TMD phenomenology and A N in pp collisions Umberto D’Alesio Physics Department & INFN University of Cagliari, Italy Workshop on Opportunities for Polarized Physics at FERMILAB based on work in collaboration with M. Anselmino, M. Boglione, E. Leader, S. Melis, F. Murgia, C. Pisano and A. Prokudin
U. D’Alesio Fermilab - 21 May 2013 Outline • A N in pp → hX – experimental status – theoretical approaches: Twist-3 vs. TMD approach • TMD approach: Collins vs. Sivers effect in pp → h X • Access to the Sivers effect: pp → jet X and pp → γ X • Access to the Collins effect: pp → jet πX • A N at midrapidity and the gluon Sivers function • Conclusions TMD phenomenology and A N in pp collisions 1
U. D’Alesio Fermilab - 21 May 2013 SSAs in p ↑ p → h X x F = 2 p L / √ s A N ≡ dσ ↑− dσ ↓ dσ ↑ + dσ ↓ s till challenging started long time ago 0.6 0.4 0.2 A N 0 -0.2 π + -0.4 π 0 π − -0.6 0 0.2 0.4 0.6 0.8 1 x F √ s = 20 GeV [E704 coll. 91] TMD phenomenology and A N in pp collisions 2
U. D’Alesio Fermilab - 21 May 2013 SSAs in p ↑ p → h X x F = 2 p L / √ s A N ≡ dσ ↑− dσ ↓ dσ ↑ + dσ ↓ s till challenging confirmed at much larger energies √ s = 200 GeV [STAR coll. 08] TMD phenomenology and A N in pp collisions 3
U. D’Alesio Fermilab - 21 May 2013 SSAs in p ↑ p → h X x F = 2 p L / √ s A N ≡ dσ ↑− dσ ↓ dσ ↑ + dσ ↓ s till challenging and at even larger energies and at large P T 0.1 0.1 70 mrad 70 mrad STAR preliminary STAR preliminary 30 mrad 30 mrad x F = 0.20 x F = 0.28 0.05 0.05 A N A N 0 0 2 3 4 5 6 7 8 2 3 4 5 6 7 8 P T (GeV) P T (GeV) √ s = 500 GeV [STAR coll. 12] [Preliminary] TMD phenomenology and A N in pp collisions 4
U. D’Alesio Fermilab - 21 May 2013 • A N : sizeable at large rapidity, increasing with x F and P T (RHIC) • Theoretical approaches 1. collinear pQCD factorization at twist-3: universal quark-gluon-quark correlators, (i.e. T F ( x, x ) ) [Efremov-Teryaev 82,85; Qiu-Sterman 91,92,98; Kouvaris et al. 06; Kanazawa- Koike 00,10; Kang et al. 11] 2. Generalized Parton Model (GPM): TMD effects ( assuming factorization) [Anselmino-Boglione-Murgia 95, Anselmino et al. 06; UD-Murgia 04,08; Anselmino et al. 12,13] TMD phenomenology and A N in pp collisions 5
U. D’Alesio Fermilab - 21 May 2013 Motivations: phenom. point of view • pp → h X – suppression of the Collins effect REVISITED! – use of phenomenological information gathered from SIDIS and e + e − data potential role of Collins and Sivers effects in A N in pp → π X – sign mismatch issue Twist-3 qgq -correlation funct. from SIDIS Sivers funct.: wrong sign in A N • other final states (jet, γ , pion-jet) – disentangling Collins and Sivers effects and approaches – study of universality-breaking effects • A N at mid-rapidity: role, if any, of the gluon Sivers function TMD phenomenology and A N in pp collisions 6
U. D’Alesio Fermilab - 21 May 2013 Twist-3 approach Three contributions to A N (schematic view) large x F Φ (3) q/p ↑ ⊗ f q/p ⊗ σ ⊗ D h/q � able [ ⋆ ] to describe A N (FIT) [Kouvaris et al. 06] q ↑ /p ⊗ σ ′ ⊗ D h/q ∆ T q ⊗ Φ (3) negligible [Kanazawa-Koike 00] � ⊗ σ ′′ ⊗ D (3) ∆ T q ⊗ f q/p h/q ↑ ? under study [Kang-Yuan-Zhou 10, Metz-Pitonyak 12] Notice: - Φ (3) q/p ↑ → T F ( x, x ) Efremov-Teryaev-Qiu-Sterman correlation function ⋆ Correction of an overall sign in the definition of gT F [Kang et al. 11] TMD phenomenology and A N in pp collisions 7
U. D’Alesio Fermilab - 21 May 2013 The sign mismatch issue Link between Sivers and ETQS functions [Boer-Mulders-Piljman 03] x gT u,F (x, x) 0.1 Q=2 GeV 0.05 ( k 2 ∫ ) d 2 k ⊥ f ⊥ q 1 T ( x, k 2 ⊥ ⊥ ) | SIDIS = − g T F ( x, x ) 0 M -0.05 ⋆ sign mismatch in A N (if only T F !) -0.1 u-quark [Kang et al. 11] 0 0.2 0.4 0.6 0.8 1 x T F from pp vs. T F via f ⊥ 1 T Solutions: - node in x [Kang-Prokudin 12] and/or in k ⊥ (likely ruled out) - TMD evolution and k ⊥ spreading - study of A N in lp → l ′ X via qγq ⇐ ⇒ qgq correlators [Metz et al. 12] - additional and LARGE twist-3 effects (fragmentation sector)? [Metz-Pitonyak 12] still an open an intriguing issue! TMD phenomenology and A N in pp collisions 8
