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Sivers and Boer-Mulders functions in SIDIS

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10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceSivers and Boer-Mulders functions in SIDIS10th International Workshop on Hadron Structure and SpectroscopyS.MelisStefano MelisDipartimento di Scienze e Tecnologie Avanzate,Università del Piemonte Orientaleand INFN, sezione di Torino&Alessandria.In collaboration with:M. Anselmino, V. Barone, M. Boglione, A. Kotzinian, A. Prokudin, U. D’Alesio, F. Murgia1


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venice⋄The asymmetry A sin(φ h−φ S )UTfor the Sivers effectOutline⋄Fit of HERMES and COMPASS data on π and K⋄Comparison with our previous fit on π data⋄Sivers effect in DY@COMPASS⋄Boer-Mulders and Cahn effect in unpolarized SIDIS⋄ConclusionsS.Melis2


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venice⋄The asymmetry A sin(φ h−φ S )UTfor the Sivers effectOutline⋄Fit of HERMES and COMPASS data on π and K⋄Comparison with our previous fit on π data⋄Sivers effect in DY@COMPASS⋄Boer-Mulders and Cahn effect in unpolarized SIDIS⋄ConclusionsS.Melis3


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venice⋄The asymmetry A sin(φ h−φ S )UTfor the Sivers effectOutline⋄Fit of HERMES and COMPASS data on π and K⋄Comparison with our previous fit on π data⋄Sivers effect in DY@COMPASS⋄Boer-Mulders and Cahn effect in unpolarized SIDIS⋄ConclusionsS.Melis4


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VenicePolarized SIDIS➢ Polarized SIDIS cross section (γ ∗ p c.m.):dσ lp↑ →l ′ hX = ∑ q f q/p ↑(x,k ⊥,Q 2 ) ⊗ dσ lq→l′q ⊗ D h q (z,p ⊥ ,Q 2 )⋄f q/p ↑(x, k ⊥ , Q 2 ) is the distribution function of parton qinside a transverse polarized proton pl l ′ φ h⋄D h q (z, p ⊥ , Q 2 ) is the fragmentation functionof a parton q into the hadron hk ⊥k ′p ⊥P TP hϕỹPSφ S˜x˜zyxzS.Melis5


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceSivers Function➢ If we introduce the transverse partonic momentum it can be builta PDF (Sivers function) with a typical azimuthal correlation:f q/p ↑(x,k ⊥ ) = f q/p (x,k ⊥ ) + 1 2 ∆N f q/p ↑(x,k ⊥ )S T · ( ˆP × ˆk ⊥ )= f q/p (x,k ⊥ ) + 1 2} {{ }∆N f q/p ↑(x,k ⊥ )} {{ }unpol. PDFSivers functionsin(ϕ − φ S )where S T is the proton transverse spin vector, with azimuthal angle φ S ,and ˆP the proton momentum direction.⋄ Other notations: 1 2 ∆N f q/p ↑(x, k ⊥ ) = − k ⊥mpf ⊥q1T (x, k ⊥)⋄ Bound: |∆N f q/p ↑(x,k ⊥ )|2f q/p (x,k ⊥ )≤ 1S.Melis6


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceThe weighted asymmetry for the Sivers effect➢ Inserting in:dσ lp↑ →l ′ hX = ∑ q f q/p ↑(x,k ⊥,Q 2 ) ⊗ dσ lq→lq ⊗ D h q (z,p ⊥ ,Q 2 )➢ ...we can build the weighted asymmetry:A sin(φ h−φ S )UT= 2RdφS dφ h [dσ ↑ −dσ ↓ ] sin(φ h −φ S )RdφS dφ h [dσ ↑ +dσ ↓ ]➢ ...that is:A sin(φ h−φ S )UT=P Rq dφS dφ h d 2 k ⊥ ∆ N f q/p ↑(x,k ⊥ ) sin(ϕ−φ S ) dˆσlq→lqPqdQ 2 Dq h (z,p ⊥)sin(φ h −φ S )RdφS dφ h d 2 k ⊥ f q/p (x,k ⊥ ) dˆσlq→lqdQ 2 Dq h(z,p ⊥)S.Melis7


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceParametrizations:➢ We assume a factorized gaussian smearing for the unpolarized PDF and FF:⋄ f q/p (x, k ⊥ ) = f q (x)1π〈k 2 ⊥ 〉 e−k2 ⊥ /〈k2 ⊥ 〉 ⋄ D h q (z, p ⊥ ) = D h q (z)1π〈p 2 ⊥ 〉 e−p2 ⊥ /〈p2 ⊥ 〉〈k 2 ⊥ 〉 = 0.25 (GeV/c)2 〈p 2 ⊥ 〉 = 0.20 (GeV/c)2 .〈k 2 ⊥〉 and 〈p 2 ⊥〉 fixed as found in Ref. [1] by analysing the cosφ Cahn effect.➢ Similarly for the Sivers function:∆ N f q/p ↑(x, k ⊥ ) = 2 N q (x) h(k ⊥ ) f q/p (x, k ⊥ )N q (x) = N q x α q(1 − x) β q (α q+β q ) (α q+βq)α α qq β β qq≤ 1 , h(k ⊥ ) = √ 2e k ⊥M1e −k2 ⊥ /M2 1 ≤ 1 ,where N q , α q , β q and M 1 (GeV/c) are free parametersS.Melis[1] Anselmino et al., Phys. Rev. D71,074006 (2005)8


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceFit of HERMES & COMPASS SIDIS data⋄ GRV98 set for PDF’s⋄ DSS set for FF’s⋄ 〈k 2 ⊥〉 and 〈p 2 ⊥〉 from the Cahn Effect➢ “Broken sea“ ansatz, 11 free parameters:N uN d∆ N f q/p ↑(x, k ⊥ ) = 2 N q (x) h(k ⊥ ) f q/p (x, k ⊥ )N q (x) = N q x α q(1 − x) β q (α q+β q ) (α q+βq)α α qq β β qqh(k ⊥ ) = √ 2e k ⊥M1e −k2 ⊥ /M2 1NūN sN ¯dN¯sα u α d α seaβ M 1Anselmino et al., ArXiv:0805.2677S.Melis9


