Transverse Momentum Dependent distributions:theory...phenomenology, future

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1 Transverse Momentum Dependent distributions:theory...phenomenology, future Umberto D Alesio Physics Department and INFN University of Cagliari, Italy QCD-N6, 2 nd Workshop on the QCD structure of the nucleon June 12-16, 26 Monte Porzio Catone, Rome, Italy [ M. Anselmino, M. Boglione, A. Kotzinian, E. Leader, S. Melis, F. Murgia, A. Prokudin] U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 1

2 Outline Motivations: Understanding transverse degrees of freedom in a hadron: s and k. h 1 : wanted! TMD s: tool to SSA; window on partonic orbital angular momentum? Help from: f1t (Sivers), H 1 (Collins), h 1 (Boer-Mulders), D1T (Other leading twist TMD s not considered here) Strategy: TMD process kinematics(set-ups) (polarizing ff). SSA and DSA: clear vs. involved cases (SIDIS, DY, e + e, pp CX) present vs. future Summary U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 2

3 - Formal issues of TMD s and their still open problems (gauge invariant definitions, universality, factorization, evolution, resummation, soft factor, models...) accounted in Bacchetta and Metz s talks. - Focus on TMD s within a phenomenological approach: which, where and how. 1. Processes 2. kinematics (role of phases) - Short overview on standard cases; - Deeper insight in cases where there is a not clear access to TMD s. U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 3

4 Hadronic Processes U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 4

5 SIDIS lp l hx: A UT - ok k factorization (Ji, Ma, Yuan 4, 5) - LO: partons quarks - azimuthal dependences: - φ S φ h f1t (Sivers: direct access), - φ S + φ h h 1 H1 (transversity - Collins) a) h = π: basic case b) h = K + (u s), K (ūs) same but access to strange f 1T : D s(k) different flavour weighting even in the ud sector: i.e. D u (π )/Dū(π ) < D u (K )/Dū(K ) complementary role - experim. data from: HERMES, COMPASS, CLAS - analysis: Collins et al. 5, Efremov et al. 5, Vogelsang and Yuan 5, Anselmino et al. 5 accounted in Schweitzer, Boglione, Elschenbroich talks U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 5

6 e + e ππx - ok k factorization - LO: partons quarks - azimuthal dependences: cos(2φ): H1 H1 (Collins: direct access) data from BELLE analysis: Efremov et al. 6, Anselmino et al. (in progress) accounted in Schweitzer, Boglione, Seidl talks U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 6

7 DY: pp l + l X : A T T, A N p p l + l X [A T T ]: - azimuthal dependence: cos(2φ) : h 1 h 1 (transversity: direct access) but - pp case at large s (RHIC): sea region and h 1 q small values (statistics) - p p case at moderate s (PAX): valence and quadratic h 1q large values (resummation?) estimates: Martin et al. 98, 99, Anselmino et al. 5, Shimizu et al. 5, Barone et al. 6 accounted in Metz talk U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 7

8 p p l + l X [A N ] - ok k factorization (Ji, Ma, Yuan 4, 5) - LO: partons quarks - azimuthal dependence: - dφ e+ e f 1T (Sivers: direct access) - φ e+ e h 1 h 1 (transversity - Boer-Mulders) estimates: Efremov et al. 5, Anselmino et al 3, 5 Unpolarized SIDIS and DY - azimuthal dependences: cos(2φ) : h 1 H1 (mixed with Cahn effect) cos(2φ) : h 1 h 1 estimates: Boer 99, Gamberg et al. 3, Anselmino et al. 5 data: EMC, FNAL-E665 accounted in Boglione, Gamberg, Goldstein talks U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 8

9 p p CX : A N - the dirty case - k factorization still UNKNOWN, but: 1. first data on SSA and more are coming 2. if universality is broken in a stronger way (not simply a change of sign), possible well defined prescription and/or channel selection - LO: partons quarks and gluons - no azimuthal dependences...not really true (see below) - many effects at work...but help from C(= π, D, Λ, γ) and kinematics (Anselmino et al. 5, 6) U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 9

