Transversity: present and future. Alessandro Bacchetta

Transcription

1 Transversity: present and future Alessandro Bacchetta

2 Outline Trento, Alessandro Bacchetta Transversity: present and future 2

3 Outline Overview of experimental possibilities Trento, Alessandro Bacchetta Transversity: present and future 2

4 Outline Overview of experimental possibilities First extraction from SIDIS Trento, Alessandro Bacchetta Transversity: present and future 2

5 Outline Overview of experimental possibilities First extraction from SIDIS New SIDIS data Trento, Alessandro Bacchetta Transversity: present and future 2

6 Outline Overview of experimental possibilities First extraction from SIDIS New SIDIS data Other observables Trento, Alessandro Bacchetta Transversity: present and future 2

7 Outline Overview of experimental possibilities First extraction from SIDIS New SIDIS data Other observables Some other issues worth mentioning Trento, Alessandro Bacchetta Transversity: present and future 2

8 Outline Overview of experimental possibilities First extraction from SIDIS New SIDIS data Other observables Some other issues worth mentioning Not much on TMD functions Trento, Alessandro Bacchetta Transversity: present and future 2

9 Warning In the talk, I ll make use of three notations for transversity: q h1 δ q Δ q T Trento, Alessandro Bacchetta Transversity: present and future 3

10 Overview of experimental possibilities

11 Where to observe it: SIDIS Process Experiment Observable Grade lp lπ X lp l( ππ) X lp lλx Hermes, Compass, JLab, EIC Hermes, Compass, JLab@12GeV, EIC Hermes, Compass, JLab@12GeV, EIC h H h H h1 H1 h1 H1 Trento, Alessandro Bacchetta Transversity: present and future 5

12 Where to observe it: SIDIS CAVEAT: grades reflect my personal opinion! It would be nice to discuss them together Process Experiment Observable Grade lp lπ X lp l( ππ) X lp lλx Hermes, Compass, JLab, EIC Hermes, Compass, JLab@12GeV, EIC Hermes, Compass, JLab@12GeV, EIC h H h H h1 H1 h1 H1 Trento, Alessandro Bacchetta Transversity: present and future 5

13 Where to observe it: SIDIS CAVEAT: grades reflect my personal opinion! It would be nice to discuss them together Process Experiment Observable Grade lp lπ X lp l( ππ) X lp lλx Hermes, Compass, JLab, EIC Hermes, Compass, JLab@12GeV, EIC Hermes, Compass, JLab@12GeV, EIC h H h H h1 H1 h1 H1 Talks by Miller, Bradamante, Grosse-Perdekamp, Jiang Trento, Alessandro Bacchetta Transversity: present and future 5

14 Hadron-hadron scattering Doubly polarized Singly polarized Process Experiment Observable Grade Rhic p ( p p) l l X JParc h1 h1 Pax Rhic p ( p p) π X ( p p π) p ( ππ) X ( π p) p JParc Pax Rhic, JParc Compass, Panda Rhic, JParc Compass, Panda Compass, JParc, Panda Rhic, Compass, JParc, Panda h h D fh 1 1 H 1 ( p p π ) p ΛX fh 1 1 H1 l l X h 1 h1 ( p p π ) p j( j γ ) X π( j γ) X ( π j γ) X h 1 h1 f h H h h D Trento, Alessandro Bacchetta Transversity: present and future 6

15 Hadron-hadron scattering Doubly polarized Singly polarized Process Experiment Observable Grade Rhic p ( p p) l l X JParc h1 h1 Pax Rhic p ( p p) π X JParc Pax h1 h1 D1 ( p p π) p ( ππ) X ( p p π ) p ΛX ( π p) p l l X Rhic, JParc fh 1 1 H 1 Compass, Panda Rhic, JParc fh 1 1 H1 Compass, Panda Compass, JParc, h 1 h1 Panda Talks by Bland, Grosse-Perdekamp, Goto, Dalpiaz ( p p π ) p j( j γ ) X π( j γ) X ( π j γ) X Rhic, Compass, JParc, Panda h 1 h1 f h H h h D Trento, Alessandro Bacchetta Transversity: present and future 6

