Mini-review of experimental results on TMDs. Wen-Chen Chang Institute of Physics, Academia Sinica

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1 Mini-review of experimental results on MDs Wen-Cen Cang Institute of Pysics, cademia inica 1

2 Outline Introduction: Wy MDs? Leading-twist structures Experimental approaces Mini-review of experimental results: Polarization independent MDs: number density and Boer-Mulders functions Polarization dependent MDs: transversity and ivers functions ummary & experimental prospects

3 Factorization of Hard Processes σ proton Q = f parton (x, Q ) σ parton (Q ) 3

4 Universality of Parton Density Functions (PDFs) ea quarks Valance quarks x: momentum fraction of partons 4

5 Wy MDs? e Z-boson transverse momentum q spectrum in pp collisions at te LHC PRD 85, 0300 (01) t large q, te fixed-order pqcd describes te data very well. For q<10 GeV, pqcd calculation fails: multi-parton QCD radiation. ngeles-martinez et al., arxiv:

6 Multi-dimensional Partonic tructures Beyond collinear approximation Related to te orbital motion and spin-orbit effects. ttp:// 6

7 Leading-wist ransverse-momentum Dependent Parton Density Function (MDs) spin of te nucleon Nucleon Quark, Gluon U L spin of te parton k of te parton U number density f 1 q,g (x, k ) Boer-Mulders 1 q,g (x, k ) L Helicity q,g (x, k ) g 1L worm-gear L q,g 1L (x, k ) ivers q,g (x, k ) f 1 Kotzinian- Mulders worm-gear q,g g 1 (x, k ) ransversity 1 q,g (x, k ) Pretzelosity q,g (x, k ) 1 7

8 Leading-wist ransverse-momentum Dependent Fragmentation Function (MDs) spin of te nucleon Nucleon Quark, Gluon U L spin of te parton k of te parton U unpolarized D 1 q,g (x, k ) Collins H 1 q,g (x, k ) L q,g G 1L (x, k ) q,g H 1L (x, k ) H 1 q,g (x, k ) q,g D 1 (x, k ) q,g G 1 (x, k ) q,g H 1 (x, k ) 8

9 ccessing MDs IDI: ep ex Drell-Yan: pp e + e - X Diadron in e+e-: e + e - 1 X Hadron production in pp: pp X

10 IDI cross-sections cos(φ) sin(φ φ F UU, s ) sin(φ+φ FU, s ) FU : tructure Functions vakian et al., Eur. Pys.J. 5 (016)

11 Polarization-dependent erms: ransverse pin symmetry U U F 1 N N U F f N N UU f: dilution factor due to non-polarizable component of te target : polarization degree of transverse spin dvantage: most of te systematics due to instrumental artifacts cancel. Disadvantage: te unpolarized structure function F UU as to be well known. 11

12 5 pril 017 Bakur Parsamyan DI017 1 IDI x-section.kotzinian, Nucl. Pys. B441, 34 (1995). Baccetta, Diel, Goeke, Metz, Mulders and clegel JHEP 070:093 (007). l l' γ * X P,, ( ), ( ),,, ;, s s w w U L U L UU UU L y y F Mx F F Q y y y c cos sin os sin sin cos,, cos cos sin sin sin cos 1 1 U UU UU L L UU LU U U L L L L L L U L d dxdydzdp d d y F F xyq x sin s sin in co si n sin 3 co s s 1 sin sin sin 3 sin sin cos cos U U L U U U L cos cos 1 L

13 c cos sin os sin sin cos,, cos cos sin sin sin cos 1 1 U UU UU L L UU LU U U L L L L L L U L d dxdydzdp d d y F F xyq x sin s sin in co si n sin 3 co s s 1 sin sin sin 3 sin sin cos cos U U L U U U L cos cos 1 L 5 pril 017 Bakur Parsamyan DI IDI x-section and MDs at twist- Quark Nucleon U L U number density Boer-Mulders L elicity worm-gear L ivers Kotzinian-Mulders worm-gear transversity pretzelosity 1 (, ) q g x k 1 (, ) q L x k 1 (, ) q f x k 1 (, ) q f x k 1 (, ) q x k 1 (, ) q x k 1 (, ) q x k 1 (, ) q g x k DF FF l l' γ * X P two FFs: and q q D z P H z P (, ) (, )

