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(tr "/tr ),, d(x)[1 p(x}p(A)]. The average nuclearwasgivendensitybyp( A ) 3 & /4 &„&, 5(r )/3. The quantity (r ) is the rms electronscattering radius of the nucleus [48]. The values of p( & )J. GOMEZnucleons/fm ) used in the fits were 0.024 forof al.(in units etA-Dependence of EMC Effect4366IIIIIIIIIIIIIlllllx 0.22z Ab1.0 2}. TheIIIIIIIIvalues(1.Inparamempirical parametrizationIIIIII0.60(b)1.00.8—497. 237x 1013.129x 775. 767x —205. 872x0.600(b) 145.291x—1208. 393x0 0.90The1.0 fit values of C are close to unity everywheregood empirical parametrization0.9—is0.9 lnC(x} 0.017 0.018 lnx 0. 005(lnxIIIIIIIIIIIII10Nuclear Weight AIII100thistracteandmodeThby eof a(x) and C(x) are listed heavyin TIX, and the former is plotted in Fig. 19. The y Beperax 0.220(a)haveisshownin Fig. 19Alsoisgree of freedom(A1.0 a(x) —0. 070 2. 189x —24. 667xo 0.9Ft/FanZOU)These parametrizations also characterize the NMCon0.8He, C, andvalid in the ra0.05Ca [6]0.and10 are 0.only150.01(x &0. 88.NuclearDensityThe cross-section ratios can also be examinedFIG. function20. Ratiosof(cr"/crversus nuclearat and(a) Table2indensitynuclearFig.3)- densityFIG. 18. Ratios (o "/0");, versus atomic weight A at x(a) 0.pe2asRlines 5⟨r⟩/3the20ρ 3A/4πR220Someand (b) x 0.600.FIThesolidparepresentedescribed below, predict that the probabx 0.220 and (b) x 0.600. The solid lines are a parametriza-rametrization models,(cr"/od) d( )[1xP( )p(xA)]. The errorsaveragof nucleons systematic,within thenucleus(whicoverlap point-to-pointty of statistical,tion of the data in terms of (cr "/cr );, C(x) A '"'. The errorsshown includetarget(12).and r2 RMSscatteringradiusto thenuclearis relatedEtoelectronshown include statistical, point-to-point systematic, and targetto-target proportionalerrors.The overallfunctiuncertaintydensity)due to thedeuteriumratiosTheat the Qs-averaged(rr "1'o );,shownwto-target errors. The overall uncertainty due to the deuteriumincluded onlytarget is efFect.A 2 point.is includedat the A 2targetin terms of average nuclear densitySLACE139:onlyGomezet point.al, PRD 49, 4348 (1992)parametrizedTABLE IX. Fit coeScients versus x. The coefBcients are from the fits (0 "/cr );, C(x) A '"' and(o "iver d);, d(x) [1 p(x)p( A )] are shown for both coarse and fine x bins. The fits include A 2.22

JLab E03103REMC (FA2/FD2)/(A/2)E03103 in Hall C at Jefferson Lab ran Fall 2004à Measured EMC ratios for light nuclei (3He, 4He, Be, and C)à Results consistent with previous world dataà Examined nuclear dependence a la E139New definition of “size” of theEMC effectà Slope of line fit fromx 0.35 to 0.71.1 dREMC/dx 0.280 /- 0.02810.9Normalization (1.6%)0.30.40.50.60.70.80.9xDefinition assumes shape ofthe EMC effect is universalfor nucleià Data consistent with thisassumptionà Normalization errors meanwe can only confirm this at1-1.5% level23

EMC Effect and Local Nuclear Density9Behas low average densityà Large component of structure is2α nà Most nucleons in tight, α-likeconfigurationsEMC effect driven by local ratherthan average nuclear density“Local density” is appealing inthat it makes sense intuitively –can we make this morequantitative?24