10 a) p p πx : phases f1t (Sivers) ***** h 1 H1 (transversity - Collins) ** h 1 h 1 (transversity - Boer-Mulders) * f1t h 1 H1 (Sivers - Boer-Mulders - Collins) - Phenomenological ansatz, Anselmino et al. 5, 6 dσ A,S A+B,S B C+X = ρ a/a,s A λ a,λ ˆf a/a,sa (x a a, k a ) ρ b/b,s B λ b,λ b a,b,c,d,{λ} ˆf b/b,sb (x b, k b ) ˆM λc,λ d ;λ a,λ b ˆM λ c,λ d ;λ a,λ b ˆD λ C,λ C λ c,λ c non-planar partonic scattering: relative azimuthal phases at work! (z, k C) U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 1

11 b) p p DX: phases f1t (Sivers) ***** partonic subprocesses: q q c c, gg c c = dσ dσ = Anselmino et al. 5 c) pp Λ X: P T phases D1T (polarizing ff) ***** h 1 H 1 (Boer-Mulders - transversity ff) ** h 1 h 1 D1T (Boer-Mulders - polar. ff) * UD et al. in progress U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 11

12 p p γx : A N phases f1t (Sivers) ***** h 1 h 1 (transversity - Boer-Mulders) *** - partonic subprocesses: q q γg, qg γq - one vertex is QED e 2 q p p jetx : A N f 1T (Sivers) h 1 h 1 (transversity - Boer-Mulders) U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 12

13 p p C 1 C 2 X : A N p p jet jet X nearly back-to-back gluon, Boer and Vogelsang 4 f 1T p p π jetx separation of contributions: f 1T h 1 H 1 U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 13

14 help from kinematics U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 14

15 SIDIS and e + e : ok - a combined analysis h 1 and H1 ; - universality of H1 SIDIS and DY: ok - f1t for quarks; - universality (sign change) of f1t : a crucial test. - new data from COMPASS on H targets and CLAS relevant to cover different and complementary x regions; - estimates for RHIC, JPARC, PAX; U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 15

16 .1.5 (1)q x f 1T (x) d-quark Ref.[18] Ref.[21] x f 1T (1/2)q (x) Ref.[18] Ref.[19] d-quark u-quark HERMES x-range x u-quark HERMES x-range x Comparison of different extractions of the Sivers function (1-σ). [18] Anselmino et al., [19] Vogelsang and Yuan, [21] Collins et al., 5 U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 16

17 s = GeV -.5 <A N > -.1 4<M<6 GeV, y < x F y < M (GeV) -.5 <A N > s = 2 GeV 4<M<2 GeV, <y< x F <y<3 y < M (GeV) Predictions for A N in DY at PAX and RHIC (Anselmino et al. 5) U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 17

18 pp πx: high vs. moderate energies, forward, backward and central rapidity many contributions to A N, BUT - Sivers effect alone can describe E74 data (UD and Murgia 4). - Collins effect suppressed (other contrib.s vanishing) Anselmino et al STAR, PHENIX data on π and BRAHMS data on K ± can be explained in terms of the Sivers effect (as extracted from E74). - Forward rapidities: valence dominated; - Sensitivity to the gluon Sivers function? a) high energies (RHIC): midrapidity (PHENIX): gluon dominated [backward rapidities less useful due to phases cancellation] b) moderate energies (PAX, JPARC): backward rapidities gluon dominated and large [mid rap. valence contaminated] U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 18

19 .6.4 π + π π.6.4 π + π π A N A N (max) p T = 1.5 GeV/c KKP-LSS BBS x F x F A N at E = 2 GeV vs. x F at p T = 1.5 GeV/c. Data are from [E74] PLB (1991). Sivers effect [left] (valence-like). N u = +.4 a u = 2. b u =.3 N d =.9 a d = 2. b d =.2 Collins effect [right](full saturated). Transversity funct. and Collins funct. full saturated CONSISTENCY with SIDIS U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 19

20 .5.4 KKP-1 KKP-2 Kretzer A N.1 A N x F x F Predictions of A N (pp π X) in terms of Sivers effect alone [U.D. and F. Murgia PRD7 (5)] at s = 2 GeV and η = 3.8 vs. x F Data are from [STAR] PRL92 (4). Predictions of A N (pp π X) in terms of Sivers effect alone at s = 2 GeV and η = 4.1 vs. x F. STAR preliminary data. U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 2