14 IDI x-section: transverse spin dependent part d FUU, FUU, L 1... dxdydzdp d d sin U sin sin U sin sin3 U sin 3 sin 1 U sin sin 1 U sin cos 1 L cos cos 1 L cos cos 1 L cos Eigt transverse-spin-dependent azimutal asymmetries () appear in IDI x-section Four twist- s (ivers, Collins, pretzelosity, Kotzinian-Mulders) Four iger-twist sin( s) U sin( s) U sin(3 s) U q 1 1q q 1 1q q 1 1q WW sin( s ) 1 q q U Q 1 H1 q f1 D1 q WW sin( s) U cos( s ) L WW cos( s ) L f Q 1 q q Q 1 H1 q f1 D1 q g 1 q 1 D H H WW cos(s) L D g q 1 1q D 1q q Q g1 D1 q +... wist- wist pril 017 Bakur Parsamyan DI017 14

15 IDI and single-polarized DY x-sections d FUU, FUU, L 1... dxdydzdp d d IDI d d sin U sin sin U sin sin3 U sin 3 sin 1 U sin sin 1 U sin cos 1 L cos cos 1 L cos cos 1 L cos F 1 U F U 1 1 U cos C cosc sin C U sin cos C sinc sin C sinc sin C sin DY cosc cosc sin C U cos sinc sin C L sin C L sinc sin C L sin sin sinc C C sin sinc sin C sin C sin C C 5 pril 017 Bakur Parsamyan DI017 15

16 IDI and single-polarized DY x-sections at twist- (LO) LO d dxdydzdp d d cos 1 UU cos sin UL UU, UU, L sin sin U sin sin U sin sin3 U sin 3 L F cos L F L 1 1 cos LL IDI IDI-DY bridge d d LO F 1cos 1 U C cosc 1 D sin U cos C C sinc L sin C L sin C sin sin sinc sin C D sin C sinc sin C were D sin / 1cos sin C C DY C cos UU sin( s) U sin( s) U sin( 3 s) U sin UL H q 1 1q f D q 1 1q H q 1 1q H q 1 1q H q 1L 1q... Boer-Mulders ivers ransversity Pretzelosity Worm-gear L cos U sin sin( C ) sin( sin L C C C f q q 1, 1,p q q 1, 1,p q 1, q q 1, 1,p ) q q 1, 1, p f q 1 L, p 5 pril 017 LL g D, g D q cos ( s) q 1L 1q L 1 1q : FFs, furter constrained by te e+e- process. Bakur Parsamyan DI017 Double polarized DY only 16

17 Key Issues of MDs to be nswered/ested by Experiments ignals Factorization and universality: different processes Properties of QCD evolution: different energies Flavor dependence (u, d, തu, d, ҧ s, s, ҧ g): different targets and tagged adrons 17

18 Leading-wist ransverse-momentum Dependent Parton Density Function (MDs) spin of te nucleon Nucleon Quark, Gluon U L spin of te parton k of te parton U number density f 1 q,g (x, k ) Boer-Mulders 1 q,g (x, k ) L Helicity q,g (x, k ) g 1L worm-gear L q,g 1L (x, k ) ivers q,g (x, k ) f 1 Kotzinian- Mulders worm-gear q,g g 1 (x, k ) ransversity 1 q,g (x, k ) Pretzelosity q,g (x, k ) 1 18

19 UNPOLRIZED RNVERE MOMENUM DIRIBUION 19

20 Unpolarized Quark ransverse Momentum distributions f 1 q (x, k ) IDI P zk P k : intrinsice parton transverse momentum : transverse momentum gained during fragmentation Drell-Yan q k k B P Difficult to separate k and P in IDI only. 0