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceFit: HERMES data➢ HERMES data ⋄ fitep → eπXp lab = 27.57 GeV/cep → eKX- φ S)sin (φ hA UT0.15 00.10.0500.10.050ππ0.15 +0.1 -0.050-0.1π0 0.1 0.2 0.3 0.4 0.5HERMESpreliminary2002-20050.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1P Tx z (GeV)⋄ Diefenthaler, hep-ex/0612010 (2006)- φ S)sin (φ hA UT0.20.10-0.10KS-0.20.2 +0.10-0.1K-0.20.2 -0.10-0.1K-0.20 0.1 0.2 0.3 0.4 0.5HERMESpreliminary2002-20050.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1P Tx z (GeV)S.Melis10


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceFit: COMPASS data➢ COMPASS data ⋄ fiteD → eπXp lab = 160 GeV/ceD → eKX0.1 00.050π COMPASS 2003-20040.10.0500K COMPASS 2003-2004S- φ S)sin (φ hA UT-0.10.1 +0.050-0.1ππ0.1 -0.050- φ S)sin (φ hA UT-0.10.050K0.1 +-0.10.1 -K0.050-0.1-310-210-110 10.2 0.4 0.6 0.8 0.5 1 1.5P Tx z (GeV)⋄ A. Martin (COMPASS), Czech. J. Phys. 56, F33 (2006)-0.1-310-210-110 10.2 0.4 0.6 0.8 0.5 1 1.5P Tx z (GeV)S.Melis11


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceBurkardt sum rule⋄ P aRdx d 2 k ⊥ k ⊥ f a/p ↑(x, k ⊥ ) ≡ P a 〈ka ⊥〉 = 0where 〈k a ⊥〉 is related to the first moment of the Sivers function by:h R〈k a π 1⊥〉 = dx R i∞dk 2 0 0 ⊥ k⊥ 2 ∆ N f a/p ↑(x, k ⊥ ) (S × ˆP )= m pR 10 dx∆N f (1)q/p ↑ (x) (S × ˆP ) ≡ 〈k a ⊥〉 (S × ˆP )⋄ It is almost saturated by u and d quarks alone at Q 2 = 2.4 (GeV/c) 2 :〈k u ⊥ 〉 + 〈kd ⊥ 〉 = −17+37 −55 (MeV/c) 〈kū⊥ 〉 + 〈k ¯d⊥ 〉 + 〈k s ⊥ 〉 + 〈k¯s ⊥ 〉 = −14+43 −66 (MeV/c).⋄ The individual contribution for quarks are:〈k u ⊥ 〉 = 96+60 −28 (MeV/c) 〈kd ⊥ 〉 = −113+45 −51 (MeV/c)〈kū⊥ 〉 = 2+24 −11 (MeV/c) 〈k ¯d⊥ 〉 = −28 +20−60 (MeV/c)〈k⊥ s 〉 =−4+11 −15 (MeV/c) 〈k¯s ⊥ 〉 = 17+30 −8 (MeV/c).thus leaving little room for a gluon Sivers functionS.Melis−10 ≤ 〈k g ⊥ 〉 ≤ 48 (MeV/c) 14


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VenicePrediction K 0 s HERMES➢ HERMES K 0 sp lab = 27.57 GeV/cep → eKX- φ S)sin (φ hA UT0.20.10-0.10KS-0.20.2 +0.10-0.1-0.20.2 -0.10-0.1KK-0.20 0.1 0.2 0.3 0.4 0.5HERMESpreliminary2002-20050.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1P Tx z (GeV)S.Melis15


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VenicePrediction COMPASS-Deuterium: π 0 and K 0 s➢ COMPASS: π 0 and K 0 seD → eπXp lab = 160 GeV/ceD → eKX0.1 00.050π COMPASS 2003-20040.10.0500K COMPASS 2003-2004S- φ S)sin (φ hA UT-0.10.1 +0.050-0.1ππ0.1 -0.050- φ S)sin (φ hA UT-0.10.050K0.1 +-0.10.1 -K0.050-0.1-0.1-310-210-110 10.2 0.4 0.6 0.8 0.5 1 1.5P Tx z (GeV)-310-210-110 10.2 0.4 0.6 0.8 0.5 1 1.5P Tx z (GeV)⋄ M. Alekseev ArXiv:0802.2160(2008)S.Melis16


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VenicePredictions: COMPASS Hydrogen target➢ Predictions for the COMPASS hydrogen targetep → eπXep → eKX- φ S)sin (φ hA UT0.1π+0.050-0.05-0.1- φ S)sin (φ hA UT0.1 +K0.050-0.05-0.1- φ S)0.1π-0.05- φ S)0.1 -K0.05sin (φ hA UT0-0.05-0.1sin (φ hA UT0-0.05-0.1-310-210-110 10.2 0.4 0.6 0.8 0.5 1 1.5x z (GeV)P T-310-210-110 10.2 0.4 0.6 0.8 0.5 1 1.5x z (GeV)P TS.Melis17


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VenicePredictions: COMPASS Hydrogen target➢ COMPASS hydrogen target-h + , h −ep → ehX➢ Preliminary COMPASS proton dataS. Levorato, Transversity08, Ferrara⋄h − data fully described⋄h + data overestimatedS.Melis18


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VenicePredictions: HERMES proton data 2009➢ HERMES hydrogen targetHERMES Protonsin(φA h -φ S )UTsin(φA h -φ S )UTsin(φA h -φ S )UT0.150.10.050-0.05-0.1-0.150.150.10.050-0.05-0.1-0.150.150.10.050-0.05-0.1-0.15π 0 π 0π +π −π +π 0π − π +sin(φA h -φ S )UTsin(φA h -φ S )UT0.150.10.05π − -0.05-0.1-0.150-0.05-0.1-0.150.150.10.050Κ + Κ +Κ −0.1 0.2 0.3 0.4xHERMES ProtonΚ − Κ +0.3 0.4 0.5 0.6 0.7zΚ −0.1 0.3 0.5 0.7 0.9 1.1P (GeV) T0.1 0.2 0.3 0.4x0.3 0.4 0.5 0.6 0.7z0.1 0.3 0.5 0.7 0.9 1.1P (GeV) TA. Airapetian et al, Phys. Rev. Lett. 103 (2009) 152002S.Melis19