Local Density à Short Range CorrelationsWhat drives high “local” density in the nucleus?More complex calculations start from realistic NN potentialsTensor interaction and short range repulsive core lead to highmomentum tail in nuclear wave function à correlated nucleons25

Measuring Short Range CorrelationsTo measure the (relative) probability of finding a correlated pair, ratios ofheavy to light nuclei are taken at x 1 à QE scatteringIf high momentum nucleons in nuclei come from correlated pairs, ratio of A/Dshould show a plateau (assumes FSIs cancel, etc.)2N SRC3N SRC2 σA a2 (A)A σD1.4 x 2 2 nucleon correlation2.4 x 3 3 nucleon correlation26

Weinstein et al firstobserved linear correlationbetween size of EMCeffect and Short RangeCorrelation “plateau”Correlation strengthenedwith addition of Berylliumdata-dREMC/dxEMC Effect and SRC0.520.4/ ndfp04.895 / 5197Au-0.08426 0.0038695612C0.3Fe9Be4He0.230.10.0HedO. Hen et al, Phys.Rev. C85 (2012) 047301-0.10123456a2(A/d)This result provides a quantitative test of level of correlationbetween the two effects27

Origin of the EMC Effect Observation of correlation between size of EMC effectand SRCs interesting – but still does not explain theorigin of the EMC effect Seems odd that an effect observed in QE scatteringperhaps has common origin with modification of quarkdistributions Nonetheless, this correlation can be used to gleaninformation about nucleon structure28

EMC-SRC correlationused by Weinstein et al toextract the “in-mediumcorrection” byextrapolating to a2 0-dREMC/dxEMC Effect in Deuteron from SRCs0.520.4/ ndfp04.895 / 5IMC à 5612C0.3Fe9Be4He0.2AnAu-0.08426 0.00386930.12A1970.0HedO. Hen et al, Phys.Rev. C85 (2012) 047301p-0.10123IMC(D) EMC(N) – EMC(D)456a2(A/d)dRIM C 0.079 0.006dx29

EMC Effect in DeuteriumFrom BONUS: F2n/F2pUse world data from FD2and F2pCJ12systematic errorsKulagin and PettiW 1.4 GeV; 4 GeV data24 5 GeV; W 1.4 GeV; Q 1 GeV2-0.10(5)x 1.03(2)1.061.04F2d/(F2p F2n)EMC effect in deuteriumalso recently extractedusing data from BONUSexperiment (seeyesterday)1.0210.980.960.940.92Size of EMC “slope” extractedfrom this analysis consistentwith that extracted from EMCSRC correlation0.90.10.20.30.40.50.60.70.8xGriffioen et al, arXiv:1506.00871 [hep-ph]30

Future of the EMC Effect A key question moving forward is exploration of the roleof SRCs in the EMC effect New observables may be needed to gain further insight– Flavor dependence of the EMC effect (valence andsea quarks)– EMC effect in polarized quark distributions? Quark-meson inspired coupling models of the EMCeffect seem to bridge the gap between quark andnucleon degrees of freedom– These models do not include or give rise to SRCs31

Semi-inclusive DISSIDIS à production of one ormore hadrons in DIS reactionSimple picture:1. Electron scatters from quarkin nucleon2. Quark is kicked out à subsequently hadronizes,ending up in bound stateIn this simple picture, SIDIS canbe used to “tag” the flavor of thestruck quark in DIS process(E,’ p’ )e(E, p)qγ*Nuudhhπ πFragmentation function32

Semi-inclusive DISIn principle SIDIS can also beused to gain information aboutspatial distributions of quarks innucleonsà This requires measurements/observation of transversedegrees of freedom(E,’ p’ )e(E, p)qγ*Nuudhhπ π33

SIDIS KinematicsUseful kinematics related to outgoing hadron:q·pEhz q·Pp·qp q cos Fraction of virtual photon energy transferred to hadronpT (p( q qk) · ( qk qp )22ph )ph 12Components of hadron momentumrelative to qAzimuthal angle between electronscattering plane and hadron reactionplane34