U. D’Alesio Fermilab - 21 May 2013 TMD approach Many contributions from nonplanar partonic kinematics (helicity formalism) [Anselmino et al. 06] ∆ N f q/p ↑ ⊗ Sivers funct. ( f ⊥ f q/p ⊗ σ ⊗ D cos φ q 1 T ) ⊗ ∆ N f q ↑ /p ⊗ σ ′ ⊗ D h/q cos ψ ′ Boer-Mulders funct. ( h ⊥ ∆ T q 1 ) ⊗ σ ′′ ⊗ ∆ N D h/q ↑ cos ψ ′′ Collins funct. ( H ⊥ ∆ T q ⊗ f q/p 1 ) plus others and plus contributions from gluon TMDs ⊗ : convolutions on x , k ⊥ ; ψ ’s complicate calculable azimuthal phases Only Sivers and Collins effects survive under integration over angular depend.s Let’s consider separately the Collins and Sivers effects TMD phenomenology and A N in pp collisions 9
U. D’Alesio Fermilab - 21 May 2013 Collins effect (revisited) original claimed suppression due - to wrong sign in the spin transfer for qg → qg : one of the most important channels - to relative cancelation with other channels: qq → qq and q ¯ q → q ¯ q . Role of intrinsic azimuthal phases: relevant but not totally suppressing ⇒ a new realistic reanalysis [Anselmino-Boglione-UD-Leader-Melis-Murgia-Prokudin 12] TMD phenomenology and A N in pp collisions 10
U. D’Alesio Fermilab - 21 May 2013 Phenomenology of the Collins effect - use of available information on the Collins effect from SIDIS and e + e − data - global fit not worth at this stage (non separable effects in pp ) - universality of the Collins function [Collins-Metz 04, Yuan 08] - ∆ T q not constrained at large x (SIDIS data x ≤ 0 . 3 ) impact on A N at large x F 0.5 0.4 u(x) 0.3 Present status - large errors 0.2 T ∆ 0.1 x 0 large x behaviour ≃ (1 − x ) β with −0.1 0.1 1. β =4 . 74 ± 5 . 45 [Anselmino et al. 07] d(x) 0.05 2. β =0 . 84 ± 2 . 30 [Anselmino et al. 09] ⇐ 0 T −0.05 ∆ 3. β =3 . 64 +5 . 80 [Anselmino et al. 13] x −0.1 − 3 . 37 −0.15 −0.2 0.2 0.4 0.6 0.8 1 x TMD phenomenology and A N in pp collisions 11
U. D’Alesio Fermilab - 21 May 2013 Large- x behaviour of the transversity q x αq (1 − x ) βq [ q ( x ) + ∆ q ( x )] ∆ T q ( x, k ⊥ ) ≃ N T g ( k ⊥ ) q = u, d 2 - use of isospin symmetry + only favoured and disfavoured FFs - flavour independent parameters except β q - proper evolution for ∆ T q , DGLAP for ∆ N D - 9 parameters to be fitted: ... β u , β d ... TMD phenomenology and A N in pp collisions 12
U. D’Alesio Fermilab - 21 May 2013 Scan Procedure I step 1. 9-parameter reference fit on SIDIS (HERMES, COMPASS) and e + e − (Belle) data 2. grid (scan) of the parameters, β u , β d within the range (0.0–4.0) 3. 7-parameter fit to SIDIS and e + e − data adopting the β q -grid 4. selection via χ 2 scan ≤ χ 2 min + ∆ χ 2 | ref . fit (stat. uncert. band) [fulfilled by all fits] 5. computation of Collins pion SSA for pp collisions HERMES ) h ↑ → π + φ lP l X + 0.1 s = 7.25374 (GeV) S φ sin ( UT 0.05 A example of the fit with β fixed: scan band on HERMES π + data 0 −0.05 0.05 0.1 0.15 0.2 0.25 0.3 0.35 x TMD phenomenology and A N in pp collisions 13
U. D’Alesio Fermilab - 21 May 2013 Results Collins contribution Envelope curves (scan band) 0.2 0.15 π + π 0 π − 0.1 0.1 0 0.05 A N A N -0.1 0 θ = 2.3 ° θ = 4.0 ° η = 3.3 η = 3.7 -0.2 -0.05 0.2 0.3 0.4 0.1 0.2 0.3 0.4 0.2 0.4 0.6 0.2 0.4 0.6 x F x F x F x F √ s = 200 GeV BRAHMS@RHIC 2007 STAR@RHIC 2008 able to describe A N for charged pions, but not the large- x F neutral pion SSA data TMD phenomenology and A N in pp collisions 14
U. D’Alesio Fermilab - 21 May 2013 II step: further tests 1. best curve within the scan and computation of its statistical error band ( π 0 -STAR) 2. allowance for full flavour dependence and back to step I (13-parameter fit) 3. also tried: a transversity-like evolution for the Collins function (not relevant) TMD phenomenology and A N in pp collisions 15
U. D’Alesio Fermilab - 21 May 2013 Statistical uncertainty bands Collins contribution 0.15 0.15 π 0 π 0 0.1 0.1 0.05 0.05 A N A N 0 0 η = 3.3 η = 3.7 η = 3.3 η = 3.7 -0.05 -0.05 0.2 0.4 0.6 0.2 0.4 0.6 0.2 0.4 0.6 0.2 0.4 0.6 x F x F x F x F flavour-independent par. free parameters ∄ a single curve good at low and large x F Same conclusions for E704 data at √ s = 20 GeV TMD phenomenology and A N in pp collisions 16
U. D’Alesio Fermilab - 21 May 2013 Collins effect: conclusions • The Collins effect, corrected, is sizeable 1. able to reproduce the low x F RHIC data. 2. not sufficient at large x F , where A N increases • Additional mechanisms are required: the Sivers effect? Let’s consider it along the same lines TMD phenomenology and A N in pp collisions 17
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