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3D structure of the nucleon and Transverse single-spin asymmetries

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1 3D structure of the nucleon and Transverse single-spin asymmetries
Motivations 3D nucleon structure TMDs (Transverse momentum dependent distributions) Transverse single-spin asymmetries in various (SEMI-) INCLUSIVE processes Open issues 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

2 such as a nucleon Motivations (general statements)
Nucleon: still a mysterious object despite 50 years of studies, yet the most abundant piece of matter in the visible Universe QCD and confinement: still to be understood Spin: fundamental quantum degree of freedom a tool to study the inner structure of a composite system such as a nucleon 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

3 Transverse Spin effects
𝐴 𝑁 in 𝑝 ↑ 𝑝 β†’ Ο€ X… a long-standing puzzle 𝒙 𝑭 =𝟐 𝑷 𝑳 / 𝒔 Collinear twist-2 QCD: 𝐴 𝑁 ≀ few % Almost energy independent 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

4 1-D picture of the nucleon
inclusive DIS DIS Structure Functions Collinear PDFs 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

5 Orbital motion of quarks/gluons Its correlation to proton spin
(open) Physics issues Orbital motion of quarks/gluons Its correlation to proton spin Intrinsic transverse momentum of quarks/gluons Spatial distribution of quarks/gluons 3D structure Non perturbative effects in high-energy processes Origin of transverse/azimuthal spin asymmetries Observables Role of local colour gauge invariance of QCD Factorization, universality, resummation QCD at work 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

6 This talk 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

7 Proton spin puzzle TMDs (or IPDs)
Non trivial decomposition [Leader, LorcΓ© (2014)] 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

8 TMDs: How can we access them?
A step backward: Collinear approach The key point is: Factorization (separation btw large/short distance physics) Evolution with hard scale β†’ DGLAP eqs. A cornerstone in pQCD 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

9 To access directly the TMDs:
Two-scale processes: 𝑄 2 ≫ π‘˜ 𝑇 2 β‰ˆ Ξ› 𝑄𝐢𝐷 2 Drell-Yan 𝑝𝑝 β†’ 𝑙 + 𝑙 βˆ’ 𝑋 𝑒 + 𝑒 βˆ’ β†’ πœ‹πœ‹ 𝑋 SIDIS 𝑙𝑝→ 𝑙 β€² β„Ž 𝑋 TMD factorization proven 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

10 And possibly in processes like
And more 𝑝𝑝 β†’πœ‹ 𝑋 (𝑝𝑝 β†’ 𝛾 𝑋, 𝑝𝑝→𝑗𝑒𝑑 𝑋) Single scale processes 𝑝𝑝→ πœ‹ 𝑗𝑒𝑑 𝑋 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

11 EIC Where can we access TMDs? SIDIS Drell-Yan 𝑒 + 𝑒 βˆ’ β†’ Ο€ Ο€ X
𝑝𝑝→ πœ‹ 𝑋 , 𝑝𝑝→ πœ‹ 𝑗𝑒𝑑 𝑋 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

12 Spread all over the world
3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

13 TMDs and unpolarized cross sections
SIDIS multiplicities 𝑙 𝑝 β†’ 𝑙 β€² β„Ž 𝑋 π‘₯,𝑧: Β«longitudinalΒ» momentum fractions of the quark within its parent proton and of the hadron w.r.t. the fragmenting parent quark (collinear parton model) Factorized Gaussian forms 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

14 Signori, Bacchetta, Radici, Schnell (2013)
<π‘˜ βŠ₯ 2 > = 𝐺𝑒𝑉 2 < 𝑝 βŠ₯ 2 > = 𝐺𝑒𝑉 2 Anselmino, et al. (2014) Signori, Bacchetta, Radici, Schnell (2013) 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

15 TMDs: flavour structure
Gaussian widths up < down < sea ???? to be further explored Signori, Bacchetta, Radici, Schnell (2013) 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

16 Theory: factorization and evolution
Collinear approach Evolution β†’ DGLAP eqs. TMD approach…more involved 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

17 An example: DY process Extra gluons:
Wilson lines, operators between parton fields in the correlator function Soft factors, vacuum expectation values of further Wilson lines, absorbed in the TMDs) DY processes: 𝑝𝑝→ 𝑙 + 𝑙 βˆ’ 𝑋 Wilson lines: path-ordered exponential of the gauge field ensuring local gauge invariance, but inducing some process dependence 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

18 TMD factorization approaches
Seminal paper TMD framework Tremendous progress 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

19 TMD Factorization and evolution (I)
DY processes Collins approach (2011) Collinear PDF pQCD Non perturbative parts 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