21 Parameterizations of MDs a: parton flavor Baccetta et al., arxiv:

22 HERME: IDI Carged Hadron Multiplicities PRD 87, (013) [arxiv: ]

23 COMP: IDI Carged Hadron Multiplicities Eur. Pys. J. C73, 531 (013) [arxiv: ] 3

24 Fixed-arget Drell-Yan Experiments 800 GeV E615, Pys. Rev. D43, 815 (1991) E88, Pys. Rev. D3, 604 (1981) 4

25 ransverse Momentum Distribution of Z Production Baccetta et al., arxiv:

26 Global nalysis of f 1 q (x, k ) FFs for IDI: NLO DEH for π; LO D for K. P and k are correlated in te extraction. average values arxiv: arxiv: arxiv: arxiv: arxiv: arxiv: arxiv: Baccetta et al., arxiv: ignals of intrinsic k and IDI processes. No flavor dependence. in DY 6

27 BOER-MULDER FUNCION 7

28 qq O Drell-Yan decay angular distributions annilation parton model: 0 ( s ) =1, = =0; and are te decay polar and azimutal angles of te μ + in te dilepton rest-frame Collins-oper frame d (1 cos sin cos sin cos ) d 0 ((1 cos ) (1 3cos ) 1 sin cos sin cos ) Lam-ung relation (1978) Collinear pqcd 1 : O( ), 1 =0 ; s 0 8

29 CERN: Violation of L Relation Z. Pys. 37 (1988) 545 +W 140 GeV +W 194 GeV +W 86 GeV 1 =0 P [GeV] 9

30 FNL: Violation of Lam-ung Relation PRD 39, 9 (1989) 5-GeV +W 1 =0 cos modulation at large p 30

31 zimutal symmetries Require Nontrivial pin Correlation e most general q തq spin density matrix ( qq, ) 1 {1 1 Fj ( e j ) 1 Gj 1 ( e j ) H ij ( ei ) ( e j )} 4 1 H H Violation of L relation: (1 ) 4 1 H Collinear case: H H, H H 0, 0 Brandenburg, Nactmann & Mirkes, ZPC 60 (1993) 697 Nonzero κ requires te correlation of te spins of quark and antiquark. 33 Wat will be te mecanism? 31

32 Brandenburg, Nactmann & Mirkes [Z. Py. C 60 (1993) 697]: QCD Vacuum Effect O. Nactmann, EC DY worksop, fm spin-flip syncrotron gluons O. Nactmann / nnals of Pysics 350 (014)

33 Boer [PRD 60, (1999)]: Hadronic Effect, Boer-Mulders Functions pin-orbit correlation of transversely polarized noncollinear partons inside an unpolarized adron Boer-Mulders Function : a correlation between quark's k and transverse spin 1 in an unpolarized adron (, q ) (B,q) (, q ) (B,q) UU f1 f1 1 1 cos ; 1 ( N) 1 ( ) 0 for large k Consistency of factorization in term of MDs 33

34 Consistency of L relation in p+p and p+d DY: E866 (PRL 99 (007) 08301; PRL 10 (009) 18001) ν(π - Wµ + µ - X)~ [valence 1 (π)] * [valence 1 (p)] ν(pdµ+µ-x) ~ [valence 1 (p)] * [sea 1 (p)] ea-quark BM functions are muc smaller tan valence quarks. 34

35 Boer-Mulders functions from unpolarized pd and pp Drell-Yan data Z. Lu and I. cmidt, PRD 81, (010) V. Barone et al., PRD 8, (010) ignal of Boer-Mulders functions in Drell-Yan processes. Flavor dependence. 35

36 IDI: cos φ modulation 1 :Boer-Mulders distribution H 1 :Collins fragmentation function twist- BM contribution flavor dependent twist-4 Can contribution (te noncollinear kinematics of quarks) flavor blind 36