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VenicePredictions: JLAB@12 GeV-PIONS➢ Predictions for the JLAB@12 GeV for hydrogen and He 3 (neutron) targets:Hydrogen He 3- φ S)0.150.1π+JLab 12 GeV- φ S)0.1 π+JLab N 12 GeV-0sin (φ hA UT0.050sin (φ hA UT-0.1-0.2-0.3- φ S)0.10.05- φ S)0.1-0sin (φ hA UT0-0.05-0.1π -sin (φ hA UT-0.1-0.2-0.3π -0.2 0.4 0.6 0.8 10.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 10.2 0.4 0.6 0.8 10.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1x z P T(GeV)x z P T(GeV)➢ JLAB can improve our knowledge of the Sivers functions at medium/large xand of the d quark Sivers function by means of the neutron target.S.Melis20


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VenicePredictions: JLAB@12 GeV-KAONS➢ Predictions for the JLAB@12 GeV for hydrogen and He 3 (neutron) targets:Hydrogen He 3- φ S)0.150.1+K JLab 12 GeV- φ S)0.1-0+K JLab N 12 GeVsin (φ hA UT0.050sin (φ hA UT-0.1-0.2-0.3- φ S)0.10.05- φ S)0.1-0sin (φ hA UT0-0.05-0.1-Ksin (φ hA UT-0.1-0.2-0.3-K0.2 0.4 0.6 0.8 10.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 10.2 0.4 0.6 0.8 10.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1x z P T(GeV)x z P T(GeV)➢ JLAB can improve our knowledge of the Sivers functions at medium/large xand of the d quark Sivers function by means of the neutron target.S.Melis21


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceDrell-Yan!S.Melis22


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceDrell-YanA + B −→ l + + l − + XB(P B ) l +b(p b )γ ∗ (q)A(P A )a(p a )l −S.Melis23


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceSivers Function in the DY process➢ If hadron A is transversely polarized then the DY cross section can be written as:d 4 σ ↑d 4 q = P ∫abdx a d 2 k ⊥a dx b d 2 k ⊥b f a/A ↑(x a , k ⊥a ) f b/B (x b , k ⊥b ) δ 4 (p a + p b − q) ˆσ ab→l+ l −0where f q/p ↑(x, k ⊥ ) = f q/p (x, k ⊥ ) + 1 2 ∆N f q/p ↑(x, k ⊥ )| {z }Sivers functionsin(φ S − ϕ)A sin(φ γ−φ S )N≡∫ 2πdφ0 γ [dσ ↑ − dσ ↓ ] sin(φ γ − φ S )∫1 2π2dφ0 γ [dσ ↑ + dσ ↓ ]A sin(φ γ−φ S )N(A ↑ B → γ ∗ X; x F , M, q T ) = −A sin(φ γ−φ S )N(B A ↑ → γ ∗ X; −x F , M, q T )S.Melis24


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceSivers Effect-COMPASSτ = x a x b = M 2 /s ≃ 0.16COMPASS: π pCOMPASS: π p ↑0.40.30.3π -π +0.2π -π +0.2A Nsin(φ γ -φ S )0.10-0.1A Nsin(φ γ -φ S )0.10-0.1-0.2-0.34


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceSivers Effect-COMPASSτ = x a x b = M 2 /s ≃ 0.16Assuming ∆ N f q/p ↑ DY = −∆ N f q/p ↑ SIDIS:⋄ π − = |dū〉0.30.20.1COMPASS: π p ↑π -π +π − p ↑ ≃ fū/π − ⊗ ∆f u/p↑ < 0A Nsin(φ γ -φ S )0⋄ π + = |u ¯d〉π + p ↑ ≃ f ¯d/π + ⊗ ∆f d/p ↑ > 0-0.1-0.2-0.34


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceCahn and Boer-Mulders effect in A cos2φ 27S.Melis


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venicecos 2φThe azimuthal asymmetry A➢ The general structure for the unpolarized SIDIS cross section is:⋄ dσ = A + B cos φ + C cos2φ• A =∝ f 1 ⊗ D 1 is the usual φ-independent contribution• B ∝ 1 Q (f 1 ⊗ D 1 + h ⊥ 1 ⊗ H ⊥ 1 ) sub-leading Cahn+BM effect• C ∝ h ⊥ 1 ⊗ H ⊥ 1 + 1Q 2 f 1 ⊗ D 1 BM effect+ Twist-4 CahnS.Melis28


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venicecos 2φThe azimuthal asymmetry A➢ The general structure for the unpolarized SIDIS cross section is:⋄ dσ = A + B cos φ + C cos2φ• A =∝ f 1 ⊗ D 1 is the usual φ-independent contribution• B ∝ 1 Q (f 1 ⊗ D 1 + h ⊥ 1 ⊗ H ⊥ 1 ) sub-leading Cahn+BM effect• C ∝ h ⊥ 1 ⊗ H ⊥ 1 + 1Q 2 f 1 ⊗ D 1 BM effect+ Twist-4 CahnS.Melis29


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venicecos 2φThe azimuthal asymmetry A➢ The general structure for the unpolarized SIDIS cross section is:⋄ dσ = A + B cos φ + C cos2φ• A =∝ f 1 ⊗ D 1 is the usual φ-independent contribution• B ∝ 1 Q (f 1 ⊗ D 1 + h ⊥ 1 ⊗ H ⊥ 1 ) sub-leading Cahn+BM effect• C ∝ h ⊥ 1 ⊗ H ⊥ 1 + 1Q 2 f 1 ⊗ D 1 BM effect+ Twist-4 Cahnunpolarized PDFS.Melis30


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venicecos 2φThe azimuthal asymmetry A➢ The general structure for the unpolarized SIDIS cross section is:⋄ dσ = A + B cos φ + C cos2φ• A =∝ f 1 ⊗ D 1 is the usual φ-independent contribution• B ∝ 1 Q (f 1 ⊗ D 1 + h ⊥ 1 ⊗ H ⊥ 1 ) sub-leading Cahn+BM effect• C ∝ h ⊥ 1 ⊗ H ⊥ 1 + 1Q 2 f 1 ⊗ D 1 BM effect+ Twist-4 Cahnunpolarized FFS.Melis31


