Deeply Virtual Meson Production and Transversity GPDs Valery Kubarovsky Jefferson Lab 1 Exclusive Meson Production and Short-Range Hadron Structure January 22-24, 2015, Jlab Outline Physics motivation CLAS data on pseudoscalar meson electroproduction Transversity GPD and structure functions Flavor decomposition of Transversity GPDs Conclusion 2 Description of hadron structure in terms of GPDs Nucleon form factors transverse charge & current densities Nobel prize R. Hofstadter Structure functions quark longitudinal momentum (polarized and unpolarized) distributions Nobel prize 1990 J.Friedman, H. Kendall, R. Taylor GPDs correlated quark momentum distributions (polarized and unpolarized) in transverse space 3 D. Mu ller 94, X. Ji 96, A. Radyushkin 96 Picture from the review: Belitsky, Radyushkin (2005) Generalized Parton Distributions GPDs are functions of three kinematic variables: x, and t, x-quark momentum fraction of the nucleon, skewedness xB/(2-x B ), t=(p-p) 2. There are 4 chiral even GPDs where partons do not flip helicity H, H, E, E 4 chiral odd GPDs flip the parton helicity H T, H T, E T, E T The chiral-odd GPDs are difficult to access since subprocesses with quark helicity-flip are suppressed ~ ~ ~ ~ 4 Chiral-odd GPDs Very little known about the chiral-odd GPDs Anomalous tensor magnetic moment (Compare with anomalous magnetic moment) Transversity distribution The transversity describes the distribution of transversely polarized quarks in a transversely polarized nucleon 5 Structure functions and GPDs Leading twist L The brackets denote the convolution of the elementary process with the GPD F (generalized form factors) The brackets denote the convolution of the elementary process with the GPD F (generalized form factors) 6 Structure functions and GPDs Leading twist L The brackets denote the convolution of the elementary process with the GPD F (generalized form factors) The brackets denote the convolution of the elementary process with the GPD F (generalized form factors) 7 S. Goloskokov and P. Kroll S. Liuti and G. Goldstein L suppressed by a factor coming from: Structure functions and GPDs Leading twist L The brackets denote the convolution of the elementary process with the GPD F (generalized form factors) The brackets denote the convolution of the elementary process with the GPD F (generalized form factors) 8 S. Goloskokov and P. Kroll S. Liuti and G. Goldstein L suppressed by a factor coming from: Transversity in electroproduction of pseudoscalar mesons Leading twist pion wave function dynamically suppressed Twist-3 pion wave function suppressed by, however (enhanced by chiral condensate) 10 A. Kim, to be published Structure functions and GPDs t-dependence at t=t min is determined by the interplay between Direct access to the Transversity GPDs 11 H T and E T =2H T +E T _ ~ Transversity GPD model S. Goloskokov and P. Kroll S. Liuti and G. Goldstein L > T ) Eides,Frankfurt,Strikman PRD 59,114025(1998) Structure functions and GFFs The brackets denote the convolution of the elementary process with the GPD F (Generalized form factors GFFs) 26 CLAS did not separate T and L However in the approximation of the transversity GPDs dominance, that is supported by CLAS data, L H T for and t-dependence is steeper for E T than for H T Estimation of the systematic uncertainties connected with the used approximation is in progress Generalized Form Factors 27 Q 2 GeV 2 xBxB _ _ 0 Generalized Form Factors 28 Q 2 =2.2 GeV 2, x B =0.27 E T > H T t-dependence is steeper for E T than for H T _ _ | |~ e bt b(E T )=1.27 GeV -2 b(H T )=0.98 GeV -2 GPD Flavor Decomposition 29 Similar expressions for E T _ GPDs appear in different flavor combinations for 0 and The combined 0 and data permit the flavor (u and d) decomposition for GPDs H T and E T The u/d decomposition was done under simple assumption that the relative phase between u and d is 0 or 180 degrees. _ / GPDs 30 Q 2 =2.2 GeV 2, x B =0.27 correction factor 31 Octet-singlet mixing angle Chiral condensate Decay constants 1/K | | d and | | u seem to have the same signs _ _ Flavor Decomposition of the Transversity GPDs 32 u quarks d quarks u quarks d quarks u and d have different signs for u and d- quarks in accordance with the transversity function h 1 (Anselmino et al.) Q 2 =1.8 GeV 2, x B =0.22 Decisions shown with positive values of u- quarks GPDs only _ Flavor Decomposition of the Transversity GPDs u quarks d quarks u quarks d quarks Q 2 =2.2 GeV 2, x B =0.27 _ _ u and d have different signs for u and d- quarks in accordance with the transversity function h 1 (Anselmino et al.) | | d and | | u seem to have the same signs _ _ Decisions shown with positive values of u- quarks GPDs only Jlab 12 GeV upgrade CLAS12 High luminosity Large acceptance Wide kinematic coverage High precision Improved particle ID CLAS6 Kinematics coverage for deeply exclusive experiments no overlap with other existing experiments compete with other experiments 12GeV complementary & unique Kinematic Coverage at 11 GeV Statistics at W=2.75 GeV vs Q 2 11 GeV 8.8 GeV 6.6 GeV 00 x B =0.35 x B =0.1 Rosenbluth L/T Separation CLAS 0 and data support the dominance of the transversity GPDs in the processes of the pseudoscalar meson electroproduction The generalized form factors and are directly connected to the structure functions T and TT within handbag approach Exclusive electroproduction of 0 and mesons allows to extract generalized form factors and The combined 0 and data will provide the way for the flavor decomposition of the transversity GPDs CLAS12 will continue the GPD study with broader kinematics and higher statistics. Summary 39 _ _ The End p p z x+ LL (z)(z) x- + = Generalized Form factors 41 HTHT ETET _ Generalized Form factors (extracted in the approximation of the transverse dominance) vs theoretical input to the model The comparison shows that the approximation is reasonable