Unpolarized TMD fits Cristian Pisano Workshop TMDs at JLab: present and future Pavia, 19-20 December 2018
Motivation ◮ Are unpolarized quark TMDs universal? ◮ Does TMD evolution allow for a description of the data at different Q 2 ? ◮ How wide is the transverse momentum distribution? Is it wider at low x ? Pavia 2017 : Bacchetta, Delcarro, CP, Radici, Signori, JHEP 1706 (2017) 2/23
TMD factorization Two scale processes Q 2 ≫ p 2 T Factorization proven 3/23
Semi-inclusive DIS vs DY Electron-positron annihilation data are still missing 4/23
Experiments 5/23
Extraction of unpolarized quark TMDs State of the art courtesy of A. Bacchetta 6/23
SIDIS structure function � F UU , T ( x , z , P 2 hT , Q 2 ) = H a UU , T ( Q 2 ; µ 2 ) d 2 k T d 2 P T f a x , k 2 T ; µ 2 � D h / a z , P 2 T ; µ 2 � δ 2 � � � � z k T − P hT + P T � 1 1 a Q 2 , P 2 M 2 / Q 2 � + Y UU , T � � + O � hT H a UU , T ≈ O ( α 0 Q 2 , P 2 � � S ), Y UU , T ≈ 0 in Pavia 2016 hT 2 π | P hT | F UU , T ( x , z , P 2 hT , Q 2 ) d σ h N / d x d z d P 2 hT d Q 2 Multiplicities: m h N ( x , z , P 2 hT , Q 2 ) = ≈ d σ DIS / d x d Q 2 F T ( x , Q 2 ) 7/23
TMD evolution Fourier transform Rogers, Aybat, PRD 83 (11) Collins, Foundations of Perturbative QCD (11) Different schemes have been suggested Collins, Soper, Sterman, NPB 250 (85) Laenen, Sterman, Vogelsang, PRL 84 (00) Echevarria, Idilbi, Schaefer, Scimemi, EPJ C73 (13) b 2 Assumption for nonperturbative evolution: g K = − g 2 T 2 8/23
TMD evolution Effects of ¯ b ⋆ prescription These choices are arbitrary: they should be checked/challenged in the future � 1 � 1 − e − b 4 T / b 4 4 µ b = 2 e − γ E max ¯ b max = 2 e − γ E b ⋆ ≡ b max ¯ 1 − e − b 4 T / b 4 b ⋆ min b min = 2 e − γ E Q ◮ Low b T modification: integrated result is recovered (unitarity constraint) ◮ µ b never bigger than Q now ◮ Large effect at low Q (inhibits gluon radiation) 9/23
Functional form of TMDs Input distributions at Q 2 = 1 GeV 2 x -dependent width: g 1 ( x ) = N 1 (1 − x ) α x σ x ) α ˆ (1 − ˆ x σ where N 1 ≡ g 1 (ˆ x ) with x = 0 . 1 ˆ α, σ, N 1 , λ : free parameters (4 for TMD PDFs, 6 for TMD FFs) 10/23
Data selection and analysis Q 2 > 1.4 GeV 2 0 . 2 < z < 0 . 7 P hT , q T < Min[0 . 2 Q , 0 . 7 Qz ] + 0 . 5 GeV Problems in separating the fragmentation regions in SIDIS at low Q 2 Boglione, Collins, Gamberg, Gonzalez-Hernandez, Rogers, Sato, PLB 766 (2017) Fit of 200 replicas of the data 11/23
Summary of the results Total number of data points: 8059 Total number of free parameters: 11 ◮ 4 for TMD PDFs ◮ 6 for TMD FFs ◮ 1 for TMD evolution Total χ 2 /dof = 1.55 ± 0.05 12/23
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