20 TMD Factorization and evolution (II)
DY processes: 𝑝𝑝→ 𝑙 + 𝑙 βˆ’ 𝑋 Echevarria, Idilbi, Scimemi (2012,13,14) UD, Echevarria, Melis, Scimemi (2014) TMD in b space 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

21 Non-perturbative input and accuracy
Both needed Relevant for 𝑍 0 data Sensitive to low-energy/low- π‘ž 𝑇 data 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

22 Fit to Drell-Yan and 𝒁 𝟎 production data Low energy Tevatron
TMD evolution at NNLL (SCET) UD, Echevarria, Melis, Scimemi (2014) (223 data points) Low energy Tevatron 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

23 Scale dependence: NLL vs. NNLL
Low energy NLL NNLL Tevatron Strong reduction at NNLL 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC 3D PDFs: Path to the LHC

24 Predictions from NNLL fit
TMDs at LHC Predictions from NNLL fit 𝑝𝑝→𝑍 𝑋 Pure resummed pQCD Inclusion of the non Perturbative piece ( π‘˜ 𝑇 ) 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

25 TMDs and spin collinear T-odd
3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

26 surviving in the collinear limit, there are 5 TMDs more, in particular
Beyond the unpol ( 𝑓 1 ), helicity ( 𝑔 1 ) and transversity ( β„Ž 1 ) distributions, surviving in the collinear limit, there are 5 TMDs more, in particular The Sivers function 𝑓 1𝑇 βŠ₯ Sivers (1989) Correlation between the spin of the proton and the parton transverse momentum 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

27 Analogously, one can define TMDs in the fragmentation process.
In particular, for its relevance The Collins function 𝐻 1 βŠ₯π‘ž Collins (1992) Correlation between the spin of the fragmenting quark and the hadron transverse momentum 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

28 Sivers and Collins functions extensively studied
theoretically, experimentally and phenomenologically CLEAR evidence from data HERMES, COMPASS SIDIS Collins Sivers First phase: analysis with DGLAP evolution Second phase (just started): TMD evolution 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

29 Extracted Sivers functions
TO-CA and PV groups large-π‘₯ region: unconstrained [β†’ JLab] sea region: unconstrained [β†’ EIC] Aybat, Collins, Qiu, Rogers (2012) Effect of the TMD evolution 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

30 Distortion in the transverse plane
Non zero Sivers effect related to parton orbital angular momentum 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

31 Modified universality of the Sivers function
Collins (2012) Final state interactions in SIDIS Initial state interactions in DY A clear-cut test If falsified: - misunderstanding of final-state interacts. leading to T-odd effects - missing points in QCD factorization (TMD and collinear) [most severe scenario] 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

32 First results from RHIC: 𝒑 ↑ 𝒑→ 𝑾 Β± 𝑿
STAR Collaboration (2016) No TMD evolution First hint at the sign change, but large exp. errors and … Kang et al (2016) 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

33 New analysis: Anselmino, Boglione, UD, Murgia, Prokudin (2016)
Sign reversed 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

34 Collins function & transversity
Combined analysis of Without TMD evolution SIDIS and 𝑒 + 𝑒 βˆ’ β†’πœ‹πœ‹ 𝑋 Anselmino, Boglione, UD, Melis, Murgia, Prokudin (2015) 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

35 Same analysis but with TMD evolution
Kang, Prokudin, Sun, Yuan (2015) Same analysis but with TMD evolution No compelling TMD evolution yet Remember: SSAs are ratios…. 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

36 Back to 𝐴 𝑁 : further evidence of Sivers and Collins effects
+ transversity Collins + … Non separable In a phenomenological TMD scheme From SIDIS extractions to 𝑝𝑝 data (STAR (2008)): scan procedure Anselmino, Boglione, UD, Leader, Melis, Murgia, Prokudin (2012 & 13) Collins effect alone Sivers effect alone Proper combination? in progress 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

37 Higher-twist contributions to 𝑨 𝑡
Collinear factorization: proven Qiu, Sterman (1991) Twist-three functions corresponding, and related, to the TMDs, like Boer, Mulders, Piljman (2003) Using these relations one is not able to describe 𝐴 𝑁 (sign mismatch issue) A completely new twist-3 fragm. function seems to be able (necessary) to explain 𝐴 𝑁 𝐴 𝑁 in 𝑝𝑝→𝛾 𝑋 ideal to disentangle the two approaches ( 𝐴 𝑁 with different sign) 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