16 First extraction from SIDIS

17 Transversity in SIDIS A ( x, y, z, P ) sin( φh+ φs) 2 UT h = (1 y ) C 2 2 x y kt P M P h 2 1 y + y 2 C 2 2 [ fd 1 1 ] x y h h h 1 H 1 Trento, Alessandro Bacchetta Transversity: present and future 8

18 Convolution Trento, Alessandro Bacchetta Transversity: present and future 9

19 Convolution (2) q 2 q 2 C[ fd] = x eq d ptd ktδ ( pt kt Ph z) f ( xp, T ) D ( z, k T ) q Trento, Alessandro Bacchetta Transversity: present and future 9

20 Convolution (2) q 2 q 2 C[ fd] = x eq d ptd ktδ ( pt kt Ph z) f ( xp, T ) D ( z, k T ) q Gaussian Ansatz 1 f ( x, p ) = f ( x) e 2 1 T 1 2 π pt p p 2 T 2 T D( z) 1 D ( z, k ) = e T 2 2 z π kt k k 2 T 2 T Trento, Alessandro Bacchetta Transversity: present and future 9

21 Convolution (2) q 2 q 2 C[ fd] = x eq d ptd ktδ ( pt kt Ph z) f ( xp, T ) D ( z, k T ) q Gaussian Ansatz 1 f ( x, p ) = f ( x) e 2 1 T 1 2 π pt p p 2 T 2 T D( z) 1 D ( z, k ) = e T 2 2 z π kt k k 2 T 2 T 2 q q 1 C[ fd 1 1] = x eq f1 ( xd ) 1( z) e 2 q π P h P P 2 h 2 h Trento, Alessandro Bacchetta Transversity: present and future 9

22 Data from BELLE BELLE, PRL 96 (06) Trento, Alessandro Bacchetta Transversity: present and future 10

23 Collins function Anselmino et al., PRD 75 (07) Trento, Alessandro Bacchetta Transversity: present and future 11

24 Collins function Efremov, Goeke, Schweitzer, PRD 73 (06) Anselmino et al., PRD 75 (07) Trento, Alessandro Bacchetta Transversity: present and future 11

25 Collins function Efremov, Goeke, Schweitzer, PRD 73 (06) Vogelsang, Yuan, PRD 73 (06) Anselmino et al., PRD 75 (07) Trento, Alessandro Bacchetta Transversity: present and future 11

26 Collins function Efremov, Goeke, Schweitzer, PRD 73 (06) Vogelsang, Yuan, PRD 73 (06) Anselmino et al., PRD 75 (07) Talks by Boglione, Efremov Trento, Alessandro Bacchetta Transversity: present and future 11

27 Data from Hermes and Compass PROTON HERMES, hep-ex/ HERMES, PRL 94 (05) DEUTERON COMPASS, NPB 765 (07) COMPASS, PRL 94 (05) Trento, Alessandro Bacchetta Transversity: present and future 12

28 First extraction of transversity Anselmino et al., PRD 75, (07) Trento, Alessandro Bacchetta Transversity: present and future 13

29 First extraction of transversity MILESTONE Anselmino et al., PRD 75, (07) Trento, Alessandro Bacchetta Transversity: present and future 13

30 First extraction of transversity MILESTONE Anselmino et al., PRD 75, (07) Trento, Alessandro Bacchetta Transversity: present and future 13

31 First extraction of transversity MILESTONE Anselmino et al., PRD 75, (07) Talk by Boglione Trento, Alessandro Bacchetta Transversity: present and future 13

32 For comparison: helicity distribution AAC, Hirai et al. PRD 69 (04) Trento, Alessandro Bacchetta Transversity: present and future 14

33 For comparison: helicity distribution NOTE: treatment of statistical uncertainty? AAC, Hirai et al. PRD 69 (04) Trento, Alessandro Bacchetta Transversity: present and future 14