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venicecos 2φThe azimuthal asymmetry A➢ The general structure for the unpolarized SIDIS cross section is:⋄ dσ = A + B cos φ + C cos2φ• A =∝ f 1 ⊗ D 1 is the usual φ-independent contribution• B ∝ 1 Q (f 1 ⊗ D 1 + h ⊥ 1 ⊗ H ⊥ 1 ) sub-leading Cahn+BM effect• C ∝ h ⊥ 1 ⊗ H ⊥ 1 + 1Q 2 f 1 ⊗ D 1 BM effect+ Twist-4 CahnS.Melis32


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venicecos 2φThe azimuthal asymmetry A➢ The general structure for the unpolarized SIDIS cross section is:⋄ dσ = A + B cos φ + C cos2φ• A =∝ f 1 ⊗ D 1 is the usual φ-independent contribution• B ∝ 1 Q (f 1 ⊗ D 1 + h ⊥ 1 ⊗ H ⊥ 1 ) sub-leading Cahn+BM effect• C ∝ h ⊥ 1 ⊗ H ⊥ 1 + 1Q 2 f 1 ⊗ D 1 BM effect+ Twist-4 CahnS.Melis33


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venicecos 2φThe azimuthal asymmetry A➢ The general structure for the unpolarized SIDIS cross section is:⋄ dσ = A + B cos φ + C cos2φ• A =∝ f 1 ⊗ D 1 is the usual φ-independent contribution• B ∝ 1 Q (f 1 ⊗ D 1 + h ⊥ 1 ⊗ H ⊥ 1 ) sub-leading Cahn+BM effect• C ∝ h ⊥ 1 ⊗ H ⊥ 1 + 1Q 2 f 1 ⊗ D 1 BM effect+ Twist-4 CahnS.Melis34


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venicecos 2φThe azimuthal asymmetry A➢ The general structure for the unpolarized SIDIS cross section is:⋄ dσ = A + B cos φ + C cos2φ• A =∝ f 1 ⊗ D 1 is the usual φ-independent contribution• B ∝ 1 Q (f 1 ⊗ D 1 + h ⊥ 1 ⊗ H ⊥ 1 ) sub-leading Cahn+BM effect• C ∝ h ⊥ 1 ⊗ H ⊥ 1 + 1Q 2 f 1 ⊗ D 1 BM effect+ Twist-4 CahnS.Melis35


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venicecos 2φThe azimuthal asymmetry A➢ The general structure for the unpolarized SIDIS cross section is:⋄ dσ = A + B cos φ + C cos2φ• A =∝ f 1 ⊗ D 1 is the usual φ-independent contribution• B ∝ 1 Q (f 1 ⊗ D 1 + h ⊥ 1 ⊗ H ⊥ 1 ) sub-leading Cahn+BM effect• C ∝ h ⊥ 1 ⊗ H ⊥ 1 + 1Q 2 f 1 ⊗ D 1 BM effect+ Twist-4 CahnBoer-Mulders functionS.Melis36


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venicecos 2φThe azimuthal asymmetry A➢ The general structure for the unpolarized SIDIS cross section is:⋄ dσ = A + B cos φ + C cos2φ• A =∝ f 1 ⊗ D 1 is the usual φ-independent contribution• B ∝ 1 Q (f 1 ⊗ D 1 + h ⊥ 1 ⊗ H ⊥ 1 ) sub-leading Cahn+BM effect• C ∝ h ⊥ 1 ⊗ H ⊥ 1 + 1Q 2 f 1 ⊗ D 1 BM effect+ Twist-4 CahnCollins fragmentation functionS.Melis37


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venicecos 2φThe azimuthal asymmetry A➢ The general structure for the unpolarized SIDIS cross section is:⋄ dσ = A + B cos φ + C cos2φ• A =∝ f 1 ⊗ D 1 is the usual φ-independent contribution• B ∝ 1 Q (f 1 ⊗ D 1 + h ⊥ 1 ⊗ H ⊥ 1 ) sub-leading Cahn+BM effect• C ∝ h ⊥ 1 ⊗ H ⊥ 1 + 1Q 2 f 1 ⊗ D 1 BM effect+ Twist-4 CahnS.Melis38


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venicecos 2φThe azimuthal asymmetry A➢ The general structure for the unpolarized SIDIS cross section is:⋄ dσ = A + B cos φ + C cos2φ• A =∝ f 1 ⊗ D 1 is the usual φ-independent contribution• B ∝ 1 Q (f 1 ⊗ D 1 + h ⊥ 1 ⊗ H ⊥ 1 ) sub-leading Cahn+BM effect• C ∝ h ⊥ 1 ⊗ H ⊥ 1 + 1Q 2 f 1 ⊗ D 1 BM effect+ Twist-4 CahnS.Melis39


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venicecos 2φThe azimuthal asymmetry A➢ The general structure for the unpolarized SIDIS cross section is:⋄ dσ = A + B cos φ + C cos2φ• A =∝ f 1 ⊗ D 1 is the usual φ-independent contribution• B ∝ 1 Q (f 1 ⊗ D 1 + h ⊥ 1 ⊗ H ⊥ 1 ) sub-leading Cahn+BM effectTwist-2• C ∝ h ⊥ 1 ⊗ H ⊥ 1 + 1Q 2 f 1 ⊗ D 1 BM effect+ Twist-4 CahnS.Melis40


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venicecos 2φThe azimuthal asymmetry A➢ The general structure for the unpolarized SIDIS cross section is:⋄ dσ = A + B cos φ + C cos2φ• A =∝ f 1 ⊗ D 1 is the usual φ-independent contribution• B ∝ 1 Q (f 1 ⊗ D 1 + h ⊥ 1 ⊗ H ⊥ 1 ) sub-leading Cahn+BM effect• C ∝ h ⊥ 1 ⊗ H ⊥ 1 + 1Q 2 f 1 ⊗ D 1 BM effect+ Twist-4 CahnS.Melis41


