Light-front densities for transversely

polarized hadrons Lorcé CédricMainz UniversityGermany

*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 PictureBreit frame

BUT Lorentz contraction

Creation/annihilation of pairsNO 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)]

Bint

Transverse Charge Densities

Monopole Anomalous!

Interpretation:

Transversity basis

S

d

Induced EDM

Dipole

u

d

X

dipole

Similarly for higher spins

quadrupolemonopole octupole

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)]

ChargeChargenormalizationnormalization

UniversalUniversalg=2 factorg=2 factor

Dirac

EWSMSM

SupergravitySupergravity

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!

E E E

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