34 Comparison with some models [1] Soffer et al. PRD 65 (02) [2] Korotkov et al. EPJC 18 (01) [3] Schweitzer et al., PRD 64 (01) [4] Wakamatsu, PLB 509 (01) [5] Pasquini et al., PRD 72 (05) [6] Anselmino et al., PRD 75 (07) Trento, Alessandro Bacchetta Transversity: present and future 15

35 Comparison of tensor charges χ quark spectator lattice non-relativistic bag χ quark soliton 2 χ quark soliton 1 Barone, Drago, Ratcliffe, PR 359 (2002) Trento, Alessandro Bacchetta Transversity: present and future 16

36 Comparison of tensor charges 2.4 GeV GeV 2 χ quark lattice spectator non-relativistic bag χ quark soliton 2 χ quark soliton 1 Wakamatsu, [hep-ph] Barone, Drago, Ratcliffe, PR 359 (2002) Trento, Alessandro Bacchetta Transversity: present and future 16

37 Limits of the extraction Trento, Alessandro Bacchetta Transversity: present and future 17

38 Limits of the extraction Evolution equations for unintegrated distribution function see e.g. Ceccopieri, Trentadue, PLB 636 (06) Trento, Alessandro Bacchetta Transversity: present and future 17

39 Limits of the extraction Evolution equations for unintegrated distribution function see e.g. Ceccopieri, Trentadue, PLB 636 (06) Talk by Boer Trento, Alessandro Bacchetta Transversity: present and future 17

40 Limits of the extraction Evolution equations for unintegrated distribution function see e.g. Ceccopieri, Trentadue, PLB 636 (06) Talk by Boer Gaussian transverse-momentum Ansatz Trento, Alessandro Bacchetta Transversity: present and future 17

41 Limits of the extraction Evolution equations for unintegrated distribution function see e.g. Ceccopieri, Trentadue, PLB 636 (06) Talk by Boer Gaussian transverse-momentum Ansatz No sea quarks taken into consideration Trento, Alessandro Bacchetta Transversity: present and future 17

42 Limits of the extraction Evolution equations for unintegrated distribution function see e.g. Ceccopieri, Trentadue, PLB 636 (06) Talk by Boer Gaussian transverse-momentum Ansatz No sea quarks taken into consideration Limited x-range Trento, Alessandro Bacchetta Transversity: present and future 17

43 New SIDIS data

44 Recent data from HERMES OLD Trento, Alessandro Bacchetta Transversity: present and future 19

45 Recent data from HERMES OLD NEW M. Diefenthaler, talk at DIS07 Trento, Alessandro Bacchetta Transversity: present and future 19

46 Recent data from HERMES OLD NEW M. Diefenthaler, talk at DIS07 Talk by Miller Trento, Alessandro Bacchetta Transversity: present and future 19

47 Recent data from HERMES KAONS Trento, Alessandro Bacchetta Transversity: present and future 20

48 Recent data from HERMES KAONS π 0 M. Diefenthaler, talk at DIS07 Trento, Alessandro Bacchetta Transversity: present and future 20

49 Recent data from HERMES KAONS π 0 M. Diefenthaler, talk at DIS07 Talk by Miller Trento, Alessandro Bacchetta Transversity: present and future 20

50 Recent data from COMPASS IDENTIFIED CHARGED HADRONS A. Bressan, talk at DIS07 Trento, Alessandro Bacchetta Transversity: present and future 21

51 Recent data from COMPASS IDENTIFIED CHARGED HADRONS A. Bressan, talk at DIS07 Talk by Bradamante Trento, Alessandro Bacchetta Transversity: present and future 21

52 Recent data from BELLE OLD Trento, Alessandro Bacchetta Transversity: present and future 22

53 Recent data from BELLE OLD NEW R. Seidl, talk at DIS07 Trento, Alessandro Bacchetta Transversity: present and future 22

54 Recent data from BELLE OLD NEW R. Seidl, talk at DIS07 Talk by R. Seidl Trento, Alessandro Bacchetta Transversity: present and future 22