38 𝑨 𝑡 in 𝒍 𝒑→ 𝝅 𝑿 (single-scale process)
Inclusive process One hard scale 𝑃 𝑇 A bridge between SIDIS and π‘π‘β†’β„Ž 𝑋 From SIDIS to 𝑙 π‘β†’β„Ž 𝑋: test of a unified TMD approach Anselmino, Boglione, UD, Melis, Murgia, Prokudin (2010&14) LO: π‘™π‘žβ†’π‘™q Fairly good description of HERMES data but Inclusive events: final lepton scattered almost collinear 𝑄 2 β‰ˆ0 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

39 Quasi-real photon exchange
Lepton as a source of quasi-real 𝛾 𝑙→𝑙′ 𝛾 final lepton almost collinear WeizsΓ€cker-Williams approximation Reanalysis of SSAs (and unpol. xsecs): UD, Flore, Murgia 2017 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

40 SSAs: Only Sivers and (marginally) Collins effects sizeable
HERMES data (2014) Predictions from SIDIS extractions 0.1 Inclusive data πœ‹ βˆ’ 0.1 Anti-tagged πœ‹ + πœ‹ βˆ’ -0.1 -0.1 TMD scheme seems fine WW: big improvement! 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC 3D PDFs: Path to the LHC

41 Collins effect: from SIDIS to 𝒑𝒑→ 𝝅 𝒋𝒆𝒕 𝑿
𝐴 𝑁 π‘Š = Collins effect Sivers effect Collins-like effect 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC UD, Murgia, Pisano (2011)

42 Universality of the Collins function
< 𝑝 𝑇 𝐽𝑒𝑑 > = 13 GeV < 𝑝 𝑇 𝐽𝑒𝑑 > = 31 GeV 200 GeV 500 GeV UD, Murgia, Pisano, in progress Data: PHENIX Coll. (2015) Predictions without TMD evolution Universality of the Collins function mild (or no) TMD evolution 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

43 Collins-like contribution
sin( Ξ¦ 𝑆 βˆ’2 Ξ¦ πœ‹ 𝐻 ) Defined modulation 𝐴 𝑁 sin( Ξ¦ 𝑆 βˆ’2 Ξ¦ πœ‹ 𝐻 ) Positivity bound helicity flip of the gluon Towards a first constraint of the product of TMDs for linearly polarized gluons inside 𝑝 ↑ and linearly pol. gluons fragm. into a πœ‹ PHENIX 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

44 Open issues in TMD phenomenology
TMD evolution and its relevance An example Kang (2015) w/o TMD evolution Role of non perturbative input choices Transverse momentum dependence in SIDIS and its consistency with DY TMD factorization breaking effects in 𝑝𝑝→ Ο€ 𝑋 , 𝑝𝑝→𝑗𝑒𝑑 𝑗𝑒𝑑 𝑋 (are they sizeable???) Gluon TMDs at low x and parton saturation, TMD factor. vs. Color Glass Condensate 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

45 Future β†’ EIC access to small-π‘₯ domain: JLAB
Space, (transv.) momentum and spin distributions of gluon and sea quarks Missing and complementary information on TMDs and GPDs JLAB 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

46 Conclusions and open issues
3D image of the nucleon: mysterious and fascinating Experimental evidence to go beyond a simple collinear (1D) picture CRUCIAL TASK: DATA Interpretation towards a true 3D image of the nucleon Transverse single-spin asymmetries: challenging and tool to learn deeper on the nucleon structure and QCD Spin-TMD effects well established: orbital angular momentum combined analysis OF SIDIS, DY and 𝑒 + 𝑒 βˆ’ DATA Waiting for COMPASS, Jlab-12, RHIC, and eventually EIC results Phenomenology and theory issues: factorization (break.), evolution and non perturbative inputs THANK YOU 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

47 BACK-UP SLIDES 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

48 Reanalysis within a TMD scheme + WeizsΓ€cker-Williams approx.
UD, Flore, Murgia (in preparation) - Evolution 2016 Unpolarized cross sections LO + WW LO π‘™π‘žβ†’π‘™π‘ž 𝑃 𝑇 =1.4 GeV WW π›Ύπ‘žβ†’π‘”π‘ž π›Ύπ‘”β†’π‘ž π‘ž πœ‹ + πœ‹ βˆ’ NOTICE 𝒙 𝑭 >𝟎 backward scattering LO WW piece: 50-70% of the total 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

49 Access to the gluon Sivers function
𝐴 𝑁 at mid-rapidity PHENIX Collaboration data (2014) All other effects are washed out UD, Murgia, Pisano JHEP09 (2015) 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

50 TMDs at LHC (II) Ferrera (2014) 𝑝𝑝→𝑍 𝑋 uncertainties in 𝑝𝑝→𝐻 𝑋
Inclusion of the non perturbative piece 3D structure of the nucleon and transverse SSAs -- U. D'Alesio (Cagliari University & INFN) 1/02/2017 HEPC

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