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venicecos 2φThe azimuthal asymmetry A➢ The general structure for the unpolarized SIDIS cross section is:⋄ dσ = A + B cos φ + C cos2φ• A =∝ f 1 ⊗ D 1 is the usual φ-independent contribution• B ∝ 1 Q (f 1 ⊗ D 1 + h ⊥ 1 ⊗ H ⊥ 1 ) sub-leading Cahn+BM effectTwist-4• C ∝ h ⊥ 1 ⊗ H ⊥ 1 + 1Q 2 f 1 ⊗ D 1 BM effect+ Twist-4 CahnS.Melis42


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venicecos 2φThe azimuthal asymmetry A➢ The general structure for the unpolarized SIDIS cross section is:⋄ dσ = A + B cos φ + C cos2φ• A =∝ f 1 ⊗ D 1 is the usual φ-independent contribution• B ∝ 1 Q (f 1 ⊗ D 1 + h ⊥ 1 ⊗ H ⊥ 1 ) sub-leading Cahn+BM effectTwist-4• C ∝ h ⊥ 1 ⊗ H ⊥ 1 + ( 1Q 2 f 1 ⊗ D 1 + 1Q 2 [...]) BM effect+ Twist-4 Cahn+ ...S.Melis43


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venicecos 2φThe azimuthal asymmetry A➢ The general structure for the unpolarized SIDIS cross section is:⋄ dσ = A + B cos φ + C cos2φ• A =∝ f 1 ⊗ D 1 is the usual φ-independent contribution• B ∝ 1 Q (f 1 ⊗ D 1 + h ⊥ 1 ⊗ H ⊥ 1 ) sub-leading Cahn+BM effect• C ∝ h ⊥ 1 ⊗ H ⊥ 1 + 1Q 2 f 1 ⊗ D 1 BM effect+ Twist-4 CahnA cos 2φ = 2Rdσ cos2φRdσ= C AS.Melis44


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venicecos 2φThe azimuthal asymmetry A➢ The general structure for the unpolarized SIDIS cross section is:⋄ dσ = A + B cos φ + C cos2φ• A =∝ f 1 ⊗ D 1 is the usual φ-independent contribution• B ∝ 1 Q (f 1 ⊗ D 1 + h ⊥ 1 ⊗ H ⊥ 1 ) sub-leading Cahn+BM effect• C ∝ h ⊥ 1 ⊗ H ⊥ 1 + 1Q 2 f 1 ⊗ D 1 BM effect+ Twist-4 Cahnwell known in x,z, gaussian in k ⊥ and p ⊥S.Melis45


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venicecos 2φThe azimuthal asymmetry A➢ The general structure for the unpolarized SIDIS cross section is:⋄ dσ = A + B cos φ + C cos2φ• A =∝ f 1 ⊗ D 1 is the usual φ-independent contribution• B ∝ 1 Q (f 1 ⊗ D 1 + h ⊥ 1 ⊗ H ⊥ 1 ) sub-leading Cahn+BM effect• C ∝ h ⊥ 1 ⊗ H ⊥ 1 + 1Q 2 f 1 ⊗ D 1 BM effect+ Twist-4 Cahnfrom the fit of e + e − +SIDIS data[*][*]Anselmino et al., ArXiv:0812.4366v1S.Melis46


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceParametrizations of the Collins function➢ We fitted BELLE e + e − data + COMPASS and HERMES SIDIS dataassuming a factorized gaussian smearing for ∆ N D π/q ↑ = p ⊥zM hH ⊥ 1 (z,p ⊥ ):⋄∆ N D π/q ↑(z,p ⊥ ) = 2N C q (z) h(p ⊥ ) D π/q (z)1π〈p 2 ⊥ 〉 e−p2 ⊥ /〈p2 ⊥ 〉•N C q (x) = N C q z γ (1 − z) δ (γ+δ)(γ+δ)γ γ δ δ•h(p ⊥ ) = √ 2e p ⊥MCe −p2 ⊥ /M2 C⋄ Favored:D π + /u = D π + / ¯d = D favD π − /d = D π − /ū = D fav⋄ Unfavored:D π + /d = D π + /ū = D π + /s(¯s) = D unfD π − /u = D π − / ¯d = D π − /s(¯s) = D unfAnselmino et al., ArXiv:0812.4366v1S.Melis47


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceThe Collins functions⋄ Collins functions: favored and unfavored− ∆ D unf(z)/2D (z) ∆ D fav(z)/2D (z)NNfavunf10.80.60.40.2010.80.60.40.2− ∆ D unf(z, p ) ∆ D fav(z, p )NN0.80.60.40.200.80.60.40.21 22Q = 2.4 GeVz = 0.361 22Q = 2.4 GeVz = 0.3600.2 0.4 0.6 0.800 0.2 0.4 0.6 0.8 1z p (GeV)Anselmino et al., ArXiv:0812.4366v1S.Melis48


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, Venicecos 2φThe azimuthal asymmetry A➢ The general structure for the unpolarized SIDIS cross section is:⋄ dσ = A + B cos φ + C cos2φ• A =∝ f 1 ⊗ D 1 is the usual φ-independent contribution• B ∝ 1 Q (f 1 ⊗ D 1 + h ⊥ 1 ⊗ H ⊥ 1 ) sub-leading Cahn+BM effect• C ∝ h ⊥ 1 ⊗ H ⊥ 1 + 1Q 2 f 1 ⊗ D 1 BM effect+ Twist-4 Cahnunknown ⇒ extracted from the A cos 2φ dataS.Melis49


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceThe Boer-Mulders function➢ We adopt for the BM function a very simple parametrization:⋄h ⊥q1 (x, k ⊥) = λ q f ⊥q1T (x, k ⊥) for u and d⋄h ⊥q1 (x, k ⊥) = −|f ⊥q1T (x, k ⊥)| for sea quarks➢ Motivated by the necessity to have few free parameters,inspired by impact parameter approach ∗ :⋄h ⊥q1 (x, k ⊥) = Kq TK q f ⊥q1T (x, k ⊥) for u and d*see for instance, M. Burkardt, Phys. Rev. D72, 094020 (2005), hep-ph/0505189.S.Melis50


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceThe Boer-Mulders function➢ We adopt for the BM function a very simple parametrization:⋄h ⊥q1 (x, k ⊥) = λ q f ⊥q1T (x, k ⊥) for u and d⋄h ⊥q1 (x, k ⊥) = −|f ⊥q1T (x, k ⊥)| for sea quarks➢ Motivated by the necessity to have few free parameters,inspired by impact parameter approach:⋄h ⊥q1 (x, k ⊥) = Kq TK q f ⊥q1T (x, k ⊥) for u and dtensor magnetic momentS.Melis51