SIDIS Cross SectionGeneral form of unpolarized cross section:2dy2 FT FL 22dxdydzdpT dxyQ 2(1)2 (1 ) cos FLT cos 2 FT TIntegrate over pT and ϕ, cross section can be expressed in terms of quarkparton model:d dxdydz1DISdDISdzd dzwhere22heq(x,Q)Df (z)f q f22)eq(x,Qf f f35

Fragmentation FunctionsDqh(z,Q2) à probability to form hadron (h) after quarkof flavor (q) is struckIn Quark-Parton Model, fragmentation functions Q2 independentà In reality, evolve with Q2 like quark PDFsFragmentation functions can be measured in e e- reactions à nocomplication due to hadron structureà Only average FF accessible – need other information for flavordependenceFor pion production, charge and isospin symmetry reduce number of FF’s needed D Du Dd D Du Dd Dū Dd Dū Dd 36

à Assumes leading orderfactorizationà Do not need knowledge ofabsolute fragmentation functions,but do need FF ratio: D-/D D favored fragmentationfunction (uà π )D- unfavored fragmentationfunction (uà π-)0.60.50.40.30.20.10 -2101.41.210.80.60.40.20-0.2 -21010-1d-uLight quark sea flavor asymmetrycan be extracted using semiinclusive pion production(d-u)/(u-d)SIDIS Examples1x22HERMES Q 2.3 GeV22E866 Q 54.0 GeV10-11x37

Strange quarkdistributions from(K K-) productionxS(x)SIDIS Examples22〈Q 〉 2.5 GeV0.42HERMES with DKS(z,Q )dz 1.27FitCTEQ6L––x(u(x) d(x))S(x) s(x) s̄(x)CTEQ6.5S-0NNPDF2.30.200.020.1Phys.Rev. D89 (2014) 9, 097101S(x)DSK (z, Q2 )dzK2dN(x,Q)2Q(x, Q ) 5dN DIS (x, Q20.6xKDQ(z, Q2 )dz38

SIDIS Examplesx u0.2Polarized quark distributionsd0hx d1 32(2)dxdQ2 dze2q q ( ) Dqh (z, Q2 )-0.2qq(x) q (x)0q (x)0–-0.2HERMES used a “purity” analysis sothey wouldn’t have to measure theabsolute magnitude of fragmentationfunctionx u–x d0-0.20-0.2x s0.030.10.6xHERMES, Phys.Rev. D71 (2005) 01200339

SIDIS with Transverse Degrees ofFreedomIn the more general case, allowing fortarget and beam polarizations, the crosssection is a bit more complicatedà Measurement of the transversemomentum of the hadron also allowsfor access to information regarding theinitial transverse momentum of thequarkà Transverse momentum dependentdistributions – TMDsà Azimuthal asymmetries key toaccessing TMDsSTk′kSPh qPhExample: Transversely polarized target, unpolarized beam2dy2sin ( hsin ( hS) S [sin()F FunpolhSU T,TU T,Ldxdyd S dzd h dp2hxyQ2 2(1)sin ( )sin (3 hS)S sin ( h S )FU T h S sin (3 h2 (1 ) sin S FUsin S )FU TTsin (2 hS)2 (1 ) sin (2 h]S )FU TS)40

TMDsIn the inclusive/forward hadron production case, we sample onedimensional parton distribution functionsTMDs allows us to explore the distributions of partons in the transversedirectionq(x)q(x, kT )Transverse momentumalso generated duringfragmentationD(z)D(z, pT )41

TMDsq(x)q(x, kT )D(z)D(z, pT )Probability of producing hadron withtransverse momentum PT comesfrom a convolution of kT dependentparton distribution and pT dependentfragmentation functionPT pT zkT 22O(kT /Q )42