55 Future data from SIDIS COMPASS proton data JLab HallA neutron data data Trento, Alessandro Bacchetta Transversity: present and future 23

56 Other observables

57 Transversity and dihadron FF Efremov, Mankiewicz, Tornquist, PLB 284 (92) Collins, Heppelmann, Ladinsky, NPB 420 (94) Jaffe, Jin, Tang, PRL 80 (98) A ( x, y, z, θ, M ) sin( φs+ φr) 2 UT ππ (1 y ) x e h ( x) H ( z, θ, M ) 2 2 x y q = q 2 q 1 1 ππ 1 y y 2 2 x e 2 2 q f x D zθ M x y q 2 1( ) 1(,, ππ ) Trento, Alessandro Bacchetta Transversity: present and future 25

58 Theoretical advantages Trento, Alessandro Bacchetta Transversity: present and future 26

59 Theoretical advantages Collinear factorization Trento, Alessandro Bacchetta Transversity: present and future 26

60 Theoretical advantages Collinear factorization No convolution in transverse momentum Trento, Alessandro Bacchetta Transversity: present and future 26

61 Theoretical advantages Collinear factorization No convolution in transverse momentum Evolution equations known Ceccopieri, Radici, Bacchetta, PLB 650 (07) Trento, Alessandro Bacchetta Transversity: present and future 26

62 Preliminary data P. van der Nat, hep-ex/ Trento, Alessandro Bacchetta Transversity: present and future 27

63 Preliminary data P. van der Nat, hep-ex/ Based on Bacchetta, Radici, PRD 74 (06) Trento, Alessandro Bacchetta Transversity: present and future 27

64 Preliminary data P. van der Nat, hep-ex/ Based on Bacchetta, Radici, PRD 74 (06) Talk by M. Radici Trento, Alessandro Bacchetta Transversity: present and future 27

65 Transversity and twist-3 FF Jaffe, Ji, PRL 71 (93) Mulders, Tangerman, NPB 461 (96) A sinφs UT ( x, y, z) = (2 y) 1 y 2 M H ( z) q 2 2 x y h 2 q x eq h1 ( x) Q q z 2 1 y + y 2 2 x e 2 2 q f1( x) D1( z) x y q Trento, Alessandro Bacchetta Transversity: present and future 28

66 Transversity in Drell-Yan Ralston, Soper, NPB 152 (79) y(1 y ) x x q 1 2 ) = 2 A ( x, x, y TT (1 2 y + y ) x x e xh ( x ) x h ( x ) 2 q q q q e xf ( x ) x f ( x ) 2 q q q Trento, Alessandro Bacchetta Transversity: present and future 29

67 Drell-Yan at RHIC Martin, Schäfer, Stratmann, Vogelsang, PRD60 (99) Trento, Alessandro Bacchetta Transversity: present and future 30

68 Jet and photon production at RHIC Soffer, Stratmann, Vogelsang, PRD65 (02) Mukherjee, Stratmann, Vogelsang, PRD72 (05) Trento, Alessandro Bacchetta Transversity: present and future 31

69 Drell-Yan at PAX PAX, hep-ex/ Efremov, Goeke, Schweitzer, EPJ C35 (04) Trento, Alessandro Bacchetta Transversity: present and future 32

70 J/ψ production at PAX Anselmino, Barone, Drago, Nikolaev, PLB594 (04) Trento, Alessandro Bacchetta Transversity: present and future 33

71 Jet and photon production at PAX Mukherjee, Stratmann, Vogelsang, PRD72 (05) Trento, Alessandro Bacchetta Transversity: present and future 34

72 Drell-Yan at JPARC Contalbrigo, Drago, Lenisa, hep-ph/ Trento, Alessandro Bacchetta Transversity: present and future 35

73 A few other issues

74 Evolution equations Barone, Drago, Ratcliffe, PR 359 (2002) Hayashigaki, Kanazawa, Koike, PRD56 (97) Trento, Alessandro Bacchetta Transversity: present and future 37