21 .15.1 π + π Sivers effect (from fit) θ = 4 pp --> K X -- RHIC - BRAHMS K + K A N A N θ = 2.3 (2.6) deg 1 < p T < 2 GeV/c x F x F Estimates for A N (π ± ) (left) and A N (K ± ) (right) at RHIC. Notice: K (ūs) positive: large non leading ff and no strange Sivers function (as in Anselmino, Murgia 98). U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 21

22 A N STAR - saturated Sivers functions s = 2 2 GeV 2 η = -4.1 quark gluon A N PAX - saturated Sivers functions quark gluon s = 196 GeV 2 p T = 1.5 GeV pp --> π + X pp --> π X Test of relevance of contributions: 2k M f a 1T = 2f a/p (positivity bound) x F x F U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 22

23 A N PHENIX from fit quark-sat gl-sat gl p T (GeV/c) A N x F = Sivers effect pp --> π X -- E74 from fit q g p T (GeV/c) PHENIX data (left): Constraint on the gluon f1t at x <.1: its positivity bound. Anselmino et al., in preparation. (E74, right) U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 23

24 her (future) measurements: p p DX: high vs. moderate energies, pp vs. p p Remember: for D: q q c c and gg c c Test of the relevance of different contributions: saturation of positivity bounds U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 24

25 E cm =2 GeV A N max p T (GeV) Maximized A N (D) at RHIC, s = 2 GeV. Sivers effect, saturated: g (thick lines), q (thin lines). U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 25

26 pp --> D X -- JPARC p T =1.5 GeV/c from fit q g PAX - saturated Sivers functions quark gluon A N.25 A N.25 p pbar --> D X s = 196 GeV 2.15 p T = 1.9 GeV x F x F Maximized A N (D) at JPARC, s = 1 GeV and PAX s = 14 GeV. U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 26

27 pp γx: high vs. moderate energies, pp vs. p p - Sivers effect dominance - sensitivity to gluon Sivers function - sensitivity to h 1 (and h 1 )?!?! q q: q e2 qf q f q qg: q e2 qf q f g Notice: easier case (w.r.t pp hx) to check k -factorization; U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 27

28 .5.4 x F = -.3 pp --> γ X -- RHIC f 1T [fit] f 1T [q] f 1T [g] h 1.3 h 1T A N p T (GeV/c) gluon f 1T dominance at large energies, x F > and moderate p T (cfr. Schmidt et al. 5) U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 28

29 pp --> γ X -- JPARC E lab = 5 GeV pp --> γ X -- JPARC E lab = 5 GeV f 1T [fit] f 1T [q] f 1T [g] h 1 h 1T f 1T [fit] f 1T [q] f 1T [g] h 1 h 1T A N.3 A N x F =.1 x F = p T (GeV/c) Maximized A N (γ) at JPARC, s = 1 GeV, x F = (left) and x F =.2 (right) p T (GeV/c) U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 29

30 ppbar --> γ X -- PAX E CM = 14 GeV ppbar --> γ X -- PAX E CM = 14 GeV f 1T [fit] f 1T [q] f 1T [g] h 1 h 1T x F = f 1T [fit] f 1T [q] f 1T [g] h 1 h 1T x F =.2 A N A N p T (GeV/c) Maximized A N (γ) at PAX, s = 14 GeV, x F = (left) and x F =.2 (right) p T (GeV/c) U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 3

31 Summary TMD s: a new window into the QCD hadron structure h 1 : fundamental quantity: a) direct access through A T T in DY ( p enhancement of valence region) b) help from TMD s: SIDIS and e + e H 1 f 1T : a) direct access through A N in SIDIS and DY (quark) b) role in pp CX (C = π, D, γ) (quark and gluon) - Interplay of different processes and different kinem. set-ups: - high vs. moderate energies, forward, backward and mid-rapididy, pp vs. p p h 1 : a) direct access through A N in DY (quark) b) role in (un)polarized hadronic processes U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 31

32 - QCD vs. phenomenological models - physical interpretation (OAM...) - k - factorization in pp CX - Twist-three vs. TMD s phenomenology - evolution... TMD s: a more and more exciting field... U. D Alesio (Univ. and INFN, Cagliari) TMD s Phenomenolgy, future 32