SIDIS and gmentationfunctionBeam polarization 3FU Ucos (2 h )FU Usin (2 h )FU LFLLsin ( hFU T,TS)sin ( h S )FU TTarget polarizationsin (3 hS)FU Tcos ( hS)FLTf1 D1h1 H 1h1L H1g1L D1f1T D1Unpolarized TMDBoer-Mulders TMDWorm gear TMDHelicityTMDSivers TMDh1 H 1Transversity TMDh1T H1Pretzelosity TMDg1T D1Worm gear TMD43

Distribution FunctionsN/qULTquarksUh1f1U unpolarizedL long. polarizedg1h1LLT trans. polarizedTf1T g1T h1 h1TnucleonDiagonal elements usual PDFsOff-diagonal elements transverse momentum distributions, requirenon-zero angular momentumf1Tà Sivers function, describes unpolarized quark in trans. pol. nucleonh1 , h1L , h1Tà Boer-Mulders functions describe transversely polarizedquarks in un/long./trans./polarized nucleon44

Unpolarized SIDISHall C @ JLAB: E00-108Measured PTdependence ofunpolarized SIDIScross sections for:π and π- fromH and D45

Model PT dependence of SIDISGaussian distributions for PT dependence, no sea quarks, and leading order in (kT/q)Inverse of total width for each combination of quark flavorand fragmentation function given by:Simple model, with several assumptions:à factorization validà fragmentation functions do not depend on quark flavorà transverse momentum widths of quark and fragmentationfunctions are Gaussian and can be added in quadratureà more 46

Unpolarized SIDISµ2u 0.07 0.03 (GeV/c)2µu µdµ2d 0.01 0.05 (GeV/c)2µ µ-47

A1 PT-Dependence in SIDISm02 0.25GeV2mD2 0.2GeV2M.Anselmino et alhep-ph/0608048In perturbative limit predicted to be constantNew eg1dvcs data allowmultidimensional binning to studykT-dependence for fixed xπ ALL can be explained in terms of broader kTdistributions for f1 compared to g148

Proton Single-Spin Asymmetries with CLASTransversely polarizedquarks in the longitudinallypolarized nucleonW2 4 GeV2Q2 1.1 GeV2y 0.850.4 z 0.7MX 1.4 GeVPT 1 GeV0.12 x 0.48ep e’pX 10% ofE05-113 dataMuch higher statistics from 2009 run49

Transverse Target AsymmetriesCollins asymmetrysin (h S)h1 H 1Provides access to “transversity” distribution à linked to tensor charge ofthe proton1q 0hq1 (x)Sivers asymmetryFundamental property of nucleon,sin (hS)f1T D1Quark distributions in a transversely polarized nucleon50

Transverse Target asymmetries fromCOMPASSCollins asymmetriesPLB 744 (2015) 25051

Transverse Target asymmetries fromCOMPASS and HERMESSiversasymmetriesPLB 744 (2015) 25052

SIDIS Summary Semi-inclusive DIS a powerful tool for exploring howquarks are distributed in the nucleon– Flavor tagging for polarized and unpolarized PDFs– TMDs allow exploration of transverse structure à linkto orbital angular momentum Most SIDIS data has been acquired at fixed targetfacilities à HERMES, JLab, COMPASS– JLab has a large SIDIS program planned for Halls A,B, and C as part of 12 GeV Upgrade– A future EIC would provide a huge amount of data inthe “sea-quark” regime53

EXTRA54

DIS Cross SectionReminder: Inclusive cased4 2 22 yxF(x,Q) (1122dxdQxQy)F2 (x, Q2 )Quark parton-modelF2 2xF1F2 (x) xd2 2 [1 (124dxdQxQd2 2 xs [1 (14dxdyQe2f qf (x)fy)2 ]e2f qf (x)fy)2 ]e2f qf (x)f55

CJ12 PDFsNuclear effects in deuteron lead to significant uncertainties in quark PDFs atlarge xà This has been studied in some depth by the CTEQ-JLAB collaborationJ. F. Owens, A. Accardi and W. Melnitchouk, Phys. Rev. D 87, 094012 (2013)56

1 Deep Inelastic Scattering Part 2 Dave Gas