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceThe Boer-Mulders function➢ We adopt for the BM function a very simple parametrization:⋄h ⊥q1 (x, k ⊥) = λ q f ⊥q1T (x, k ⊥) for u and d⋄h ⊥q1 (x, k ⊥) = −|f ⊥q1T (x, k ⊥)| for sea quarks➢ Motivated by the necessity to have few free parameters,inspired by impact parameter approach:⋄h ⊥q1 (x, k ⊥) = Kq TK q f ⊥q1T (x, k ⊥) for u and danomalous magnetic momentS.Melis52


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceThe Boer-Mulders function➢ We adopt for the BM function a very simple parametrization:⋄h ⊥q1 (x, k ⊥) = λ q f ⊥q1T (x, k ⊥) for u and d⋄h ⊥q1 (x, k ⊥) = −|f ⊥q1T (x, k ⊥)| for sea quarks➢ Motivated by the necessity to have few free parameters,inspired by impact parameter approach:⋄h ⊥q1 (x, k ⊥) = Kq TK q f ⊥q1T (x, k ⊥) for u and d•h ⊥u1 (x, k ⊥ ) ≃ 1.80f ⊥u1T (x, k ⊥ ) < 0•h ⊥d1 (x, k ⊥ ) ≃ −0.94f ⊥d1T (x, k ⊥ ) < 0S.Melis53


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceResults FIT I➢ We fitted the HERMES and COMPASS SIDIS data on A cos 2φ :warning: data are still preliminary!⋄h ⊥q1 (x, k ⊥) = λ q f ⊥q1T (x, k ⊥) for u and d⋄χ 2 /d.o.f. = 3.73•λ u = 2.0 ± 0.1•λ d = −1.11 +0.00−0.02⇒ h ⊥d1 and h ⊥u1 are both negativeS.Melis[1] Barone, Melis, Prokudin, arXiv:0912.519454


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceResults FIT I➢ We fitted the HERMES and COMPASS SIDIS data on A cos 2φ :HERMES Proton0.150.1π +π +π +π +⋄χ 2 /d.o.f. = 3.73cos 2φA0.050-0.05•λ u = 2.0 ± 0.1•λ d = −1.11 +0.00−0.02cos 2φA-0.1-0.150.150.10.050-0.05π −CahnBoer-MuldersCahn+BMπ −CahnBoer-MuldersCahn+BMπ −CahnBoer-MuldersCahn+BMπ −CahnBoer-MuldersCahn+BM-0.1-0.15CahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BM0.1 0.2 0.3 0.4 0.50.3 0.4 0.5 0.6 0.7 0.80.1 0.3 0.5 0.70.4 0.5 0.6 0.7 0.8xzP (GeV) TyS.Melis[1] Barone, Melis, Prokudin, arXiv:0912.519455


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceResults FIT I➢ We fitted the HERMES and COMPASS SIDIS data on A cos 2φ :twist-4 comparable with twist-2HERMES Proton0.150.1π +π +π +π +⋄χ 2 /d.o.f. = 3.73cos 2φA0.050-0.05•λ u = 2.0 ± 0.1•λ d = −1.11 +0.00−0.02cos 2φA-0.1-0.150.150.10.050-0.05π −CahnBoer-MuldersCahn+BMπ −CahnBoer-MuldersCahn+BMπ −CahnBoer-MuldersCahn+BMπ −CahnBoer-MuldersCahn+BM-0.1-0.15CahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BM0.1 0.2 0.3 0.4 0.50.3 0.4 0.5 0.6 0.7 0.80.1 0.3 0.5 0.70.4 0.5 0.6 0.7 0.8xzP (GeV) TyS.Melis[1] Barone, Melis, Prokudin, arXiv:0912.519456


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceResults FIT I➢ We fitted the HERMES and COMPASS SIDIS data on A cos 2φ :Cahn effect (f 1 ⊗ D 1 ) is the same for π + and π −HERMES Proton0.150.1π +π +π +π +⋄χ 2 /d.o.f. = 3.73cos 2φA0.050-0.05•λ u = 2.0 ± 0.1•λ d = −1.11 +0.00−0.02cos 2φA-0.1-0.150.150.10.050-0.05π −CahnBoer-MuldersCahn+BMπ −CahnBoer-MuldersCahn+BMπ −CahnBoer-MuldersCahn+BMπ −CahnBoer-MuldersCahn+BM-0.1-0.15CahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BM0.1 0.2 0.3 0.4 0.50.3 0.4 0.5 0.6 0.7 0.80.1 0.3 0.5 0.70.4 0.5 0.6 0.7 0.8xzP (GeV) TyS.Melis[1] Barone, Melis, Prokudin, arXiv:0912.519457


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceResults FIT I➢ We fitted the HERMES and COMPASS SIDIS data on A cos 2φ :BM effect: different sign π + /π −HERMES Proton⋄χ 2 /d.o.f. = 3.73•λ u = 2.0 ± 0.1•λ d = −1.11 +0.00−0.02〈cos 2φ〉 π+BM ∼ e2 u h⊥u 1cos 2φAcos 2φA0.150.10.050-0.05-0.1-0.150.150.10.050-0.05-0.1-0.15(x) H⊥fav1π +π −CahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BM0.1 0.2 0.3 0.4 0.5x(z) + e 2 d h⊥d 1π +π −(x) H⊥unf1(z)CahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BM0.3 0.4 0.5 0.6 0.7 0.8zπ +π −CahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BM0.1 0.3 0.5 0.7P (GeV) T⇒H ⊥fav1π +π −positive, H ⊥unf1CahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BM0.4 0.5 0.6 0.7 0.8ynegativeS.Melis〈cos 2φ〉 π−BM ∼ e2 u h⊥u 1(x) H⊥unf1(z) + e 2 d h⊥d 1(x) H⊥fav1(z)⇒ u and d BM functions both negative[1] Barone, Melis, Prokudin, arXiv:0912.519458