37 Extraction of Boer-Mulders function from IDI HERME, IP Conf. Proc. 1149, 43 (009). Barone et al., PRD 81, (010) [arxiv: ] 37

38 Extraction of Boer-Mulders function from IDI HERME, IP Conf. Proc. 1149, 43 (009). Barone et al., PRD 81, (010) [arxiv: ] 38

39 Extraction of Boer-Mulders function from IDI COMP, arxiv: ; arxiv: wist-4 Can contribution comparable to twist- Boer-Mulders contribution Barone et al., PRD 81, (010) [arxiv: ] 39

40 Extraction of Boer-Mulders function from IDI and Drell-Yan data IDI Barone et al., PRD 81, (010) [arxiv: ] DY u p d p u p d p DY u p d p u p d p Barone et al., PRD 8, (010) [arxiv: ] Lu et al., PRD 81, (010) [arxiv: ] ignals of Boer-Mulders functions in Drell-Yan and IDI processes. Flavor dependence. 40

41 HERME: cos φ modulation in IDI off unpolarized Protons PRD 87, (013) [arxiv: ] 41

42 HERME: cos φ modulation in IDI off unpolarized Deuterons PRD 87, (013) [arxiv: ] 4

43 COMP: cos φ modulation in IDI off unpolarized Deuterons NPB 886, 1046 (014) [arxiv: ] 43

44 Extraction of Boer-Mulders function from IDI COMP HERME Barone et al., PRD 91, (015) [arxiv: ] 44

45 Extraction of Boer-Mulders function from IDI someow disappointing output of our fits is te indeterminacy on te extraction of te Boer-Mulders function, wic seems to play a minor role in te asymmetries. Barone et al., PRD 91, (015) [arxiv: ] ignals of Boer-Mulders functions in IDI processes??? 45

46 RNVERIY 46

47 IDI x-section: transverse spin dependent part d FUU, FUU, L 1... dxdydzdp d d sin U sin sin U sin sin3 U sin 3 sin 1 U sin sin 1 U sin cos 1 L cos cos 1 L cos cos 1 L cos Eigt transverse-spin-dependent azimutal asymmetries () appear in IDI x-section Four twist- s (ivers, Collins, pretzelosity, Kotzinian-Mulders) Four iger-twist 5 pril 017 Bakur Parsamyan DI017 sin( s) U sin( s) U sin(3 s) U q 1 1q q 1 1q q 1 1q WW sin( s ) 1 q q U Q 1 H1 q f1 D1 q WW sin( s) U cos( s ) L WW cos( s ) L f Q 1 q q Q 1 H1 q f1 D1 q g 1 q 1 D H H WW cos(s) L D g q 1 1q D 1q q Q g1 D1 q +... wist- wist e 1 ( x) H (, z p q sin( ) 1 q q q s U q eq q( x) Dq ( z, p ) 1 q : ransversity H 1q :Collins FFs Collins asymmetry +... ) 47

48 HERME: Collins asymmetry off polarized Protons PRL 94, 0100 (005) [ep-ex/ ] PLB 693, 11 (010) [arxiv: ] 48

49 COMP: Collins asymmetry off polarized Deuterons and Protons PLB 673, 17 (009) [arxiv: ] PLB 744, 50 (015) [arxiv: ] 49

50 HLL : Collins asymmetry off polarized Helium PRL 107, (011) [arxiv: ] PRC 90, (014) [arxiv: ] 50

51 Belle: wo-pion zimutal Correlation H 1q :Collins FFs R R sin 1 cos( ) 1 cos unlike sign like sign 0, 1 51

52 Extraction of ransversity and Collins FFs from IDI and Belle data ransversity Collins FFs Favored u quark d quark Unfavored nselmino et al., PRD 87, (013) [arxiv: ] ignals of transversity and Collins FFs s in IDI and ee processes. Flavor dependence. 5

