Light-front densities for transversely polarized hadrons Lorcé Cédric Mainz University Germany *4th Workshop on ERHMT, JLAb, Newport News, Virginia USA (May 18-21, 2010) *

Outline Picture in the transverse plane Form Factors Generalized Polarizabilities GTMDs & Co.

Standard Picture Breit frame BUT Lorentz contraction Creation/annihilation of pairs NO probability/charge density interpretation [Ernst, Sachs, Wali (1960)] [Sachs (1962)]

Correct Picture Extreme Lorentz contraction 2D picture No creation/annihilation of massive pairs Light-front frame [Burkardt (2001,2003)]

Transverse Charge Densities p n Long. pol.Transv. pol. Electric dipole! [Miller (2007)][Carlson & Vdh (2008)]

B int Transverse Charge Densities MonopoleAnomalous! Interpretation: Transversity basis S d Induced EDM Dipole u d X

dipole Similarly for higher spins quadrupolemonopoleoctupole 2j+1 circular multipoles! =+++ Transverse Charge Densities [Lorcé (2009)] [Alexandrou et al. (2008,2009)] Distortions of transverse charge densities due to anomalous values of EM moments Claim:

Higher Spins 2j+1 circular multipoles! [Lorcé (2009)] ChargenormalizationUniversal g=2 factor Dirac EW SM Supergravity

Generalized Polarizabilities VCS in low limit described by 6 GPs Linear response to external quasi-static dipole electric field

Generalized Polarizabilities [Gorchtein, Lorcé, Pasquini, Vdh (2010)] dipole quadrupole monopole Only 3 linear combinations available! EEE

GTMDs (Generalized Transverse Momentum dependent parton Distributions) Complete parametrization [Meißner, Metz, Schlegel (2009)] Probabilistic interpretation in impact-parameter space with dd

,  GCDs (Generalized transverse Charge Densities) [Lorcé, Pasquini (in preparation)] k T b Unpolarized u quark in unpolarized proton k T  fixed

GCDs (Generalized transverse Charge Densities) [Lorcé, Pasquini (in preparation)] k T Unpolarized u quark in unpolarized proton k T fixed =+

GCDs (Generalized transverse Charge Densities) [Lorcé, Pasquini (in preparation)],k T  fixed k T k T k T k T Unpolarized u quark in unpolarized proton

GCDs (Generalized transverse Charge Densities) [Lorcé, Pasquini (in preparation)] Unpolarized u and d quarks in unpolarized proton  u  d More u than d in central region!

FFs  Correct picture on the light front  Distortions of densities due to anomalous moments  « Natural » EM moments form a pseudo-Pascal triangle GPs  VCS amplitude in the light front  3 out of 6 mapped out GTMDs & Co.  Full information  Anisotropic distribution of  u/d quarks dominance in central region of proton/neutron Summary k T