A first determination of the unpolarized quark TMDs from a global analysis

A first determination of the unpolarized quark TMDs from a global analysis Cristian Pisano QCD Evolution 2017 Thomas Jefferson National Accelerator Facility Newport News, VA (USA) May 22-26, 2017 In collaboration with A. Bacchetta, F. Delcarro, M. Radici, A. Signori

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? Bacchetta, Delcarro, CP, Radici, Signori (Pavia 2016) ArXiv:1703.10157 [hep-ph] Submitted to JHEP 2/22

Semi-inclusive DIS vs DY 3/22

Experiments 4/22

Extraction of unpolarized quark TMDs State of the art 5/22

SIDIS structure function F UU,T (x, z, P 2 ht, Q2 ) = a H a UU,T (Q2 ; µ 2 ) ( 2 2 ) ( 2 2 +Y ) UU,T Q, P ht +O M /Q d 2 k T d 2 P T f a ( 2 1 x, k T ; µ2) D h/a 1 ( z, P 2 T ; µ2) δ 2( zk T P ht + P T ) H a UU,T O(α 0 S), Y UU,T ( Q 2, P 2 ht ) 0 in Pavia 2016 Multiplicities: mn(x, h z, PhT 2, Q 2 ) = dσh N /dx dz dp2 ht dq2 2π P ht F UU,T (x,z,p 2 dσ DIS /dx dq 2 ht,q2 ) F T (x,q 2 ) 6/22

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) 7/22 Assumption for nonperturbative evolution: g K = g 2 b 2 T 2

TMD evolution Effects of b prescription These choices are arbitrary: they should be checked/challenged in the future ( ) 1 1 e b b4 T /b4 4 max b max b max = 2e γe µ b = 2e γ E 1 e b4 T /b4 min b b min = 2e 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) 8/22

Functional form of TMDs Input distributions at Q 2 = 1 GeV 2 x-dependent width: where g 1(x) = N 1 (1 x) α x σ (1 ˆx) α ˆx σ N 1 g 1(ˆx) with ˆx = 0.1 α, σ, N 1, λ: free parameters (4 for TMD PDFs, 6 for TMD FFs) 9/22

Data selection and analysis Q 2 > 1.4 GeV 2 0.2 < z < 0.7 P ht, q T < Min[0.2Q, 0.7Qz] + 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 10/22

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 11/22

HERMES data = = Pion production π + [ - ] = = = = = = = = χ 2 /dof 4.83 π - [ - ] 2.47 π + = (=) = (=) = (=) = (=) = (=) = (=) [ - ] 3.46 π - [ - ] 2.00 [] [] [] [] [] 12/22 = (=) = (=) = (=) = (=) = (=) = (=)

HERMES data = = Kaon production + [ - ] = = = = = = = = χ 2 /dof 0.91 - [ - ] 0.82 + = (=) = (=) = (=) = (=) = (=) = (=) [ - ] 1.31 - [ - ] 2.54 [] [] [] [] [] 13/22 = (=) = (=) = (=) = (=) = (=) = (=)

SIDIS h + COMPASS data = = = = = = = = = (=) = (=) = (=) = (=) = (=) = (=) = (=) = = = = χ 2 /dof = 1.01 = = = = = = = = [] = = = = = = = = = = = = [] [] [] [] [] [] 14/22

SIDIS h COMPASS data = = = = = = = = = (=) = (=) = (=) = (=) = (=) = (=) = (=) = = = = χ 2 /dof = 1.61 = = = = = = = = [] = = = = = = = = = = = = [] [] [] [] [] [] 15/22

Drell-Yan data χ 2 /dof 0.32 0.84 0.99 1.12 = = = = = = = = σ / () - - [] [] [] [] = ( =) = ( =) = ( =) = ( =) = ( =) = ( =-) = ( =-) = ( =-) = ( =-) The peak is now at about 1 GeV, it was at 0.4 GeV 16/22

Z-boson production χ 2 /dof 1.36 1.11 2.00 1.73 = = = = σ / [ - ] CDF [] [] [] [] The peak is now at 4 GeV Most of the χ 2 is due to normalization 17/22

Nonperturbative evolution TMD evolution is not uniquely determined by pqcd calculations Different schemes may behave differently Nonperturbative input is needed to determine evolution precisely Faster evolution: transverse momentum increases faster due to gluon radiation Slower evolution: the effect of gluon radiation is weaker 18/22

Correlation between transverse momenta Pavia 2016 results Anticorrelation between transverse momentum in TMD PDFs and in TMD FFs 19/22

Mean transverse momentum Q 2 = 1 GeV 2 In TMD distribution functions In TMD fragmentation functions [ ] [ ] - - 20/22

Stability of the results How does the χ 2 of a single replica change if we modify our default choices? Original χ 2 /dof = 1.51 Normalization of HERMES data as done for COMPASS: χ 2 /dof 1.27 Parametrizations for collinear PDFs (NLO GJR 2008 default choice): NLO MSTW 2008 (1.84), NLO CJ12 (1.85) More stringent cuts (TMD factorization better under control) χ 2 /dof 1 Ex: Q 2 > 1.5 GeV 2, 0.25 < z < 0.6, P ht < 0.2Qz = χ 2 /dof = 1.02 (477 bins) 21/22

Conclusions We demonstrated for the first time that it is possible to fit simultaneously SIDIS, DY, and Z boson production data We extracted unpolarized quark TMDs using more than eight thousand data points The TMD framework seems to work quite well Most of the discrepancies come from the normalizations The Y term still needs to be implemented 22/22