53 Extraction of ransversity and Collins FFs from IDI, Belle and Barbar data ransversity Collins FFs Favored u quark d quark Unfavored nselmino et al., PRD 9, (015) [arxiv: ] ignals of transversity and Collins FFs s in IDI and ee processes. Flavor dependence. 53

54 Nucleon ensor Carge from Extracted ransversity ensor Carge q [ q( x) q( x)] dx 1 0 ensor carges: 1 : Extractions from global fits (using two different Collins FF parameterizations) -10: Predictions from various models (including LQCD) Discrepancy could be caused by neglecting sea quark transversity in te fit ensor carges are smaller tan axial carge. u d

55 Diadron IDI: ransversity and DiFFs φ : azimutal angle of diadron φ R : azimutal angle of target-polarization transversity Polarized diadron Fragmentation Functions 55

56 rtru Collins symmetry of Diadron Pairs in e+e- Process ee ( ) jet ( ) jet X 1 Polarized diadron Fragmentation Functions Unpolarized diadron Fragmentation Functions 56

57 Belle: rtru Collins symmetry of Dipion Pairs PRL 107, (011) [arxiv: ] 57

58 Extraction of DiFFs from rtru Collins symmetry Courtoy et al., PRD 85, (01) [arxiv: ] 58

59 HERME: IDI Diadron zimutal symmetry off Unpolarized Protons HERME, JHEP 06 (008) 017, [arxiv: ] 59

60 COMP: IDI Diadron zimutal symmetry off Unpolarized Deuterons and Protons PLB 713, 10 (01) [arxiv: ] 60

61 Extraction of ransversity and DiFFs from IDI and Belle data Baccetta et al., PRL 107, (011) [arxiv: ]; JHEP 03, 119 (013) [arxiv: ] 61

62 Extraction of ransversity from single-adron and diadron IDI transversity extraction from te Collins effect of single-adron IDI [arxiv: ] offer bound Baccetta et al., PRL 107, (011) [arxiv: ]; JHEP 03, 119 (013) [arxiv: ] Universality of transversity in te single-adron and diadron IDI. Flavor dependence. 6

63 IVER FUNCION 63

64 IDI x-section: transverse spin dependent part d FUU, FUU, L 1... dxdydzdp d d sin U sin sin U sin sin3 U sin 3 sin 1 U sin sin 1 U sin cos 1 L cos cos 1 L cos cos 1 L cos Eigt transverse-spin-dependent azimutal asymmetries () appear in IDI x-section Four twist- s (ivers, Collins, pretzelosity, Kotzinian-Mulders) Four iger-twist sin( s) U sin( s) U sin(3 s) U q 1 1q q 1 1q q 1 1q WW sin( s ) 1 q q U Q 1 H1 q f1 D1 q WW sin( s) U cos( s ) L WW cos( s ) L f Q 1 q q Q 1 H1 q f1 D1 q g 1 q 1 D H H WW cos(s) L D g q 1 1q D 1q q Q g1 D1 q f 1 q : ivers D 1q : FFs wist ivers asymmetry wist-3 q sin( ) q q 1 1q s U q eq 1q e f ( x, p / z) D ( z, p ) q( x, p / z) D ( z) 5 pril 017 Bakur Parsamyan DI017 64

65 MD ivers Function 1 q f ( x, k, ) ˆ / fq/ p( x, k ) f1 (, ) ( N ) q p x k p k M Unpolarized proton ransversely-polarized proton k y k y k x nonzero ivers function is considered to be strong evidence for te presence of quark orbital angular momentum. kx 65

66 HERME: ivers symmetry off Polarized Protons PRL 103, 1500 (009) [arxiv: ] 66

67 COMP: ivers symmetry off Polarized Deuterons PLB 673, 17 (009) [arxiv: ] 67

68 COMP: ivers symmetry off Polarized Protons PLB 744, 50 (015) [arxiv: ] 68

69 Nonzero ivers symmetries from IDI COMP, PLB 744 (015) 50 ivers Functions ignals of ivers functions in IDI. Flavor dependence. PRD 86, (01) [arxiv: ] 69