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceResults FIT I➢ We fitted the HERMES and COMPASS SIDIS data on A cos 2φ :HERMES Proton0.150.1π +π +π +π +⋄χ 2 /d.o.f. = 3.73cos 2φA0.050-0.05•λ u = 2.0 ± 0.1•λ d = −1.11 +0.00−0.02cos 2φA-0.1-0.150.150.10.050-0.05π −CahnBoer-MuldersCahn+BMπ −CahnBoer-MuldersCahn+BMπ −CahnBoer-MuldersCahn+BMπ −CahnBoer-MuldersCahn+BM-0.1-0.15CahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BM0.1 0.2 0.3 0.4 0.50.3 0.4 0.5 0.6 0.7 0.80.1 0.3 0.5 0.70.4 0.5 0.6 0.7 0.8xzP (GeV) TyS.Melis[1] Barone, Melis, Prokudin, arXiv:0912.519459


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceResults FIT I➢ We fitted the HERMES and COMPASS SIDIS data on A cos 2φ :HERMES Deuteron0.150.1π +π +π +π +⋄χ 2 /d.o.f. = 3.73cos 2φA0.050-0.05•λ u = 2.0 ± 0.1•λ d = −1.11 +0.00−0.02cos 2φA-0.1-0.150.150.10.050-0.05π −CahnBoer-MuldersCahn+BMπ −CahnBoer-MuldersCahn+BMπ −CahnBoer-MuldersCahn+BMπ −CahnBoer-MuldersCahn+BM-0.1-0.15CahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BM0.1 0.2 0.3 0.4 0.50.3 0.4 0.5 0.6 0.7 0.80.1 0.3 0.5 0.70.4 0.5 0.6 0.7 0.8xzP (GeV) TyS.Melis[1] Barone, Melis, Prokudin, arXiv:0912.519460


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceResults FIT I➢ We fitted the HERMES and COMPASS SIDIS data on A cos 2φ :COMPASS Deuteron⋄χ 2 /d.o.f. = 3.73•λ u = 2.0 ± 0.1cos 2φA0.150.10.050-0.05-0.1-0.15π +CahnBoer-MuldersCahn+BMπ +CahnBoer-MuldersCahn+BMπ +CahnBoer-MuldersCahn+BM•λ d = −1.11 +0.00−0.02cos 2φA0.150.10.050-0.05-0.1-0.15π −CahnBoer-MuldersCahn+BM10 -2 10 -1xπ −CahnBoer-MuldersCahn+BM0.3 0.4 0.5 0.6 0.7zπ −CahnBoer-MuldersCahn+BM0.1 0.3 0.5 0.7 0.9P (GeV) TS.Melis[1] Barone, Melis, Prokudin, arXiv:0912.519461


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceResults FIT I➢ We fitted the HERMES and COMPASS SIDIS data on A cos 2φ :⇒ strong role of Cahn effect...COMPASS Deuteron⋄χ 2 /d.o.f. = 3.73•λ u = 2.0 ± 0.1cos 2φA0.150.10.050-0.05-0.1-0.15π +CahnBoer-MuldersCahn+BMπ +CahnBoer-MuldersCahn+BMπ +CahnBoer-MuldersCahn+BM•λ d = −1.11 +0.00−0.02cos 2φA0.150.10.050-0.05-0.1-0.15π −CahnBoer-MuldersCahn+BM10 -2 10 -1xπ −CahnBoer-MuldersCahn+BM0.3 0.4 0.5 0.6 0.7zπ −CahnBoer-MuldersCahn+BM0.1 0.3 0.5 0.7 0.9P (GeV) TS.Melis[1] Barone, Melis, Prokudin, arXiv:0912.519462


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceCahn effect remind➢ The general structure for the unpolarized SIDIS cross section is:⋄ dσ = A + B cos φ + C cos2φ• C ∝ h ⊥ 1 ⊗ H ⊥ 1 + 1Q 2 f 1 ⊗ D 1 BM effect+ Twist-4 Cahn⋄ f q/p (x, k ⊥ ) = f q (x)1π〈k 2 ⊥ 〉 e−k2 ⊥ /〈k2 ⊥ 〉 ⋄ D h q (z, p ⊥ ) = D h q (z)1π〈p 2 ⊥ 〉 e−p2 ⊥ /〈p2 ⊥ 〉〈k 2 ⊥〉 and 〈p 2 ⊥〉 fixed as found in Ref. [1] by analysing the Cahn cos φ effect.〈k 2 ⊥ 〉 = 0.25 (GeV/c)2 〈p 2 ⊥ 〉 = 0.20 (GeV/c)2 .S.Melis[1] Anselmino et al., Phys. Rev. D71,074006 (2005)63


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceResults FIT II➢ The Cahn is a crucial ingredient, let us change it:〈k 2 ⊥〉 = 0.25 (GeV/c) 2 for COMPASS and 〈k 2 ⊥〉 = 0.18 (GeV/c) 2 for HERMES⋄χ 2 /d.o.f. = 2.41•λ u = 2.1 ± 0.1•λ d = −1.11 +0.00−0.02⇒ Better description, h ⊥d1 and h ⊥u1 do not change!S.Melis[1] Barone, Melis, Prokudin, arXiv:0912.519464


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceResults FIT II➢ We fitted the HERMES and COMPASS SIDIS data on A cos 2φ :HERMES Proton0.150.1π +π +π +π +⋄χ 2 /d.o.f. = 2.41cos 2φA0.050-0.05•λ u = 2.1 ± 0.1•λ d = −1.11 +0.00−0.02cos 2φA-0.1-0.150.150.10.050-0.05π −CahnBoer-MuldersCahn+BMπ −CahnBoer-MuldersCahn+BMπ −CahnBoer-MuldersCahn+BMπ −CahnBoer-MuldersCahn+BM-0.1-0.15CahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BM0.1 0.2 0.3 0.4 0.50.3 0.4 0.5 0.6 0.7 0.80.1 0.3 0.5 0.70.4 0.5 0.6 0.7 0.8xzP (GeV) TyS.Melis[1] Barone, Melis, Prokudin, arXiv:0912.519465


