Modification of transverse momentum distributions in nuclei Harut

Modification of transverse momentum distributions in nuclei Harut Avakian (JLab) Workshop on Nuclear Chromo-Dynamic Studies with a Future Electron Ion Collider Argonne National Laboratory, April 7 - 9, 2010 • TMDs and spin-orbit correlations • k. T-distributions • Higher twists in SIDIS • MC-simulations • Projections for observables • Conclusions H. Avakian, Argonne, April 8 1

Structure of the Nucleon Wpu(k, r. T) “Mother” Wigner distributions d 2 k. T d 2 r. T GPDs/IPDs TMD PDFs f 1 u(x, k. T), . . h 1 u(x, k. T) quark polarization d 2 k. T PDFs f 1 u(x), . . h 1 u(x) ØGauge invariant definition (Belitsky, Ji, Yuan 2003) ØUniversality of k. T-dependent PDFs (Collins, Metz 2003) ØFactorization for small k. T. (Ji, Ma, Yuan 2005) H. Avakian, Argonne, April 8 2

Tang, Wang & Zhou Phys. Rev. D 77: 125010, 2008 k. T and FSI l l’ BHS 2002 Collins 2002 Ji, Yuan 2002 x, k. T proton l’ l total transverse momentum broadening squared l. T x, k’T spectator system nucleus l’T spectator system soft gluon exchanges included in the distribution function (gauge link) • The difference is coming from final state interactions (different remnant) H. Avakian, Argonne, April 8 3

SIDIS: partonic cross sections k. T p┴ PT = p┴ +z k. T Ji, Ma, Yuan Phys. Rev. D 71: 034005, 2005 Is the info on x-k. T correlations accessible in k. T integrated observables? H. Avakian, Argonne, April 8 4

Quark distributions at large k. T: models q JMR model MR , R=s, a Dq Effect of the orbital motion on the q- may be most significant Du/u (H. A. , S. Brodsky, A. Deur, F. Yuan 2007) Higher probability to find a quark anti-aligned with proton spin at large k. T (dipole formfactor), J. Ellis, D-S. Hwang, A. Kotzinian H. Avakian, Argonne, April 8 5

Quark distributions at large k. T: lattice B. Musch ar. Xiv: 0907. 2381 Higher probability to find a quark antialigned with proton spin at large k. T Higher probability to find a d -quark at large k. T Understanding the transverse structure is crucial! H. Avakian, Argonne, April 8 6

A 1 PT-dependence ar. Xiv: 1003. 4549 Lattice Anselmino Collins PT PT CLAS data suggests that width of g 1 is less than the width of f 1 New CLAS data would allow multidimensional binning to study k. T-dependence for fixed x H. Avakian, Argonne, April 8 7

H. Avakian, Argonne, April 8 8

Quark distributions at large k. T bigger effect at large z PT = p┴ +z k. T Higher probability to find a hadron at large PT in nuclei k. T-distributions may be wider in nuclei? H. Avakian, Argonne, April 8 9

Jet limit: Higher Twist azimuthal asymmetries Twist-2 Twist-3 T-odd “interaction dependent” No leading twist, provide access to quarkgluon correlations H. A. , A. Efremov, P. Schweitzer, F. Yuan ar. Xiv: 1001. 5467 H. Avakian, Argonne, April 8 10

Modification of Cahn effect Bag model Gao, Liang & Wang ar. Xiv: 1001. 3146 • Nuclear Large cosnf moments COMPASS modification ofobserved Cahn mayatprovide info on k. T broadening and proton TMDs H. Avakian, Argonne, April 8 11

Collins mechanism for SSA FC fs Fragmenting quark polarization PT fragmentation of transversely polarized quarks into unpolarized FC hadrons fh x f. S = p/2+fh y PT f. S fh x PT PT fh fh y f. S=p/2 y x f. S=p x HT function related to force on the quark. M. Burkardt (2008) H. Avakian, Argonne, April 8 12

Electroproduction kinematics: JLab 12→EIC Q 2 collider experiments EIC (4 x 60): H 1, ZEUS 10 -4<x. B<0. 02 gluons (and quarks) EIC 10 -4<x. B<0. 3 fixed target experiments COMPASS 0. 006<x. B<0. 3 EIC HERMES 0. 02<x. B<0. 3 gluons/valence and sea quarks JLab 12 JLab 0. 1<x. B<0. 7 JLab@12 Ge. V valence quarks Study of high x domain requires high luminosity, low x higher energies H. Avakian, Argonne, April 8 13

LEPTO/PEPSI: quark distributions Event Generator with polarized electron and nucleon: PEPSI, …. MC with Cahn Acceptance check Design parameters Smearing/resolution routines Use GEANT as input z>0. 1 Physics analysis using the “reconstructed” event sample z>0. 3 • Implemented in PEPSI modification to LEPTO done by A. Kotzinian • Add different widths for q+ and q- Need to model TMDs in LUND MC H. Avakian, Argonne, April 8 14

