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Semi-Inclusive Charged-Pion Electro-production off Protons and Deuterons: Cross Sections, Ratios and Transverse Momentum Dependence Rolf Ent (Jefferson Lab) Baryons 2013 Glasgow, UK June 27

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Semi-Inclusive Charged-Pion Electro-production off Protons and Deuterons: Cross Sections, Ratios and Transverse Momentum Dependence HERMES data established the potential for semi-inclusive DIS (SIDIS) JLab/Hall C’s basic SIDIS cross section data at a 6-GeV JLab showed agreement with partonic expectations and hints at a flavor dependence in transverse momentum dependence, laying the foundation for a vigorous 12-GeV SIDIS program. T. Navasardyan et al., Phys. Rev. Lett. 98 (2007) 022001; H. Mkrtchyan et al., Phys. Lett. B665 (2008) 20; R. Asaturyan et al., Phys. Rev. C 85 (2012) 015202. AlsoM. Osipenko et al. (CLAS), Phys. Rev. D 80 (2009) 032004. Recently also extensive set of unpolarized SIDIS cross section data from both HERMES and COMPASS: A. Airapetyan et al., Phys. Rev. D 87 (2013) 074029. C. Adolph et al., arXiv:1305.7317v1 (2013). Pre-Amble

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Outline Semi-Inclusive Deep Inelastic Scattering – Introduction Towards a Partonic Description Semi-Inclusive Deep Inelastic Scattering – Formalism Transverse Momentum Dependence – Flavor Dependence Unpolarized SIDIS Cross Section Measurements @12 GeV Charged Pions and Neutral Pions Semi-Inclusive Charged-Pion Electro-production off Protons and Deuterons: Cross Sections, Ratios and Transverse Momentum Dependence

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Beyond form factors and quark distributions Generalized Parton and Transverse Momentum Distributions Proton form factors, transverse charge & current densities Structure functions, quark longitudinal momentum & helicity distributions Correlated quark momentum and helicity distributions in transverse space - GPDs Extend longitudinal quark momentum & helicity distributions to transverse momentum distributions - TMDs 2000’s 1990’s

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The road to orbital motion The difference between the +, –, and K + asymmetries reveals that quarks and anti-quarks of different flavor are orbiting in different ways within the proton. Swing to the left, swing to the right: A surprise of transverse-spin experiments d h ~ e q 2 q(x) d f D f h (z) Sivers distribution

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The Incomplete Nucleon: Spin Puzzle LqLq JgJg ++ 1 2 = 1 2 ~ 0.25(world DIS) G small(RHIC+DIS) L q ? Longitudinal momentum fraction x and transverse momentum images Longitudinal momentum fraction x and transverse spatial images Up quark Sivers Function 12 GeV projections: valence quarks well mapped

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Solution: Detect a final state hadron in addition to scattered electron Can ‘tag’ the flavor of the struck quark by measuring the hadrons produced: ‘flavor tagging’ DIS probes only the sum of quarks and anti-quarks requires assumptions on the role of sea quarks Measure inclusive (e,e’) at same time as (e,e’h) SIDIS SIDIS – Flavor Decomposition Leading-Order (LO) QCD after integration over p T and NLO: gluon radiation mixes x and z dependences Target-Mass corrections at large z ln(1-z) corrections at large z : parton distribution function : fragmentation function M x 2 = W’ 2 ~ M 2 + Q 2 (1/x – 1)(1 - z) z = E h /

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E00-108 Experiment in Hall C/JLab 1) Probe + and - final states 2) Use both proton and neutron (deuteron) targets 3) Combination of precise cross sections and ratios allows confirmation of interpretation in terms of convolution of quark distribution and fragmentation function 4) Combination allows, naively, a separation of quark k t -widths from fragmentation p t -widths (if sea quark contributions small) M x 2 = W’ 2 ~ M 2 + Q 2 (1/x – 1)(1 - z) z = E h / Mx2Mx2 region Convolution of CTEQ5 quark distribution and BKK fragmentation function x ~ 0.3, Q 2 ~ 2.3 (GeV/c) 2 0.2 < x < 0.6, 2 < Q 2 < 4, 0.3 < z < 1