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceResults FIT II➢ We fitted the HERMES and COMPASS SIDIS data on A cos 2φ :HERMES Deuteron0.150.1π +π +π +π +⋄χ 2 /d.o.f. = 2.41cos 2φA0.050-0.05•λ u = 2.1 ± 0.1•λ d = −1.11 +0.00−0.02cos 2φA-0.1-0.150.150.10.050-0.05π −CahnBoer-MuldersCahn+BMπ −CahnBoer-MuldersCahn+BMπ −CahnBoer-MuldersCahn+BMπ −CahnBoer-MuldersCahn+BM-0.1-0.15CahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BMCahnBoer-MuldersCahn+BM0.1 0.2 0.3 0.4 0.50.3 0.4 0.5 0.6 0.7 0.80.1 0.3 0.5 0.70.4 0.5 0.6 0.7 0.8xzP (GeV) TyS.Melis[1] Barone, Melis, Prokudin, arXiv:0912.519466


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceResults FIT II➢ We fitted the HERMES and COMPASS SIDIS data on A cos 2φ :COMPASS Deuteron⋄χ 2 /d.o.f. = 2.41•λ u = 2.1 ± 0.1cos 2φA0.150.10.050-0.05-0.1-0.15π +CahnBoer-MuldersCahn+BMπ +CahnBoer-MuldersCahn+BMπ +CahnBoer-MuldersCahn+BM•λ d = −1.11 +0.00−0.02cos 2φA0.150.10.050-0.05-0.1-0.15π −CahnBoer-MuldersCahn+BM10 -2 10 -1xπ −CahnBoer-MuldersCahn+BM0.3 0.4 0.5 0.6 0.7zπ −CahnBoer-MuldersCahn+BM0.1 0.3 0.5 0.7 0.9P (GeV) TS.Melis[1] Barone, Melis, Prokudin, arXiv:0912.519467


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceSummary and Conclusions➢ We performed a fit of HERMES and COMPASS data on π and Kin order to extract Sivers functions.⋄ u and d quark Sivers functions are similar to those extracted previously by consideringonly pion data;⋄ a positive ¯s Sivers function is required to explain K + data.⋄ the other sea Sivers functions are not well constrained by data;⋄ Burkardt sum rule is saturated by quarks contributions, leaving little room for the gluonSivers function;⋄ In DY A sin(φ S−φ γ )Ncan be at least of order of 10% for COMPASS kinematics.⋄ The COMPASS DY explored x region is close to that explored in SIDIS (Direct comparison).⋄ It can be tested the qcd prediction: ∆ N f q/p ↑ DY = −∆ N f q/p ↑ SIDIS .S.Melis68


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceSummary and Conclusions➢ Boer-Mulders function⋄ We fitted preliminary data of HERMES and COMPASS⋄ The Cahn effect is not negligible and is comparable with BM effect⋄ u and d Boer-Mulders functions are both negative and compatible with impact parameterapproach predictions.⋄ Some evidences that 〈k⊥〉 2 are different for the different kinematics(as in the case ofof HERMES and COMPASS), see recent paper by Schweitzer, Teckentrup and Metz(arXiv:1003.2190) .S.Melis69


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceS.Melis 70


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceBack-up slidesS.Melis71


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceDetails of the fit: fragmentation functions➢ Fragmentation function are a crucial ingredient for our fit.➢ We have considered three different FF set:⋄ KRE set (Kretzer, Phys. Rev. D62, 054001, 2000)⋄ HKNS set (Hirai et al., hep-ph/0702250, 2007)⋄ DSS set (De Florian et al., Phys. Rev. D75 114010,2007)➢ All these sets are equivalent with regard to their impact in the extractionof the Sivers functions from SIDIS pion data from HERMES and COMPASS➢ However there are important differences with regard to the description of kaons dataS.Melis72


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceFragmentation functions IIDSS KRE HKNS Q 2 = 2.4 GeV 2z D(z)u0.51π+01z D(z)u0.51 +K01d0.5d0.50101u0.5u0.50101d0.5d0.50101s0.5s0.50101s0.5s0.500 0.2 0.4 0.6 0.8 1z00 0.2 0.4 0.6 0.8 1zS.Melis73


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceFragmentation functions IIDSS KRE HKNSQ 2 = 2.4 GeV 21 +0.5⋄ For the DSS set D K+0over the whole 1 z range:z D(z)u0.5K + → (u¯s) and the probability of01producing from the vacuum an uū pairdu0.501π¯s (z) > DuK+ (z)than a heavier s¯s pair is higher.z D(z)udu0.51 +K010.5010.501d0.5⋄ DSS set can0reproduce kaons1multiplicity at HERMESss0.5(HERMES Coll., arXiv:0803.2993)010.5dss0.5010.5010.500 0.2 0.4 0.6 0.8 1z00 0.2 0.4 0.6 0.8 1zS.Melis74


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceFragmentation functions III2 〈sin(φ-φ S)〉 h UT0.250.20.15K +π +HERMES PRELIMINARYIII2002-2005lepton beam asymmetry, Sivers amplitudes8.1% scale uncertainty➢ A big D K+¯s can help to explain whythe asymmetry for K + is greaterthan that for π + .2 〈sin(φ-φ S)〉 h UT0.10.0500.150.10.05K -π - x 0.2 0.3 0.4 0.5 0.6 z0-0.05-0.1-0.150.1 0.2 0.30.2 0.4 0.6 0.8 1P h⊥[GeV]S.Melis75


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceSivers functions & FF setsDSS KRE HKNS- φ S)sin (φ hA UT0.2 +K0.10-0.1HERMES preliminary 2002-2005- φ S)sin (φ hA UT-0.20.20.10-0.1-0.2-K0 0.1 0.2 0.3 0.4 0.50.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1x z P T(GeV)S.Melis76


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceSign of the Sivers function in DYFSIISISIDISCollins: Phys.Lett.B536:43-48,2002DY➢ The sign of the gauge link is related to time direction of the Wilson line.For a T-odd function, it implies that the function changes signfor a past/future pointing Wilson line⋄∆ N f q/p ↑(x, k ⊥ ) SIDIS = −∆ N f q/p ↑(x, k ⊥ ) DYS.Melis77


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceS.Melis 78


10th International Workshop on Hadron Structure and Spectroscopy, 14th-17th March 2010, VeniceS.Melis 79

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