EIC 4 x 60 (Lumi 1033, cm-2 sec-1 , ~1 hour) <x>=0. 1, <Q 2>=4 s(p) = 0. 05 + 0. 06*p [Ge. V] % K*s can be studied with EIC H. Avakian, Argonne, April 8 15

PT-dependence of beam SSA ssinf. LU~FLU~ 1/Q (Twist-3) In the perturbative limit 1/PT behavior expected 4 x 60 100 days, L=1033 cm-2 s-1 Nonperturbative TMD Perturbative region Study for SSA transition from non-perturbative to perturbative regime. EIC will significantly increase the PT range. H. Avakian, Argonne, April 8 16

Boer-Mulders Asymmetry with CLAS 12 & EIC 5 -Ge. V - e p 50 Ge. V Transversely polarized quarks in the unpolarized nucleon sin(f. C) =cos(2 fh) CLAS 12 EIC Perturbative limit calculations available for Nonperturbative TMD Perturbative region : J. Zhou, F. Yuan, Z Liang: ar. Xiv: 0909. 2238 CLAS 12 and EIC studies of transition from non-perturbative to perturbative regime will provide complementary info on spin-orbit correlations and test unified theory (Ji et al) H. Avakian, Argonne, April 8 17

Summary Studies of spin and azimuthal asymmetries in semi-inclusive processes at EIC : • Measure nuclear modification of transverse momentum distributions and spin-orbit correlations of partons at small x, in a wide range of Q • Study quark-gluon correlations (HT) in nucleon and nucleus • Provide information on correlations of longitudinal and transverse degrees of freedom ØEIC: Studies of nuclear modifications of spin orbit and quark-gluon correlations combined with JLab 12 data will help construct a more complete picture about the structure of the nucleon and nuclei. H. Avakian, Argonne, April 8 18

Support slides…. H. Avakian, Argonne, April 8 19

Struck quark kinematics (EIC 4 x 60) qq High energy quarks at small angles H. Avakian, Argonne, April 8 20

SIDIS (g*p->p. X) x-section at leading twist TMD PDFs • Measure Boer-Mulders distribution functions and probe the polarized fragmentation function • Measurements from different experiments consistent H. Avakian, Argonne, April 8 21

Tang, Wang & Zhou Phys. Rev. D 77: 125010, 2008 k. T and FSI l l’ BHS 2002 Collins 2002 Ji, Yuan 2002 x, k. T proton l’ l total transverse momentum broadening squared l. T spectator system x, k’T nucleus l’T spectator system • The difference is coming from final state interactions (different remnant) H. Avakian, Argonne, April 8 22

Transverse force on the polarized quarks Quark polarized in the x-direction with k. T in the y-direction Force on the active quark right after scattering (t=0) Interpreting HT (quark-gluon-quark correlations) as force on the quarks (Burkardt hep-ph: 0810. 3589) H. Avakian, Argonne, April 8 23

EIC: Kinematics Coverage 5 Ge. V e p 50 Ge. V e’p+X x. F>0 (CFR) EIC-MC x. F<0 ( TFR) all x. F>0 z>0. 3 EIC-MC Major part of current particles at large angles in Lab frame (PID at large angles crucial). H. Avakian, Argonne, April 8 24

Q 2 -dependence of beam SSA ssinf. LU(UL) ~FLU(UL)~ 1/Q (Twist-3) 1/Q behavior expected (fixed x bin) Study for Q 2 dependence of beam SSA allows to check the higher twist nature and access quark-gluon correlations. H. Avakian, Argonne, April 8 25

EIC medium energy EIC@JLab EIC@RHIC • Electron energy: 4 -20 Ge. V • Proton energy: 50 -250 Ge. V – • • Electron energy: 3 -11 Ge. V • Proton energy: 20 -60 Ge. V – More symmetric kinematics provides better resolution and particle id Luminosity: ~ 1033 cm-2 s-1 – Main Features • Luminosity: ~ 1034 cm-2 s-1 – in range around s ~ 1000 -10000 Ge. V 2 More symmetric kinematics provides better resolution and particle id in range around s ~ 1000 Ge. V 2 • Polarized electrons and light ions • 90% of hardware can be reused • Potential upgrade with high-energy ring Slides are for a “generic” US version of an EIC (5 x 50 or 4 x 60): – longitudinal and transverse polarized > 70%) • Limited R&D needs • • Limited R&D needsbeams (longitudinal and transverse, 33 luminosities of at least 10 • 3 interaction regions (detectors) • • ? interaction regions (detectors) H. Avakian, Argonne, April 8 26

JETSET: Single particle production in hard scattering LUND Fragmentation Functions - Before - After Target remnant quark Lund-MC should be modified to allow checks of sensitivity of measurements to different effects related to the transverse structure H. Avakian, Argonne, April 8 27

