TMDs from Hard Scattering Processes Umberto DAlesio University

TMDs from Hard Scattering Processes Umberto D’Alesio University and INFN, Cagliari q TMDs & Unpolarized cross sections: evolution, accuracy and non perturbative inputs q TMDs & Transverse single-spin asymmetries: Universality, evolution, and (factorization in) inclusive processes q Conclusions 30/11/2016 3 D Parton Distributions: path to the LHC TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 1

TMDs: How can we access them? TMD factorization proven 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 2

And possibly in processes like And more 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 3

SIDIS multiplicities TMDs and unpolarized cross sections Anselmino et al. (2014) 30/11/2016 Signori, Bacchetta, Radici, Schnell (2013) TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 4

Theory: factorization and evolution Collinear approach Factorization Evolution → DGLAP eqs. A cornerstone in p. QCD TMD approach…more involved 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 5

TMD Factorization and evolution DY processes Echevarria, Idilbi, Scimemi (2012, 13, 14) UD, Echevarria, Melis, Scimemi (2014) TMD in b space Collinear PDF RG eq 30/11/2016 Scale independent Theo. Equiv. with Collins approach TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 6

Non-perturbative input and accuracy Both needed 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 7

TMD evolution at NNLL (SCET) UD, Echevarria, Melis, Scimemi (2014) (223 data points) Tevatron Low energy 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 8

Scale dependence: NLL vs. NNLL Low energy Tevatron Strong reduction at NNLL 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 9

TMDs at LHC (I) Predictions from NNLL fit Pure resummed p. QCD 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 10

TMDs at LHC (II) Inclusion of the non perturbative piece 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) Ferrera (2014) 11

TMDs and spin For its relevance, among the eight TMD-PDFs Sivers (1989) Correlation between the spin of the proton and the parton transverse momentum 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 12

Analogously, among the TMD-FFs, for its relevance Collins (1992) Correlation between the spin of the fragmenting quark and the hadron transverse momentum Crucial for the first ever extraction of transversity 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 13

Sivers and Collins functions extensively studied theoretically, experimentally and phenomenologically SIDIS CLEAR evidence from data HERMES, COMPASS, JLab Collins Sivers First phase: analysis with DGLAP evolution Second phase (just started): TMD evolution 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 14

Modified universality of the Sivers function Collins (2002) Final state interactions in SIDIS Initial state interactions in DY If falsified: A clear-cut test - missing points in QCD factorization (TMD and collinear) [most severe scenario] 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 15

STAR Collaboration (2016) Kang et al. (2016) without TMD evolution First hint at the sign change, but large exp. errors and … 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 16

New analysis: Anselmino, Boglione, UD, Murgia, Prokudin, in progress q New extraction of the Sivers funct. : why? Role of antiquarks domin ant Role of unpolarized TMDs 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 17

q Sign reversed q Without TMD evolution To be further explored 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 18

Collins function & transversity Combined analysis of SIDIS without TMD evolution Anselmino, Boglione, UD, Gonzalez, Melis, Murgia, Prokudin (2007, 09, 13, 15) Differences due to a more flexible Collins param. 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 19

Analysis with TMD evolution Kang, Prokudin, Sun, Yuan (2015) NO evidence of TMD evolution yet SSAs are (double)ratios… 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 20

In a phenomenological TMD scheme Sivers effect alone Non separable Collins effect alone Proper combination? in progress 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 21

q Collinear factorization: proven Qiu, Sterman (1991) q Twist-3 funct. s corresponding, and related, to TMDs, like Boer, Mulders, Piljman (2003) Kanazawa, Koike, Metz, Pitonyak (2014) 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 22

Anselmino, Boglione, UD, Melis, Murgia, Prokudin (2010&14) Fairly good description of HERMES data but 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 23

Quasi-real photon exchange Hinderer, Schlegel, Vogelsang (2015) Weizsäcker-Williams approximation 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 24

Reanalysis within a TMD scheme + Weizsäcker-Williams approx. UD, Flore, Murgia (in preparation) - UD@QCD Evolution 2016 Unpolarized cross sections LO + WW LO WW piece: 5070% of the total 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 25

SSAs: Only Sivers and (marginally) Collins effects sizeable Predictions from SIDIS extractions 0. 1 Inclusive data 0. 1 0 -0. 1 WW: big improvement! 30/11/2016 Anti-tagged 0 HERMES data (2014) -0. 1 TMD scheme seems to work TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 26

Sivers effect Collins-like effect Collins effect UD, Murgia, Pisano (2011) 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 27

200 Ge. V Predictions without TMD evolution 30/11/2016 500 Ge. V Data: PHENIX Collaboration (2015) UD, Murgia, Pisano, in progress Ø Universality of the Collins function Ø mild (or no) TMD evolution TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 28

Collins-like contribution Defined modulation Positivity bound helicity flip of the gluon PHENIX 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 29

q Unpolarized cross sections: YO U K factorization, evolution and universality AN progress of theory and phenomenology of TMDs TH q Tremendous ! Conclusions and open issues role of non perturbative inputs from low to high energies transv. momentum dependence in SIDIS and DY (consistency ? ? ? ) q Transverse single-spin asymmetries: NO compelling effects of TMD evolution from data NO evidence of factor. breaking in inclusive (one-large scale) processes Sign change of the Sivers funct. under study, Collins function universal q More data expected: COMPASS, Jlab, RHIC, and eventually EIC In other words: more challenging and exciting work… 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 30

BACK-UP SLIDES 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 31

TMD factorization approaches Seminal paper s s e TMD framework s u o r g o r p d n e em Tr 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 32

Collins approach (2011) Theoretcal equivalent with SCET but potentially different in phenomenology Collinear PDF p. QCD Non perturbative parts Role of NON perturbative input 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 33

Open issues in TMD phenomenology TMD evolution and its relevance An example w/o TMD evolution Kang (2015) Role of non perturbative input choices Transverse momentum dep. in SIDIS and its consistency with DY Gluon TMDs at low x and parton saturation, TMD factorization vs. Color Glass Condensate 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 34

TMDs: flavour structure Gaussian widths Signori, Bacchetta, Radici, Schnell (2013) up <<down <<sea 30/11/2016 ? ? to be further explored TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 35

Where can we access TMDs? EIC SIDIS Drell-Yan 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 36

Extracted Sivers functions TO-CA and PV groups sea region: unconstrained [→EIC] Effect of TMD evolution Aybat, Collins, Qiu, Rogers (2012) 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 37

Distortion in the transverse plane Non zero Sivers effect related to parton orbital angular momentum 30/11/2016 TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 38

Access to the gluon Sivers function PHENIX Coll data (2014) All other effects are washed out 30/11/2016 UD, Murgia, Pisano (2015) TMDS FROM HARD SCATTERING PROCESSES U. D'ALESIO (CAGLIARI UNIVERSITY & INFN) 39