70 ivers symmetries of π + (u ҧ in IDI d) and K + (us) ҧ K+ iv > π+ iv : ivers functions of sea quarks ( ҧ PLB 744, 50 (015) [arxiv: ] s, d) ҧ migt be large. 70

71 ign Cange of ivers Functions J.C. Collins, Pys. Lett. B 536 (00) 43.V. Belitsky, X. Ji, F. Yuan, Nucl. Pys. B 656 (003) 165 D. Boer, P.J. Mulders, F. Pijlman, Nucl. Pys. B 667 (003) 01 Z.B. Kang, J.W. Qiu, Pys. Rev. Lett. 103 (009) Drell-Yan IDI ivers 1*ivers DY IDI QCD gluon gauge link (Wilson line) in te initial state (DY) vs. final state interactions (IDI). Fundamental predictions from perturbative QCD and MD pysics will be tested. 71

72 015 U.. Long Range Plan ttps://science.energy.gov/~/media/np/nsac/pdf/015lrp/015_lrpn_ pdf 7

73 B. Parsamyan, DI017 73

74 ransverse of W in polarized pp collisions at RHIC R, PRL 116 (016)

75 Predicted ivers asymmetry N, assuming a sign cange of te IDI ivers functions nselmino et al.,, JHEP04 (017) 046 [arxiv: ] ignals of ivers functions in W production. Hints of (non)universality. 75

76 QCD Evolution of MDs ybat, Collins, Qiu and Rogers, PRD 85, (01) 76

77 Predicted ivers symmetries in COMP wit QCD Evolution un and Yuan, PRD 88, (013) Ecevarria, Idilbi, Kang and Vitev, PRD 89, (014) 77

78 ivers symmetries (x,z,p,q ) COMP, PLB 770 (017)

79 ivers symmetry in Drell-Yan: dσ LO d 4 qdω = α em Fq σ U LO LO ቄ 1 + D sin θ sin s f1 f 1 U cos φ cos φ Density( ) ivers( ) B + Ԧ ቂ sin φ s sin φ s COMP, arxiv: [ep-ex] 79

80 ivers symmetry in Drell-Yan sign cange no sign cange COMP, arxiv: [ep-ex]. PRL accepted. ignals of ivers functions in Drell-Yan process. Evidence of universality and MD factorization. 80

81 ummary tatus k Boer- Mulders ignals Factorization and universality QCD evolution Flavor dependence IDI: YE DY: YE YE for bot IDI and DY? IDI:? DY: YE ransversity IDI: YE DY:?? YE for IDI ivers IDI: YE DY: YE YE for bot IDI and DY? Under study Under study Under study Under study Quark: NO Gluon:? Quark: YE Gluon:? Quark: YE Gluon:? Quark: YE Gluon:? 81

82 Experimental Prospects COMP-II: polarized DY wit polarized targets JLB1: IDI wit polarized targets RHIC: DY and W production wit polarized proton beam Fermilab: polarized DY wit polarized targets EIC: IDI wit polarized proton beam LHC: DY and DY+jets 8

83 Explored Regions Gluon and sea quarks Valence quarks arxiv:

84 Electron Ion Collider Improved precision of ivers Functions ccess to te Gluon MDs arxiv:

85 References vakian et al., Experimental results on MDs, Eur. Pys. J. 5 (016) no.6, 150. Boglione and Prokudin, Penomenology of transverse spin: past, present and future, arxiv: Perdekamp and Yuan, ransverse pin tructure of te Nucleon, arxiv: J.C. Peng s talk in Worksop on adron tomograpy at J-PRC and KEKB, MDs: Present and Future. opical issue on te 3-D structure of te nucleon, Eur. Pys. J. 5 (016) no.6 (June 016). 85

86 ank you for attending! 86