listed in Table 1. The systematic errors will be of orderAPV 6%.for The a present hydrogen data target.from E94-017 extend to Q2 =5GeV2/c2 with a statistical error of about 0.043 in the highest

62 2.5.2 Induced Nuclear Isospin Violation The ratio of the structure functions between complex nuclei and deuterium

4u (x)+d (x) R = A A (2.11) EMC 4u(x)+d(x)

where u(d)A is the normalized PDF for quarks in the nucleus, have been observed to depend on x. For parity violation, the PDFs are weighted di↵erently:

1.16u (x)+d (x) RZ = A A (2.12) EMC 1.16u(x)+d(x)

The quantity that is practical to measure is the super-ratio

A Z APV REMC RSuper = D = Z (2.13) APV REMC Transition to the perturbative regime

• DIS often viewed as simply a “tool” to gain access to parton distributions in the perturbative regime • Understanding the transition to this regime is also of key interest, and one of the reasons JLab was built

CEBAF’s original mission statement Key Mission and Principal Focus (1987): The study of the largely unexplored transition between the nucleon-meson and the quark-gluon descriptions of nuclear matter.

41 The Strong Force at Long and Short Distances

Confinement Constituent Quarks Asymptotically Protons & Neutrons Free Quarks Q < Λ Q > Λ Q >> Λ α(Q) large αs(Q) > 1 αs(Q) small

One parameter, ΛQCD, ~ Mass Scale or Inverse Distance Scale q where αs(Q) = infinity

g “Separates” Confinement q and Perturbative Regions

Mass and Radius of the Proton are (almost) completely governed by

ΛQCD≈0.213 GeV

Quark Model Quark Parton Model

42 The Quark Parton Model is well defined in the limit of large Q2 and large υ (or W2). Empirically, deep inelastic scattering (or quark parton model) descriptions seem to work well down to modest energy scales: Q2 ~ 1 GeV2, W2 ~ 4 GeV2.

Why is the Quark-Hadron Transition in QCD so smooth, and occurring at such low energy scales?

The underlying reason is the Quark-Hadron Duality phenomenon.

43 Quark Hadron Duality At high enough energy:

Hadronic Cross Sections Perturbative averaged over appropriate Quark-Gluon Theory energy range

= Σhadrons Σquarks+gluons Can use either set of complete basis states to describe physical phenomena

In different energy regimes one description is more “economical” than the other: how can we understand the transition between these 2 regimes?

44 Duality in the F2 Structure Function

First observed ~1970 by Bloom and Gilman at SLAC by comparing resonance production data with

deep inelastic scattering data 2 F • Integrated F2 strength in Nucleon Resonance region equals strength under scaling curve. Integrated strength (over all ω’) is Q2 = 0.5 2 called Bloom-Gilman integral Q = 0.9

Shortcomings: • Only a single scaling curve and no 2 Q evolution (Theory inadequate in 2 pre-QCD era) F

• No σL/σT separation à F2 data depend on assumption of R = σL/σT 2 2 • Only moderate statistics Q = 1.7 Q = 2.4

ω’ = 1+W2/Q2 45 Quark-Hadron Duality

I. Niculescu et al., PRL85:1182 (2000)

• In the late 90s, a large body of data in the resonance region was acquired at JLab

• High statistics, large phase space allowed the examination of duality with high precision

• Most interesting – duality was observed to hold even when looking at individual resonances above Q2=1-2 GeV2!

46 Duality in Separated Structure Functions

The resonance region is, on average, well described by NNLO QCD fits for separated structure functions as well.

This implies that Higher-Twist (FSI) 2 contributions cancel, and are on average small. “Quark-Hadron Duality” F 1 The result is a smooth transition from Quark Model Excitations to a Parton Model description, or a smooth quark-hadron transition. 2xF L F This explains the success of the parton model at relatively low W2 (=4 GeV2) and Q2 (=1 GeV2). JLab, Hall C: E94-110 47 Duality Summary

• In addition to unpolarized proton structure functions, duality has been observed to manifest for: – Neutron structure functions p n – Asymmetries (A 1 and A 1) – Semi-inclusive DIS (SIDIS) • Other duality-like manifestations – Approach to scaling of charged pion form-factor – Scaling of deep-exclusive reactions • The dual nature of these reactions (globally) is not so surprising – its required • But why does it work so well locally? – Experimentally, we may have done as much as we can – need new theoretical insight to understand the detailed behavior

48 Summary – Part 1

• Deep Inelastic Scattering is a powerful tool for probing the quark-gluon structure of nucleons • DIS gave us first evidence that the partonic picture of the nucleon was accurate • Since then, unpolarized and polarized DIS has provided a huge body of data that has constrained PDFs – Polarized data not yet achieved same kinematic reach and coverage as unpolarized • While DIS itself is useful – understanding the transition from the non-perturbative to the perturbative regime is a key issue • What about the 3D structure of nucleons?

49 EXTRA

50 Physics Motivations Hadron Physics Quark Flavor Dependent Eﬀects on Proton

! Measurement of d(x)/u(x) ratio for the proton u(x)+0.912d(x) ap(x) at high x 1 ∼ u(x)+0.25d(x) ! Acleanmeasurementfreefromanynuclearcorrections ! Uncertainties of set of PVDIS measurements are shown in the plot (red dots) ! Provides high precision measurements in range of x

Projected 12 GeV d/u Extractions

1 CJ12 - PDF + nucl uncert. BigBite 3H/ 3He DIS CLAS12 BoNuS 0.8 CLAS12 BoNuS, relaxed cuts SoLID PVDIS 0.6 SU(6) d/u 0.4 DSE

0.2 pQCD BoNuS sys. uncert. Broken SU(6) 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x

th Rakitha S. Beminiwattha DIS 2015 April 29 ,2015 14/2051