SIDIS kinematical plane and observables Cross section is a function of scale variables x, y, z z Target polarization Beam polarization U unpolarized L long. polarized T trans. polarized sin 2 f moment of the cross section for unpolarized beam and long. polarized target H. Avakian, Argonne, April 8 28

Kaon production in SIDIS FAST-MC L S CLAS 12 S* EIC 4 x 60 detected s(p) = 0. 05 + 0. 06*p [Ge. V] % Identification using the missing mass may be possible H. Avakian, Argonne, April 8 29

Azimuthal moments with unpolarized target quark polarization H. Avakian, JLab, Argonne, Nov 25 April 8 30

Azimuthal moments with unpolarized target quark polarization H. Avakian, JLab, Argonne, Nov 25 April 8 31

SSA with unpolarized target quark polarization H. Avakian, JLab, Argonne, Nov 25 April 8 32

SSA with unpolarized target quark polarization H. Avakian, JLab, Argonne, Nov 25 April 8 33

SSA with long. polarized target quark polarization H. Avakian, Argonne, April 8 34

SSA with long. polarized target quark polarization H. Avakian, Argonne, April 8 35

SSA with unpolarized target quark polarization H. Avakian, Argonne, April 8 36

SSA with unpolarized target quark polarization H. Avakian, Argonne, April 8 37

Single hadron production in hard scattering x. F>0 (current fragmentation) h x. F<0 (target fragmentation) x. F - momentum in the CM frame Target fragmentation Current fragmentation semi-inclusive semi-exclusive FF h M Fracture Functions h h DA DA h -1 exclusive PDF 0 k. T-dependent PDFs PDF GPD 1 x. F Generalized PDFs Measurements in different kinematical regions provide complementary information on the complex nucleon structure. H. Avakian, Argonne, April 8 38

L production in the target fragmentation L polarization in TFR provides information on contribution of strange sea to proton spin (ud)-diquark is a spin and isospin singlet s-quark carries whole spin of L x. F - momentum x. F(L) in the CM frame Study polarized diquark fracture functions sensitive to the correlations between struck quark transverse momentum and the diquark spin. EIC CLAS 12 Wide kinematical coverage of EIC would allow studies of hadronization in the target fragmentation region (fracture functions) H. Avakian, Argonne, April 8 39

Collins effect p+ Simple string fragmentation for pions (Artru model) z leading pion out of page L r production may produce an opposite sign AUT Fraction of r in ep. X % left from ep. X asm 20% 40% ~75% ~50% L r z Leading r opposite to leading p(into page) hep-ph/9606390 Fraction of direct kaons may be significantly higher than the fraction of direct pions. H. Avakian, Argonne, April 8 LUND-MC 40

K/K* and L/S separations Detection of K+ crucial for separation of different final states (L, S, K*) H. Avakian, Argonne, April 8 41

Sivers effect in the target fragmentation A. Kotzinian High statistics of CLAS 12 will allow studies of kinematic dependences of the Sivers effect in target fragmentation region H. Avakian, Argonne, April 8 42

collider experiments H 1, ZEUS (EIC) 10 -4<x. B<0. 02 (0. 3): gluons (and quarks) in the proton 27 Ge V HERA Q 2 EIC ENC ra s 60 ) ab L J V 6 Ge 4 x es ) JL ab C( EN C( 15 @ 3 x b JLa 12 as mp co d de g (up m r e h EI Q 2 Hard Scattering Processes: Kinematics Coverage ) fixed target experiments COMPASS, HERMES 0. 006/0. 02<x. B<0. 3 : gluons/valence and sea quarks JLab/JLab@12 Ge. V 0. 1<x. B<0. 7 : valence quarks Study of high x domain requires high luminosity, low x higher energies H. Avakian, Argonne, April 8 43

collider experiments H 1, ZEUS (EIC) 10 -4<x. B<0. 02 (0. 3): gluons (and quarks) in the proton Ge V HERA 27 Q 2 Hard Scattering Processes: Kinematics Coverage Q 2 EIC ENC EIC ra s as mp co ENC d de es ab L J V 6 Ge rm e h JLab 12 b@ JLa g (up ) fixed target experiments COMPASS, HERMES 0. 006/0. 02<x. B<0. 3 : gluons/valence and sea quarks JLab/JLab@12 Ge. V 0. 1<x. B<0. 7 : valence quarks Study of high x domain requires high luminosity, low x higher energies H. Avakian, Argonne, April 8 44

hep: ar. Xiv-09092238 H. Avakian, Argonne, April 8 45

TMDs: QCD based predictions Large-x limit Burkardt (2007) Brodsky & Yuan (2006) Large-Nc limit (Pobilitsa) Do not change sign (isoscalar) All others change sign u→d (isovector) H. Avakian, Argonne, April 8 46