75 Transverse momentum dependence Kawamura, Kodaira, Tanaka, hep-ph/ Trento, Alessandro Bacchetta Transversity: present and future 38

76 Transversity sum rule = dx g ( x) + L + L 2 2 a= q, q, g a= q, q a q g 1 z z 1 1 = dx h ( x) + L + L 2 2 a q g 1 T T Bakker, Leader, Trueman, PRD 70 (04) Trento, Alessandro Bacchetta Transversity: present and future 39

77 Transversity sum rule = dx g ( x) + L + L 2 2 a= q, q, g a= q, q a q g 1 z z 1 1 = dx h ( x) + L + L 2 2 a q g 1 T T Bakker, Leader, Trueman, PRD 70 (04) CRITICISM: sum rule should be derived from hadronic matrix elements of conserved quark-gluon operators. There is no such operator for transversity. Trento, Alessandro Bacchetta Transversity: present and future 39

78 A possible compromise There is another sum rule, derived in the standard way 1 1 = dx g ( x) + L + L 2 2 a= q, q, g a q g T T T O. Teryaev, B. Pire and J. Soffer, hep-ph/ P.G. Ratcliffe, hep-ph/ Trento, Alessandro Bacchetta Transversity: present and future 40

79 A possible compromise There is another sum rule, derived in the standard way 1 1 = dx g ( x) + L + L 2 2 a= q, q, g a q g T T T O. Teryaev, B. Pire and J. Soffer, hep-ph/ P.G. Ratcliffe, hep-ph/ These sum rule could correspond to BLT sum rule if g ( x) = h ( x) a T a= q, q, g a= q, q What kind of approximation is this? Free quarks? Wandzura--Wilczek like? a 1 Trento, Alessandro Bacchetta Transversity: present and future 40

80 Gluon transversity (linearity) Artru, Mekhfi, ZPC 45 (90) Trento, Alessandro Bacchetta Transversity: present and future 41

81 Gluon transversity (linearity) Artru, Mekhfi, ZPC 45 (90) Requires linearly polarized spin-1 target Trento, Alessandro Bacchetta Transversity: present and future 41

82 Gluon transversity (linearity) Artru, Mekhfi, ZPC 45 (90) Requires linearly polarized spin-1 target Gluon linearity in the photon: dihadron photoproduction Trento, Alessandro Bacchetta Transversity: present and future 41

83 Gluon transversity (linearity) Artru, Mekhfi, ZPC 45 (90) Requires linearly polarized spin-1 target Gluon linearity in the photon: dihadron photoproduction Gluon linearity in the deuteron: DIS with linearly polarized deuteron Trento, Alessandro Bacchetta Transversity: present and future 41

84 Conclusions Trento, Alessandro Bacchetta Transversity: present and future 42

85 Conclusions With present data, there is already work for the next few years Trento, Alessandro Bacchetta Transversity: present and future 42

86 Conclusions With present data, there is already work for the next few years More data will come in the near future from Hermes, Compass, JLab, Rhic Trento, Alessandro Bacchetta Transversity: present and future 42

87 Conclusions With present data, there is already work for the next few years More data will come in the near future from Hermes, Compass, JLab, Rhic Hopefully, contributions from future facilities (JParc, Fair, EIC) Trento, Alessandro Bacchetta Transversity: present and future 42

88 Conclusions With present data, there is already work for the next few years More data will come in the near future from Hermes, Compass, JLab, Rhic Hopefully, contributions from future facilities (JParc, Fair, EIC) It s the beginning of a transverse era! Trento, Alessandro Bacchetta Transversity: present and future 42

89 Transversity in SIDIS (1 y ) kt Ph dσ dσ... sin( φ ) C 2 2 h φs 1 H1... x y M P h y y 2 dσ + dσ + C 2 2 [ fd 1 1 ] + cos2 φh... + cos φh... x y h h Trento, Alessandro Bacchetta Transversity: present and future 43