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How Can We Verify Factorization? Neglect sea quarks and assume no k t dependence to parton distribution functions Fragmentation function dependence drops out in Leading Order [ p ( + ) + p ( - )]/[ d ( + ) + d ( - )] = [4u(x) + d(x)]/[5(u(x) + d(x))] ~ p / d independent of z and k t [ p ( + ) - p ( - )]/[ d ( + ) - d ( - )] = [4u(x) - d(x)]/[3(u(x) + d(x))] independent of z and k t, but more sensitive to assumptions

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Closed (open) symbols reflect data after (before) events from coherent production are subtracted GRV & CTEQ, @ LO or NLO (Note: z = 0.65 ~ M x 2 = 2.5 GeV 2 ) E00-108: Onset of the Parton Model Good description for p and d targets for 0.4 < z < 0.65

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E00-108: Onset of the Parton Model (Resonances cancel (in SU(6)) in D - /D + ratio extracted from deuterium data) (Deuterium data) quark Collinear Fragmentation factorization e q 2 q(x) D q (z)

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Destructive interference leads to factorization and duality F. Close et al : SU(6) Quark Model How many resonances does one need to average over to obtain a complete set of states to mimic a parton model? 56 and 70 states o.k. for closure From deuterium data: D - /D + = (4 – N + /N - )/(4N + /N - - 1) Resonances cancel in D - /D + ratio extracted from deuterium!

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E00-108: Onset of the Parton Model in SIDIS Curves are parton model calculations using CTEQ5M parton distributions at NLO and BKK fragmentation functions. Agreement with the parton model expectation is always far better for ratios, also for D/H, Al/D, or for ratios versus z or Q 2. Bodes well for SIDIS at 12 GeV x = 0.4 x = 0.32 N- region Solid (open) symbols are after (before) subtraction of diffractive events Phys. Rev. C85: 015202 (2012) CTEQ5M d v /u v extracted from differences and ratios of + and - cross sections off H and D targets

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New Observable Reveals Interesting Behavior of Quarks Target: (transversely) polarized 3 He ~ polarized neutron J. Huang et al., PRL 108, (2012) 052001 1 st measurement of A LT beam-target double-spin asymmetry Indications: A non-vanishing quark “transversal helicity” distribution, reveals alignment of quark spin transverse to neutron spin direction Quark orbital motions 1 st measurement of 3 He (neutron) single-spin asymmetries (SSA) Measurement of Sivers & Collins SSA’s in X. Qian et al., PRL 107, (2011) 072003

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P t = p t + z k t + O(k t 2 /Q 2 ) p m x TMD TMD u (x,k T ) f 1,g 1,f 1T,g 1T h 1, h 1T,h 1L,h 1 Final transverse momentum of the detected pion P t arises from convolution of the struck quark transverse momentum k t with the transverse momentum generated during the fragmentation p t. Linked to framework of Transverse Momentum Dependent Parton Distributions SIDIS – k T Dependence

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TMD q (x,k T ) p m X TMD Transverse momentum dependence of SIDIS Linked to framework of Transverse Momentum Dependent Parton Distributions Unpolarized k T -dependent SIDIS: in framework of Anselmino et al. described in terms of convolution of quark distributions f and (one or more) fragmentation functions D, each with own characteristic (Gaussian) width Emerging new area of study Unpolarized target Longitudinally pol. target Transversely pol. target N q ULT Uf1f1 h1h1 Lg1g1 h 1 L Tf 1T g 1T h 1 h 1T Basic precision cross section measurements: Crucial information to validate theoretical understanding -Convolution framework requires validation for most future SIDIS experiments and their interpretation -Can constrain TMD evolution -Questions on target-mass corrections and ln(1-z) re-summations require precision large-z data f

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SIDIS Formalism General formalism for (e,e’h) coincidence reaction with polarized beam: ( = azimuthal angle of e’ around the electron beam axis w.r.t. an arbitrary fixed direction) [A. Bacchetta et al., JHEP 0702 (2007) 093] Use of polarized beams will provide useful azimuthal beam asymmetry measurements (F LU ) at low P T Unpolarized k T -dependent SIDIS: F UU cos( ) and F UU cos(2 ), in framework of Anselmino et al. described in terms of convolution of quark distributions f and (one or more) fragmentation functions D, each with own characteristic (Gaussian) width. If beam is unpolarized, and the (e,e’h) measurements are fully integrated over , only the F UU,T and F UU,L responses, or the usual transverse ( T ) and longitudinal ( L ) cross section pieces, survive.

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Transverse momentum dependence of SIDIS General formalism for (e,e’h) coincidence reaction with polarized beam: ( = azimuthal angle of e’ around the electron beam axis w.r.t. an arbitrary fixed direction) Azimuthal h dependence crucial to separate out kinematic effects (Cahn effect) from twist-2 correlations and higher twist effects. data fit on EMC (1987) and Fermilab (1993) data assuming Cahn effect → = 0.25 GeV 2 (assuming 0,u = 0,d ) [A. Bacchetta et al., JHEP 0702 (2007) 093]

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Hall C: Transverse momentum dependence P t dependence very similar for proton and deuterium targets, but deuterium slopes systematically smaller? E00- 108 P t dependence very similar for proton and deuterium targets

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Unpolarized SIDIS – Simple Analysis Constrain k T dependence of up and down quarks separately 1) Probe + and - final states 2) Use both proton and neutron (d) targets 4) Combination allows, in principle, separation of quark width from fragmentation widths (if sea quark contributions small) 1 st example: Hall C, Phys. Lett. B665 (2008) 20 Numbers are close to expectations! But, simple model only with many assumptions (factorization valid, fragmentation functions do not depend on quark flavor, transverse momentum widths of quark and fragmentation functions are gaussian and can be added in quadrature, sea quarks are negligible, assume Cahn effect, etc.), incomplete cos( ) coverage, uncertainties in exclusive event & diffractive contributions. Example x = 0.32 z = 0.55 (favored) (up)

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Unpolarized SIDIS – Transverse Momentum Warning: we used here an overly simplistic model analysis in an early effort to show the perspective of P t -dependent SIDIS experiments. An alternate analysis was performed in Schweitzer, Teckentrup and Metz, PRD 81 (2010) 094019 Gauss model for P t distributions - Do not assume kinematic dominance of Cahn effect Showing consistency of CLAS, Hall C, HERMES data Gaussian approach also describes Drell-Yan data, giving credence to the factorization approach used Warning again: a gaussian approach can formally not be correct For instance, the assumption of Cahn dominance may not be justified. But, the P t dependence of D seems shallower than H, with an intriguing explanation in terms of flavor/k t deconvolution.

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Transverse momentum dependence of SIDIS CLAS Gauss: 2 = /4 HERMES (also consistent with CLAS) Gaussian approach of Schweitzer, Teckentrup and Metz, PRD 81 (2010) 094019 E00 -108 Curves are from the Gauss model with the Gauss width fixed from CLAS data x = 0.32

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Transverse momentum dependence of SIDIS Intrinsic value of SIDIS to establish transverse momentum widths of quarks with different flavor and polarization now well established (and they can be different). Steps towards QCD evolution taken. Need precision at large z to validate fragmentation process, verify target-mass correction and ln(1-z) re- summation, etc. Double Spin Asymmetry Avakian et al., PRL 105 (2010) 262002 Adolph et al., arXiv:1305.7317v1 (2013) CLASCOMPASS

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Transverse momentum dependence of SIDIS Intrinsic value of SIDIS to establish transverse momentum widths of quarks with different flavor and polarization now well established (and they can be different). Steps towards QCD evolution taken. Need precision at large z to validate fragmentation process, verify target-mass correction and ln(1-z) re- summation, etc. HERMES Hall C Airapetian et al., PRD 107 (2013) 074029 Asaturyan et al., PRC 105 (2012) 015202 Solid (open) triangles: Cornell data @ x = 0.24 & x = 0,50

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Hall C SIDIS Program – basic (e,e’ ) cross sections Why need for (e,e’ 0 ) beyond (e,e’ +/- )? Low-energy (x,z) factorization, or possible convolution in terms of quark distribution and fragmentation functions, at JLab-12 GeV must be well validated to substantiate the SIDIS science output. Many questions at intermediate-large z (~0.2-1) and low- intermediate Q 2 (~2-10 GeV 2 ) remain. (At a 12-GeV JLab, Hall C’s role will be again to provide basis SIDIS cross sections.) (e,e’ 0 ): no diffractive contributions no exclusive pole contributions reduced resonance contributions proportional to average D Solid (open) symbols are after (before) subtraction of exclusive events Ratio of after (before) subtraction of exclusive events HERMES PRD87 (2013) 074029

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JLab Unpolarized SIDIS Program Kinematics 6 GeV phase space 11 GeV phase space E00-108 E12-09-017 Scan in (x,z,P T ) + scan in Q 2 at fixed x E12-09-002 + scans in z E12-06-104 L/T scan in (z,P T ) No scan in Q 2 at fixed x: R DIS (Q 2 ) known E12-13-007 Neutral pions: Scan in (x,z,P T ) Overlap with E12-09-017 & E12-09-002 Charged pions: Parasitic with E12-13-010 Accessible Phase Space for SIDIS (and Deep Exclusive Scattering) at 12-GeV JLab Typical z range: 0.2 to 0.7 (up to 1.0 for smaller M x 2 )

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R DIS R DIS (Q 2 = 2 GeV 2 ) Only existing data: Cornell 70’s data R = L / T in SIDIS (ep e’ +/- X) Conclusion: “data consistent with both R = 0 and R = R DIS ” Some hint of large R at large z in Cornell data? Example projections given for E12-06-104 assuming R SIDIS = R DIS

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E12-09-017 Projected Results - Kaons III II I IV VI V

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Semi-Inclusive Charged-Pion Electro-production off Protons and Deuterons: Cross Sections, Ratios and Transverse Momentum Dependence Hall C/E00-108 1,2 H(e,e’ +/- ) cross section data provided the foundation of the SIDIS framework in terms of convolution at lower energies. Agreement with parton model expectations is always far better for ratios. Transverse momentum dependence of cross section (and asymmetry data) led to consideration of flavor dependence. Now the stage of precision data enters, to provide answers to questions of1) experimental issues such as contributions, L/T ratios, etc. 2) flavor dependence of transverse momentum widths (and fragmentation functions) 3) QCD evolution and ln(1-z) re-summation At a 12-GeV JLab precision unpolarized SIDIS experiments approved for: -Measurement of ratio R = L / T in SIDIS (E12-06-104) -Measurement of Transverse Momentum Dependence of Charged-Pion and Kaon Production (E12-09-017) -Precise Measurement of Charged-Pion Ratios to High Q 2 (E12-09-002) -Measurement of Semi-Inclusive Neutral-Pion Production (E12-13-007)

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E12-09-017 Projected Results - Pions III II I IV VI V

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R = L / T in (e,e’ ) SIDIS quark Knowledge on R = L / T in SIDIS is essentially non-existing! If integrated over z (and p T, , hadrons), R SIDIS = R DIS R SIDIS = R DIS test of dominance of quark fragmentation R SIDIS may vary with z At large z, there are known contributions from exclusive and diffractive channels: e.g., pions from and + - R SIDIS may vary with transverse momentum p T Is R SIDIS + = R SIDIS - ? Is R SIDIS H = R SIDIS D ? Is R SIDIS K + = R SIDIS + ? Is R SIDIS K + = R SIDIS K - ? E2-06-104 measure kaons too! (with about 10% of pion statistics) e q 2 q(x) D q (z) “A skeleton in our closet”

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